Mammalian Cell Culture Process for Monoclonal Antibody Production: Nonlinear Modelling and Parameter Estimation

Directory of Open Access Journals (Sweden)

Dan Selişteanu

2015-01-01

Full Text Available Monoclonal antibodies (mAbs are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies.

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

Science.gov (United States)

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

Science.gov (United States)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Parameter Estimation

DEFF Research Database (Denmark)

Sales-Cruz, Mauricio; Heitzig, Martina; Cameron, Ian

2011-01-01

of optimisation techniques coupled with dynamic solution of the underlying model. Linear and nonlinear approaches to parameter estimation are investigated. There is also the application of maximum likelihood principles in the estimation of parameters, as well as the use of orthogonal collocation to generate a set......In this chapter the importance of parameter estimation in model development is illustrated through various applications related to reaction systems. In particular, rate constants in a reaction system are obtained through parameter estimation methods. These approaches often require the application...... of algebraic equations as the basis for parameter estimation.These approaches are illustrated using estimations of kinetic constants from reaction system models....

Nonlinear systems time-varying parameter estimation: Application to induction motors

Energy Technology Data Exchange (ETDEWEB)

Kenne, Godpromesse [Laboratoire d' Automatique et d' Informatique Appliquee (LAIA), Departement de Genie Electrique, IUT FOTSO Victor, Universite de Dschang, B.P. 134 Bandjoun (Cameroon); Ahmed-Ali, Tarek [Ecole Nationale Superieure des Ingenieurs des Etudes et Techniques d' Armement (ENSIETA), 2 Rue Francois Verny, 29806 Brest Cedex 9 (France); Lamnabhi-Lagarrigue, F. [Laboratoire des Signaux et Systemes (L2S), C.N.R.S-SUPELEC, Universite Paris XI, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France); Arzande, Amir [Departement Energie, Ecole Superieure d' Electricite-SUPELEC, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France)

2008-11-15

In this paper, an algorithm for time-varying parameter estimation for a large class of nonlinear systems is presented. The proof of the convergence of the estimates to their true values is achieved using Lyapunov theories and does not require that the classical persistent excitation condition be satisfied by the input signal. Since the induction motor (IM) is widely used in several industrial sectors, the algorithm developed is potentially useful for adjusting the controller parameters of variable speed drives. The method proposed is simple and easily implementable in real-time. The application of this approach to on-line estimation of the rotor resistance of IM shows a rapidly converging estimate in spite of measurement noise, discretization effects, parameter uncertainties (e.g. inaccuracies on motor inductance values) and modeling inaccuracies. The robustness analysis for this IM application also revealed that the proposed scheme is insensitive to the stator resistance variations within a wide range. The merits of the proposed algorithm in the case of on-line time-varying rotor resistance estimation are demonstrated via experimental results in various operating conditions of the induction motor. The experimental results obtained demonstrate that the application of the proposed algorithm to update on-line the parameters of an adaptive controller (e.g. IM and synchronous machines adaptive control) can improve the efficiency of the industrial process. The other interesting features of the proposed method include fault detection/estimation and adaptive control of IM and synchronous machines. (author)

Applied parameter estimation for chemical engineers

CERN Document Server

Englezos, Peter

2000-01-01

Formulation of the parameter estimation problem; computation of parameters in linear models-linear regression; Gauss-Newton method for algebraic models; other nonlinear regression methods for algebraic models; Gauss-Newton method for ordinary differential equation (ODE) models; shortcut estimation methods for ODE models; practical guidelines for algorithm implementation; constrained parameter estimation; Gauss-Newton method for partial differential equation (PDE) models; statistical inferences; design of experiments; recursive parameter estimation; parameter estimation in nonlinear thermodynam

Determination of power system component parameters using nonlinear dead beat estimation method

Science.gov (United States)

Kolluru, Lakshmi

Power systems are considered the most complex man-made wonders in existence today. In order to effectively supply the ever increasing demands of the consumers, power systems are required to remain stable at all times. Stability and monitoring of these complex systems are achieved by strategically placed computerized control centers. State and parameter estimation is an integral part of these facilities, as they deal with identifying the unknown states and/or parameters of the systems. Advancements in measurement technologies and the introduction of phasor measurement units (PMU) provide detailed and dynamic information of all measurements. Accurate availability of dynamic measurements provides engineers the opportunity to expand and explore various possibilities in power system dynamic analysis/control. This thesis discusses the development of a parameter determination algorithm for nonlinear power systems, using dynamic data obtained from local measurements. The proposed algorithm was developed by observing the dead beat estimator used in state space estimation of linear systems. The dead beat estimator is considered to be very effective as it is capable of obtaining the required results in a fixed number of steps. The number of steps required is related to the order of the system and the number of parameters to be estimated. The proposed algorithm uses the idea of dead beat estimator and nonlinear finite difference methods to create an algorithm which is user friendly and can determine the parameters fairly accurately and effectively. The proposed algorithm is based on a deterministic approach, which uses dynamic data and mathematical models of power system components to determine the unknown parameters. The effectiveness of the algorithm is tested by implementing it to identify the unknown parameters of a synchronous machine. MATLAB environment is used to create three test cases for dynamic analysis of the system with assumed known parameters. Faults are

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

Directory of Open Access Journals (Sweden)

Afnizanfaizal Abdullah

Full Text Available The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

Science.gov (United States)

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

Robust nonlinear autoregressive moving average model parameter estimation using stochastic recurrent artificial neural networks

DEFF Research Database (Denmark)

Chon, K H; Hoyer, D; Armoundas, A A

1999-01-01

In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic...... part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction...... error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate...

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

Science.gov (United States)

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

DEFF Research Database (Denmark)

Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas

2018-01-01

. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....

Performance emulation and parameter estimation for nonlinear fibre-optic links

DEFF Research Database (Denmark)

Piels, Molly; Porto da Silva, Edson; Zibar, Darko

2016-01-01

Fibre-optic communication systems, especially when operating in the nonlinear regime, generally do not perform exactly as theory would predict. A number of methods for data-based evaluation of nonlinear fibre-optic link parameters, both for accurate performance emulation and optimization...

Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

Science.gov (United States)

Vasta, M.; Roberts, J. B.

1998-06-01

Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

Science.gov (United States)

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

On-line scheme for parameter estimation of nonlinear lithium ion battery equivalent circuit models using the simplified refined instrumental variable method for a modified Wiener continuous-time model

International Nuclear Information System (INIS)

Allafi, Walid; Uddin, Kotub; Zhang, Cheng; Mazuir Raja Ahsan Sha, Raja; Marco, James

2017-01-01

Highlights: •Off-line estimation approach for continuous-time domain for non-invertible function. •Model reformulated to multi-input-single-output; nonlinearity described by sigmoid. •Method directly estimates parameters of nonlinear ECM from the measured-data. •Iterative on-line technique leads to smoother convergence. •The model is validated off-line and on-line using NCA battery. -- Abstract: The accuracy of identifying the parameters of models describing lithium ion batteries (LIBs) in typical battery management system (BMS) applications is critical to the estimation of key states such as the state of charge (SoC) and state of health (SoH). In applications such as electric vehicles (EVs) where LIBs are subjected to highly demanding cycles of operation and varying environmental conditions leading to non-trivial interactions of ageing stress factors, this identification is more challenging. This paper proposes an algorithm that directly estimates the parameters of a nonlinear battery model from measured input and output data in the continuous time-domain. The simplified refined instrumental variable method is extended to estimate the parameters of a Wiener model where there is no requirement for the nonlinear function to be invertible. To account for nonlinear battery dynamics, in this paper, the typical linear equivalent circuit model (ECM) is enhanced by a block-oriented Wiener configuration where the nonlinear memoryless block following the typical ECM is defined to be a sigmoid static nonlinearity. The nonlinear Weiner model is reformulated in the form of a multi-input, single-output linear model. This linear form allows the parameters of the nonlinear model to be estimated using any linear estimator such as the well-established least squares (LS) algorithm. In this paper, the recursive least square (RLS) method is adopted for online parameter estimation. The approach was validated on experimental data measured from an 18650-type Graphite

Application of the Elitist-Mutated PSO and an Improved GSA to Estimate Parameters of Linear and Nonlinear Muskingum Flood Routing Models.

Directory of Open Access Journals (Sweden)

Ling Kang

Full Text Available Heuristic search algorithms, which are characterized by faster convergence rates and can obtain better solutions than the traditional mathematical methods, are extensively used in engineering optimizations. In this paper, a newly developed elitist-mutated particle swarm optimization (EMPSO technique and an improved gravitational search algorithm (IGSA are successively applied to parameter estimation problems of Muskingum flood routing models. First, the global optimization performance of the EMPSO and IGSA are validated by nine standard benchmark functions. Then, to further analyse the applicability of the EMPSO and IGSA for various forms of Muskingum models, three typical structures are considered: the basic two-parameter linear Muskingum model (LMM, a three-parameter nonlinear Muskingum model (NLMM and a four-parameter nonlinear Muskingum model which incorporates the lateral flow (NLMM-L. The problems are formulated as optimization procedures to minimize the sum of the squared deviations (SSQ or the sum of the absolute deviations (SAD between the observed and the estimated outflows. Comparative results of the selected numerical cases (Case 1-3 show that the EMPSO and IGSA not only rapidly converge but also obtain the same best optimal parameter vector in every run. The EMPSO and IGSA exhibit superior robustness and provide two efficient alternative approaches that can be confidently employed to estimate the parameters of both linear and nonlinear Muskingum models in engineering applications.

Online Parameter Identification and State of Charge Estimation of Lithium-Ion Batteries Based on Forgetting Factor Recursive Least Squares and Nonlinear Kalman Filter

Directory of Open Access Journals (Sweden)

Bizhong Xia

2017-12-01

Full Text Available State of charge (SOC estimation is the core of any battery management system. Most closed-loop SOC estimation algorithms are based on the equivalent circuit model with fixed parameters. However, the parameters of the equivalent circuit model will change as temperature or SOC changes, resulting in reduced SOC estimation accuracy. In this paper, two SOC estimation algorithms with online parameter identification are proposed to solve this problem based on forgetting factor recursive least squares (FFRLS and nonlinear Kalman filter. The parameters of a Thevenin model are constantly updated by FFRLS. The nonlinear Kalman filter is used to perform the recursive operation to estimate SOC. Experiments in variable temperature environments verify the effectiveness of the proposed algorithms. A combination of four driving cycles is loaded on lithium-ion batteries to test the adaptability of the approaches to different working conditions. Under certain conditions, the average error of the SOC estimation dropped from 5.6% to 1.1% after adding the online parameters identification, showing that the estimation accuracy of proposed algorithms is greatly improved. Besides, simulated measurement noise is added to the test data to prove the robustness of the algorithms.

Diffraction corrections for second harmonic beam fields and effects on the nonlinearity parameter evaluation

Energy Technology Data Exchange (ETDEWEB)

Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

2016-04-15

The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.

Multi-objective optimization in quantum parameter estimation

Science.gov (United States)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

2014-01-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

A different approach to estimate nonlinear regression model using numerical methods

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics

Science.gov (United States)

Kukreja, Sunil L.; Boyle, Richard D.

2014-01-01

Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.

Parameter Estimation for a Computable General Equilibrium Model

DEFF Research Database (Denmark)

Arndt, Channing; Robinson, Sherman; Tarp, Finn

We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of nonlinear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...

A new method to estimate parameters of linear compartmental models using artificial neural networks

International Nuclear Information System (INIS)

Gambhir, Sanjiv S.; Keppenne, Christian L.; Phelps, Michael E.; Banerjee, Pranab K.

1998-01-01

At present, the preferred tool for parameter estimation in compartmental analysis is an iterative procedure; weighted nonlinear regression. For a large number of applications, observed data can be fitted to sums of exponentials whose parameters are directly related to the rate constants/coefficients of the compartmental models. Since weighted nonlinear regression often has to be repeated for many different data sets, the process of fitting data from compartmental systems can be very time consuming. Furthermore the minimization routine often converges to a local (as opposed to global) minimum. In this paper, we examine the possibility of using artificial neural networks instead of weighted nonlinear regression in order to estimate model parameters. We train simple feed-forward neural networks to produce as outputs the parameter values of a given model when kinetic data are fed to the networks' input layer. The artificial neural networks produce unbiased estimates and are orders of magnitude faster than regression algorithms. At noise levels typical of many real applications, the neural networks are found to produce lower variance estimates than weighted nonlinear regression in the estimation of parameters from mono- and biexponential models. These results are primarily due to the inability of weighted nonlinear regression to converge. These results establish that artificial neural networks are powerful tools for estimating parameters for simple compartmental models. (author)

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

Science.gov (United States)

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

State and parameter estimation in biotechnical batch reactors

NARCIS (Netherlands)

Keesman, K.J.

2000-01-01

In this paper the problem of state and parameter estimation in biotechnical batch reactors is considered. Models describing the biotechnical process behaviour are usually nonlinear with time-varying parameters. Hence, the resulting large dimensions of the augmented state vector, roughly > 7, in

Parameter Estimation for a Computable General Equilibrium Model

DEFF Research Database (Denmark)

Arndt, Channing; Robinson, Sherman; Tarp, Finn

2002-01-01

We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of non-linear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...

Spatio-temporal modeling of nonlinear distributed parameter systems

CERN Document Server

Li, Han-Xiong

2011-01-01

The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

Science.gov (United States)

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Robust Parameter and Signal Estimation in Induction Motors

DEFF Research Database (Denmark)

Børsting, H.

This thesis deals with theories and methods for robust parameter and signal estimation in induction motors. The project originates in industrial interests concerning sensor-less control of electrical drives. During the work, some general problems concerning estimation of signals and parameters...... in nonlinear systems, have been exposed. The main objectives of this project are: - analysis and application of theories and methods for robust estimation of parameters in a model structure, obtained from knowledge of the physics of the induction motor. - analysis and application of theories and methods...... for robust estimation of the rotor speed and driving torque of the induction motor based only on measurements of stator voltages and currents. Only contimuous-time models have been used, which means that physical related signals and parameters are estimated directly and not indirectly by some discrete...

ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2014-12-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.

Parameter Estimation in Stochastic Grey-Box Models

DEFF Research Database (Denmark)

Kristensen, Niels Rode; Madsen, Henrik; Jørgensen, Sten Bay

2004-01-01

An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended...... Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool...... and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term....

Genetic Algorithms for a Parameter Estimation of a Fermentation Process Model: A Comparison

Directory of Open Access Journals (Sweden)

Olympia Roeva

2005-12-01

Full Text Available In this paper the problem of a parameter estimation using genetic algorithms is examined. A case study considering the estimation of 6 parameters of a nonlinear dynamic model of E. coli fermentation is presented as a test problem. The parameter estimation problem is stated as a nonlinear programming problem subject to nonlinear differential-algebraic constraints. This problem is known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based local optimization methods fail to arrive satisfied solutions. To overcome their limitations, the use of different genetic algorithms as stochastic global optimization methods is explored. These algorithms are proved to be very suitable for the optimization of highly non-linear problems with many variables. Genetic algorithms can guarantee global optimality and robustness. These facts make them advantageous in use for parameter identification of fermentation models. A comparison between simple, modified and multi-population genetic algorithms is presented. The best result is obtained using the modified genetic algorithm. The considered algorithms converged very closely to the cost value but the modified algorithm is in times faster than other two.

Application of spreadsheet to estimate infiltration parameters

Directory of Open Access Journals (Sweden)

Mohammad Zakwan

2016-09-01

Full Text Available Infiltration is the process of flow of water into the ground through the soil surface. Soil water although contributes a negligible fraction of total water present on earth surface, but is of utmost importance for plant life. Estimation of infiltration rates is of paramount importance for estimation of effective rainfall, groundwater recharge, and designing of irrigation systems. Numerous infiltration models are in use for estimation of infiltration rates. The conventional graphical approach for estimation of infiltration parameters often fails to estimate the infiltration parameters precisely. The generalised reduced gradient (GRG solver is reported to be a powerful tool for estimating parameters of nonlinear equations and it has, therefore, been implemented to estimate the infiltration parameters in the present paper. Field data of infiltration rate available in literature for sandy loam soils of Umuahia, Nigeria were used to evaluate the performance of GRG solver. A comparative study of graphical method and GRG solver shows that the performance of GRG solver is better than that of conventional graphical method for estimation of infiltration rates. Further, the performance of Kostiakov model has been found to be better than the Horton and Philip's model in most of the cases based on both the approaches of parameter estimation.

Characteristics and Impact Factors of Parameter Alpha in the Nonlinear Advection-Aridity Method for Estimating Evapotranspiration at Interannual Scale in the Loess Plateau

Science.gov (United States)

Zhou, H.; Liu, W.; Ning, T.

2017-12-01

Land surface actual evapotranspiration plays a key role in the global water and energy cycles. Accurate estimation of evapotranspiration is crucial for understanding the interactions between the land surface and the atmosphere, as well as for managing water resources. The nonlinear advection-aridity approach was formulated by Brutsaert to estimate actual evapotranspiration in 2015. Subsequently, this approach has been verified, applied and developed by many scholars. The estimation, impact factors and correlation analysis of the parameter alpha (αe) of this approach has become important aspects of the research. According to the principle of this approach, the potential evapotranspiration (ETpo) (taking αe as 1) and the apparent potential evapotranspiration (ETpm) were calculated using the meteorological data of 123 sites of the Loess Plateau and its surrounding areas. Then the mean spatial values of precipitation (P), ETpm and ETpo for 13 catchments were obtained by a CoKriging interpolation algorithm. Based on the runoff data of the 13 catchments, actual evapotranspiration was calculated using the catchment water balance equation at the hydrological year scale (May to April of the following year) by ignoring the change of catchment water storage. Thus, the parameter was estimated, and its relationships with P, ETpm and aridity index (ETpm/P) were further analyzed. The results showed that the general range of annual parameter value was 0.385-1.085, with an average value of 0.751 and a standard deviation of 0.113. The mean annual parameter αe value showed different spatial characteristics, with lower values in northern and higher values in southern. The annual scale parameter linearly related with annual P (R2=0.89) and ETpm (R2=0.49), while it exhibited a power function relationship with the aridity index (R2=0.83). Considering the ETpm is a variable in the nonlinear advection-aridity approach in which its effect has been incorporated, the relationship of

Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

Directory of Open Access Journals (Sweden)

Lan Wang

2017-01-01

Full Text Available Quasi-linear autoregressive with exogenous inputs (Quasi-ARX models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.

Sensorless Estimation and Nonlinear Control of a Rotational Energy Harvester

Science.gov (United States)

Nunna, Kameswarie; Toh, Tzern T.; Mitcheson, Paul D.; Astolfi, Alessandro

2013-12-01

It is important to perform sensorless monitoring of parameters in energy harvesting devices in order to determine the operating states of the system. However, physical measurements of these parameters is often a challenging task due to the unavailability of access points. This paper presents, as an example application, the design of a nonlinear observer and a nonlinear feedback controller for a rotational energy harvester. A dynamic model of a rotational energy harvester with its power electronic interface is derived and validated. This model is then used to design a nonlinear observer and a nonlinear feedback controller which yield a sensorless closed-loop system. The observer estimates the mechancial quantities from the measured electrical quantities while the control law sustains power generation across a range of source rotation speeds. The proposed scheme is assessed through simulations and experiments.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

Science.gov (United States)

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter

Directory of Open Access Journals (Sweden)

Xuegang Song

2017-10-01

Full Text Available This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

Science.gov (United States)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using laguerre functions

DEFF Research Database (Denmark)

Chon, K H; Cohen, R J; Holstein-Rathlou, N H

1997-01-01

A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving...... average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre...

Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects

Directory of Open Access Journals (Sweden)

Yi Hu

2014-01-01

Full Text Available This paper suggests a generalized method of moments (GMM based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999 original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991 are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.

Statistics of Parameter Estimates: A Concrete Example

KAUST Repository

Aguilar, Oscar

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise levels, models, or prior knowledge. But what can we say about the validity of such estimates, and the influence of these assumptions? This paper is concerned with methods to address these questions, and for didactic purposes it is written in the context of a concrete nonlinear parameter estimation problem. We will use the results of a physical experiment conducted by Allmaras et al. at Texas A&M University [M. Allmaras et al., SIAM Rev., 55 (2013), pp. 149-167] to illustrate the importance of validation procedures for statistical parameter estimation. We describe statistical methods and data analysis tools to check the choices of likelihood and prior distributions, and provide examples of how to compare Bayesian results with those obtained by non-Bayesian methods based on different types of assumptions. We explain how different statistical methods can be used in complementary ways to improve the understanding of parameter estimates and their uncertainties.

Tracking of nuclear reactor parameters via recursive non linear estimation

International Nuclear Information System (INIS)

Pages Fita, J.; Alengrin, G.; Aguilar Martin, J.; Zwingelstein, M.

1975-01-01

The usefulness of nonlinear estimation in the supervision of nuclear reactors, as well for reactivity determination as for on-line modelisation in order to detect eventual and unwanted changes in working operation is illustrated. It is dealt with the reactivity estimation using an a priori dynamical model under the hypothesis of one group of delayed neutrons (measurements were done with an ionisation chamber). The determination of the reactivity using such measurements appears as a nonlinear estimation procedure derived from a particular form of nonlinear filter. Observed inputs being demand of power and inside temperature, and output being the reactivity balance, a recursive algorithm is derived for the estimation of the parameters that define the actual behavior of the reactor. Example of treatment of real data is given [fr

Nonlinear Bayesian Algorithms for Gas Plume Detection and Estimation from Hyper-spectral Thermal Image Data

Energy Technology Data Exchange (ETDEWEB)

Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L.; Anderson, Kevin K.

2007-06-13

This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.

State, Parameter, and Unknown Input Estimation Problems in Active Automotive Safety Applications

Science.gov (United States)

Phanomchoeng, Gridsada

A variety of driver assistance systems such as traction control, electronic stability control (ESC), rollover prevention and lane departure avoidance systems are being developed by automotive manufacturers to reduce driver burden, partially automate normal driving operations, and reduce accidents. The effectiveness of these driver assistance systems can be significant enhanced if the real-time values of several vehicle parameters and state variables, namely tire-road friction coefficient, slip angle, roll angle, and rollover index, can be known. Since there are no inexpensive sensors available to measure these variables, it is necessary to estimate them. However, due to the significant nonlinear dynamics in a vehicle, due to unknown and changing plant parameters, and due to the presence of unknown input disturbances, the design of estimation algorithms for this application is challenging. This dissertation develops a new approach to observer design for nonlinear systems in which the nonlinearity has a globally (or locally) bounded Jacobian. The developed approach utilizes a modified version of the mean value theorem to express the nonlinearity in the estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). A number of illustrative examples are presented to show that the developed approach is less conservative and more useful than the standard Lipschitz assumption based nonlinear observer. The developed nonlinear observer is utilized for estimation of slip angle, longitudinal vehicle velocity, and vehicle roll angle. In order to predict and prevent vehicle rollovers in tripped situations, it is necessary to estimate the vertical tire forces in the presence of unknown road disturbance inputs. An approach to estimate unknown disturbance inputs in nonlinear systems using dynamic model inversion and a modified version of the mean value theorem is

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

Science.gov (United States)

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

Parameter estimation in X-ray astronomy

International Nuclear Information System (INIS)

Lampton, M.; Margon, B.; Bowyer, S.

1976-01-01

The problems of model classification and parameter estimation are examined, with the objective of establishing the statistical reliability of inferences drawn from X-ray observations. For testing the validities of classes of models, the procedure based on minimizing the chi 2 statistic is recommended; it provides a rejection criterion at any desired significance level. Once a class of models has been accepted, a related procedure based on the increase of chi 2 gives a confidence region for the values of the model's adjustable parameters. The procedure allows the confidence level to be chosen exactly, even for highly nonlinear models. Numerical experiments confirm the validity of the prescribed technique.The chi 2 /sub min/+1 error estimation method is evaluated and found unsuitable when several parameter ranges are to be derived, because it substantially underestimates their joint errors. The ratio of variances method, while formally correct, gives parameter confidence regions which are more variable than necessary

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

Science.gov (United States)

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

2011-01-01

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

Parameter estimation in space systems using recurrent neural networks

Science.gov (United States)

Parlos, Alexander G.; Atiya, Amir F.; Sunkel, John W.

1991-01-01

The identification of time-varying parameters encountered in space systems is addressed, using artificial neural systems. A hybrid feedforward/feedback neural network, namely a recurrent multilayer perception, is used as the model structure in the nonlinear system identification. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard back-propagation-learning algorithm is modified and it is used for both the off-line and on-line supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying parameters of nonlinear dynamic systems is investigated by estimating the mass properties of a representative large spacecraft. The changes in the spacecraft inertia are predicted using a trained neural network, during two configurations corresponding to the early and late stages of the spacecraft on-orbit assembly sequence. The proposed on-line mass properties estimation capability offers encouraging results, though, further research is warranted for training and testing the predictive capabilities of these networks beyond nominal spacecraft operations.

Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

Directory of Open Access Journals (Sweden)

Su Young Yu

2015-03-01

Full Text Available In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear para- meters of soil models was investigated by Dynamic Embedment Factor (DEF concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.

PWR system simulation and parameter estimation with neural networks

Energy Technology Data Exchange (ETDEWEB)

Akkurt, Hatice; Colak, Uener E-mail: uc@nuke.hacettepe.edu.tr

2002-11-01

A detailed nonlinear model for a typical PWR system has been considered for the development of simulation software. Each component in the system has been represented by appropriate differential equations. The SCILAB software was used for solving nonlinear equations to simulate steady-state and transient operational conditions. Overall system has been constructed by connecting individual components to each other. The validity of models for individual components and overall system has been verified. The system response against given transients have been analyzed. A neural network has been utilized to estimate system parameters during transients. Different transients have been imposed in training and prediction stages with neural networks. Reactor power and system reactivity during the transient event have been predicted by the neural network. Results show that neural networks estimations are in good agreement with the calculated response of the reactor system. The maximum errors are within {+-}0.254% for power and between -0.146 and 0.353% for reactivity prediction cases. Steam generator parameters, pressure and water level, are also successfully predicted by the neural network employed in this study. The noise imposed on the input parameters of the neural network deteriorates the power estimation capability whereas the reactivity estimation capability is not significantly affected.

PWR system simulation and parameter estimation with neural networks

International Nuclear Information System (INIS)

Akkurt, Hatice; Colak, Uener

2002-01-01

A detailed nonlinear model for a typical PWR system has been considered for the development of simulation software. Each component in the system has been represented by appropriate differential equations. The SCILAB software was used for solving nonlinear equations to simulate steady-state and transient operational conditions. Overall system has been constructed by connecting individual components to each other. The validity of models for individual components and overall system has been verified. The system response against given transients have been analyzed. A neural network has been utilized to estimate system parameters during transients. Different transients have been imposed in training and prediction stages with neural networks. Reactor power and system reactivity during the transient event have been predicted by the neural network. Results show that neural networks estimations are in good agreement with the calculated response of the reactor system. The maximum errors are within ±0.254% for power and between -0.146 and 0.353% for reactivity prediction cases. Steam generator parameters, pressure and water level, are also successfully predicted by the neural network employed in this study. The noise imposed on the input parameters of the neural network deteriorates the power estimation capability whereas the reactivity estimation capability is not significantly affected

Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

Science.gov (United States)

Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano

2012-05-10

The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

Overview and benchmark analysis of fuel cell parameters estimation for energy management purposes

Science.gov (United States)

Kandidayeni, M.; Macias, A.; Amamou, A. A.; Boulon, L.; Kelouwani, S.; Chaoui, H.

2018-03-01

Proton exchange membrane fuel cells (PEMFCs) have become the center of attention for energy conversion in many areas such as automotive industry, where they confront a high dynamic behavior resulting in their characteristics variation. In order to ensure appropriate modeling of PEMFCs, accurate parameters estimation is in demand. However, parameter estimation of PEMFC models is highly challenging due to their multivariate, nonlinear, and complex essence. This paper comprehensively reviews PEMFC models parameters estimation methods with a specific view to online identification algorithms, which are considered as the basis of global energy management strategy design, to estimate the linear and nonlinear parameters of a PEMFC model in real time. In this respect, different PEMFC models with different categories and purposes are discussed first. Subsequently, a thorough investigation of PEMFC parameter estimation methods in the literature is conducted in terms of applicability. Three potential algorithms for online applications, Recursive Least Square (RLS), Kalman filter, and extended Kalman filter (EKF), which has escaped the attention in previous works, have been then utilized to identify the parameters of two well-known semi-empirical models in the literature, Squadrito et al. and Amphlett et al. Ultimately, the achieved results and future challenges are discussed.

Nonlinear Parameter Estimation in Microbiological Degradation Systems and Statistic Test for Common Estimation

DEFF Research Database (Denmark)

Sommer, Helle Mølgaard; Holst, Helle; Spliid, Henrik

1995-01-01

Three identical microbiological experiments were carried out and analysed in order to examine the variability of the parameter estimates. The microbiological system consisted of a substrate (toluene) and a biomass (pure culture) mixed together in an aquifer medium. The degradation of the substrate...

Reactivity estimation using digital nonlinear H∞ estimator for VHTRC experiment

International Nuclear Information System (INIS)

Suzuki, Katsuo; Nabeshima, Kunihiko; Yamane, Tsuyoshi

2003-01-01

On-line and real-time estimation of time-varying reactivity in a nuclear reactor in necessary for early detection of reactivity anomaly and safe operation. Using a digital nonlinear H ∞ estimator, an experiment of real-time dynamic reactivity estimation was carried out in the Very High Temperature Reactor Critical Assembly (VHTRC) of Japan Atomic Energy Research Institute. Some technical issues of the experiment are described, such as reactivity insertion, data sampling frequency, anti-aliasing filter, experimental circuit and digitalising nonlinear H ∞ reactivity estimator, and so on. Then, we discussed the experimental results obtained by the digital nonlinear H ∞ estimator with sampled data of the nuclear instrumentation signal for the power responses under various reactivity insertions. Good performances of estimated reactivity were observed, with almost no delay to the true reactivity and sufficient accuracy between 0.05 cent and 0.1 cent. The experiment shows that real-time reactivity for data sampling period of 10 ms can be certainly realized. From the results of the experiment, it is concluded that the digital nonlinear H ∞ reactivity estimator can be applied as on-line real-time reactivity meter for actual nuclear plants. (author)

State of charge estimation of lithium-ion batteries based on an improved parameter identification method

International Nuclear Information System (INIS)

Xia, Bizhong; Chen, Chaoren; Tian, Yong; Wang, Mingwang; Sun, Wei; Xu, Zhihui

2015-01-01

The SOC (state of charge) is the most important index of the battery management systems. However, it cannot be measured directly with sensors and must be estimated with mathematical techniques. An accurate battery model is crucial to exactly estimate the SOC. In order to improve the model accuracy, this paper presents an improved parameter identification method. Firstly, the concept of polarization depth is proposed based on the analysis of polarization characteristics of the lithium-ion batteries. Then, the nonlinear least square technique is applied to determine the model parameters according to data collected from pulsed discharge experiments. The results show that the proposed method can reduce the model error as compared with the conventional approach. Furthermore, a nonlinear observer presented in the previous work is utilized to verify the validity of the proposed parameter identification method in SOC estimation. Finally, experiments with different levels of discharge current are carried out to investigate the influence of polarization depth on SOC estimation. Experimental results show that the proposed method can improve the SOC estimation accuracy as compared with the conventional approach, especially under the conditions of large discharge current. - Highlights: • The polarization characteristics of lithium-ion batteries are analyzed. • The concept of polarization depth is proposed to improve model accuracy. • A nonlinear least square technique is applied to determine the model parameters. • A nonlinear observer is used as the SOC estimation algorithm. • The validity of the proposed method is verified by experimental results.

A robust methodology for kinetic model parameter estimation for biocatalytic reactions

DEFF Research Database (Denmark)

Al-Haque, Naweed; Andrade Santacoloma, Paloma de Gracia; Lima Afonso Neto, Watson

2012-01-01

lead to globally optimized parameter values. In this article, a robust methodology to estimate parameters for biocatalytic reaction kinetic expressions is proposed. The methodology determines the parameters in a systematic manner by exploiting the best features of several of the current approaches...... parameters, which are strongly correlated with each other. State-of-the-art methodologies such as nonlinear regression (using progress curves) or graphical analysis (using initial rate data, for example, the Lineweaver-Burke plot, Hanes plot or Dixon plot) often incorporate errors in the estimates and rarely...

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

Energy Technology Data Exchange (ETDEWEB)

Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir

2009-08-30

This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

International Nuclear Information System (INIS)

Ayati, Moosa; Khaki-Sedigh, Ali

2009-01-01

This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

Beyer's non-linearity parameter (B/A) in benzylidene aniline Schiff base liquid crystalline systems

International Nuclear Information System (INIS)

Nagi Reddy, M.V.V.; Pisipati, V.G.K.M.; Madhavi Latha, D.; Datta Prasad, P.V.

2011-01-01

The non-linearity parameter B/A is estimated for a number of liquid crystal materials of the type N-(p-n-alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO.m, where n and m are the aliphatic chains on either side of the rigid core, which can be varied from 1 to 18 to realize a number of LC materials with a variety LC phase variants. The B/A values are computed from both density and sound velocity data following standard relations reported in literature. This systematic study in a homologous series provides an opportunity to study how this parameter behaves with (1) either the alkoxy and/or alkyl chain number, (2) with the total chain number (n+m), (3) with increase in molecular weight and (4) whether the linear relations reported in literature either with αT [thermal expansion coefficient (α) and temperature (T)] and sound velocity (u) will hold good or not and if so to what extent. The results are discussed with the body of data available in literature on liquids, liquid mixtures and other LC materials. -- Research highlights: → The Bayer's non-linearity parameter (B/A) is estimated for the first time for a number liquid crystal materials of the type N-(p-n-alkoxy benzylidene)-p-nalkyl anilines. → The magnitude of B/A estimated from sound velocity data is higher compared to that estimated thermal expansion data. → The B/A value decreases with increase in molecular weight with an even odd fashion and reaches a minimum value and saturates. → These studies reveal that both the thermal expansion coefficient and sound velocity are the tools to estimate the non-linear parameter B/A in the case of liquid crystals.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

A software for parameter estimation in dynamic models

Directory of Open Access Journals (Sweden)

M. Yuceer

2008-12-01

Full Text Available A common problem in dynamic systems is to determine parameters in an equation used to represent experimental data. The goal is to determine the values of model parameters that provide the best fit to measured data, generally based on some type of least squares or maximum likelihood criterion. In the most general case, this requires the solution of a nonlinear and frequently non-convex optimization problem. Some of the available software lack in generality, while others do not provide ease of use. A user-interactive parameter estimation software was needed for identifying kinetic parameters. In this work we developed an integration based optimization approach to provide a solution to such problems. For easy implementation of the technique, a parameter estimation software (PARES has been developed in MATLAB environment. When tested with extensive example problems from literature, the suggested approach is proven to provide good agreement between predicted and observed data within relatively less computing time and iterations.

Nonlinear estimation of weathering rate parameters for uranium in surface soil near a nuclear facility

International Nuclear Information System (INIS)

Killough, G.G.; Rope, S.K.; Shleien, B.; Voilleque, P.G.

1999-01-01

A dynamic mass-balance model has been calibrated by a nonlinear parameter estimation method, using time-series measurements of uranium in surface soil near the former Feed Materials Production Center (FMPC) near Fernald, Ohio, USA. The time-series data, taken at six locations near the site boundary since 1971, show a statistically significant downtrend of above-background uranium concentration in surface soil for all six locations. The dynamic model is based on first-order kinetics in a surface-soil compartment 10 cm in depth. Median estimates of weathering rate coefficients for insoluble uranium in this soil compartment range from about 0.065-0.14 year -1 , corresponding to mean transit times of about 7-15 years, depending on the location sampled. The model, calibrated by methods similar to those discussed in this paper, has been used to simulate surface soil kinetics of uranium for a dose reconstruction study. It was also applied, along with other data, to make confirmatory estimates of airborne releases of uranium from the FMPC between 1951 and 1988. Two soil-column models (one diffusive and one advective, the latter similar to a catenary first-order kinetic box model) were calibrated to profile data taken at one of the six locations in 1976. The temporal predictions of the advective model approximate the trend of the time series data for that location. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

Science.gov (United States)

Hamim, Salah Uddin Ahmed

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

Iterative method of the parameter variation for solution of nonlinear functional equations

International Nuclear Information System (INIS)

Davidenko, D.F.

1975-01-01

The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

Evaluation of unconfined-aquifer parameters from pumping test data by nonlinear least squares

Science.gov (United States)

Heidari, Manoutchehr; Wench, Allen

1997-05-01

Nonlinear least squares (NLS) with automatic differentiation was used to estimate aquifer parameters from drawdown data obtained from published pumping tests conducted in homogeneous, water-table aquifers. The method is based on a technique that seeks to minimize the squares of residuals between observed and calculated drawdown subject to bounds that are placed on the parameter of interest. The analytical model developed by Neuman for flow to a partially penetrating well of infinitesimal diameter situated in an infinite, homogeneous and anisotropic aquifer was used to obtain calculated drawdown. NLS was first applied to synthetic drawdown data from a hypothetical but realistic aquifer to demonstrate that the relevant hydraulic parameters (storativity, specific yield, and horizontal and vertical hydraulic conductivity) can be evaluated accurately. Next the method was used to estimate the parameters at three field sites with widely varying hydraulic properties. NLS produced unbiased estimates of the aquifer parameters that are close to the estimates obtained with the same data using a visual curve-matching approach. Small differences in the estimates are a consequence of subjective interpretation introduced in the visual approach.

Estimation of Parameters in Mean-Reverting Stochastic Systems

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Tianhai Tian

2014-01-01

Full Text Available Stochastic differential equation (SDE is a very important mathematical tool to describe complex systems in which noise plays an important role. SDE models have been widely used to study the dynamic properties of various nonlinear systems in biology, engineering, finance, and economics, as well as physical sciences. Since a SDE can generate unlimited numbers of trajectories, it is difficult to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. Although substantial research efforts have been made to develop effective methods, it is still a challenge to infer unknown parameters in SDE models from observations that may have large variations. Using an interest rate model as a test problem, in this work we use the Bayesian inference and Markov Chain Monte Carlo method to estimate unknown parameters in SDE models.

A Novel Methodology for Estimating State-Of-Charge of Li-Ion Batteries Using Advanced Parameters Estimation

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Ibrahim M. Safwat

2017-11-01

Full Text Available State-of-charge (SOC estimations of Li-ion batteries have been the focus of many research studies in previous years. Many articles discussed the dynamic model’s parameters estimation of the Li-ion battery, where the fixed forgetting factor recursive least square estimation methodology is employed. However, the change rate of each parameter to reach the true value is not taken into consideration, which may tend to poor estimation. This article discusses this issue, and proposes two solutions to solve it. The first solution is the usage of a variable forgetting factor instead of a fixed one, while the second solution is defining a vector of forgetting factors, which means one factor for each parameter. After parameters estimation, a new idea is proposed to estimate state-of-charge (SOC of the Li-ion battery based on Newton’s method. Also, the error percentage and computational cost are discussed and compared with that of nonlinear Kalman filters. This methodology is applied on a 36 V 30 A Li-ion pack to validate this idea.

PARAMETER ESTIMATION OF VALVE STICTION USING ANT COLONY OPTIMIZATION

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S. Kalaivani

2012-07-01

Full Text Available In this paper, a procedure for quantifying valve stiction in control loops based on ant colony optimization has been proposed. Pneumatic control valves are widely used in the process industry. The control valve contains non-linearities such as stiction, backlash, and deadband that in turn cause oscillations in the process output. Stiction is one of the long-standing problems and it is the most severe problem in the control valves. Thus the measurement data from an oscillating control loop can be used as a possible diagnostic signal to provide an estimate of the stiction magnitude. Quantification of control valve stiction is still a challenging issue. Prior to doing stiction detection and quantification, it is necessary to choose a suitable model structure to describe control-valve stiction. To understand the stiction phenomenon, the Stenman model is used. Ant Colony Optimization (ACO, an intelligent swarm algorithm, proves effective in various fields. The ACO algorithm is inspired from the natural trail following behaviour of ants. The parameters of the Stenman model are estimated using ant colony optimization, from the input-output data by minimizing the error between the actual stiction model output and the simulated stiction model output. Using ant colony optimization, Stenman model with known nonlinear structure and unknown parameters can be estimated.

Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data

Science.gov (United States)

Klein, Vladislav; Murphy, Patrick C.

1998-01-01

Aerodynamic equations were formulated for an aircraft in one-degree-of-freedom large amplitude motion about each of its body axes. The model formulation based on indicial functions separated the resulting aerodynamic forces and moments into static terms, purely rotary terms and unsteady terms. Model identification from experimental data combined stepwise regression and maximum likelihood estimation in a two-stage optimization algorithm that can identify the unsteady term and rotary term if necessary. The identification scheme was applied to oscillatory data in two examples. The model identified from experimental data fit the data well, however, some parameters were estimated with limited accuracy. The resulting model was a good predictor for oscillatory and ramp input data.

Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems

International Nuclear Information System (INIS)

Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris

2011-01-01

Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)

Nonlinearity Analysis and Parameters Optimization for an Inductive Angle Sensor

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Lin Ye

2014-02-01

Full Text Available Using the finite element method (FEM and particle swarm optimization (PSO, a nonlinearity analysis based on parameter optimization is proposed to design an inductive angle sensor. Due to the structure complexity of the sensor, understanding the influences of structure parameters on the nonlinearity errors is a critical step in designing an effective sensor. Key parameters are selected for the design based on the parameters’ effects on the nonlinearity errors. The finite element method and particle swarm optimization are combined for the sensor design to get the minimal nonlinearity error. In the simulation, the nonlinearity error of the optimized sensor is 0.053% in the angle range from −60° to 60°. A prototype sensor is manufactured and measured experimentally, and the experimental nonlinearity error is 0.081% in the angle range from −60° to 60°.

New developments in state estimation for Nonlinear Systems

DEFF Research Database (Denmark)

Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole

2000-01-01

Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a mult......-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications....

Estimating Multivariate Exponentail-Affine Term Structure Models from Coupon Bound Prices using Nonlinear Filtering

DEFF Research Database (Denmark)

Baadsgaard, Mikkel; Nielsen, Jan Nygaard; Madsen, Henrik

2000-01-01

An econometric analysis of continuous-timemodels of the term structure of interest rates is presented. A panel of coupon bond prices with different maturities is used to estimate the embedded parameters of a continuous-discrete state space model of unobserved state variables: the spot interest rate...... noise term should account for model errors. A nonlinear filtering method is used to compute estimates of the state variables, and the model parameters are estimated by a quasimaximum likelihood method provided that some assumptions are imposed on the model residuals. Both Monte Carlo simulation results...

A MIT-Based Nonlinear Adaptive Set-Membership Filter for the Ellipsoidal Estimation of Mobile Robots' States

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Dalei Song

2012-10-01

Full Text Available The adaptive extended set-membership filter (AESMF for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method-based adaptive set-membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time-varying states and parameters. As a result of using the proposed MIT-AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.

Nonlinear estimation and control of automotive drivetrains

CERN Document Server

Chen, Hong

2014-01-01

Nonlinear Estimation and Control of Automotive Drivetrains discusses the control problems involved in automotive drivetrains, particularly in hydraulic Automatic Transmission (AT), Dual Clutch Transmission (DCT) and Automated Manual Transmission (AMT). Challenging estimation and control problems, such as driveline torque estimation and gear shift control, are addressed by applying the latest nonlinear control theories, including constructive nonlinear control (Backstepping, Input-to-State Stable) and Model Predictive Control (MPC). The estimation and control performance is improved while the calibration effort is reduced significantly. The book presents many detailed examples of design processes and thus enables the readers to understand how to successfully combine purely theoretical methodologies with actual applications in vehicles. The book is intended for researchers, PhD students, control engineers and automotive engineers. Hong Chen is a professor at the State Key Laboratory of Automotive Simulation and...

The influence of different PAST-based subspace trackers on DaPT parameter estimation

Science.gov (United States)

Lechtenberg, M.; Götze, J.

2012-09-01

In the context of parameter estimation, subspace-based methods like ESPRIT have become common. They require a subspace separation e.g. based on eigenvalue/-vector decomposition. In time-varying environments, this can be done by subspace trackers. One class of these is based on the PAST algorithm. Our non-linear parameter estimation algorithm DaPT builds on-top of the ESPRIT algorithm. Evaluation of the different variants of the PAST algorithm shows which variant of the PAST algorithm is worthwhile in the context of frequency estimation.

Simultaneous identification of unknown groundwater pollution sources and estimation of aquifer parameters

Science.gov (United States)

Datta, Bithin; Chakrabarty, Dibakar; Dhar, Anirban

2009-09-01

Pollution source identification is a common problem encountered frequently. In absence of prior information about flow and transport parameters, the performance of source identification models depends on the accuracy in estimation of these parameters. A methodology is developed for simultaneous pollution source identification and parameter estimation in groundwater systems. The groundwater flow and transport simulator is linked to the nonlinear optimization model as an external module. The simulator defines the flow and transport processes, and serves as a binding equality constraint. The Jacobian matrix which determines the search direction in the nonlinear optimization model links the groundwater flow-transport simulator and the optimization method. Performance of the proposed methodology using spatiotemporal hydraulic head values and pollutant concentration measurements is evaluated by solving illustrative problems. Two different decision model formulations are developed. The computational efficiency of these models is compared using two nonlinear optimization algorithms. The proposed methodology addresses some of the computational limitations of using the embedded optimization technique which embeds the discretized flow and transport equations as equality constraints for optimization. Solution results obtained are also found to be better than those obtained using the embedded optimization technique. The performance evaluations reported here demonstrate the potential applicability of the developed methodology for a fairly large aquifer study area with multiple unknown pollution sources.

Assessing robustness of designs for random effects parameters for nonlinear mixed-effects models.

Science.gov (United States)

Duffull, Stephen B; Hooker, Andrew C

2017-12-01

Optimal designs for nonlinear models are dependent on the choice of parameter values. Various methods have been proposed to provide designs that are robust to uncertainty in the prior choice of parameter values. These methods are generally based on estimating the expectation of the determinant (or a transformation of the determinant) of the information matrix over the prior distribution of the parameter values. For high dimensional models this can be computationally challenging. For nonlinear mixed-effects models the question arises as to the importance of accounting for uncertainty in the prior value of the variances of the random effects parameters. In this work we explore the influence of the variance of the random effects parameters on the optimal design. We find that the method for approximating the expectation and variance of the likelihood is of potential importance for considering the influence of random effects. The most common approximation to the likelihood, based on a first-order Taylor series approximation, yields designs that are relatively insensitive to the prior value of the variance of the random effects parameters and under these conditions it appears to be sufficient to consider uncertainty on the fixed-effects parameters only.

Frequency-Domain Maximum-Likelihood Estimation of High-Voltage Pulse Transformer Model Parameters

CERN Document Server

Aguglia, D; Martins, C.D.A.

2014-01-01

This paper presents an offline frequency-domain nonlinear and stochastic identification method for equivalent model parameter estimation of high-voltage pulse transformers. Such kinds of transformers are widely used in the pulsed-power domain, and the difficulty in deriving pulsed-power converter optimal control strategies is directly linked to the accuracy of the equivalent circuit parameters. These components require models which take into account electric fields energies represented by stray capacitance in the equivalent circuit. These capacitive elements must be accurately identified, since they greatly influence the general converter performances. A nonlinear frequency-based identification method, based on maximum-likelihood estimation, is presented, and a sensitivity analysis of the best experimental test to be considered is carried out. The procedure takes into account magnetic saturation and skin effects occurring in the windings during the frequency tests. The presented method is validated by experim...

Estimation methods for nonlinear state-space models in ecology

DEFF Research Database (Denmark)

Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro

2011-01-01

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...

Nonlinear parameter estimation in inviscid compressible flows in presence of uncertainties

International Nuclear Information System (INIS)

Jemcov, A.; Mathur, S.

2004-01-01

The focus of this paper is on the formulation and solution of inverse problems of parameter estimation using algorithmic differentiation. The inverse problem formulated here seeks to determine the input parameters that minimize a least squares functional with respect to certain target data. The formulation allows for uncertainty in the target data by considering the least squares functional in a stochastic basis described by the covariance of the target data. Furthermore, to allow for robust design, the formulation also accounts for uncertainties in the input parameters. This is achieved using the method of propagation of uncertainties using the directional derivatives of the output parameters with respect to unknown parameters. The required derivatives are calculated simultaneously with the solution using generic programming exploiting the template and operator overloading features of the C++ language. The methodology described here is general and applicable to any numerical solution procedure for any set of governing equations but for the purpose of this paper we consider a finite volume solution of the compressible Euler equations. In particular, we illustrate the method for the case of supersonic flow in a duct with a wedge. The parameter to be determined is the inlet Mach number and the target data is the axial component of velocity at the exit of the duct. (author)

Riccati-parameter solutions of nonlinear second-order ODEs

International Nuclear Information System (INIS)

Reyes, M A; Rosu, H C

2008-01-01

It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure

Adaptive estimation for control of uncertain nonlinear systems with applications to target tracking

Science.gov (United States)

Madyastha, Venkatesh Kattigari

2005-08-01

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems

Repetitive Identification of Structural Systems Using a Nonlinear Model Parameter Refinement Approach

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Jeng-Wen Lin

2009-01-01

Full Text Available This paper proposes a statistical confidence interval based nonlinear model parameter refinement approach for the health monitoring of structural systems subjected to seismic excitations. The developed model refinement approach uses the 95% confidence interval of the estimated structural parameters to determine their statistical significance in a least-squares regression setting. When the parameters' confidence interval covers the zero value, it is statistically sustainable to truncate such parameters. The remaining parameters will repetitively undergo such parameter sifting process for model refinement until all the parameters' statistical significance cannot be further improved. This newly developed model refinement approach is implemented for the series models of multivariable polynomial expansions: the linear, the Taylor series, and the power series model, leading to a more accurate identification as well as a more controllable design for system vibration control. Because the statistical regression based model refinement approach is intrinsically used to process a “batch” of data and obtain an ensemble average estimation such as the structural stiffness, the Kalman filter and one of its extended versions is introduced to the refined power series model for structural health monitoring.

Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models

DEFF Research Database (Denmark)

Gerhard, Daniel; Bremer, Melanie; Ritz, Christian

2014-01-01

A unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real-time PCR experiments. Focus is on estimating the marginal or population-based derived parameters: cycle thresholds and ΔΔc(t), but retaining the conditional mixed mod...

Parameter Identification for Nonlinear Circuit Models of Power BAW Resonator

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CONSTANTINESCU, F.

2011-02-01

Full Text Available The large signal operation of the bulk acoustic wave (BAW resonators is characterized by the amplitude-frequency effect and the intermodulation effect. The measurement of these effects, together with that of the small signal frequency characteristic, are used in this paper for the parameter identification of the nonlinear circuit models developed previously by authors. As the resonator has been connected to the measurement bench by wire bonding, the parasitic elements of this connection have been taken into account, being estimated solving some electrical and magnetic field problems.

Parameter estimation for lithium ion batteries

Science.gov (United States)

Santhanagopalan, Shriram

With an increase in the demand for lithium based batteries at the rate of about 7% per year, the amount of effort put into improving the performance of these batteries from both experimental and theoretical perspectives is increasing. There exist a number of mathematical models ranging from simple empirical models to complicated physics-based models to describe the processes leading to failure of these cells. The literature is also rife with experimental studies that characterize the various properties of the system in an attempt to improve the performance of lithium ion cells. However, very little has been done to quantify the experimental observations and relate these results to the existing mathematical models. In fact, the best of the physics based models in the literature show as much as 20% discrepancy when compared to experimental data. The reasons for such a big difference include, but are not limited to, numerical complexities involved in extracting parameters from experimental data and inconsistencies in interpreting directly measured values for the parameters. In this work, an attempt has been made to implement simplified models to extract parameter values that accurately characterize the performance of lithium ion cells. The validity of these models under a variety of experimental conditions is verified using a model discrimination procedure. Transport and kinetic properties are estimated using a non-linear estimation procedure. The initial state of charge inside each electrode is also maintained as an unknown parameter, since this value plays a significant role in accurately matching experimental charge/discharge curves with model predictions and is not readily known from experimental data. The second part of the dissertation focuses on parameters that change rapidly with time. For example, in the case of lithium ion batteries used in Hybrid Electric Vehicle (HEV) applications, the prediction of the State of Charge (SOC) of the cell under a variety of

Using linear time-invariant system theory to estimate kinetic parameters directly from projection measurements

International Nuclear Information System (INIS)

Zeng, G.L.; Gullberg, G.T.

1995-01-01

It is common practice to estimate kinetic parameters from dynamically acquired tomographic data by first reconstructing a dynamic sequence of three-dimensional reconstructions and then fitting the parameters to time activity curves generated from the time-varying reconstructed images. However, in SPECT, the pharmaceutical distribution can change during the acquisition of a complete tomographic data set, which can bias the estimated kinetic parameters. It is hypothesized that more accurate estimates of the kinetic parameters can be obtained by fitting to the projection measurements instead of the reconstructed time sequence. Estimation from projections requires the knowledge of their relationship between the tissue regions of interest or voxels with particular kinetic parameters and the project measurements, which results in a complicated nonlinear estimation problem with a series of exponential factors with multiplicative coefficients. A technique is presented in this paper where the exponential decay parameters are estimated separately using linear time-invariant system theory. Once the exponential factors are known, the coefficients of the exponentials can be estimated using linear estimation techniques. Computer simulations demonstrate that estimation of the kinetic parameters directly from the projections is more accurate than the estimation from the reconstructed images

The performance of simulated annealing in parameter estimation for vapor-liquid equilibrium modeling

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A. Bonilla-Petriciolet

2007-03-01

Full Text Available In this paper we report the application and evaluation of the simulated annealing (SA optimization method in parameter estimation for vapor-liquid equilibrium (VLE modeling. We tested this optimization method using the classical least squares and error-in-variable approaches. The reliability and efficiency of the data-fitting procedure are also considered using different values for algorithm parameters of the SA method. Our results indicate that this method, when properly implemented, is a robust procedure for nonlinear parameter estimation in thermodynamic models. However, in difficult problems it still can converge to local optimums of the objective function.

Recursive prediction error methods for online estimation in nonlinear state-space models

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Dag Ljungquist

1994-04-01

Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.

A hybrid optimization approach to the estimation of distributed parameters in two-dimensional confined aquifers

Science.gov (United States)

Heidari, M.; Ranjithan, S.R.

1998-01-01

In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

Science.gov (United States)

Abhinav, S.; Manohar, C. S.

2018-03-01

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

Measurement of the Acoustic Nonlinearity Parameter for Biological Media.

Science.gov (United States)

Cobb, Wesley Nelson

In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.

NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP

Institute of Scientific and Technical Information of China (English)

ZHOU Bo; HAN Jianda

2007-01-01

In order to achieve precise, robust autonomous guidance and control of a tracked vehicle, a kinematic model with longitudinal and lateral slip is established. Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly. The first filter is the well-known extended Kalman filter. The second filter is an unscented version of the Kalman filter. The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution. The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies. The four different approaches have different complexities, behavior and advantages that are surveyed and compared.

Estimation of real-time runway surface contamination using flight data recorder parameters

Science.gov (United States)

Curry, Donovan

Within this research effort, the development of an analytic process for friction coefficient estimation is presented. Under static equilibrium, the sum of forces and moments acting on the aircraft, in the aircraft body coordinate system, while on the ground at any instant is equal to zero. Under this premise the longitudinal, lateral and normal forces due to landing are calculated along with the individual deceleration components existent when an aircraft comes to a rest during ground roll. In order to validate this hypothesis a six degree of freedom aircraft model had to be created and landing tests had to be simulated on different surfaces. The simulated aircraft model includes a high fidelity aerodynamic model, thrust model, landing gear model, friction model and antiskid model. Three main surfaces were defined in the friction model; dry, wet and snow/ice. Only the parameters recorded by an FDR are used directly from the aircraft model all others are estimated or known a priori. The estimation of unknown parameters is also presented in the research effort. With all needed parameters a comparison and validation with simulated and estimated data, under different runway conditions, is performed. Finally, this report presents results of a sensitivity analysis in order to provide a measure of reliability of the analytic estimation process. Linear and non-linear sensitivity analysis has been performed in order to quantify the level of uncertainty implicit in modeling estimated parameters and how they can affect the calculation of the instantaneous coefficient of friction. Using the approach of force and moment equilibrium about the CG at landing to reconstruct the instantaneous coefficient of friction appears to be a reasonably accurate estimate when compared to the simulated friction coefficient. This is also true when the FDR and estimated parameters are introduced to white noise and when crosswind is introduced to the simulation. After the linear analysis the

Non-linear corrections to the cosmological matter power spectrum and scale-dependent galaxy bias: implications for parameter estimation

International Nuclear Information System (INIS)

Hamann, Jan; Hannestad, Steen; Melchiorri, Alessandro; Wong, Yvonne Y Y

2008-01-01

We explore and compare the performances of two non-linear correction and scale-dependent biasing models for the extraction of cosmological information from galaxy power spectrum data, especially in the context of beyond-ΛCDM (CDM: cold dark matter) cosmologies. The first model is the well known Q model, first applied in the analysis of Two-degree Field Galaxy Redshift Survey data. The second, the P model, is inspired by the halo model, in which non-linear evolution and scale-dependent biasing are encapsulated in a single non-Poisson shot noise term. We find that while the two models perform equally well in providing adequate correction for a range of galaxy clustering data in standard ΛCDM cosmology and in extensions with massive neutrinos, the Q model can give unphysical results in cosmologies containing a subdominant free-streaming dark matter whose temperature depends on the particle mass, e.g., relic thermal axions, unless a suitable prior is imposed on the correction parameter. This last case also exposes the danger of analytic marginalization, a technique sometimes used in the marginalization of nuisance parameters. In contrast, the P model suffers no undesirable effects, and is the recommended non-linear correction model also because of its physical transparency

Non-linear corrections to the cosmological matter power spectrum and scale-dependent galaxy bias: implications for parameter estimation

Science.gov (United States)

Hamann, Jan; Hannestad, Steen; Melchiorri, Alessandro; Wong, Yvonne Y. Y.

2008-07-01

We explore and compare the performances of two non-linear correction and scale-dependent biasing models for the extraction of cosmological information from galaxy power spectrum data, especially in the context of beyond-ΛCDM (CDM: cold dark matter) cosmologies. The first model is the well known Q model, first applied in the analysis of Two-degree Field Galaxy Redshift Survey data. The second, the P model, is inspired by the halo model, in which non-linear evolution and scale-dependent biasing are encapsulated in a single non-Poisson shot noise term. We find that while the two models perform equally well in providing adequate correction for a range of galaxy clustering data in standard ΛCDM cosmology and in extensions with massive neutrinos, the Q model can give unphysical results in cosmologies containing a subdominant free-streaming dark matter whose temperature depends on the particle mass, e.g., relic thermal axions, unless a suitable prior is imposed on the correction parameter. This last case also exposes the danger of analytic marginalization, a technique sometimes used in the marginalization of nuisance parameters. In contrast, the P model suffers no undesirable effects, and is the recommended non-linear correction model also because of its physical transparency.

Joint state and parameter estimation for a class of cascade systems: Application to a hemodynamic model

KAUST Repository

Zayane, Chadia

2014-06-01

In this paper, we address a special case of state and parameter estimation, where the system can be put on a cascade form allowing to estimate the state components and the set of unknown parameters separately. Inspired by the nonlinear Balloon hemodynamic model for functional Magnetic Resonance Imaging problem, we propose a hierarchical approach. The system is divided into two subsystems in cascade. The state and input are first estimated from a noisy measured signal using an adaptive observer. The obtained input is then used to estimate the parameters of a linear system using the modulating functions method. Some numerical results are presented to illustrate the efficiency of the proposed method.

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

International Nuclear Information System (INIS)

Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

2013-01-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

Parameter and State Estimation of Large-Scale Complex Systems Using Python Tools

Directory of Open Access Journals (Sweden)

M. Anushka S. Perera

2015-07-01

Full Text Available This paper discusses the topics related to automating parameter, disturbance and state estimation analysis of large-scale complex nonlinear dynamic systems using free programming tools. For large-scale complex systems, before implementing any state estimator, the system should be analyzed for structural observability and the structural observability analysis can be automated using Modelica and Python. As a result of structural observability analysis, the system may be decomposed into subsystems where some of them may be observable --- with respect to parameter, disturbances, and states --- while some may not. The state estimation process is carried out for those observable subsystems and the optimum number of additional measurements are prescribed for unobservable subsystems to make them observable. In this paper, an industrial case study is considered: the copper production process at Glencore Nikkelverk, Kristiansand, Norway. The copper production process is a large-scale complex system. It is shown how to implement various state estimators, in Python, to estimate parameters and disturbances, in addition to states, based on available measurements.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

Science.gov (United States)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking

Applicability of genetic algorithms to parameter estimation of economic models

Directory of Open Access Journals (Sweden)

Marcel Ševela

2004-01-01

Full Text Available The paper concentrates on capability of genetic algorithms for parameter estimation of non-linear economic models. In the paper we test the ability of genetic algorithms to estimate of parameters of demand function for durable goods and simultaneously search for parameters of genetic algorithm that lead to maximum effectiveness of the computation algorithm. The genetic algorithms connect deterministic iterative computation methods with stochastic methods. In the genteic aůgorithm approach each possible solution is represented by one individual, those life and lifes of all generations of individuals run under a few parameter of genetic algorithm. Our simulations resulted in optimal mutation rate of 15% of all bits in chromosomes, optimal elitism rate 20%. We can not set the optimal extend of generation, because it proves positive correlation with effectiveness of genetic algorithm in all range under research, but its impact is degreasing. The used genetic algorithm was sensitive to mutation rate at most, than to extend of generation. The sensitivity to elitism rate is not so strong.

An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation

Institute of Scientific and Technical Information of China (English)

Xiaogu ZHENG

2009-01-01

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.

Determination of the Nonlinearity Parameter in the TNM Model of Structural Recovery

Science.gov (United States)

Bari, Rozana; Simon, Sindee

Structural recovery of non-equilibrium glassy materials takes place by evolution of volume and enthalpy as the glass attempts to reach to equilibrium. Structural recovery is nonlinear, nonexponential, and depends on thermal history and the process can be described by phenomenological models of structural recovery, such as the Tool-Narayanaswamy-Moynihan (TNM) and the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) models. The goal of the present work is to analyze methods to determine the nonlinearity parameter x and activation energy Δh/R. The methods to determine x includes the inflectional analysis, time-temperature superposition, and two-step temperature jump methods. The activation energy Δh/R can also be obtained by the first two methods. The TNM model is used to simulate structural recovery data, which are then used to test the accuracy of the methods to determine x and Δh/R, with a particular interest in data obtained after cooling at high rates as can be obtained in the Flash DSC. The nonlinearity parameter x by the inflectional analysis and two-step temperature methods are accurate for exponential recovery. However, for real systems with nonexponential relaxation, methods to determine x are not reliable. The activation energy is well estimated by both the time-temperature superposition and inflectional analysis methods, with the former being slightly better.

HIV Model Parameter Estimates from Interruption Trial Data including Drug Efficacy and Reservoir Dynamics

Science.gov (United States)

Luo, Rutao; Piovoso, Michael J.; Martinez-Picado, Javier; Zurakowski, Ryan

2012-01-01

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients. PMID:22815727

Optimization-based particle filter for state and parameter estimation

Institute of Scientific and Technical Information of China (English)

Li Fu; Qi Fei; Shi Guangming; Zhang Li

2009-01-01

In recent years, the theory of particle filter has been developed and widely used for state and parameter estimation in nonlinear/non-Gaussian systems. Choosing good importance density is a critical issue in particle filter design. In order to improve the approximation of posterior distribution, this paper provides an optimization-based algorithm (the steepest descent method) to generate the proposal distribution and then sample particles from the distribution. This algorithm is applied in 1-D case, and the simulation results show that the proposed particle filter performs better than the extended Kalman filter (EKF), the standard particle filter (PF), the extended Kalman particle filter (PF-EKF) and the unscented particle filter (UPF) both in efficiency and in estimation precision.

Identification and estimation of nonlinear models using two samples with nonclassical measurement errors

KAUST Repository

Carroll, Raymond J.

2010-05-01

This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest - the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates - is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

Science.gov (United States)

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

Science.gov (United States)

Su, Fei; Wang, Jiang; Deng, Bin; Wei, Xi-Le; Chen, Ying-Yuan; Liu, Chen; Li, Hui-Yan

2015-02-01

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

Effect of conjugation length on nonlinear optical parameters of anthraquinone dyes investigated using He-Ne laser operating in CW mode

Science.gov (United States)

Pramodini, S.; Poornesh, P.

2014-10-01

We report the studies on third-order optical nonlinearity and optical limiting of anthraquinone dyes. Z-scan technique was employed to evaluate the nonlinear parameters such as nonlinear absorption coefficient βeff and nonlinear index of refraction n2. Continuous wave He-Ne laser was used as the source of excitation. The estimated values of βeff, n2 and χ(3) are of the order of 10-3 cm/W, 10-5 esu and 10-7 esu respectively. The presence of donor and acceptor groups in the structure results in increase in conjugation length. This resulted in the enhancement of nonlinear optical parameters values of the dye. Multiple diffraction rings were observed when the samples were exposed to laser beam due to thermal lensing. Dyes exhibited good optical limiting behavior under the experimental conditions. The results indicate that the dyes investigated here are materialise as candidates for photonics device applications such as optical power limiters.

Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation

Directory of Open Access Journals (Sweden)

Xiaoyan Deng

2009-01-01

into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.

Synchronous Generator Model Parameter Estimation Based on Noisy Dynamic Waveforms

Science.gov (United States)

Berhausen, Sebastian; Paszek, Stefan

2016-01-01

In recent years, there have occurred system failures in many power systems all over the world. They have resulted in a lack of power supply to a large number of recipients. To minimize the risk of occurrence of power failures, it is necessary to perform multivariate investigations, including simulations, of power system operating conditions. To conduct reliable simulations, the current base of parameters of the models of generating units, containing the models of synchronous generators, is necessary. In the paper, there is presented a method for parameter estimation of a synchronous generator nonlinear model based on the analysis of selected transient waveforms caused by introducing a disturbance (in the form of a pseudorandom signal) in the generator voltage regulation channel. The parameter estimation was performed by minimizing the objective function defined as a mean square error for deviations between the measurement waveforms and the waveforms calculated based on the generator mathematical model. A hybrid algorithm was used for the minimization of the objective function. In the paper, there is described a filter system used for filtering the noisy measurement waveforms. The calculation results of the model of a 44 kW synchronous generator installed on a laboratory stand of the Institute of Electrical Engineering and Computer Science of the Silesian University of Technology are also given. The presented estimation method can be successfully applied to parameter estimation of different models of high-power synchronous generators operating in a power system.

Estimating the parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistic

OpenAIRE

McDonald, A. David; Sandal, Leif Kristoffer

1998-01-01

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic, put forward by Hurn and Lin...

Convergent Cross Mapping: Basic concept, influence of estimation parameters and practical application.

Science.gov (United States)

Schiecke, Karin; Pester, Britta; Feucht, Martha; Leistritz, Lutz; Witte, Herbert

2015-01-01

In neuroscience, data are typically generated from neural network activity. Complex interactions between measured time series are involved, and nothing or only little is known about the underlying dynamic system. Convergent Cross Mapping (CCM) provides the possibility to investigate nonlinear causal interactions between time series by using nonlinear state space reconstruction. Aim of this study is to investigate the general applicability, and to show potentials and limitation of CCM. Influence of estimation parameters could be demonstrated by means of simulated data, whereas interval-based application of CCM on real data could be adapted for the investigation of interactions between heart rate and specific EEG components of children with temporal lobe epilepsy.

DYNAMIC ESTIMATION FOR PARAMETERS OF INTERFERENCE SIGNALS BY THE SECOND ORDER EXTENDED KALMAN FILTERING

Directory of Open Access Journals (Sweden)

P. A. Ermolaev

2014-03-01

Full Text Available Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.

Application of the Generalized Nonlinear Complementary Relationship for Estimating Evaporation in North China

Science.gov (United States)

Yu, M.; Wu, B.

2017-12-01

As an important part of the coupled Eco-Hydrological processes, evaporation is the bond for exchange of energy and heat between the surface and the atmosphere. However, the estimation of evaporation remains a challenge compared with other main hydrological factors in water cycle. The complementary relationship which proposed by Bouchet (1963) has laid the foundation for various approaches to estimate evaporation from land surfaces, the essence of the principle is a relationship between three types of evaporation in the environment. It can simply implemented with routine meteorological data without the need for resistance parameters of the vegetation and bare land, which are difficult to observed and complicated to estimate in most surface flux models. On this basis the generalized nonlinear formulation was proposed by Brutsaert (2015). The daily evaporation can be estimated once the potential evaporation (Epo) and apparent potential evaporation (Epa) are known. The new formulation has a strong physical basis and can be expected to perform better under natural water stress conditions, nevertheless, the model has not been widely validated over different climate types and underlying surface patterns. In this study, we attempted to apply the generalized nonlinear complementary relationship in North China, three flux stations in North China are used for testing the universality and accuracy of this model against observed evaporation over different vegetation types, including Guantao Site, Miyun Site and Huailai Site. Guantao Site has double-cropping systems and crop rotations with summer maize and winter wheat; the other two sites are dominated by spring maize. Detailed measurements of meteorological factors at certain heights above ground surface from automatic weather stations offered necessary parameters for daily evaporation estimation. Using the Bowen ratio, the surface energy measured by the eddy covariance systems at the flux stations is adjusted on a daily scale

Optomechanical parameter estimation

International Nuclear Information System (INIS)

Ang, Shan Zheng; Tsang, Mankei; Harris, Glen I; Bowen, Warwick P

2013-01-01

We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cramér–Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of radiometer and expectation–maximization (EM) algorithms in the estimation of the force noise power. When applied to experimental data, the EM estimator is found to have the lowest error and follow the Cramér–Rao bound most closely. Our analytic results are envisioned to be valuable to optomechanical experiment design, while the EM algorithm, with its ability to estimate most of the system parameters, is envisioned to be useful for optomechanical sensing, atomic magnetometry and fundamental tests of quantum mechanics. (paper)

A parameter estimation for DC servo motor by using optimization process

International Nuclear Information System (INIS)

Arjoni Amir

2010-01-01

Modeling and simulation parameters of DC servo motor using Matlab Simulink software have been done. The objective to define the DC servo motor parameter estimation is to get DC servo motor parameter values (B, La, Ra, Km, J) which are significant value that can be used for actuation process of control systems. In the analysis of control systems DC the servo motor expressed by transfer function equation to make faster to be analyzed as a component of the actuator. To obtain the data model parameters and initial conditions of the DC servo motors is then carried out the processor modeling and simulation in which the DC servo motor combined with other components. To obtain preliminary data of the DC servo motor parameters as estimated venue, it is obtained from the data factory of the DC servo motor. The initial data parameters of the DC servo motor are applied for the optimization process by using nonlinear least square algorithm and minimize the cost function value so that the DC servo motors parameter values are obtained significantly. The result of the optimization process of the DC servo motor parameter values are B = 0.039881, J= 1.2608e-007, Km = 0.069648, La = 2.3242e-006 and Ra = 1.8837. (author)

State and parameter estimation based on a nonlinear filter applied to an industrial process control of ethanol production

Directory of Open Access Journals (Sweden)

Meleiro L.A.C.

2000-01-01

Full Text Available Most advanced computer-aided control applications rely on good dynamics process models. The performance of the control system depends on the accuracy of the model used. Typically, such models are developed by conducting off-line identification experiments on the process. These experiments for identification often result in input-output data with small output signal-to-noise ratio, and using these data results in inaccurate model parameter estimates [1]. In this work, a multivariable adaptive self-tuning controller (STC was developed for a biotechnological process application. Due to the difficulties involving the measurements or the excessive amount of variables normally found in industrial process, it is proposed to develop "soft-sensors" which are based fundamentally on artificial neural networks (ANN. A second approach proposed was set in hybrid models, results of the association of deterministic models (which incorporates the available prior knowledge about the process being modeled with artificial neural networks. In this case, kinetic parameters - which are very hard to be accurately determined in real time industrial plants operation - were obtained using ANN predictions. These methods are especially suitable for the identification of time-varying and nonlinear models. This advanced control strategy was applied to a fermentation process to produce ethyl alcohol (ethanol in industrial scale. The reaction rate considered for substratum consumption, cells and ethanol productions are validated with industrial data for typical operating conditions. The results obtained show that the proposed procedure in this work has a great potential for application.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics.

Science.gov (United States)

Madi, Mahmoud K; Karameh, Fadi N

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

Science.gov (United States)

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate

Describing pediatric dysphonia with nonlinear dynamic parameters

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Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

2008-01-01

Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

Numerical simulation of electro-osmotic consolidation coupling non-linear variation of soil parameters

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Wu, Hui; Hu, Liming; Wen, Qingbo

2017-06-01

Electro-osmotic consolidation is an effective method for soft ground improvement. A main limitation of previous numerical models on this technique is the ignorance of the non-linear variation of soil parameters. In the present study, a multi-field numerical model is developed with the consideration of the non-linear variation of soil parameters during electro-osmotic consolidation process. The numerical simulations on an axisymmetric model indicated that the non-linear variation of soil parameters showed remarkable impact on the development of the excess pore water pressure and degree of consolidation. A field experiment with complex geometry, boundary conditions, electrode configuration and voltage application was further simulated with the developed numerical model. The comparison between field and numerical data indicated that the numerical model coupling of the non-linear variation of soil parameters gave more reasonable results. The developed numerical model is capable to analyze engineering cases with complex operating conditions.

Nonlinear observer to estimate polarization phenomenon in membrane distillation

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Khoukhi Billal

2015-01-01

Full Text Available This paper presents a bi-dimensional dynamic model of Direct Contact Membrane Desalination (DCMD process. Most of the MD configuration processes have been modeled as steady-state one-dimensional systems. Stationary two-dimensional MD models have been considered only in very few studies. In this work, a dynamic model of a DCMD process is developed. The model is implemented using Matlab/Simulink environment. Numerical simulations are conducted for different operational parameters at the module inlets such as the feed and permeate temperature or feed and permeate flow rate. The results are compared with experimental data published in the literature. The work presents also a feed forward control that compensates the possible decrease of the temperature gradient by increasing the flow rate. This work also deals with a development of nonlinear observer to estimate temperature polarization inside the membrane. The observer gives a good profile and longitudinal temperature estimations and shows a good prediction of pure water flux production.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

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Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints

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Adom Giffin

2014-09-01

Full Text Available In this paper, we continue our efforts to show how maximum relative entropy (MrE can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF. However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA. Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.

Chloramine demand estimation using surrogate chemical and microbiological parameters.

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Moradi, Sina; Liu, Sanly; Chow, Christopher W K; van Leeuwen, John; Cook, David; Drikas, Mary; Amal, Rose

2017-07-01

A model is developed to enable estimation of chloramine demand in full scale drinking water supplies based on chemical and microbiological factors that affect chloramine decay rate via nonlinear regression analysis method. The model is based on organic character (specific ultraviolet absorbance (SUVA)) of the water samples and a laboratory measure of the microbiological (F m ) decay of chloramine. The applicability of the model for estimation of chloramine residual (and hence chloramine demand) was tested on several waters from different water treatment plants in Australia through statistical test analysis between the experimental and predicted data. Results showed that the model was able to simulate and estimate chloramine demand at various times in real drinking water systems. To elucidate the loss of chloramine over the wide variation of water quality used in this study, the model incorporates both the fast and slow chloramine decay pathways. The significance of estimated fast and slow decay rate constants as the kinetic parameters of the model for three water sources in Australia was discussed. It was found that with the same water source, the kinetic parameters remain the same. This modelling approach has the potential to be used by water treatment operators as a decision support tool in order to manage chloramine disinfection. Copyright © 2017. Published by Elsevier B.V.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

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Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Improved Estimates of Thermodynamic Parameters

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Lawson, D. D.

1982-01-01

Techniques refined for estimating heat of vaporization and other parameters from molecular structure. Using parabolic equation with three adjustable parameters, heat of vaporization can be used to estimate boiling point, and vice versa. Boiling points and vapor pressures for some nonpolar liquids were estimated by improved method and compared with previously reported values. Technique for estimating thermodynamic parameters should make it easier for engineers to choose among candidate heat-exchange fluids for thermochemical cycles.

Estimating Lithium-Ion Battery State of Charge and Parameters Using a Continuous-Discrete Extended Kalman Filter

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Yasser Diab

2017-07-01

Full Text Available A real-time determination of battery parameters is challenging because batteries are non-linear, time-varying systems. The transient behaviour of lithium-ion batteries is modelled by a Thevenin-equivalent circuit with two time constants characterising activation and concentration polarization. An experimental approach is proposed for directly determining battery parameters as a function of physical quantities. The model’s parameters are a function of the state of charge and of the discharge rate. These can be expressed by regression equations in the model to derive a continuous-discrete extended Kalman estimator of the state of charge and of other parameters. This technique is based on numerical integration of the ordinary differential equations to predict the state of the stochastic dynamic system and the corresponding error covariance matrix. Then a standard correction step of the extended Kalman filter (EKF is applied to increase the accuracy of estimated parameters. Simulations resulting from this proposed estimator model were compared with experimental results under a variety of operating scenarios—analysis of the results demonstrate the accuracy of the estimator for correctly identifying battery parameters.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

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Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

International Nuclear Information System (INIS)

Sharma, Mamta; Tripathi, S. K.

2015-01-01

CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n 2 ) and nonlinear susceptibility (χ 3 ) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n 2 and β and is found to be of the order of 10 −7 – 10 −8 m 2 /V 2 . The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect

Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization

International Nuclear Information System (INIS)

Gao Fei; Tong Hengqing; Li Zhuoqiu

2008-01-01

This paper proposes a novel quantum-behaved particle swarm optimization (NQPSO) for the estimation of chaos' unknown parameters by transforming them into nonlinear functions' optimization. By means of the techniques in the following three aspects: contracting the searching space self-adaptively; boundaries restriction strategy; substituting the particles' convex combination for their centre of mass, this paper achieves a quite effective search mechanism with fine equilibrium between exploitation and exploration. Details of applying the proposed method and other methods into Lorenz systems are given, and experiments done show that NQPSO has better adaptability, dependability and robustness. It is a successful approach in unknown parameter estimation online especially in the cases with white noises

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

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Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification

Parameters estimation for reactive transport: A way to test the validity of a reactive model

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Aggarwal, Mohit; Cheikh Anta Ndiaye, Mame; Carrayrou, Jérôme

The chemical parameters used in reactive transport models are not known accurately due to the complexity and the heterogeneous conditions of a real domain. We will present an efficient algorithm in order to estimate the chemical parameters using Monte-Carlo method. Monte-Carlo methods are very robust for the optimisation of the highly non-linear mathematical model describing reactive transport. Reactive transport of tributyltin (TBT) through natural quartz sand at seven different pHs is taken as the test case. Our algorithm will be used to estimate the chemical parameters of the sorption of TBT onto the natural quartz sand. By testing and comparing three models of surface complexation, we show that the proposed adsorption model cannot explain the experimental data.

Stable Parameter Estimation for Autoregressive Equations with Random Coefficients

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V. B. Goryainov

2014-01-01

Full Text Available In recent yearsthere has been a growing interest in non-linear time series models. They are more flexible than traditional linear models and allow more adequate description of real data. Among these models a autoregressive model with random coefficients plays an important role. It is widely used in various fields of science and technology, for example, in physics, biology, economics and finance. The model parameters are the mean values of autoregressive coefficients. Their evaluation is the main task of model identification. The basic method of estimation is still the least squares method, which gives good results for Gaussian time series, but it is quite sensitive to even small disturbancesin the assumption of Gaussian observations. In this paper we propose estimates, which generalize the least squares estimate in the sense that the quadratic objective function is replaced by an arbitrary convex and even function. Reasonable choice of objective function allows you to keep the benefits of the least squares estimate and eliminate its shortcomings. In particular, you can make it so that they will be almost as effective as the least squares estimate in the Gaussian case, but almost never loose in accuracy with small deviations of the probability distribution of the observations from the Gaussian distribution.The main result is the proof of consistency and asymptotic normality of the proposed estimates in the particular case of the one-parameter model describing the stationary process with finite variance. Another important result is the finding of the asymptotic relative efficiency of the proposed estimates in relation to the least squares estimate. This allows you to compare the two estimates, depending on the probability distribution of innovation process and of autoregressive coefficients. The results can be used to identify an autoregressive process, especially with nonGaussian nature, and/or of autoregressive processes observed with gross

Automated Land Cover Change Detection and Mapping from Hidden Parameter Estimates of Normalized Difference Vegetation Index (NDVI) Time-Series

Science.gov (United States)

Chakraborty, S.; Banerjee, A.; Gupta, S. K. S.; Christensen, P. R.; Papandreou-Suppappola, A.

2017-12-01

Multitemporal observations acquired frequently by satellites with short revisit periods such as the Moderate Resolution Imaging Spectroradiometer (MODIS), is an important source for modeling land cover. Due to the inherent seasonality of the land cover, harmonic modeling reveals hidden state parameters characteristic to it, which is used in classifying different land cover types and in detecting changes due to natural or anthropogenic factors. In this work, we use an eight day MODIS composite to create a Normalized Difference Vegetation Index (NDVI) time-series of ten years. Improved hidden parameter estimates of the nonlinear harmonic NDVI model are obtained using the Particle Filter (PF), a sequential Monte Carlo estimator. The nonlinear estimation based on PF is shown to improve parameter estimation for different land cover types compared to existing techniques that use the Extended Kalman Filter (EKF), due to linearization of the harmonic model. As these parameters are representative of a given land cover, its applicability in near real-time detection of land cover change is also studied by formulating a metric that captures parameter deviation due to change. The detection methodology is evaluated by considering change as a rare class problem. This approach is shown to detect change with minimum delay. Additionally, the degree of change within the change perimeter is non-uniform. By clustering the deviation in parameters due to change, this spatial variation in change severity is effectively mapped and validated with high spatial resolution change maps of the given regions.

METAHEURISTIC OPTIMIZATION METHODS FOR PARAMETERS ESTIMATION OF DYNAMIC SYSTEMS

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V. Panteleev Andrei

2017-01-01

Full Text Available The article considers the usage of metaheuristic methods of constrained global optimization: “Big Bang - Big Crunch”, “Fireworks Algorithm”, “Grenade Explosion Method” in parameters of dynamic systems estimation, described with algebraic-differential equations. Parameters estimation is based upon the observation results from mathematical model behavior. Their values are derived after criterion minimization, which describes the total squared error of state vector coordinates from the deduced ones with precise values observation at different periods of time. Paral- lelepiped type restriction is imposed on the parameters values. Used for solving problems, metaheuristic methods of constrained global extremum don’t guarantee the result, but allow to get a solution of a rather good quality in accepta- ble amount of time. The algorithm of using metaheuristic methods is given. Alongside with the obvious methods for solving algebraic-differential equation systems, it is convenient to use implicit methods for solving ordinary differen- tial equation systems. Two ways of solving the problem of parameters evaluation are given, those parameters differ in their mathematical model. In the first example, a linear mathematical model describes the chemical action parameters change, and in the second one, a nonlinear mathematical model describes predator-prey dynamics, which characterize the changes in both kinds’ population. For each of the observed examples there are calculation results from all the three methods of optimization, there are also some recommendations for how to choose methods parameters. The obtained numerical results have demonstrated the efficiency of the proposed approach. The deduced parameters ap- proximate points slightly differ from the best known solutions, which were deduced differently. To refine the results one should apply hybrid schemes that combine classical methods of optimization of zero, first and second orders and

Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

Energy Technology Data Exchange (ETDEWEB)

Sharma, Mamta [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India); Department of Applied Sciences (Physics), UIET, Panjab University, Chandigarh-160014 (India); Tripathi, S. K., E-mail: surya@pu.ac.in, E-mail: surya-tr@yahoo.com [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India)

2015-06-24

CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n{sub 2}) and nonlinear susceptibility (χ{sup 3}) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n{sub 2} and β and is found to be of the order of 10{sup −7} – 10{sup −8} m{sup 2}/V{sup 2}. The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect.

Noise level estimation in weakly nonlinear slowly time-varying systems

International Nuclear Information System (INIS)

Aerts, J R M; Dirckx, J J J; Lataire, J; Pintelon, R

2008-01-01

Recently, a method using multisine excitation was proposed for estimating the frequency response, the nonlinear distortions and the disturbing noise of weakly nonlinear time-invariant systems. This method has been demonstrated on the measurement of nonlinear distortions in the vibration of acoustically driven systems such as a latex membrane, which is a good example of a time-invariant system [1]. However, not all systems are perfectly time invariant, e.g. biomechanical systems. This time variation can be misinterpreted as an elevated noise floor, and the classical noise estimation method gives a wrong result. Two improved methods to retrieve the correct noise information from the measurements are presented. Both of them make use of multisine excitations. First, it is demonstrated that the improved methods give the same result as the classical noise estimation method when applied to a time-invariant system (high-quality microphone membrane). Next, it is demonstrated that the new methods clearly give an improved estimate of the noise level on time-varying systems. As an application example results for the vibration response of an eardrum are shown

Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

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Ding, Bo; Fang, Huajing

2017-05-01

This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

International Nuclear Information System (INIS)

Banerjee, Amit; Abu-Mahfouz, Issam

2014-01-01

The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm

Linear parameter varying representations for nonlinear control design

Science.gov (United States)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that

Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia

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Cândea, Doina; Halanay, Andrei; Rǎdulescu, Rodica; Tǎlmaci, Rodica

2017-01-01

We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. For the most significant parameters of the model which affect the evolution of CML disease during Imatinib treatment we try to estimate the realistic values using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

Directory of Open Access Journals (Sweden)

A. M. López Jiménez

2002-01-01

Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

Robust and efficient parameter estimation in dynamic models of biological systems.

Science.gov (United States)

Gábor, Attila; Banga, Julio R

2015-10-29

Dynamic modelling provides a systematic framework to understand function in biological systems. Parameter estimation in nonlinear dynamic models remains a very challenging inverse problem due to its nonconvexity and ill-conditioning. Associated issues like overfitting and local solutions are usually not properly addressed in the systems biology literature despite their importance. Here we present a method for robust and efficient parameter estimation which uses two main strategies to surmount the aforementioned difficulties: (i) efficient global optimization to deal with nonconvexity, and (ii) proper regularization methods to handle ill-conditioning. In the case of regularization, we present a detailed critical comparison of methods and guidelines for properly tuning them. Further, we show how regularized estimations ensure the best trade-offs between bias and variance, reducing overfitting, and allowing the incorporation of prior knowledge in a systematic way. We illustrate the performance of the presented method with seven case studies of different nature and increasing complexity, considering several scenarios of data availability, measurement noise and prior knowledge. We show how our method ensures improved estimations with faster and more stable convergence. We also show how the calibrated models are more generalizable. Finally, we give a set of simple guidelines to apply this strategy to a wide variety of calibration problems. Here we provide a parameter estimation strategy which combines efficient global optimization with a regularization scheme. This method is able to calibrate dynamic models in an efficient and robust way, effectively fighting overfitting and allowing the incorporation of prior information.

Parameter estimation in plasmonic QED

Science.gov (United States)

Jahromi, H. Rangani

2018-03-01

We address the problem of parameter estimation in the presence of plasmonic modes manipulating emitted light via the localized surface plasmons in a plasmonic waveguide at the nanoscale. The emitter that we discuss is the nitrogen vacancy centre (NVC) in diamond modelled as a qubit. Our goal is to estimate the β factor measuring the fraction of emitted energy captured by waveguide surface plasmons. The best strategy to obtain the most accurate estimation of the parameter, in terms of the initial state of the probes and different control parameters, is investigated. In particular, for two-qubit estimation, it is found although we may achieve the best estimation at initial instants by using the maximally entangled initial states, at long times, the optimal estimation occurs when the initial state of the probes is a product one. We also find that decreasing the interqubit distance or increasing the propagation length of the plasmons improve the precision of the estimation. Moreover, decrease of spontaneous emission rate of the NVCs retards the quantum Fisher information (QFI) reduction and therefore the vanishing of the QFI, measuring the precision of the estimation, is delayed. In addition, if the phase parameter of the initial state of the two NVCs is equal to πrad, the best estimation with the two-qubit system is achieved when initially the NVCs are maximally entangled. Besides, the one-qubit estimation has been also analysed in detail. Especially, we show that, using a two-qubit probe, at any arbitrary time, enhances considerably the precision of estimation in comparison with one-qubit estimation.

Parameter Estimation in Continuous Time Domain

Directory of Open Access Journals (Sweden)

Gabriela M. ATANASIU

2016-12-01

Full Text Available This paper will aim to presents the applications of a continuous-time parameter estimation method for estimating structural parameters of a real bridge structure. For the purpose of illustrating this method two case studies of a bridge pile located in a highly seismic risk area are considered, for which the structural parameters for the mass, damping and stiffness are estimated. The estimation process is followed by the validation of the analytical results and comparison with them to the measurement data. Further benefits and applications for the continuous-time parameter estimation method in civil engineering are presented in the final part of this paper.

A Novel Non-Iterative Method for Real-Time Parameter Estimation of the Fricke-Morse Model

Directory of Open Access Journals (Sweden)

SIMIC, M.

2016-11-01

Full Text Available Parameter estimation of Fricke-Morse model of biological tissue is widely used in bioimpedance data processing and analysis. Complex nonlinear least squares (CNLS data fitting is often used for parameter estimation of the model, but limitations such as high processing time, converging into local minimums, need for good initial guess of model parameters and non-convergence have been reported. Thus, there is strong motivation to develop methods which can solve these flaws. In this paper a novel real-time method for parameter estimation of Fricke-Morse model of biological cells is presented. The proposed method uses the value of characteristic frequency estimated from the measured imaginary part of bioimpedance, whereupon the Fricke-Morse model parameters are calculated using the provided analytical expressions. The proposed method is compared with CNLS in frequency ranges of 1 kHz to 10 MHz (beta-dispersion and 10 kHz to 100 kHz, which is more suitable for low-cost microcontroller-based bioimpedance measurement systems. The obtained results are promising, and in both frequency ranges, CNLS and the proposed method have accuracies suitable for most electrical bioimpedance (EBI applications. However, the proposed algorithm has significantly lower computation complexity, so it was 20-80 times faster than CNLS.

Parameter sensitivity analysis of nonlinear piezoelectric probe in tapping mode atomic force microscopy for measurement improvement

Energy Technology Data Exchange (ETDEWEB)

McCarty, Rachael; Nima Mahmoodi, S., E-mail: nmahmoodi@eng.ua.edu [Department of Mechanical Engineering, The University of Alabama, Box 870276, Tuscaloosa, Alabama 35487 (United States)

2014-02-21

The equations of motion for a piezoelectric microcantilever are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are obtained. Then, the method of multiple scales is used to analyze the analytical frequency response of the piezoelectric probe. The effects of nonlinear excitation force on the microcantilever beam's frequency and amplitude are analytically studied. The results show a frequency shift in the response resulting from the force nonlinearities. This frequency shift during contact mode is an important consideration in the modeling of AFM mechanics for generation of more accurate imaging. Also, a sensitivity analysis of the system parameters on the nonlinearity effect is performed. The results of a sensitivity analysis show that it is possible to choose parameters such that the frequency shift minimizes. Certain parameters such as tip radius, microcantilever beam dimensions, and modulus of elasticity have more influence on the nonlinearity of the system than other parameters. By changing only three parameters—tip radius, thickness, and modulus of elasticity of the microbeam—a more than 70% reduction in nonlinearity effect was achieved.

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

Science.gov (United States)

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

Non-linearity parameter of binary liquid mixtures at elevated pressures

Indian Academy of Sciences (India)

. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter / of four binary liquid ...

Nonlinear models for autoregressive conditional heteroskedasticity

DEFF Research Database (Denmark)

Teräsvirta, Timo

This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discu...

ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS

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muhammad zahid rashid

2011-04-01

Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR,  moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes

Parameter estimation techniques for LTP system identification

Science.gov (United States)

Nofrarias Serra, Miquel

LISA Pathfinder (LPF) is the precursor mission of LISA (Laser Interferometer Space Antenna) and the first step towards gravitational waves detection in space. The main instrument onboard the mission is the LTP (LISA Technology Package) whose scientific goal is to test LISA's drag-free control loop by reaching a differential acceleration noise level between two masses in √ geodesic motion of 3 × 10-14 ms-2 / Hz in the milliHertz band. The mission is not only challenging in terms of technology readiness but also in terms of data analysis. As with any gravitational wave detector, attaining the instrument performance goals will require an extensive noise hunting campaign to measure all contributions with high accuracy. But, opposite to on-ground experiments, LTP characterisation will be only possible by setting parameters via telecommands and getting a selected amount of information through the available telemetry downlink. These two conditions, high accuracy and high reliability, are the main restrictions that the LTP data analysis must overcome. A dedicated object oriented Matlab Toolbox (LTPDA) has been set up by the LTP analysis team for this purpose. Among the different toolbox methods, an essential part for the mission are the parameter estimation tools that will be used for system identification during operations: Linear Least Squares, Non-linear Least Squares and Monte Carlo Markov Chain methods have been implemented as LTPDA methods. The data analysis team has been testing those methods with a series of mock data exercises with the following objectives: to cross-check parameter estimation methods and compare the achievable accuracy for each of them, and to develop the best strategies to describe the physics underlying a complex controlled experiment as the LTP. In this contribution we describe how these methods were tested with simulated LTP-like data to recover the parameters of the model and we report on the latest results of these mock data exercises.

Bayesian Parameter Estimation for Heavy-Duty Vehicles

Energy Technology Data Exchange (ETDEWEB)

Miller, Eric; Konan, Arnaud; Duran, Adam

2017-03-28

Accurate vehicle parameters are valuable for design, modeling, and reporting. Estimating vehicle parameters can be a very time-consuming process requiring tightly-controlled experimentation. This work describes a method to estimate vehicle parameters such as mass, coefficient of drag/frontal area, and rolling resistance using data logged during standard vehicle operation. The method uses Monte Carlo to generate parameter sets which is fed to a variant of the road load equation. Modeled road load is then compared to measured load to evaluate the probability of the parameter set. Acceptance of a proposed parameter set is determined using the probability ratio to the current state, so that the chain history will give a distribution of parameter sets. Compared to a single value, a distribution of possible values provides information on the quality of estimates and the range of possible parameter values. The method is demonstrated by estimating dynamometer parameters. Results confirm the method's ability to estimate reasonable parameter sets, and indicates an opportunity to increase the certainty of estimates through careful selection or generation of the test drive cycle.

An improved fuzzy Kalman filter for state estimation of nonlinear systems

International Nuclear Information System (INIS)

Zhou, Z-J; Hu, C-H; Chen, L; Zhang, B-C

2008-01-01

The extended fuzzy Kalman filter (EFKF) is developed recently and used for state estimation of the nonlinear systems with uncertainty. Based on extension of the orthogonality principle and the extended fuzzy Kalman filter, an improved fuzzy Kalman filters (IFKF) is proposed in this paper, which is more applicable and can deal with the state estimation of the nonlinear systems better than the EFKF. A simulation study is provided to verify the efficiency of the proposed method

MANOVA, LDA, and FA criteria in clusters parameter estimation

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Stan Lipovetsky

2015-12-01

Full Text Available Multivariate analysis of variance (MANOVA and linear discriminant analysis (LDA apply such well-known criteria as the Wilks’ lambda, Lawley–Hotelling trace, and Pillai’s trace test for checking quality of the solutions. The current paper suggests using these criteria for building objectives for finding clusters parameters because optimizing such objectives corresponds to the best distinguishing between the clusters. Relation to Joreskog’s classification for factor analysis (FA techniques is also considered. The problem can be reduced to the multinomial parameterization, and solution can be found in a nonlinear optimization procedure which yields the estimates for the cluster centers and sizes. This approach for clustering works with data compressed into covariance matrix so can be especially useful for big data.

Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring

Science.gov (United States)

Li, Y. J.; Kokkinaki, Amalia; Darve, Eric F.; Kitanidis, Peter K.

2017-08-01

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts.

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

Bierens, Herman J

1981-01-01

This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

Sensitivity of acoustic nonlinearity parameter to the microstructural changes in cement-based materials

Science.gov (United States)

Kim, Gun; Kim, Jin-Yeon; Kurtis, Kimberly E.; Jacobs, Laurence J.

2015-03-01

This research experimentally investigates the sensitivity of the acoustic nonlinearity parameter to microcracks in cement-based materials. Based on the second harmonic generation (SHG) technique, an experimental setup using non-contact, air-coupled detection is used to receive the consistent Rayleigh surface waves. To induce variations in the extent of microscale cracking in two types of specimens (concrete and mortar), shrinkage reducing admixture (SRA), is used in one set, while a companion specimen is prepared without SRA. A 50 kHz wedge transducer and a 100 kHz air-coupled transducer are implemented for the generation and detection of nonlinear Rayleigh waves. It is shown that the air-coupled detection method provides more repeatable fundamental and second harmonic amplitudes of the propagating Rayleigh waves. The obtained amplitudes are then used to calculate the relative nonlinearity parameter βre, the ratio of the second harmonic amplitude to the square of the fundamental amplitude. The experimental results clearly demonstrate that the nonlinearity parameter (βre) is highly sensitive to the microstructural changes in cement-based materials than the Rayleigh phase velocity and attenuation and that SRA has great potential to avoid shrinkage cracking in cement-based materials.

Ecient Parameter Estimation and Control Based on a Modified LOS Guidance System of an Underwater Vehicle

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Elías Revestido Herrero

2017-12-01

Full Text Available In this work, a methodology is proposed for the improvement of the parameter estimation effciency of a non-linear manoeuvring model of a torpedo shaped unmanned underwater vehicle. For this purpose, data from different tests, were carried out with the aforementioned vehicle at the facilities of the Canal de Experiencias Hidrodinámicas del Pardo, Madrid. In the proposed methodology, the following aspects are taken into account in order to improve the parameter estimation effciency: selection of the sampling period, smoothing of the data acquired in the tests considering a compromise between variance and bias of the smoothing filter to be applied, analysis of the classical linear regression model proposed in each trial, from the statistical point of view for the estimation of the parameters. Improvements in effciency are verified by graphical and statistical methods. In addition, a modification of the conventional LOS method is proposed which provides satisfactory results in the presence of ocean currents by performing a simple procedure.

Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates

Science.gov (United States)

Curto Sillamoni, Ignacio J.; Idiart, Martín I.

2016-10-01

We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.

ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

KAUST Repository

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Keyes, David E.

2016-01-01

In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

KAUST Repository

Litvinenko, Alexander

2016-10-25

In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A method for nonlinear exponential regression analysis

Science.gov (United States)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations

International Nuclear Information System (INIS)

Civalek, Ö.

2014-01-01

In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied

Feasibility of Residual Stress Nondestructive Estimation Using the Nonlinear Property of Critical Refraction Longitudinal Wave

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Yu-Hua Zhang

2017-01-01

Full Text Available Residual stress has significant influence on the performance of mechanical components, and the nondestructive estimation of residual stress is always a difficult problem. This study applies the relative nonlinear coefficient of critical refraction longitudinal (LCR wave to nondestructively characterize the stress state of materials; the feasibility of residual stress estimation using the nonlinear property of LCR wave is verified. The nonlinear ultrasonic measurements based on LCR wave are conducted on components with known stress state to calculate the relative nonlinear coefficient. Experimental results indicate that the relative nonlinear coefficient monotonically increases with prestress and the increment of relative nonlinear coefficient is about 80%, while the wave velocity only decreases about 0.2%. The sensitivity of the relative nonlinear coefficient for stress is much higher than wave velocity. Furthermore, the dependence between the relative nonlinear coefficient and deformation state of components is found. The stress detection resolution based on the nonlinear property of LCR wave is 10 MPa, which has higher resolution than wave velocity. These results demonstrate that the nonlinear property of LCR wave is more suitable for stress characterization than wave velocity, and this quantitative information could be used for residual stress estimation.

Nonlinear Filtering Techniques Comparison for Battery State Estimation

Directory of Open Access Journals (Sweden)

Aspasia Papazoglou

2014-09-01

Full Text Available The performance of estimation algorithms is vital for the correct functioning of batteries in electric vehicles, as poor estimates will inevitably jeopardize the operations that rely on un-measurable quantities, such as State of Charge and State of Health. This paper compares the performance of three nonlinear estimation algorithms: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter, where a lithium-ion cell model is considered. The effectiveness of these algorithms is measured by their ability to produce accurate estimates against their computational complexity in terms of number of operations and execution time required. The trade-offs between estimators' performance and their computational complexity are analyzed.

Measurement Model Nonlinearity in Estimation of Dynamical Systems

Science.gov (United States)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

Power capability evaluation for lithium iron phosphate batteries based on multi-parameter constraints estimation

Science.gov (United States)

Wang, Yujie; Pan, Rui; Liu, Chang; Chen, Zonghai; Ling, Qiang

2018-01-01

The battery power capability is intimately correlated with the climbing, braking and accelerating performance of the electric vehicles. Accurate power capability prediction can not only guarantee the safety but also regulate driving behavior and optimize battery energy usage. However, the nonlinearity of the battery model is very complex especially for the lithium iron phosphate batteries. Besides, the hysteresis loop in the open-circuit voltage curve is easy to cause large error in model prediction. In this work, a multi-parameter constraints dynamic estimation method is proposed to predict the battery continuous period power capability. A high-fidelity battery model which considers the battery polarization and hysteresis phenomenon is presented to approximate the high nonlinearity of the lithium iron phosphate battery. Explicit analyses of power capability with multiple constraints are elaborated, specifically the state-of-energy is considered in power capability assessment. Furthermore, to solve the problem of nonlinear system state estimation, and suppress noise interference, the UKF based state observer is employed for power capability prediction. The performance of the proposed methodology is demonstrated by experiments under different dynamic characterization schedules. The charge and discharge power capabilities of the lithium iron phosphate batteries are quantitatively assessed under different time scales and temperatures.

Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise

Directory of Open Access Journals (Sweden)

Ali Fahim Khan

2015-01-01

Full Text Available Modeling the blood oxygenation level dependent (BOLD signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

Linear theory for filtering nonlinear multiscale systems with model error.

Science.gov (United States)

Berry, Tyrus; Harlim, John

2014-07-08

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

Volcano deformation source parameters estimated from InSAR: Sensitivities to uncertainties in seismic tomography

Science.gov (United States)

Masterlark, Timothy; Donovan, Theodore; Feigl, Kurt L.; Haney, Matt; Thurber, Clifford H.; Tung, Sui

2016-01-01

The eruption cycle of a volcano is controlled in part by the upward migration of magma. The characteristics of the magma flux produce a deformation signature at the Earth's surface. Inverse analyses use geodetic data to estimate strategic controlling parameters that describe the position and pressurization of a magma chamber at depth. The specific distribution of material properties controls how observed surface deformation translates to source parameter estimates. Seismic tomography models describe the spatial distributions of material properties that are necessary for accurate models of volcano deformation. This study investigates how uncertainties in seismic tomography models propagate into variations in the estimates of volcano deformation source parameters inverted from geodetic data. We conduct finite element model-based nonlinear inverse analyses of interferometric synthetic aperture radar (InSAR) data for Okmok volcano, Alaska, as an example. We then analyze the estimated parameters and their uncertainties to characterize the magma chamber. Analyses are performed separately for models simulating a pressurized chamber embedded in a homogeneous domain as well as for a domain having a heterogeneous distribution of material properties according to seismic tomography. The estimated depth of the source is sensitive to the distribution of material properties. The estimated depths for the homogeneous and heterogeneous domains are 2666 ± 42 and 3527 ± 56 m below mean sea level, respectively (99% confidence). A Monte Carlo analysis indicates that uncertainties of the seismic tomography cannot account for this discrepancy at the 99% confidence level. Accounting for the spatial distribution of elastic properties according to seismic tomography significantly improves the fit of the deformation model predictions and significantly influences estimates for parameters that describe the location of a pressurized magma chamber.

Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

DEFF Research Database (Denmark)

Vich, Catalina; Berg, Rune W.; Guillamon, Antoni

2017-01-01

Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo...... recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical...... models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures...

Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

International Nuclear Information System (INIS)

Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

2015-01-01

In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

Enzymatic Synthesis of Ampicillin: Nonlinear Modeling, Kinetics Estimation, and Adaptive Control

Directory of Open Access Journals (Sweden)

Monica Roman

2012-01-01

Full Text Available Nowadays, the use of advanced control strategies in biotechnology is quite low. A main reason is the lack of quality of the data, and the fact that more sophisticated control strategies must be based on a model of the dynamics of bioprocesses. The nonlinearity of the bioprocesses and the absence of cheap and reliable instrumentation require an enhanced modeling effort and identification strategies for the kinetics. The present work approaches modeling and control strategies for the enzymatic synthesis of ampicillin that is carried out inside a fed-batch bioreactor. First, a nonlinear dynamical model of this bioprocess is obtained by using a novel modeling procedure for biotechnology: the bond graph methodology. Second, a high gain observer is designed for the estimation of the imprecisely known kinetics of the synthesis process. Third, by combining an exact linearizing control law with the on-line estimation kinetics algorithm, a nonlinear adaptive control law is designed. The case study discussed shows that a nonlinear feedback control strategy applied to the ampicillin synthesis bioprocess can cope with disturbances, noisy measurements, and parametric uncertainties. Numerical simulations performed with MATLAB environment are included in order to test the behavior and the performances of the proposed estimation and control strategies.

On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models part 2. Parameter and state estimation

Science.gov (United States)

Fleischer, Christian; Waag, Wladislaw; Heyn, Hans-Martin; Sauer, Dirk Uwe

2014-09-01

Lithium-ion battery systems employed in high power demanding systems such as electric vehicles require a sophisticated monitoring system to ensure safe and reliable operation. Three major states of the battery are of special interest and need to be constantly monitored. These include: battery state of charge (SoC), battery state of health (capacity fade determination, SoH), and state of function (power fade determination, SoF). The second paper concludes the series by presenting a multi-stage online parameter identification technique based on a weighted recursive least quadratic squares parameter estimator to determine the parameters of the proposed battery model from the first paper during operation. A novel mutation based algorithm is developed to determine the nonlinear current dependency of the charge-transfer resistance. The influence of diffusion is determined by an on-line identification technique and verified on several batteries at different operation conditions. This method guarantees a short response time and, together with its fully recursive structure, assures a long-term stable monitoring of the battery parameters. The relative dynamic voltage prediction error of the algorithm is reduced to 2%. The changes of parameters are used to determine the states of the battery. The algorithm is real-time capable and can be implemented on embedded systems.

A Nonlinear Attitude Estimator for Attitude and Heading Reference Systems Based on MEMS Sensors

DEFF Research Database (Denmark)

Wang, Yunlong; Soltani, Mohsen; Hussain, Dil muhammed Akbar

2016-01-01

In this paper, a nonlinear attitude estimator is designed for an Attitude Heading and Reference System (AHRS) based on Micro Electro-Mechanical Systems (MEMS) sensors. The design process of the attitude estimator is stated with detail, and the equilibrium point of the estimator error model...... the problems in previous research works. Moreover, the estimation of MEMS gyroscope bias is also inclueded in this estimator. The designed nonlinear attitude estimator is firstly tested in simulation environment and then implemented in an AHRS hardware for further experiments. Finally, the attitude estimation...

Smoothing of, and parameter estimation from, noisy biophysical recordings.

Directory of Open Access Journals (Sweden)

Quentin J M Huys

2009-05-01

Full Text Available Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically detailed models are not designed to deal with this. We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo ("particle filtering" methods, in combination with a detailed biophysical description of a cell, are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a non-parametric manner. Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances, and observation noise are inferred automatically from noisy data via expectation-maximization. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.

Estimation of parameters of constant elasticity of substitution production functional model

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

Projective and hybrid projective synchronization for the Lorenz-Stenflo system with estimation of unknown parameters

International Nuclear Information System (INIS)

Mukherjee, Payel; Banerjee, Santo

2010-01-01

In this work, in the first phase, we study the phenomenon of projective synchronization in the Lorenz-Stenflo system. Synchronization is then investigated for the same system with unknown parameters. We show analytically that synchronization is possible for some proper choice of the nonlinear controller by using a suitable Lyapunov function. With the help of this result, it is also possible to estimate the values of the unknown system parameters. In the second phase as an extension of our analysis, we investigate the new hybrid projective synchronization for the same system. All our analyses are well supported with numerical evidence.

Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

Directory of Open Access Journals (Sweden)

Il Young Song

2015-01-01

Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.

Cosmological Parameter Estimation with Large Scale Structure Observations

CERN Document Server

Di Dio, Enea; Durrer, Ruth; Lesgourgues, Julien

2014-01-01

We estimate the sensitivity of future galaxy surveys to cosmological parameters, using the redshift dependent angular power spectra of galaxy number counts, $C_\\ell(z_1,z_2)$, calculated with all relativistic corrections at first order in perturbation theory. We pay special attention to the redshift dependence of the non-linearity scale and present Fisher matrix forecasts for Euclid-like and DES-like galaxy surveys. We compare the standard $P(k)$ analysis with the new $C_\\ell(z_1,z_2)$ method. We show that for surveys with photometric redshifts the new analysis performs significantly better than the $P(k)$ analysis. For spectroscopic redshifts, however, the large number of redshift bins which would be needed to fully profit from the redshift information, is severely limited by shot noise. We also identify surveys which can measure the lensing contribution and we study the monopole, $C_0(z_1,z_2)$.

Fast non-linear extraction of plasma equilibrium parameters using a neural network mapping

International Nuclear Information System (INIS)

Lister, J.B.; Schnurrenberger, H.

1990-07-01

The shaping of non-circular plasmas requires a non-linear mapping between the measured diagnostic signals and selected equilibrium parameters. The particular configuration of Neural Network known as the multi-layer perceptron provides a powerful and general technique for formulating an arbitrary continuous non-linear multi-dimensional mapping. This technique has been successfully applied to the extraction of equilibrium parameters from measurements of single-null diverted plasmas in the DIII-D tokamak; the results are compared with a purely linear mapping. The method is promising, and hardware implementation is straightforward. (author) 15 refs., 7 figs

Optimization of nonlinear wave function parameters

International Nuclear Information System (INIS)

Shepard, R.; Minkoff, M.; Chemistry

2006-01-01

An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules

Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents

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Catalina Vich

2017-07-01

Full Text Available Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.

Periodic orbits of hybrid systems and parameter estimation via AD

International Nuclear Information System (INIS)

Guckenheimer, John; Phipps, Eric Todd; Casey, Richard

2004-01-01

Rhythmic, periodic processes are ubiquitous in biological systems; for example, the heart beat, walking, circadian rhythms and the menstrual cycle. Modeling these processes with high fidelity as periodic orbits of dynamical systems is challenging because: (1) (most) nonlinear differential equations can only be solved numerically; (2) accurate computation requires solving boundary value problems; (3) many problems and solutions are only piecewise smooth; (4) many problems require solving differential-algebraic equations; (5) sensitivity information for parameter dependence of solutions requires solving variational equations; and (6) truncation errors in numerical integration degrade performance of optimization methods for parameter estimation. In addition, mathematical models of biological processes frequently contain many poorly-known parameters, and the problems associated with this impedes the construction of detailed, high-fidelity models. Modelers are often faced with the difficult problem of using simulations of a nonlinear model, with complex dynamics and many parameters, to match experimental data. Improved computational tools for exploring parameter space and fitting models to data are clearly needed. This paper describes techniques for computing periodic orbits in systems of hybrid differential-algebraic equations and parameter estimation methods for fitting these orbits to data. These techniques make extensive use of automatic differentiation to accurately and efficiently evaluate derivatives for time integration, parameter sensitivities, root finding and optimization. The boundary value problem representing a periodic orbit in a hybrid system of differential algebraic equations is discretized via multiple-shooting using a high-degree Taylor series integration method (GM00, Phi03). Numerical solutions to the shooting equations are then estimated by a Newton process yielding an approximate periodic orbit. A metric is defined for computing the distance

Efficient Ensemble State-Parameters Estimation Techniques in Ocean Ecosystem Models: Application to the North Atlantic

Science.gov (United States)

El Gharamti, M.; Bethke, I.; Tjiputra, J.; Bertino, L.

2016-02-01

Given the recent strong international focus on developing new data assimilation systems for biological models, we present in this comparative study the application of newly developed state-parameters estimation tools to an ocean ecosystem model. It is quite known that the available physical models are still too simple compared to the complexity of the ocean biology. Furthermore, various biological parameters remain poorly unknown and hence wrong specifications of such parameters can lead to large model errors. Standard joint state-parameters augmentation technique using the ensemble Kalman filter (Stochastic EnKF) has been extensively tested in many geophysical applications. Some of these assimilation studies reported that jointly updating the state and the parameters might introduce significant inconsistency especially for strongly nonlinear models. This is usually the case for ecosystem models particularly during the period of the spring bloom. A better handling of the estimation problem is often carried out by separating the update of the state and the parameters using the so-called Dual EnKF. The dual filter is computationally more expensive than the Joint EnKF but is expected to perform more accurately. Using a similar separation strategy, we propose a new EnKF estimation algorithm in which we apply a one-step-ahead smoothing to the state. The new state-parameters estimation scheme is derived in a consistent Bayesian filtering framework and results in separate update steps for the state and the parameters. Unlike the classical filtering path, the new scheme starts with an update step and later a model propagation step is performed. We test the performance of the new smoothing-based schemes against the standard EnKF in a one-dimensional configuration of the Norwegian Earth System Model (NorESM) in the North Atlantic. We use nutrients profile (up to 2000 m deep) data and surface partial CO2 measurements from Mike weather station (66o N, 2o E) to estimate

Pescara benchmarks: nonlinear identification

Science.gov (United States)

Gandino, E.; Garibaldi, L.; Marchesiello, S.

2011-07-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

Pescara benchmarks: nonlinear identification

International Nuclear Information System (INIS)

Gandino, E; Garibaldi, L; Marchesiello, S

2011-01-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled M onitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing , financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

International Nuclear Information System (INIS)

Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.; Linares-Perez, J.; Nakamori, S.

2008-01-01

This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use, a filtering algorithm based on linear approximations of the real observations is proposed.

Photogrammetric Resection Approach Using Straight Line Features for Estimation of Cartosat-1 Platform Parameters

Directory of Open Access Journals (Sweden)

Nita H. Shah

2008-08-01

Full Text Available The classical calibration or space resection is the fundamental task in photogrammetry. The lack of sufficient knowledge of interior and exterior orientation parameters lead to unreliable results in the photogrammetric process. There are several other available methods using lines, which consider the determination of exterior orientation parameters, with no mention to the simultaneous determination of inner orientation parameters. Normal space resection methods solve the problem using control points, whose coordinates are known both in image and object reference systems. The non-linearity of the model and the problems, in point location in digital images are the main drawbacks of the classical approaches. The line based approach to overcome these problems includes usage of lines in the number of observations that can be provided, which improve significantly the overall system redundancy. This paper addresses mathematical model relating to both image and object reference system for solving the space resection problem which is generally used for upgrading the exterior orientation parameters. In order to solve the dynamic camera calibration parameters, a sequential estimator (Kalman Filtering is applied; in an iterative process to the image. For dynamic case, e.g. an image sequence of moving objects, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and basic physical sensor model for each instant of time. The proposed approach is tested with three real data sets and the result suggests that highly accurate space resection parameters can be obtained with or without using the control points and progressive processing time reduction.

Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform

Science.gov (United States)

Ta, Minh-Nghi; Lardiès, Joseph

2006-05-01

We consider the free response of a nonlinear vibrating system. Using the ridges and skeletons of the continuous wavelet transform, we identify weak nonlinearities on damping and stiffness and estimate their physical parameters. The crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform. The method is applied to simulated single-degree-of-freedom systems and multi-degree-of-freedom systems with nonlinearities on damping and stiffness. Experimental validation of the nonlinear identification and parameter estimation method is presented. The experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor.

On parameter estimation in deformable models

DEFF Research Database (Denmark)

Fisker, Rune; Carstensen, Jens Michael

1998-01-01

Deformable templates have been intensively studied in image analysis through the last decade, but despite its significance the estimation of model parameters has received little attention. We present a method for supervised and unsupervised model parameter estimation using a general Bayesian form...

B-spline goal-oriented error estimators for geometrically nonlinear rods

Science.gov (United States)

2011-04-01

respectively, for the output functionals q2–q4 (linear and nonlinear with the trigonometric functions sine and cosine) in all the tests considered...of the errors resulting from the linear, quadratic and nonlinear (with trigonometric functions sine and cosine) outputs and for p = 1, 2. If the... Portugal . References [1] A.T. Adams. Sobolev Spaces. Academic Press, Boston, 1975. [2] M. Ainsworth and J.T. Oden. A posteriori error estimation in

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

Directory of Open Access Journals (Sweden)

Tashkova Katerina

2011-10-01

Full Text Available Abstract Background We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. Results We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA, particle-swarm optimization (PSO, and differential evolution (DE, as well as a local-search derivative-based algorithm 717 (A717 to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Conclusions Overall, the global meta-heuristic methods (DASA, PSO, and DE clearly and significantly outperform the local derivative-based method (A717. Among the three meta-heuristics, differential evolution (DE performs best in terms of the objective function, i.e., reconstructing the output, and in terms of

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis.

Science.gov (United States)

Tashkova, Katerina; Korošec, Peter; Silc, Jurij; Todorovski, Ljupčo; Džeroski, Sašo

2011-10-11

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and

Parameter Estimation of Partial Differential Equation Models.

Science.gov (United States)

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

Parameter identification in a nonlinear nuclear reactor model using quasilinearization

International Nuclear Information System (INIS)

Barreto, J.M.; Martins Neto, A.F.; Tanomaru, N.

1980-09-01

Parameter identification in a nonlinear, lumped parameter, nuclear reactor model is carried out using discrete output power measurements during the transient caused by an external reactivity change. In order to minimize the difference between the model and the reactor power responses, the parameter promt neutron generation time and a parameter in fuel temperature reactivity coefficient equation are adjusted using quasilinearization. The influences of the external reactivity disturbance, the number and frequency of measurements and the measurement noise level on the method accuracy and rate of convergence are analysed through simulation. Procedures for the design of the identification experiments are suggested. The method proved to be very effective for low level noise measurements. (Author) [pt

NEWBOX: A computer program for parameter estimation in diffusion problems

International Nuclear Information System (INIS)

Nestor, C.W. Jr.; Godbee, H.W.; Joy, D.S.

1989-01-01

In the analysis of experiments to determine amounts of material transferred form 1 medium to another (e.g., the escape of chemically hazardous and radioactive materials from solids), there are at least 3 important considerations. These are (1) is the transport amenable to treatment by established mass transport theory; (2) do methods exist to find estimates of the parameters which will give a best fit, in some sense, to the experimental data; and (3) what computational procedures are available for evaluating the theoretical expressions. The authors have made the assumption that established mass transport theory is an adequate model for the situations under study. Since the solutions of the diffusion equation are usually nonlinear in some parameters (diffusion coefficient, reaction rate constants, etc.), use of a method of parameter adjustment involving first partial derivatives can be complicated and prone to errors in the computation of the derivatives. In addition, the parameters must satisfy certain constraints; for example, the diffusion coefficient must remain positive. For these reasons, a variant of the constrained simplex method of M. J. Box has been used to estimate parameters. It is similar, but not identical, to the downhill simplex method of Nelder and Mead. In general, they calculate the fraction of material transferred as a function of time from expressions obtained by the inversion of the Laplace transform of the fraction transferred, rather than by taking derivatives of a calculated concentration profile. With the above approaches to the 3 considerations listed at the outset, they developed a computer program NEWBOX, usable on a personal computer, to calculate the fractional release of material from 4 different geometrical shapes (semi-infinite medium, finite slab, finite circular cylinder, and sphere), accounting for several different boundary conditions

Fast non-linear extraction of plasma equilibrium parameters using a neural network mapping

International Nuclear Information System (INIS)

Lister, J.B.; Schnurrenberger, H.

1991-01-01

The shaping of non-circular plasmas requires a non-linear mapping between the measured diagnostic signals and selected equilibrium parameters. The particular configuration of neural network known as the multilayer perceptron provides a powerful and general technique for formulating an arbitrary continuous non-linear multi-dimensional mapping. This technique has been successfully applied to the extraction of equilibrium parameters from measurements of single-null diverted plasmas in the DIII-D tokamak; the results are compared with a purely linear mapping. The method is promising, and hardware implementation is straightforward. (author). 17 refs, 8 figs, 2 tab

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

Energy Technology Data Exchange (ETDEWEB)

Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Variation of nonlinearity parameter at low fundamental amplitudes

Science.gov (United States)

Barnard, Daniel J.

1999-04-01

Recent harmonic generation measurements of the nonlinearity parameter β in polycrystalline Cu-Al alloys have shown a transition to lower values at low fundamental amplitude levels. Values for β at high (>10 Å) fundamental levels are in the range predicted by single-crystal second- and third-order elastic constants while lower fundamental levels (alloy by others. The source of the effect is unclear but initial results may require a reexamination of current methods for measurement of third-order elastic constants.

Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm

International Nuclear Information System (INIS)

Oliva, Diego; Abd El Aziz, Mohamed; Ella Hassanien, Aboul

2017-01-01

Highlights: •We modify the whale algorithm using chaotic maps. •We apply a chaotic algorithm to estimate parameter of photovoltaic cells. •We perform a study of chaos in whale algorithm. •Several comparisons and metrics support the experimental results. •We test the method with data from real solar cells. -- Abstract: The using of solar energy has been increased since it is a clean source of energy. In this way, the design of photovoltaic cells has attracted the attention of researchers over the world. There are two main problems in this field: having a useful model to characterize the solar cells and the absence of data about photovoltaic cells. This situation even affects the performance of the photovoltaic modules (panels). The characteristics of the current vs. voltage are used to describe the behavior of solar cells. Considering such values, the design problem involves the solution of the complex non-linear and multi-modal objective functions. Different algorithms have been proposed to identify the parameters of the photovoltaic cells and panels. Most of them commonly fail in finding the optimal solutions. This paper proposes the Chaotic Whale Optimization Algorithm (CWOA) for the parameters estimation of solar cells. The main advantage of the proposed approach is using the chaotic maps to compute and automatically adapt the internal parameters of the optimization algorithm. This situation is beneficial in complex problems, because along the iterative process, the proposed algorithm improves their capabilities to search for the best solution. The modified method is able to optimize complex and multimodal objective functions. For example, the function for the estimation of parameters of solar cells. To illustrate the capabilities of the proposed algorithm in the solar cell design, it is compared with other optimization methods over different datasets. Moreover, the experimental results support the improved performance of the proposed approach

Precision Parameter Estimation and Machine Learning

Science.gov (United States)

Wandelt, Benjamin D.

2008-12-01

I discuss the strategy of ``Acceleration by Parallel Precomputation and Learning'' (AP-PLe) that can vastly accelerate parameter estimation in high-dimensional parameter spaces and costly likelihood functions, using trivially parallel computing to speed up sequential exploration of parameter space. This strategy combines the power of distributed computing with machine learning and Markov-Chain Monte Carlo techniques efficiently to explore a likelihood function, posterior distribution or χ2-surface. This strategy is particularly successful in cases where computing the likelihood is costly and the number of parameters is moderate or large. We apply this technique to two central problems in cosmology: the solution of the cosmological parameter estimation problem with sufficient accuracy for the Planck data using PICo; and the detailed calculation of cosmological helium and hydrogen recombination with RICO. Since the APPLe approach is designed to be able to use massively parallel resources to speed up problems that are inherently serial, we can bring the power of distributed computing to bear on parameter estimation problems. We have demonstrated this with the CosmologyatHome project.

Nonlinear Prediction As A Tool For Determining Parameters For Phase Space Reconstruction In Meteorology

Science.gov (United States)

Miksovsky, J.; Raidl, A.

Time delays phase space reconstruction represents one of useful tools of nonlinear time series analysis, enabling number of applications. Its utilization requires the value of time delay to be known, as well as the value of embedding dimension. There are sev- eral methods how to estimate both these parameters. Typically, time delay is computed first, followed by embedding dimension. Our presented approach is slightly different - we reconstructed phase space for various combinations of mentioned parameters and used it for prediction by means of the nearest neighbours in the phase space. Then some measure of prediction's success was computed (correlation or RMSE, e.g.). The position of its global maximum (minimum) should indicate the suitable combination of time delay and embedding dimension. Several meteorological (particularly clima- tological) time series were used for the computations. We have also created a MS- Windows based program in order to implement this approach - its basic features will be presented as well.

Practical estimate of gradient nonlinearity for implementation of apparent diffusion coefficient bias correction.

Science.gov (United States)

Malkyarenko, Dariya I; Chenevert, Thomas L

2014-12-01

To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.

Levenberg-Marquardt application to two-phase nonlinear parameter estimation for finned-tube coil evaporators

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available A procedure for calculation of refrigerant mass flow rate is implemented in the distributed numerical model to simulate the flow in finned-tube coil dry-expansion evaporators, usually found in refrigeration and air-conditioning systems. Two-phase refrigerant flow inside the tubes is assumed to be one-dimensional, unsteady, and homogeneous. In the model the effects of refrigerant pressure drop and the moisture condensation from the air flowing over the external surface of the tubes are considered. The results obtained are the distributions of refrigerant velocity, temperature and void fraction, tube-wall temperature, air temperature, and absolute humidity. The finite volume method is used to discretize the governing equations. Additionally, given the operation conditions and the geometric parameters, the model allows the calculation of the refrigerant mass flow rate. The value of mass flow rate is computed using the process of parameter estimation with the minimization method of Levenberg-Marquardt minimization. In order to validate the developed model, the obtained results using HFC-134a as a refrigerant are compared with available data from the literature.

Reionization history and CMB parameter estimation

International Nuclear Information System (INIS)

Dizgah, Azadeh Moradinezhad; Kinney, William H.; Gnedin, Nickolay Y.

2013-01-01

We study how uncertainty in the reionization history of the universe affects estimates of other cosmological parameters from the Cosmic Microwave Background. We analyze WMAP7 data and synthetic Planck-quality data generated using a realistic scenario for the reionization history of the universe obtained from high-resolution numerical simulation. We perform parameter estimation using a simple sudden reionization approximation, and using the Principal Component Analysis (PCA) technique proposed by Mortonson and Hu. We reach two main conclusions: (1) Adopting a simple sudden reionization model does not introduce measurable bias into values for other parameters, indicating that detailed modeling of reionization is not necessary for the purpose of parameter estimation from future CMB data sets such as Planck. (2) PCA analysis does not allow accurate reconstruction of the actual reionization history of the universe in a realistic case

Reionization history and CMB parameter estimation

Energy Technology Data Exchange (ETDEWEB)

Dizgah, Azadeh Moradinezhad; Gnedin, Nickolay Y.; Kinney, William H.

2013-05-01

We study how uncertainty in the reionization history of the universe affects estimates of other cosmological parameters from the Cosmic Microwave Background. We analyze WMAP7 data and synthetic Planck-quality data generated using a realistic scenario for the reionization history of the universe obtained from high-resolution numerical simulation. We perform parameter estimation using a simple sudden reionization approximation, and using the Principal Component Analysis (PCA) technique proposed by Mortonson and Hu. We reach two main conclusions: (1) Adopting a simple sudden reionization model does not introduce measurable bias into values for other parameters, indicating that detailed modeling of reionization is not necessary for the purpose of parameter estimation from future CMB data sets such as Planck. (2) PCA analysis does not allow accurate reconstruction of the actual reionization history of the universe in a realistic case.

Parameter Estimation of Partial Differential Equation Models

KAUST Repository

Xun, Xiaolei

2013-09-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.

2017-07-25

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.

Two-parameter nonlinear spacetime perturbations: gauge transformations and gauge invariance

International Nuclear Information System (INIS)

Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F

2003-01-01

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Ω), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by λ) are then built on top of the axisymmetric perturbations in Ω. Clearly, any interesting physics requires nonlinear perturbations, as at least terms λΩ need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory

Sensitivity Analysis and Parameter Estimation for a Reactive Transport Model of Uranium Bioremediation

Science.gov (United States)

Meyer, P. D.; Yabusaki, S.; Curtis, G. P.; Ye, M.; Fang, Y.

2011-12-01

A three-dimensional, variably-saturated flow and multicomponent biogeochemical reactive transport model of uranium bioremediation was used to generate synthetic data . The 3-D model was based on a field experiment at the U.S. Dept. of Energy Rifle Integrated Field Research Challenge site that used acetate biostimulation of indigenous metal reducing bacteria to catalyze the conversion of aqueous uranium in the +6 oxidation state to immobile solid-associated uranium in the +4 oxidation state. A key assumption in past modeling studies at this site was that a comprehensive reaction network could be developed largely through one-dimensional modeling. Sensitivity analyses and parameter estimation were completed for a 1-D reactive transport model abstracted from the 3-D model to test this assumption, to identify parameters with the greatest potential to contribute to model predictive uncertainty, and to evaluate model structure and data limitations. Results showed that sensitivities of key biogeochemical concentrations varied in space and time, that model nonlinearities and/or parameter interactions have a significant impact on calculated sensitivities, and that the complexity of the model's representation of processes affecting Fe(II) in the system may make it difficult to correctly attribute observed Fe(II) behavior to modeled processes. Non-uniformity of the 3-D simulated groundwater flux and averaging of the 3-D synthetic data for use as calibration targets in the 1-D modeling resulted in systematic errors in the 1-D model parameter estimates and outputs. This occurred despite using the same reaction network for 1-D modeling as used in the data-generating 3-D model. Predictive uncertainty of the 1-D model appeared to be significantly underestimated by linear parameter uncertainty estimates.

Parameter Estimation for Thurstone Choice Models

Energy Technology Data Exchange (ETDEWEB)

Vojnovic, Milan [London School of Economics (United Kingdom); Yun, Seyoung [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-04-24

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one or more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.

A new Bayesian recursive technique for parameter estimation

Science.gov (United States)

Kaheil, Yasir H.; Gill, M. Kashif; McKee, Mac; Bastidas, Luis

2006-08-01

The performance of any model depends on how well its associated parameters are estimated. In the current application, a localized Bayesian recursive estimation (LOBARE) approach is devised for parameter estimation. The LOBARE methodology is an extension of the Bayesian recursive estimation (BARE) method. It is applied in this paper on two different types of models: an artificial intelligence (AI) model in the form of a support vector machine (SVM) application for forecasting soil moisture and a conceptual rainfall-runoff (CRR) model represented by the Sacramento soil moisture accounting (SAC-SMA) model. Support vector machines, based on statistical learning theory (SLT), represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology. They require estimation of three parameters. SAC-SMA is a very well known model that estimates runoff. It has a 13-dimensional parameter space. In the LOBARE approach presented here, Bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set. This is done by narrowing the sampling space through updating the "parent" bounds based on their fitness. These bounds are actually the parameter sets that were selected by BARE runs on subspaces of the initial parameter space. The new approach results in faster convergence toward the optimal parameter set using minimum training/calibration data and fewer sets of parameter values. The efficacy of the localized methodology is also compared with the previously used BARE algorithm.

Ranking as parameter estimation

Czech Academy of Sciences Publication Activity Database

Kárný, Miroslav; Guy, Tatiana Valentine

2009-01-01

Roč. 4, č. 2 (2009), s. 142-158 ISSN 1745-7645 R&D Projects: GA MŠk 2C06001; GA AV ČR 1ET100750401; GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : ranking * Bayesian estimation * negotiation * modelling Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2009/AS/karny- ranking as parameter estimation.pdf

Performance comparison of attitude determination, attitude estimation, and nonlinear observers algorithms

Science.gov (United States)

MOHAMMED, M. A. SI; BOUSSADIA, H.; BELLAR, A.; ADNANE, A.

2017-01-01

This paper presents a brief synthesis and useful performance analysis of different attitude filtering algorithms (attitude determination algorithms, attitude estimation algorithms, and nonlinear observers) applied to Low Earth Orbit Satellite in terms of accuracy, convergence time, amount of memory, and computation time. This latter is calculated in two ways, using a personal computer and also using On-board computer 750 (OBC 750) that is being used in many SSTL Earth observation missions. The use of this comparative study could be an aided design tool to the designer to choose from an attitude determination or attitude estimation or attitude observer algorithms. The simulation results clearly indicate that the nonlinear Observer is the more logical choice.

Development of a Probabilistic Technique for On-line Parameter and State Estimation in Non-linear Dynamic Systems

International Nuclear Information System (INIS)

Tunc Aldemir; Miller, Don W.; Hajek, Brian K.; Peng Wang

2002-01-01

The DSD (Dynamic System Doctor) is a system-independent, interactive software under development for on-line state/parameter estimation in dynamic systems (1), partially supported through a Nuclear Engineering Education (NEER) grant during 1998-2001. This paper summarizes the recent accomplishments in improving the user-friendliness and computational capability of DSD

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

Energy Technology Data Exchange (ETDEWEB)

Adams, Brian M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ebeida, Mohamed Salah [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Eldred, Michael S. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jakeman, John Davis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Swiler, Laura Painton [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Stephens, John Adam [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Vigil, Dena M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wildey, Timothy Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bohnhoff, William J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Eddy, John P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hu, Kenneth T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Dalbey, Keith R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bauman, Lara E [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hough, Patricia Diane [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-05-01

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

Stepwise optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

International Nuclear Information System (INIS)

Frolov, A.M.

1986-01-01

The problem of exact variational calculations of few-particle systems in the exponential basis of the relative coordinates using nonlinear parameters is studied. The techniques of stepwise optimization and global chaos of nonlinear parameters are used to calculate the S and P states of homonuclear muonic molecules with an error of no more than +0.001 eV. The global-chaos technique also has proved to be successful in the case of the nuclear systems 3 H and 3 He

Cosmological parameter estimation using Particle Swarm Optimization

Science.gov (United States)

Prasad, J.; Souradeep, T.

2014-03-01

Constraining parameters of a theoretical model from observational data is an important exercise in cosmology. There are many theoretically motivated models, which demand greater number of cosmological parameters than the standard model of cosmology uses, and make the problem of parameter estimation challenging. It is a common practice to employ Bayesian formalism for parameter estimation for which, in general, likelihood surface is probed. For the standard cosmological model with six parameters, likelihood surface is quite smooth and does not have local maxima, and sampling based methods like Markov Chain Monte Carlo (MCMC) method are quite successful. However, when there are a large number of parameters or the likelihood surface is not smooth, other methods may be more effective. In this paper, we have demonstrated application of another method inspired from artificial intelligence, called Particle Swarm Optimization (PSO) for estimating cosmological parameters from Cosmic Microwave Background (CMB) data taken from the WMAP satellite.

Cosmological parameter estimation using Particle Swarm Optimization

International Nuclear Information System (INIS)

Prasad, J; Souradeep, T

2014-01-01

Constraining parameters of a theoretical model from observational data is an important exercise in cosmology. There are many theoretically motivated models, which demand greater number of cosmological parameters than the standard model of cosmology uses, and make the problem of parameter estimation challenging. It is a common practice to employ Bayesian formalism for parameter estimation for which, in general, likelihood surface is probed. For the standard cosmological model with six parameters, likelihood surface is quite smooth and does not have local maxima, and sampling based methods like Markov Chain Monte Carlo (MCMC) method are quite successful. However, when there are a large number of parameters or the likelihood surface is not smooth, other methods may be more effective. In this paper, we have demonstrated application of another method inspired from artificial intelligence, called Particle Swarm Optimization (PSO) for estimating cosmological parameters from Cosmic Microwave Background (CMB) data taken from the WMAP satellite

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

International Nuclear Information System (INIS)

Higdon, Dave; McDonnell, Jordan D; Schunck, Nicolas; Sarich, Jason; Wild, Stefan M

2015-01-01

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model η(θ), where θ denotes the uncertain, best input setting. Hence the statistical model is of the form y=η(θ)+ϵ, where ϵ accounts for measurement, and possibly other, error sources. When nonlinearity is present in η(⋅), the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model η(⋅). This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. We also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory. (paper)

Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

CERN Document Server

Martínez-Guerra, Rafael

2017-01-01

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

Control and Estimation of Distributed Parameter Systems

CERN Document Server

Kappel, F; Kunisch, K

1998-01-01

Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.

Vibro-Impact Energy Analysis of a Geared System with Piecewise-Type Nonlinearities Using Various Parameter Values

Directory of Open Access Journals (Sweden)

Jong-Yun Yoon

2015-08-01

Full Text Available Torsional systems with gear pairs such as the gearbox of wind turbines or vehicle driveline systems inherently show impact phenomena due to clearance-type nonlinearities when the system experiences sinusoidal excitation. This research investigates the vibro-impact energy of unloaded gears in geared systems using the harmonic balance method (HBM in both the frequency and time domains. To achieve accurate simulations, nonlinear models with piecewise and clearance-type nonlinearities and drag torques are defined and implemented in the HBM. Next, the nonlinear frequency responses are examined by focusing on the resonance areas where the impact phenomena occur, along with variations in key parameters such as clutch stiffness, drag torque, and inertias of the flywheel and the unloaded gear. Finally, the effects of the parameters on the vibro-impacts at a specific excitation frequency are explained using bifurcation diagrams. The results are correlated with prior research by defining the gear rattle criteria with key parameters. This article suggests a method to simulate the impact phenomena in torsional systems using the HBM and successfully assesses vibro-impact energy using bifurcation diagrams.

Effect of window function for measurement of ultrasonic nonlinear parameter using fast fourier transform of tone-burst signal

Energy Technology Data Exchange (ETDEWEB)

Lee, Kyoung Jun; Kim, Jong Beom; Song, Dong Gil; Jhang, Kyung Young [Dept. of Mechanical Engineering, Hanyang University, Seoul (Korea, Republic of)

2015-08-15

In ultrasonic nonlinear parameter measurement using the fast Fourier transform(FFT) of tone-burst signals, the side lobe and leakage on spectrum because of finite time and non-periodicity of signals makes it difficult to measure the harmonic magnitudes accurately. The window function made it possible to resolve this problem. In this study, the effect of the Hanning and Turkey window functions on the experimental measurement of nonlinear parameters was analyzed. In addition, the effect of changes in tone burst signal number with changes in the window function on the experimental measurement was analyzed. The result for both window functions were similar and showed that they enabled reliable nonlinear parameter measurement. However, in order to restore original signal amplitude, the amplitude compensation coefficient should be considered for each window function. On a separate note, the larger number of tone bursts was advantageous for stable nonlinear parameter measurement, but this effect was more advantageous in the case of the Hanning window than the Tukey window.

Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy

Energy Technology Data Exchange (ETDEWEB)

Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)

2017-04-15

The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

Directory of Open Access Journals (Sweden)

Espen R. Jakobsen

2002-05-01

Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.

Parameter Estimation of Inverter and Motor Model at Standstill using Measured Currents Only

DEFF Research Database (Denmark)

Rasmussen, Henrik; Knudsen, Morten; Tønnes, M.

1996-01-01

Methods for estimation of the parameters in the electrical equivalent diagram for the induction motor, based on special designed experiments, are given. In all experriments two of the three phases are given the same potential, i.e., no net torque is generatedand the motor is at standstill. Input...... and 3) the referred rotor rotor resistance and magnetizing inductance. The method developed in the two last experiments is independent of the inverter nonlinearity. New methods for system identification concerning saturation of the magnetic flux are given and a reference value for the flux level...... to the system is the reference values for the stator voltages given as duty cycles for the Pulse With Modulated power device. The system output is the measured stator currents. Three experiments are describedgiving respectively 1) the stator resistance and inverter parameters, 2) the stator transient inductance...

Supervised local error estimation for nonlinear image registration using convolutional neural networks

NARCIS (Netherlands)

Eppenhof, Koen A.J.; Pluim, Josien P.W.; Styner, M.A.; Angelini, E.D.

2017-01-01

Error estimation in medical image registration is valuable when validating, comparing, or combining registration methods. To validate a nonlinear image registration method, ideally the registration error should be known for the entire image domain. We propose a supervised method for the estimation

Estimating Soil Hydraulic Parameters using Gradient Based Approach

Science.gov (United States)

Rai, P. K.; Tripathi, S.

2017-12-01

The conventional way of estimating parameters of a differential equation is to minimize the error between the observations and their estimates. The estimates are produced from forward solution (numerical or analytical) of differential equation assuming a set of parameters. Parameter estimation using the conventional approach requires high computational cost, setting-up of initial and boundary conditions, and formation of difference equations in case the forward solution is obtained numerically. Gaussian process based approaches like Gaussian Process Ordinary Differential Equation (GPODE) and Adaptive Gradient Matching (AGM) have been developed to estimate the parameters of Ordinary Differential Equations without explicitly solving them. Claims have been made that these approaches can straightforwardly be extended to Partial Differential Equations; however, it has been never demonstrated. This study extends AGM approach to PDEs and applies it for estimating parameters of Richards equation. Unlike the conventional approach, the AGM approach does not require setting-up of initial and boundary conditions explicitly, which is often difficult in real world application of Richards equation. The developed methodology was applied to synthetic soil moisture data. It was seen that the proposed methodology can estimate the soil hydraulic parameters correctly and can be a potential alternative to the conventional method.

A novel and practical approach for determination of the acoustic nonlinearity parameter using a pulse-echo method

Science.gov (United States)

Jeong, Hyunjo; Zhang, Shuzeng; Barnard, Dan; Li, Xiongbing

2016-02-01

Measurements of the acoustic nonlinearity parameter β are frequently made for early detection of damage in various materials. The practical implementation of the measurement technique has been limited to the through-transmission setup for determining the nonlinearity parameter of the second harmonic wave. In this work, a feasibility study is performed to assess the possibility of using pulse-echo methods in determining the nonlinearity parameter β of solids with a stress-free boundary. The multi-Gaussian beam model is developed based on the quasilinear theory of the KZK equation. Simulation results and discussion are presented for the reflected beam fields of the fundamental and second harmonic waves, the uncorrected β behavior and the properties of total correction that incorporate reflection, attenuation and diffraction effects.

Asymmetrical effects of mesophyll conductance on fundamental photosynthetic parameters and their relationships estimated from leaf gas exchange measurements.

Science.gov (United States)

Sun, Ying; Gu, Lianhong; Dickinson, Robert E; Pallardy, Stephen G; Baker, John; Cao, Yonghui; DaMatta, Fábio Murilo; Dong, Xuejun; Ellsworth, David; Van Goethem, Davina; Jensen, Anna M; Law, Beverly E; Loos, Rodolfo; Martins, Samuel C Vitor; Norby, Richard J; Warren, Jeffrey; Weston, David; Winter, Klaus

2014-04-01

Worldwide measurements of nearly 130 C3 species covering all major plant functional types are analysed in conjunction with model simulations to determine the effects of mesophyll conductance (g(m)) on photosynthetic parameters and their relationships estimated from A/Ci curves. We find that an assumption of infinite g(m) results in up to 75% underestimation for maximum carboxylation rate V(cmax), 60% for maximum electron transport rate J(max), and 40% for triose phosphate utilization rate T(u) . V(cmax) is most sensitive, J(max) is less sensitive, and T(u) has the least sensitivity to the variation of g(m). Because of this asymmetrical effect of g(m), the ratios of J(max) to V(cmax), T(u) to V(cmax) and T(u) to J(max) are all overestimated. An infinite g(m) assumption also limits the freedom of variation of estimated parameters and artificially constrains parameter relationships to stronger shapes. These findings suggest the importance of quantifying g(m) for understanding in situ photosynthetic machinery functioning. We show that a nonzero resistance to CO2 movement in chloroplasts has small effects on estimated parameters. A non-linear function with gm as input is developed to convert the parameters estimated under an assumption of infinite gm to proper values. This function will facilitate gm representation in global carbon cycle models. © 2013 John Wiley & Sons Ltd.

Parameter Scaling in Non-Linear Microwave Tomography

DEFF Research Database (Denmark)

Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar

2012-01-01

Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....

State Estimation-based Transmission line parameter identification

Directory of Open Access Journals (Sweden)

Fredy Andrés Olarte Dussán

2010-01-01

Full Text Available This article presents two state-estimation-based algorithms for identifying transmission line parameters. The identification technique used simultaneous state-parameter estimation on an artificial power system composed of several copies of the same transmission line, using measurements at different points in time. The first algorithm used active and reactive power measurements at both ends of the line. The second method used synchronised phasor voltage and current measurements at both ends. The algorithms were tested in simulated conditions on the 30-node IEEE test system. All line parameters for this system were estimated with errors below 1%.

Nonlinear regression analysis for evaluating tracer binding parameters using the programmable K1003 desk computer

International Nuclear Information System (INIS)

Sarrach, D.; Strohner, P.

1986-01-01

The Gauss-Newton algorithm has been used to evaluate tracer binding parameters of RIA by nonlinear regression analysis. The calculations were carried out on the K1003 desk computer. Equations for simple binding models and its derivatives are presented. The advantages of nonlinear regression analysis over linear regression are demonstrated

Kinetic parameter estimation from attenuated SPECT projection measurements

International Nuclear Information System (INIS)

Reutter, B.W.; Gullberg, G.T.

1998-01-01

Conventional analysis of dynamically acquired nuclear medicine data involves fitting kinetic models to time-activity curves generated from regions of interest defined on a temporal sequence of reconstructed images. However, images reconstructed from the inconsistent projections of a time-varying distribution of radiopharmaceutical acquired by a rotating SPECT system can contain artifacts that lead to biases in the estimated kinetic parameters. To overcome this problem the authors investigated the estimation of kinetic parameters directly from projection data by modeling the data acquisition process. To accomplish this it was necessary to parametrize the spatial and temporal distribution of the radiopharmaceutical within the SPECT field of view. In a simulated transverse slice, kinetic parameters were estimated for simple one compartment models for three myocardial regions of interest, as well as for the liver. Myocardial uptake and washout parameters estimated by conventional analysis of noiseless simulated data had biases ranging between 1--63%. Parameters estimated directly from the noiseless projection data were unbiased as expected, since the model used for fitting was faithful to the simulation. Predicted uncertainties (standard deviations) of the parameters obtained for 500,000 detected events ranged between 2--31% for the myocardial uptake parameters and 2--23% for the myocardial washout parameters

MEG and fMRI fusion for nonlinear estimation of neural and BOLD signal changes

Directory of Open Access Journals (Sweden)

Sergey M Plis

2010-11-01

Full Text Available The combined analysis of MEG/EEG and functional MRI measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the BOLD response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater SNR, that confirms the expectation arising from the nature of the experiment. The highly nonlinear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources.

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Directory of Open Access Journals (Sweden)

S. L. Han

2012-01-01

Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

Standard Errors of Estimated Latent Variable Scores with Estimated Structural Parameters

Science.gov (United States)

Hoshino, Takahiro; Shigemasu, Kazuo

2008-01-01

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte…

From spiking neuron models to linear-nonlinear models.

Science.gov (United States)

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

A numerical study of non-linear crack tip parameters

Directory of Open Access Journals (Sweden)

F.V. Antunes

2015-07-01

Full Text Available Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, different authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle, were investigated. It was demonstrated that: i LEFM concepts are applicable to the problem under study; ii the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; iii the Keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; iv the analysis of remote compliance is the best numerical parameter to quantify the crack opening level; v without contact there is no effect of stress ratio on crack tip parameters. Therefore it is proved that the crack closure concept is valid.

A combined method to estimate parameters of the thalamocortical model from a heavily noise-corrupted time series of action potential

Energy Technology Data Exchange (ETDEWEB)

Wang, Ruofan; Wang, Jiang; Deng, Bin, E-mail: dengbin@tju.edu.cn; Liu, Chen; Wei, Xile [Department of Electrical and Automation Engineering, Tianjin University, Tianjin (China); Tsang, K. M.; Chan, W. L. [Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon (Hong Kong)

2014-03-15

A combined method composing of the unscented Kalman filter (UKF) and the synchronization-based method is proposed for estimating electrophysiological variables and parameters of a thalamocortical (TC) neuron model, which is commonly used for studying Parkinson's disease for its relay role of connecting the basal ganglia and the cortex. In this work, we take into account the condition when only the time series of action potential with heavy noise are available. Numerical results demonstrate that not only this method can estimate model parameters from the extracted time series of action potential successfully but also the effect of its estimation is much better than the only use of the UKF or synchronization-based method, with a higher accuracy and a better robustness against noise, especially under the severe noise conditions. Considering the rather important role of TC neuron in the normal and pathological brain functions, the exploration of the method to estimate the critical parameters could have important implications for the study of its nonlinear dynamics and further treatment of Parkinson's disease.

A combined method to estimate parameters of the thalamocortical model from a heavily noise-corrupted time series of action potential

International Nuclear Information System (INIS)

Wang, Ruofan; Wang, Jiang; Deng, Bin; Liu, Chen; Wei, Xile; Tsang, K. M.; Chan, W. L.

2014-01-01

A combined method composing of the unscented Kalman filter (UKF) and the synchronization-based method is proposed for estimating electrophysiological variables and parameters of a thalamocortical (TC) neuron model, which is commonly used for studying Parkinson's disease for its relay role of connecting the basal ganglia and the cortex. In this work, we take into account the condition when only the time series of action potential with heavy noise are available. Numerical results demonstrate that not only this method can estimate model parameters from the extracted time series of action potential successfully but also the effect of its estimation is much better than the only use of the UKF or synchronization-based method, with a higher accuracy and a better robustness against noise, especially under the severe noise conditions. Considering the rather important role of TC neuron in the normal and pathological brain functions, the exploration of the method to estimate the critical parameters could have important implications for the study of its nonlinear dynamics and further treatment of Parkinson's disease

A combined method to estimate parameters of the thalamocortical model from a heavily noise-corrupted time series of action potential

Science.gov (United States)

Wang, Ruofan; Wang, Jiang; Deng, Bin; Liu, Chen; Wei, Xile; Tsang, K. M.; Chan, W. L.

2014-03-01

A combined method composing of the unscented Kalman filter (UKF) and the synchronization-based method is proposed for estimating electrophysiological variables and parameters of a thalamocortical (TC) neuron model, which is commonly used for studying Parkinson's disease for its relay role of connecting the basal ganglia and the cortex. In this work, we take into account the condition when only the time series of action potential with heavy noise are available. Numerical results demonstrate that not only this method can estimate model parameters from the extracted time series of action potential successfully but also the effect of its estimation is much better than the only use of the UKF or synchronization-based method, with a higher accuracy and a better robustness against noise, especially under the severe noise conditions. Considering the rather important role of TC neuron in the normal and pathological brain functions, the exploration of the method to estimate the critical parameters could have important implications for the study of its nonlinear dynamics and further treatment of Parkinson's disease.

A predictor-corrector algorithm to estimate the fractional flow in oil-water models

International Nuclear Information System (INIS)

Savioli, Gabriela B; Berdaguer, Elena M Fernandez

2008-01-01

We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.

Some nonlinear estimates for lateral propagation of self-generated B fields

International Nuclear Information System (INIS)

Goldman, S.R.

1982-01-01

We present nonlinear estimates which provide plausible guidelines and scalings for the lateral transport of magnetic fields due to laser-plasma interaction in both slab and cylindrical geometries. Limitations of the modelling are also indicated

Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm

Directory of Open Access Journals (Sweden)

V. Rajinikanth

2012-01-01

Full Text Available An enhanced bacteria foraging optimization (EBFO algorithm-based Proportional + integral + derivative (PID controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.

Dynamical System and Nonlinear Regression for Estimate Host-Parasitoid Relationship

Directory of Open Access Journals (Sweden)

Ileana Miranda Cabrera

2010-01-01

Full Text Available The complex relationships of a crop with the pest, its natural enemies, and the climate factors exist in all the ecosystems, but the mathematic models has studied only some components to know the relation cause-effect. The most studied system has been concerned with the relationship pest-natural enemies such as prey-predator or host-parasitoid. The present paper shows a dynamical system for studying the relationship host-parasitoid (Diaphorina citri, Tamarixia radiata and shows that a nonlinear model permits the estimation of the parasite nymphs using nymphs healthy as the known variable. The model showed the functional answer of the parasitoid, in which a point arrives that its density is not augmented although the number host increases, and it becomes necessary to intervene in the ecosystem. A simple algorithm is used to estimate the parasitoids level using the priori relationship between the host and the climate factors and then the nonlinear model.

Dynamic systems models new methods of parameter and state estimation

CERN Document Server

2016-01-01

This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamic...

PERTURBATION ESTIMATES FOR THE MAXIMAL SOLUTION OF A NONLINEAR MATRIX EQUATION

Directory of Open Access Journals (Sweden)

Vejdi I. Hasanov

2017-06-01

Full Text Available In this paper a nonlinear matrix equation is considered. Perturba- tion estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical ex- amples.

Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2007-01-01

In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

Parameter estimation and inverse problems

CERN Document Server

Aster, Richard C; Thurber, Clifford H

2005-01-01

Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors'' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that...

Parameter estimation and long-term process simulation of a biogas reactor operated under trace elements limitation

International Nuclear Information System (INIS)

Lübken, Manfred; Koch, Konrad; Gehring, Tito; Horn, Harald; Wichern, Marc

2015-01-01

Highlights: • Estimation of ADM1 parameter uncertainty by nonlinear, correlated parameter analysis. • Unbounded confidence regions were obtained for single hydrolysis rate constants. • ADM1 carbohydrates were divided into a slowly and readily degradable part. • Bioavailability of trace metals explained discrepancies between modeled and measured data. - Abstract: The Anaerobic Digestion Model No. 1 (ADM1) was modified to describe the long-term process stability of a two-stage agricultural biogas system operated for 494 days with a mono-substrate. The ADM1 model fraction for carbohydrates was divided into a slowly and readily degradable part. Significant different hydrolysis rate constants were found for proteins and single fractions of carbohydrates in batch experiments. Degradation of starch, xylan (hemicellulose), cellulose and zein (protein) were modeled with first order hydrolysis rate coefficients of 1.20 d −1 , 0.70 d −1 , 0.18 d −1 and 0.30 d −1 , respectively. While the hydrolysis rate coefficients found in batch experiments could be used for predicting continuous process data, the statistically calculated confidence regions (nonlinear parameter estimation) showed that the upper limits were unbounded. Single discrepancies between measured and modeled process data of the two-stage pilot system could be explained by the lack of bioavailability of trace elements. Addition of iron, as Fe(III)Cl 3 , allowed stable process conditions for an organic loading rate (OLR) up to 2.5 g VS L −1 d −1 . Additional supplement of trace elements was necessary for process operation at OLRs above 2.5 g VS L −1 d −1

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

system of the second-order with nonlinearity of the type "quadratic friction" in combination with nonlinearity of the type "dry friction", was developed a software to simulate a process for providing pseudo experimental data containing random accuracy and to determine the parameters of the system. A conducted computational experiment enabled an estimate of the accuracy with which the proposed algorithm determines the parameters of the system. The illustrative numerical simulation has demonstrated that with using the proposed nonlinear dynamic system identification algorithm in frequency hodograph the accuracy of determining the coefficient values of the frequency transfer function of the second order system with a dry and quadratic friction is comparable with the range of measurement accuracy of experimental samples of this system hodograph. Well-known publications do not mention this identification method of the nonlinear dynamic systems. The nonlinear dynamical systems identification method the article describes can find application when determining parameters of various kinds of actuators. The using method of harmonic linearization and identification of dynamical systems by hodographs is promising for solving the problem of the identification of nonlinear systems with different types of nonlinearities.

Pollen parameters estimates of genetic variability among newly ...

African Journals Online (AJOL)

Pollen parameters estimates of genetic variability among newly selected Nigerian roselle (Hibiscus sabdariffa L.) genotypes. ... Estimates of some pollen parameters where used to assess the genetic diversity among ... HOW TO USE AJOL.

A Comparative Study of Distribution System Parameter Estimation Methods

Energy Technology Data Exchange (ETDEWEB)

Sun, Yannan; Williams, Tess L.; Gourisetti, Sri Nikhil Gup

2016-07-17

In this paper, we compare two parameter estimation methods for distribution systems: residual sensitivity analysis and state-vector augmentation with a Kalman filter. These two methods were originally proposed for transmission systems, and are still the most commonly used methods for parameter estimation. Distribution systems have much lower measurement redundancy than transmission systems. Therefore, estimating parameters is much more difficult. To increase the robustness of parameter estimation, the two methods are applied with combined measurement snapshots (measurement sets taken at different points in time), so that the redundancy for computing the parameter values is increased. The advantages and disadvantages of both methods are discussed. The results of this paper show that state-vector augmentation is a better approach for parameter estimation in distribution systems. Simulation studies are done on a modified version of IEEE 13-Node Test Feeder with varying levels of measurement noise and non-zero error in the other system model parameters.

An Adaptive Gain Nonlinear Observer for State of Charge Estimation of Lithium-Ion Batteries in Electric Vehicles

Directory of Open Access Journals (Sweden)

Yong Tian

2014-09-01

Full Text Available The state of charge (SOC is important for the safety and reliability of battery operation since it indicates the remaining capacity of a battery. However, it is difficult to get an accurate value of SOC, because the SOC cannot be directly measured by a sensor. In this paper, an adaptive gain nonlinear observer (AGNO for SOC estimation of lithium-ion batteries (LIBs in electric vehicles (EVs is proposed. The second-order resistor–capacitor (2RC equivalent circuit model is used to simulate the dynamic behaviors of a LIB, based on which the state equations are derived to design the AGNO for SOC estimation. The model parameters are identified using the exponential-function fitting method. The sixth-order polynomial function is used to describe the highly nonlinear relationship between the open circuit voltage (OCV and the SOC. The convergence of the proposed AGNO is proved using the Lyapunov stability theory. Two typical driving cycles, including the New European Driving Cycle (NEDC and Federal Urban Driving Schedule (FUDS are adopted to evaluate the performance of the AGNO by comparing with the unscented Kalman filter (UKF algorithm. The experimental results show that the AGNO has better performance than the UKF algorithm in terms of reducing the computation cost, improving the estimation accuracy and enhancing the convergence ability.

Estimation of Pulse Transit Time as a Function of Blood Pressure Using a Nonlinear Arterial Tube-Load Model.

Science.gov (United States)

Gao, Mingwu; Cheng, Hao-Min; Sung, Shih-Hsien; Chen, Chen-Huan; Olivier, Nicholas Bari; Mukkamala, Ramakrishna

2017-07-01

pulse transit time (PTT) varies with blood pressure (BP) throughout the cardiac cycle, yet, because of wave reflection, only one PTT value at the diastolic BP level is conventionally estimated from proximal and distal BP waveforms. The objective was to establish a technique to estimate multiple PTT values at different BP levels in the cardiac cycle. a technique was developed for estimating PTT as a function of BP (to indicate the PTT value for every BP level) from proximal and distal BP waveforms. First, a mathematical transformation from one waveform to the other is defined in terms of the parameters of a nonlinear arterial tube-load model accounting for BP-dependent arterial compliance and wave reflection. Then, the parameters are estimated by optimally fitting the waveforms to each other via the model-based transformation. Finally, PTT as a function of BP is specified by the parameters. The technique was assessed in animals and patients in several ways including the ability of its estimated PTT-BP function to serve as a subject-specific curve for calibrating PTT to BP. the calibration curve derived by the technique during a baseline period yielded bias and precision errors in mean BP of 5.1 ± 0.9 and 6.6 ± 1.0 mmHg, respectively, during hemodynamic interventions that varied mean BP widely. the new technique may permit, for the first time, estimation of PTT values throughout the cardiac cycle from proximal and distal waveforms. the technique could potentially be applied to improve arterial stiffness monitoring and help realize cuff-less BP monitoring.

Multi-Parameter Estimation for Orthorhombic Media

KAUST Repository

Masmoudi, Nabil

2015-08-19

Building reliable anisotropy models is crucial in seismic modeling, imaging and full waveform inversion. However, estimating anisotropy parameters is often hampered by the trade off between inhomogeneity and anisotropy. For instance, one way to estimate the anisotropy parameters is to relate them analytically to traveltimes, which is challenging in inhomogeneous media. Using perturbation theory, we develop travel-time approximations for orthorhombic media as explicit functions of the anellipticity parameters η1, η2 and a parameter Δγ in inhomogeneous background media. Specifically, our expansion assumes inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. This approach has two main advantages: in one hand, it provides a computationally efficient tool to solve the orthorhombic eikonal equation, on the other hand, it provides a mechanism to scan for the best fitting anisotropy parameters without the need for repetitive modeling of traveltimes, because the coefficients of the traveltime expansion are independent of the perturbed parameters. Furthermore, the coefficients of the traveltime expansion provide insights on the sensitivity of the traveltime with respect to the perturbed parameters. We show the accuracy of the traveltime approximations as well as an approach for multi-parameter scanning in orthorhombic media.

Multi-Parameter Estimation for Orthorhombic Media

KAUST Repository

Masmoudi, Nabil; Alkhalifah, Tariq Ali

2015-01-01

Building reliable anisotropy models is crucial in seismic modeling, imaging and full waveform inversion. However, estimating anisotropy parameters is often hampered by the trade off between inhomogeneity and anisotropy. For instance, one way to estimate the anisotropy parameters is to relate them analytically to traveltimes, which is challenging in inhomogeneous media. Using perturbation theory, we develop travel-time approximations for orthorhombic media as explicit functions of the anellipticity parameters η1, η2 and a parameter Δγ in inhomogeneous background media. Specifically, our expansion assumes inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. This approach has two main advantages: in one hand, it provides a computationally efficient tool to solve the orthorhombic eikonal equation, on the other hand, it provides a mechanism to scan for the best fitting anisotropy parameters without the need for repetitive modeling of traveltimes, because the coefficients of the traveltime expansion are independent of the perturbed parameters. Furthermore, the coefficients of the traveltime expansion provide insights on the sensitivity of the traveltime with respect to the perturbed parameters. We show the accuracy of the traveltime approximations as well as an approach for multi-parameter scanning in orthorhombic media.

On the real-time estimation of the wheel-rail contact force by means of a new nonlinear estimator design model

Science.gov (United States)

Strano, Salvatore; Terzo, Mario

2018-05-01

The dynamics of the railway vehicles is strongly influenced by the interaction between the wheel and the rail. This kind of contact is affected by several conditioning factors such as vehicle speed, wear, adhesion level and, moreover, it is nonlinear. As a consequence, the modelling and the observation of this kind of phenomenon are complex tasks but, at the same time, they constitute a fundamental step for the estimation of the adhesion level or for the vehicle condition monitoring. This paper presents a novel technique for the real time estimation of the wheel-rail contact forces based on an estimator design model that takes into account the nonlinearities of the interaction by means of a fitting model functional to reproduce the contact mechanics in a wide range of slip and to be easily integrated in a complete model based estimator for railway vehicle.

Assessment of cerebrospinal fluid system dynamics : novel infusion protocol, mathematical modelling and parameter estimation for hydrocephalus investigations

OpenAIRE

Andersson, Kennet

2011-01-01

Patients with idiopathic normal pressure hydrocephalus (INPH) have a disturbance in the cerebrospinal fluid (CSF) system. The treatment is neurosurgical – a shunt is placed in the CSF system. The infusion test is used to assess CSF system dynamics and to aid in the selection of patients that will benefit from shunt surgery. The infusion test can be divided into three parts: a mathematical model, an infusion protocol and a parameter estimation method. A non-linear differential equation is used...

Modeling of Volatility with Non-linear Time Series Model

OpenAIRE

Kim Song Yon; Kim Mun Chol

2013-01-01

In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.

A Real-Time Joint Estimator for Model Parameters and State of Charge of Lithium-Ion Batteries in Electric Vehicles

Directory of Open Access Journals (Sweden)

Jianping Gao

2015-08-01

Full Text Available Accurate state of charge (SoC estimation of batteries plays an important role in promoting the commercialization of electric vehicles. The main work to be done in accurately determining battery SoC can be summarized in three parts. (1 In view of the model-based SoC estimation flow diagram, the n-order resistance-capacitance (RC battery model is proposed and expected to accurately simulate the battery’s major time-variable, nonlinear characteristics. Then, the mathematical equations for model parameter identification and SoC estimation of this model are constructed. (2 The Akaike information criterion is used to determine an optimal tradeoff between battery model complexity and prediction precision for the n-order RC battery model. Results from a comparative analysis show that the first-order RC battery model is thought to be the best based on the Akaike information criterion (AIC values. (3 The real-time joint estimator for the model parameter and SoC is constructed, and the application based on two battery types indicates that the proposed SoC estimator is a closed-loop identification system where the model parameter identification and SoC estimation are corrected mutually, adaptively and simultaneously according to the observer values. The maximum SoC estimation error is less than 1% for both battery types, even against the inaccurate initial SoC.

Parameter and State Estimator for State Space Models

Directory of Open Access Journals (Sweden)

Ruifeng Ding

2014-01-01

Full Text Available This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

CERN Document Server

Rigatos, Gerasimos G

2015-01-01

This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

Electron acoustic nonlinear structures in planetary magnetospheres

Science.gov (United States)

Shah, K. H.; Qureshi, M. N. S.; Masood, W.; Shah, H. A.

2018-04-01

In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized ( r , q ) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized ( r , q ) distribution. It has been found that the flatness parameter r , tail parameter q , and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.

Nonlinear control of linear parameter varying systems with applications to hypersonic vehicles

Science.gov (United States)

Wilcox, Zachary Donald

The focus of this dissertation is to design a controller for linear parameter varying (LPV) systems, apply it specifically to air-breathing hypersonic vehicles, and examine the interplay between control performance and the structural dynamics design. Specifically a Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded, nonvanishing disturbances. The hypersonic vehicle has time varying parameters, specifically temperature profiles, and its dynamics can be reduced to an LPV system with additive disturbances. Since the HSV can be modeled as an LPV system the proposed control design is directly applicable. The control performance is directly examined through simulations. A wide variety of applications exist that can be effectively modeled as LPV systems. In particular, flight systems have historically been modeled as LPV systems and associated control tools have been applied such as gain-scheduling, linear matrix inequalities (LMIs), linear fractional transformations (LFT), and mu-types. However, as the type of flight environments and trajectories become more demanding, the traditional LPV controllers may no longer be sufficient. In particular, hypersonic flight vehicles (HSVs) present an inherently difficult problem because of the nonlinear aerothermoelastic coupling effects in the dynamics. HSV flight conditions produce temperature variations that can alter both the structural dynamics and flight dynamics. Starting with the full nonlinear dynamics, the aerothermoelastic effects are modeled by a temperature dependent, parameter varying state-space representation with added disturbances. The model includes an uncertain parameter varying state matrix, an uncertain parameter varying non-square (column deficient) input matrix, and an additive bounded disturbance. In this dissertation, a robust dynamic controller is formulated for a uncertain and disturbed LPV system. The developed

Establishment of regression dependences. Linear and nonlinear dependences

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab

Kinetic parameter estimation from SPECT cone-beam projection measurements

International Nuclear Information System (INIS)

Huesman, Ronald H.; Reutter, Bryan W.; Zeng, G. Larry; Gullberg, Grant T.

1998-01-01

Kinetic parameters are commonly estimated from dynamically acquired nuclear medicine data by first reconstructing a dynamic sequence of images and subsequently fitting the parameters to time-activity curves generated from regions of interest overlaid upon the image sequence. Biased estimates can result from images reconstructed using inconsistent projections of a time-varying distribution of radiopharmaceutical acquired by a rotating SPECT system. If the SPECT data are acquired using cone-beam collimators wherein the gantry rotates so that the focal point of the collimators always remains in a plane, additional biases can arise from images reconstructed using insufficient, as well as truncated, projection samples. To overcome these problems we have investigated the estimation of kinetic parameters directly from SPECT cone-beam projection data by modelling the data acquisition process. To accomplish this it was necessary to parametrize the spatial and temporal distribution of the radiopharmaceutical within the SPECT field of view. In a simulated chest image volume, kinetic parameters were estimated for simple one-compartment models for four myocardial regions of interest. Myocardial uptake and washout parameters estimated by conventional analysis of noiseless simulated cone-beam data had biases ranging between 3-26% and 0-28%, respectively. Parameters estimated directly from the noiseless projection data were unbiased as expected, since the model used for fitting was faithful to the simulation. Statistical uncertainties of parameter estimates for 10 000 000 events ranged between 0.2-9% for the uptake parameters and between 0.3-6% for the washout parameters. (author)

Step-by-step optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

International Nuclear Information System (INIS)

Frolov, A.M.

1986-01-01

Exact variational calculations are treated for few-particle systems in the exponential basis of relative coordinates using nonlinear parameters. The methods of step-by-step optimization and global chaos of nonlinear parameters are applied to calculate the S and P states of ppμ, ddμ, ttμ homonuclear mesomolecules within the error ≤±0.001 eV. The global chaos method turned out to be well applicable to nuclear 3 H and 3 He systems

Traveltime approximations and parameter estimation for orthorhombic media

KAUST Repository

Masmoudi, Nabil

2016-05-30

Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters if we relate them analytically to traveltimes. Using perturbation theory, we have developed traveltime approximations for orthorhombic media as explicit functions of the anellipticity parameters η1, η2, and Δχ in inhomogeneous background media. The parameter Δχ is related to Tsvankin-Thomsen notation and ensures easier computation of traveltimes in the background model. Specifically, our expansion assumes an inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. We have used the Shanks transform to enhance the accuracy of the formulas. A homogeneous medium simplification of the traveltime expansion provided a nonhyperbolic moveout description of the traveltime that was more accurate than other derived approximations. Moreover, the formulation provides a computationally efficient tool to solve the eikonal equation of an orthorhombic medium, without any constraints on the background model complexity. Although, the expansion is based on the factorized representation of the perturbation parameters, smooth variations of these parameters (represented as effective values) provides reasonable results. Thus, this formulation provides a mechanism to estimate the three effective parameters η1, η2, and Δχ. We have derived Dix-type formulas for orthorhombic medium to convert the effective parameters to their interval values.

Grain filling parameters and yield components in wheat

OpenAIRE

Brdar Milka; Kobiljski Borislav; Balalić-Kraljević Marija

2006-01-01

Grain yield of wheat (Triticum aestivum L.) is influenced by number of grains per unit area and grain weight, which is result of grain filling duration and rate. The aim of the study was to investigate the relationships between grain filling parameters in 4 wheat genotypes of different earliness and yield components. Nonlinear regression estimated and observed parameters were analyzed. Rang of estimated parameters corresponds to rang of observed parameters. Stepwise MANOVA indicated that the ...

Likelihood-Based Inference in Nonlinear Error-Correction Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbæk, Anders

We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

Science.gov (United States)

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

Science.gov (United States)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress

Estimation of non-linear effective permeability of magnetic materials with fine structure

International Nuclear Information System (INIS)

Waki, H.; Igarashi, H.; Honma, T.

2006-01-01

This paper describes a homogenization method for magnetic materials with fine structure. In this method, the structures of the magnetic materials are assumed to be periodic, and the unit cell is defined. The effective permeability is determined on the basis of magnetic energy balance in the unit cell. This method can be applied not only for linear problems but also for non-linear ones. In this paper, estimation of the effective permeability of non-linear magnetic materials by using the homogenization method is described in detail, and then the validity for the non-liner problems is tested for two-dimensional problems. It is shown that this homogenization method gives accurate non-linear effective permeability

A dynamic load estimation method for nonlinear structures with unscented Kalman filter

Science.gov (United States)

Guo, L. N.; Ding, Y.; Wang, Z.; Xu, G. S.; Wu, B.

2018-02-01

A force estimation method is proposed for hysteretic nonlinear structures. The equation of motion for the nonlinear structure is represented in state space and the state variable is augmented by the unknown the time history of external force. Unscented Kalman filter (UKF) is improved for the force identification in state space considering the ill-condition characteristic in the computation of square roots for the covariance matrix. The proposed method is firstly validated by a numerical simulation study of a 3-storey nonlinear hysteretic frame excited by periodic force. Each storey is supposed to follow a nonlinear hysteretic model. The external force is identified and the measurement noise is considered in this case. Then a case of a seismically isolated building subjected to earthquake excitation and impact force is studied. The isolation layer performs nonlinearly during the earthquake excitation. Impact force between the seismically isolated structure and the retaining wall is estimated with the proposed method. Uncertainties such as measurement noise, model error in storey stiffness and unexpected environmental disturbances are considered. A real-time substructure testing of an isolated structure is conducted to verify the proposed method. In the experimental study, the linear main structure is taken as numerical substructure while the one of the isolations with additional mass is taken as the nonlinear physical substructure. The force applied by the actuator on the physical substructure is identified and compared with the measured value from the force transducer. The method proposed in this paper is also validated by shaking table test of a seismically isolated steel frame. The acceleration of the ground motion as the unknowns is identified by the proposed method. Results from both numerical simulation and experimental studies indicate that the UKF based force identification method can be used to identify external excitations effectively for the nonlinear

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh-Bénard convection.

Science.gov (United States)

Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F

2009-03-01

Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.

Estimates for the parameters of the heavy quark expansion

Energy Technology Data Exchange (ETDEWEB)

Heinonen, Johannes; Mannel, Thomas [Universitaet Siegen (Germany)

2015-07-01

We give improved estimates for the non-perturbative parameters appearing in the heavy quark expansion for inclusive decays. While the parameters appearing in low orders of this expansion can be extracted from data, the number of parameters in higher orders proliferates strongly, making a determination of these parameters from data impossible. Thus, one has to rely on theoretical estimates which may be obtained from an insertion of intermediate states. We refine this method and attempt to estimate the uncertainties of this approach.

On robust parameter estimation in brain-computer interfacing

Science.gov (United States)

Samek, Wojciech; Nakajima, Shinichi; Kawanabe, Motoaki; Müller, Klaus-Robert

2017-12-01

Objective. The reliable estimation of parameters such as mean or covariance matrix from noisy and high-dimensional observations is a prerequisite for successful application of signal processing and machine learning algorithms in brain-computer interfacing (BCI). This challenging task becomes significantly more difficult if the data set contains outliers, e.g. due to subject movements, eye blinks or loose electrodes, as they may heavily bias the estimation and the subsequent statistical analysis. Although various robust estimators have been developed to tackle the outlier problem, they ignore important structural information in the data and thus may not be optimal. Typical structural elements in BCI data are the trials consisting of a few hundred EEG samples and indicating the start and end of a task. Approach. This work discusses the parameter estimation problem in BCI and introduces a novel hierarchical view on robustness which naturally comprises different types of outlierness occurring in structured data. Furthermore, the class of minimum divergence estimators is reviewed and a robust mean and covariance estimator for structured data is derived and evaluated with simulations and on a benchmark data set. Main results. The results show that state-of-the-art BCI algorithms benefit from robustly estimated parameters. Significance. Since parameter estimation is an integral part of various machine learning algorithms, the presented techniques are applicable to many problems beyond BCI.

Step-by-step optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

Energy Technology Data Exchange (ETDEWEB)

Frolov, A M

1986-09-01

Exact variational calculations are treated for few-particle systems in the exponential basis of relative coordinates using nonlinear parameters. The methods of step-by-step optimization and global chaos of nonlinear parameters are applied to calculate the S and P states of pp..mu.., dd..mu.., tt..mu.. homonuclear mesomolecules within the error less than or equal to+-0.001 eV. The global chaos method turned out to be well applicable to nuclear /sup 3/H and /sup 3/He systems.

A simulation of water pollution model parameter estimation

Science.gov (United States)

Kibler, J. F.

1976-01-01

A parameter estimation procedure for a water pollution transport model is elaborated. A two-dimensional instantaneous-release shear-diffusion model serves as representative of a simple transport process. Pollution concentration levels are arrived at via modeling of a remote-sensing system. The remote-sensed data are simulated by adding Gaussian noise to the concentration level values generated via the transport model. Model parameters are estimated from the simulated data using a least-squares batch processor. Resolution, sensor array size, and number and location of sensor readings can be found from the accuracies of the parameter estimates.

Prognostic value of Poincare plot as nonlinear parameter of chaos theory in patients with myocardial infarction

Directory of Open Access Journals (Sweden)

Milovanović Branislav

2007-01-01

Full Text Available Introduction: There are different proofs about association of autonomic nervous system dysfunction, especially nonlinear parameters, with higher mortality after myocardial infarction. Objective The objective of the study was to determine predictive value of Poincare plot as nonlinear parameter and other significant standard risk predictors: ejection fraction of the left ventricle, late potentials, ventricular arrhythmias, and QT interval. Method The study included 1081 patients with mean follow up of 28 months (ranging fom 0-80 months. End-point of the study was cardiovascular mortality. The following diagnostic methods were used during the second week: ECG with commercial software Schiller AT-10: short time spectral analysis of RR variability with analysis of Poincare plot as nonlinear parameter and late potentials; 24-hour ambulatory ECG monitoring: QT interval, RR interval, QT/RR slope, ventricular arrhythmias (Lown >II; echocardiography examinations: systolic disorder (defined as EF<40 %. Results There were 103 (9.52% cardiovascular deaths during the follow-up. In univariate analysis, the following parameters were significantly correlated with mortality: mean RR interval < 800 ms, QT and RR interval space relationship as mean RR interval < 800 ms and QT interval > 350 ms, positive late potentials, systolic dysfunction, Poincare plot as a point, ventricular arrhythmias (Lown > II. In multivariate analysis, the significant risk predictors were: Poincare plot as a point and mean RR interval lower than 800 ms. Conclusion Mean RR interval lower than 800 ms and nonlinear and space presentation of RR interval as a point Poincare plot were multivariate risk predictors.

Spatial Bias in Field-Estimated Unsaturated Hydraulic Properties

Energy Technology Data Exchange (ETDEWEB)

HOLT,ROBERT M.; WILSON,JOHN L.; GLASS JR.,ROBERT J.

2000-12-21

Hydraulic property measurements often rely on non-linear inversion models whose errors vary between samples. In non-linear physical measurement systems, bias can be directly quantified and removed using calibration standards. In hydrologic systems, field calibration is often infeasible and bias must be quantified indirectly. We use a Monte Carlo error analysis to indirectly quantify spatial bias in the saturated hydraulic conductivity, K{sub s}, and the exponential relative permeability parameter, {alpha}, estimated using a tension infiltrometer. Two types of observation error are considered, along with one inversion-model error resulting from poor contact between the instrument and the medium. Estimates of spatial statistics, including the mean, variance, and variogram-model parameters, show significant bias across a parameter space representative of poorly- to well-sorted silty sand to very coarse sand. When only observation errors are present, spatial statistics for both parameters are best estimated in materials with high hydraulic conductivity, like very coarse sand. When simple contact errors are included, the nature of the bias changes dramatically. Spatial statistics are poorly estimated, even in highly conductive materials. Conditions that permit accurate estimation of the statistics for one of the parameters prevent accurate estimation for the other; accurate regions for the two parameters do not overlap in parameter space. False cross-correlation between estimated parameters is created because estimates of K{sub s} also depend on estimates of {alpha} and both parameters are estimated from the same data.

On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

International Nuclear Information System (INIS)

Xu, Meng; Droguett, Enrique López; Lins, Isis Didier; Chagas Moura, Márcio das

2017-01-01

The q-Weibull model is based on the Tsallis non-extensive entropy and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate. - Highlights: • Development of an Adaptive Hybrid ABC (AHABC) algorithm for q-Weibull distribution. • AHABC combines local Nelder-Mead simplex method with ABC to enhance local search. • AHABC efficiently finds the optimal solution for the q-Weibull ML problem. • AHABC outperforms ABC and self-adaptive hybrid ABC in accuracy and convergence speed. • Useful model for reliability data with non-monotonic hazard rate.

Estimation of Poisson-Dirichlet Parameters with Monotone Missing Data

Directory of Open Access Journals (Sweden)

Xueqin Zhou

2017-01-01

Full Text Available This article considers the estimation of the unknown numerical parameters and the density of the base measure in a Poisson-Dirichlet process prior with grouped monotone missing data. The numerical parameters are estimated by the method of maximum likelihood estimates and the density function is estimated by kernel method. A set of simulations was conducted, which shows that the estimates perform well.

Variational estimation of process parameters in a simplified atmospheric general circulation model

Science.gov (United States)

Lv, Guokun; Koehl, Armin; Stammer, Detlef

2016-04-01

Parameterizations are used to simulate effects of unresolved sub-grid-scale processes in current state-of-the-art climate model. The values of the process parameters, which determine the model's climatology, are usually manually adjusted to reduce the difference of model mean state to the observed climatology. This process requires detailed knowledge of the model and its parameterizations. In this work, a variational method was used to estimate process parameters in the Planet Simulator (PlaSim). The adjoint code was generated using automatic differentiation of the source code. Some hydrological processes were switched off to remove the influence of zero-order discontinuities. In addition, the nonlinearity of the model limits the feasible assimilation window to about 1day, which is too short to tune the model's climatology. To extend the feasible assimilation window, nudging terms for all state variables were added to the model's equations, which essentially suppress all unstable directions. In identical twin experiments, we found that the feasible assimilation window could be extended to over 1-year and accurate parameters could be retrieved. Although the nudging terms transform to a damping of the adjoint variables and therefore tend to erases the information of the data over time, assimilating climatological information is shown to provide sufficient information on the parameters. Moreover, the mechanism of this regularization is discussed.

Impact of nonlinearity on changing the a priori of trace gas profile estimates from the Tropospheric Emission Spectrometer (TES

Directory of Open Access Journals (Sweden)

S. S. Kulawik

2008-06-01

Full Text Available Non-linear maximum a posteriori (MAP estimates of atmospheric profiles from the Tropospheric Emission Spectrometer (TES contains a priori information that may vary geographically, which is a confounding factor in the analysis and physical interpretation of an ensemble of profiles. One mitigation strategy is to transform profile estimates to a common prior using a linear operation thereby facilitating the interpretation of profile variability. However, this operation is dependent on the assumption of not worse than moderate non-linearity near the solution of the non-linear estimate. The robustness of this assumption is tested by comparing atmospheric retrievals from the Tropospheric Emission Spectrometer processed with a uniform prior with those processed with a variable prior and converted to a uniform prior following the non-linear retrieval. Linearly converting the prior following a non-linear retrieval is shown to have a minor effect on the results as compared to a non-linear retrieval using a uniform prior when compared to the expected total error, with less than 10% of the change in the prior ending up as unbiased fluctuations in the profile estimate results.

Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

Directory of Open Access Journals (Sweden)

Jun Yan

2013-01-01

Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Parameter estimation in stochastic differential equations

CERN Document Server

Bishwal, Jaya P N

2008-01-01

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.

Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models

DEFF Research Database (Denmark)

Hillebrand, Eric Tobias; Medeiros, Marcelo C.

We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in ARMA time series models and apply our modeling framework to daily realized volatility. Asymptotic theory for parameter estimation is developed and two model building...

Nonlinear consider covariance analysis using a sigma-point filter formulation

Science.gov (United States)

Lisano, Michael E.

2006-01-01

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

Science.gov (United States)

Zheng, Binqi; Fu, Pengcheng; Li, Baoqing; Yuan, Xiaobing

2018-03-07

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.

How to fool cosmic microwave background parameter estimation

International Nuclear Information System (INIS)

Kinney, William H.

2001-01-01

With the release of the data from the Boomerang and MAXIMA-1 balloon flights, estimates of cosmological parameters based on the cosmic microwave background (CMB) have reached unprecedented precision. In this paper I show that it is possible for these estimates to be substantially biased by features in the primordial density power spectrum. I construct primordial power spectra which mimic to within cosmic variance errors the effect of changing parameters such as the baryon density and neutrino mass, meaning that even an ideal measurement would be unable to resolve the degeneracy. Complementary measurements are necessary to resolve this ambiguity in parameter estimation efforts based on CMB temperature fluctuations alone

Summary of the DREAM8 Parameter Estimation Challenge: Toward Parameter Identification for Whole-Cell Models.

Directory of Open Access Journals (Sweden)

Jonathan R Karr

2015-05-01

Full Text Available Whole-cell models that explicitly represent all cellular components at the molecular level have the potential to predict phenotype from genotype. However, even for simple bacteria, whole-cell models will contain thousands of parameters, many of which are poorly characterized or unknown. New algorithms are needed to estimate these parameters and enable researchers to build increasingly comprehensive models. We organized the Dialogue for Reverse Engineering Assessments and Methods (DREAM 8 Whole-Cell Parameter Estimation Challenge to develop new parameter estimation algorithms for whole-cell models. We asked participants to identify a subset of parameters of a whole-cell model given the model's structure and in silico "experimental" data. Here we describe the challenge, the best performing methods, and new insights into the identifiability of whole-cell models. We also describe several valuable lessons we learned toward improving future challenges. Going forward, we believe that collaborative efforts supported by inexpensive cloud computing have the potential to solve whole-cell model parameter estimation.

Robust Fault Estimation Design for Discrete-Time Nonlinear Systems via A Modified Fuzzy Fault Estimation Observer.

Science.gov (United States)

Xie, Xiang-Peng; Yue, Dong; Park, Ju H

2018-02-01

The paper provides relaxed designs of fault estimation observer for nonlinear dynamical plants in the Takagi-Sugeno form. Compared with previous theoretical achievements, a modified version of fuzzy fault estimation observer is implemented with the aid of the so-called maximum-priority-based switching law. Given each activated switching status, the appropriate group of designed matrices can be provided so as to explore certain key properties of the considered plants by means of introducing a set of matrix-valued variables. Owing to the reason that more abundant information of the considered plants can be updated in due course and effectively exploited for each time instant, the conservatism of the obtained result is less than previous theoretical achievements and thus the main defect of those existing methods can be overcome to some extent in practice. Finally, comparative simulation studies on the classical nonlinear truck-trailer model are given to certify the benefits of the theoretic achievement which is obtained in our study. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Parameter Estimation for Improving Association Indicators in Binary Logistic Regression

Directory of Open Access Journals (Sweden)

Mahdi Bashiri

2012-02-01

Full Text Available The aim of this paper is estimation of Binary logistic regression parameters for maximizing the log-likelihood function with improved association indicators. In this paper the parameter estimation steps have been explained and then measures of association have been introduced and their calculations have been analyzed. Moreover a new related indicators based on membership degree level have been expressed. Indeed association measures demonstrate the number of success responses occurred in front of failure in certain number of Bernoulli independent experiments. In parameter estimation, existing indicators values is not sensitive to the parameter values, whereas the proposed indicators are sensitive to the estimated parameters during the iterative procedure. Therefore, proposing a new association indicator of binary logistic regression with more sensitivity to the estimated parameters in maximizing the log- likelihood in iterative procedure is innovation of this study.

Reduced Complexity Volterra Models for Nonlinear System Identification

Directory of Open Access Journals (Sweden)

Hacıoğlu Rıfat

2001-01-01

Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.

Estimation of light transport parameters in biological media using ...

Indian Academy of Sciences (India)

Estimation of light transport parameters in biological media using coherent backscattering ... backscattered light for estimating the light transport parameters of biological media has been investigated. ... Pramana – Journal of Physics | News.

Statistics of Parameter Estimates: A Concrete Example

KAUST Repository

Aguilar, Oscar; Allmaras, Moritz; Bangerth, Wolfgang; Tenorio, Luis

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise

Parameter Estimation of Partial Differential Equation Models

KAUST Repository

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Maity, Arnab; Carroll, Raymond J.

2013-01-01

PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus

Likelihood-based inference for cointegration with nonlinear error-correction

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbek, Anders Christian

2010-01-01

We consider a class of nonlinear vector error correction models where the transfer function (or loadings) of the stationary relationships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long-run cointegration parameters, and the short-run parameters. Asymptotic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normality can be found. A simulation study...

Tail estimates for stochastic fixed point equations via nonlinear renewal theory

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.

2013-01-01

estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D; Keesman, K.J.; Zwart, Heiko J.

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D.; Keesman, K.J.; Zwart, H.

2006-01-01

Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state

Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models.

Science.gov (United States)

Huang, Guanghui; Wan, Jianping; Chen, Hui

2013-02-01

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.

Nonlinear neural network for hemodynamic model state and input estimation using fMRI data

KAUST Repository

Karam, Ayman M.

2014-11-01

Originally inspired by biological neural networks, artificial neural networks (ANNs) are powerful mathematical tools that can solve complex nonlinear problems such as filtering, classification, prediction and more. This paper demonstrates the first successful implementation of ANN, specifically nonlinear autoregressive with exogenous input (NARX) networks, to estimate the hemodynamic states and neural activity from simulated and measured real blood oxygenation level dependent (BOLD) signals. Blocked and event-related BOLD data are used to test the algorithm on real experiments. The proposed method is accurate and robust even in the presence of signal noise and it does not depend on sampling interval. Moreover, the structure of the NARX networks is optimized to yield the best estimate with minimal network architecture. The results of the estimated neural activity are also discussed in terms of their potential use.

Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel.

Science.gov (United States)

Lambert, Ronald J W; Mytilinaios, Ioannis; Maitland, Luke; Brown, Angus M

2012-08-01

This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

A stepwise regression tree for nonlinear approximation: applications to estimating subpixel land cover

Science.gov (United States)

Huang, C.; Townshend, J.R.G.

2003-01-01

A stepwise regression tree (SRT) algorithm was developed for approximating complex nonlinear relationships. Based on the regression tree of Breiman et al . (BRT) and a stepwise linear regression (SLR) method, this algorithm represents an improvement over SLR in that it can approximate nonlinear relationships and over BRT in that it gives more realistic predictions. The applicability of this method to estimating subpixel forest was demonstrated using three test data sets, on all of which it gave more accurate predictions than SLR and BRT. SRT also generated more compact trees and performed better than or at least as well as BRT at all 10 equal forest proportion interval ranging from 0 to 100%. This method is appealing to estimating subpixel land cover over large areas.

Kalman filter data assimilation: targeting observations and parameter estimation.

Science.gov (United States)

Bellsky, Thomas; Kostelich, Eric J; Mahalov, Alex

2014-06-01

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

Kalman filter data assimilation: Targeting observations and parameter estimation

International Nuclear Information System (INIS)

Bellsky, Thomas; Kostelich, Eric J.; Mahalov, Alex

2014-01-01

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation

An algorithm for robust non-linear analysis of radioimmunoassays and other bioassays

International Nuclear Information System (INIS)

Normolle, D.P.

1993-01-01

The four-parameter logistic function is an appropriate model for many types of bioassays that have continuous response variables, such as radioimmunoassays. By modelling the variance of replicates in an assay, one can modify the usual parameter estimation techniques (for example, Gauss-Newton or Marquardt-Levenberg) to produce parameter estimates for the standard curve that are robust against outlying observations. This article describes the computation of robust (M-) estimates for the parameters of the four-parameter logistic function. It describes techniques for modelling the variance structure of the replicates, modifications to the usual iterative algorithms for parameter estimation in non-linear models, and a formula for inverse confidence intervals. To demonstrate the algorithm, the article presents examples where the robustly estimated four-parameter logistic model is compared with the logit-log and four-parameter logistic models with least-squares estimates. (author)

Modeling and Parameter Estimation of a Small Wind Generation System

Directory of Open Access Journals (Sweden)

Carlos A. Ramírez Gómez

2013-11-01

Full Text Available The modeling and parameter estimation of a small wind generation system is presented in this paper. The system consists of a wind turbine, a permanent magnet synchronous generator, a three phase rectifier, and a direct current load. In order to estimate the parameters wind speed data are registered in a weather station located in the Fraternidad Campus at ITM. Wind speed data were applied to a reference model programed with PSIM software. From that simulation, variables were registered to estimate the parameters. The wind generation system model together with the estimated parameters is an excellent representation of the detailed model, but the estimated model offers a higher flexibility than the programed model in PSIM software.

Estimation of parameter sensitivities for stochastic reaction networks

KAUST Repository

Gupta, Ankit

2016-01-07

Quantification of the effects of parameter uncertainty is an important and challenging problem in Systems Biology. We consider this problem in the context of stochastic models of biochemical reaction networks where the dynamics is described as a continuous-time Markov chain whose states represent the molecular counts of various species. For such models, effects of parameter uncertainty are often quantified by estimating the infinitesimal sensitivities of some observables with respect to model parameters. The aim of this talk is to present a holistic approach towards this problem of estimating parameter sensitivities for stochastic reaction networks. Our approach is based on a generic formula which allows us to construct efficient estimators for parameter sensitivity using simulations of the underlying model. We will discuss how novel simulation techniques, such as tau-leaping approximations, multi-level methods etc. can be easily integrated with our approach and how one can deal with stiff reaction networks where reactions span multiple time-scales. We will demonstrate the efficiency and applicability of our approach using many examples from the biological literature.

Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method

Energy Technology Data Exchange (ETDEWEB)

Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)

2015-04-15

In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.

Rapid assessment of nonlinear optical propagation effects in dielectrics

Science.gov (United States)

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Load Estimation from Modal Parameters

DEFF Research Database (Denmark)

Aenlle, Manuel López; Brincker, Rune; Fernández, Pelayo Fernández

2007-01-01

In Natural Input Modal Analysis the modal parameters are estimated just from the responses while the loading is not recorded. However, engineers are sometimes interested in knowing some features of the loading acting on a structure. In this paper, a procedure to determine the loading from a FRF m...

A variational approach to parameter estimation in ordinary differential equations

Directory of Open Access Journals (Sweden)

Kaschek Daniel

2012-08-01

Full Text Available Abstract Background Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. Results The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. Conclusions The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

A variational approach to parameter estimation in ordinary differential equations.

Science.gov (United States)

Kaschek, Daniel; Timmer, Jens

2012-08-14

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

Parameter estimation in stochastic rainfall-runoff models

DEFF Research Database (Denmark)

Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur

2006-01-01

A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...

Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

International Nuclear Information System (INIS)

Xu Ruirui; Chen Tianlun; Gao Chengfeng

2006-01-01

Nonlinear time series prediction is studied by using an improved least squares support vector machine (LS-SVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization. We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.

Estimation of operational parameters for a direct injection turbocharged spark ignition engine by using regression analysis and artificial neural network

Directory of Open Access Journals (Sweden)

Tosun Erdi

2017-01-01

Full Text Available This study was aimed at estimating the variation of several engine control parameters within the rotational speed-load map, using regression analysis and artificial neural network techniques. Duration of injection, specific fuel consumption, exhaust gas at turbine inlet, and within the catalytic converter brick were chosen as the output parameters for the models, while engine speed and brake mean effective pressure were selected as independent variables for prediction. Measurements were performed on a turbocharged direct injection spark ignition engine fueled with gasoline. A three-layer feed-forward structure and back-propagation algorithm was used for training the artificial neural network. It was concluded that this technique is capable of predicting engine parameters with better accuracy than linear and non-linear regression techniques.

Identification of a Class of Non-linear State Space Models using RPE Techniques

DEFF Research Database (Denmark)

Zhou, Wei-Wu; Blanke, Mogens

1989-01-01

The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...

Acoustic nonlinearity parameter B/A determined by means of thermodynamic method under elevated pressures for alkanediols.

Science.gov (United States)

Zorębski, Edward; Zorębski, Michał

2014-01-01

The so-called Beyer nonlinearity parameter B/A is calculated for 1,2- and 1,3-propanediol, 1,2-, 1,3-, and 1,4-butanediol, as well as 2-methyl-2,4-pentanediol by means of a thermodynamic method. The calculations are made for temperatures from (293.15 to 318.15) K and pressures up to 100 MPa. The decrease in B/A values with the increasing pressure is observed. In the case of 1,3-butanediol, the results are compared with corresponding literature data. The consistency is very satisfactory. A simple relationship between the internal pressure and B/A nonlinearity parameter has also been studied. Copyright © 2013 Elsevier B.V. All rights reserved.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

Science.gov (United States)

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators. [Extended Kalman Filter

Science.gov (United States)

Hill, Bryon K.; Walker, Bruce K.

1991-01-01

When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.

Neglect Of Parameter Estimation Uncertainty Can Significantly Overestimate Structural Reliability

Directory of Open Access Journals (Sweden)

Rózsás Árpád

2015-12-01

Full Text Available Parameter estimation uncertainty is often neglected in reliability studies, i.e. point estimates of distribution parameters are used for representative fractiles, and in probabilistic models. A numerical example examines the effect of this uncertainty on structural reliability using Bayesian statistics. The study reveals that the neglect of parameter estimation uncertainty might lead to an order of magnitude underestimation of failure probability.

Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator

Directory of Open Access Journals (Sweden)

Bahita Mohamed

2011-01-01

Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.

Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...

Parameter estimation in large-scale systems biology models: a parallel and self-adaptive cooperative strategy.

Science.gov (United States)

Penas, David R; González, Patricia; Egea, Jose A; Doallo, Ramón; Banga, Julio R

2017-01-21

The development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times. Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies. The performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used. The new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Inflation and cosmological parameter estimation

Energy Technology Data Exchange (ETDEWEB)

Hamann, J.

2007-05-15

In this work, we focus on two aspects of cosmological data analysis: inference of parameter values and the search for new effects in the inflationary sector. Constraints on cosmological parameters are commonly derived under the assumption of a minimal model. We point out that this procedure systematically underestimates errors and possibly biases estimates, due to overly restrictive assumptions. In a more conservative approach, we analyse cosmological data using a more general eleven-parameter model. We find that regions of the parameter space that were previously thought ruled out are still compatible with the data; the bounds on individual parameters are relaxed by up to a factor of two, compared to the results for the minimal six-parameter model. Moreover, we analyse a class of inflation models, in which the slow roll conditions are briefly violated, due to a step in the potential. We show that the presence of a step generically leads to an oscillating spectrum and perform a fit to CMB and galaxy clustering data. We do not find conclusive evidence for a step in the potential and derive strong bounds on quantities that parameterise the step. (orig.)

A parameter tree approach to estimating system sensitivities to parameter sets

International Nuclear Information System (INIS)

Jarzemba, M.S.; Sagar, B.

2000-01-01

A post-processing technique for determining relative system sensitivity to groups of parameters and system components is presented. It is assumed that an appropriate parametric model is used to simulate system behavior using Monte Carlo techniques and that a set of realizations of system output(s) is available. The objective of our technique is to analyze the input vectors and the corresponding output vectors (that is, post-process the results) to estimate the relative sensitivity of the output to input parameters (taken singly and as a group) and thereby rank them. This technique is different from the design of experimental techniques in that a partitioning of the parameter space is not required before the simulation. A tree structure (which looks similar to an event tree) is developed to better explain the technique. Each limb of the tree represents a particular combination of parameters or a combination of system components. For convenience and to distinguish it from the event tree, we call it the parameter tree. To construct the parameter tree, the samples of input parameter values are treated as either a '+' or a '-' based on whether or not the sampled parameter value is greater than or less than a specified branching criterion (e.g., mean, median, percentile of the population). The corresponding system outputs are also segregated into similar bins. Partitioning the first parameter into a '+' or a '-' bin creates the first level of the tree containing two branches. At the next level, realizations associated with each first-level branch are further partitioned into two bins using the branching criteria on the second parameter and so on until the tree is fully populated. Relative sensitivities are then inferred from the number of samples associated with each branch of the tree. The parameter tree approach is illustrated by applying it to a number of preliminary simulations of the proposed high-level radioactive waste repository at Yucca Mountain, NV. Using a

Parameter Estimation of Permanent Magnet Synchronous Motor Using Orthogonal Projection and Recursive Least Squares Combinatorial Algorithm

Directory of Open Access Journals (Sweden)

Iman Yousefi

2015-01-01

Full Text Available This paper presents parameter estimation of Permanent Magnet Synchronous Motor (PMSM using a combinatorial algorithm. Nonlinear fourth-order space state model of PMSM is selected. This model is rewritten to the linear regression form without linearization. Noise is imposed to the system in order to provide a real condition, and then combinatorial Orthogonal Projection Algorithm and Recursive Least Squares (OPA&RLS method is applied in the linear regression form to the system. Results of this method are compared to the Orthogonal Projection Algorithm (OPA and Recursive Least Squares (RLS methods to validate the feasibility of the proposed method. Simulation results validate the efficacy of the proposed algorithm.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

Science.gov (United States)

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

Online State Space Model Parameter Estimation in Synchronous Machines

Directory of Open Access Journals (Sweden)

Z. Gallehdari

2014-06-01

The suggested approach is evaluated for a sample synchronous machine model. Estimated parameters are tested for different inputs at different operating conditions. The effect of noise is also considered in this study. Simulation results show that the proposed approach provides good accuracy for parameter estimation.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

International Nuclear Information System (INIS)

Harlim, John; Mahdi, Adam; Majda, Andrew J.

2014-01-01

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model

Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables

International Nuclear Information System (INIS)

Zwierz, Marcin; Perez-Delgado, Carlos A.; Kok, Pieter

2010-01-01

We reveal a close relationship between quantum metrology and the Deutsch-Jozsa algorithm on continuous-variable quantum systems. We develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter-estimation protocol or the Deutsch-Jozsa algorithm. The parameter-estimation part of the procedure attains the Heisenberg limit and is therefore optimal. Due to the use of approximate normalizable continuous-variable eigenstates, the Deutsch-Jozsa algorithm is probabilistic. The procedure estimates a value of an unknown parameter and solves the Deutsch-Jozsa problem without the use of any entanglement.

A Nonlinear Dynamics-Based Estimator for Functional Electrical Stimulation: Preliminary Results From Lower-Leg Extension Experiments.

Science.gov (United States)

Allen, Marcus; Zhong, Qiang; Kirsch, Nicholas; Dani, Ashwin; Clark, William W; Sharma, Nitin

2017-12-01

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.

Impacts of Different Types of Measurements on Estimating Unsaturatedflow Parameters

Science.gov (United States)

Shi, L.

2015-12-01

This study evaluates the value of different types of measurements for estimating soil hydraulic parameters. A numerical method based on ensemble Kalman filter (EnKF) is presented to solely or jointly assimilate point-scale soil water head data, point-scale soil water content data, surface soil water content data and groundwater level data. This study investigates the performance of EnKF under different types of data, the potential worth contained in these data, and the factors that may affect estimation accuracy. Results show that for all types of data, smaller measurements errors lead to faster convergence to the true values. Higher accuracy measurements are required to improve the parameter estimation if a large number of unknown parameters need to be identified simultaneously. The data worth implied by the surface soil water content data and groundwater level data is prone to corruption by a deviated initial guess. Surface soil moisture data are capable of identifying soil hydraulic parameters for the top layers, but exert less or no influence on deeper layers especially when estimating multiple parameters simultaneously. Groundwater level is one type of valuable information to infer the soil hydraulic parameters. However, based on the approach used in this study, the estimates from groundwater level data may suffer severe degradation if a large number of parameters must be identified. Combined use of two or more types of data is helpful to improve the parameter estimation.

A novel extended Kalman filter for a class of nonlinear systems

Institute of Scientific and Technical Information of China (English)

DONG Zhe; YOU Zheng

2006-01-01

Estimation of the state variables of nonlinear systems is one of the fundamental and significant problems in control and signal processing. A new extended Kalman filtering approach for a class of nonlinear discrete-time systems in engineering is presented in this paper. In contrast to the celebrated extended Kalman filter (EKF), there is no linearization operation in the design procedure of the filter, and the parameters of the filter are obtained through minimizing a proper upper bound of the mean-square estimation error. Simulation results show that this filter can provide higher estimation precision than that provided by the EKF.

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

Directory of Open Access Journals (Sweden)

Daigle Bernie J

2012-05-01

Full Text Available Abstract Background A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs. MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2: an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods

Postprocessing MPEG based on estimated quantization parameters

DEFF Research Database (Denmark)

Forchhammer, Søren

2009-01-01

the case where the coded stream is not accessible, or from an architectural point of view not desirable to use, and instead estimate some of the MPEG stream parameters based on the decoded sequence. The I-frames are detected and the quantization parameters are estimated from the coded stream and used...... in the postprocessing. We focus on deringing and present a scheme which aims at suppressing ringing artifacts, while maintaining the sharpness of the texture. The goal is to improve the visual quality, so perceptual blur and ringing metrics are used in addition to PSNR evaluation. The performance of the new `pure......' postprocessing compares favorable to a reference postprocessing filter which has access to the quantization parameters not only for I-frames but also on P and B-frames....

Nonlinear Quantum Metrology of Many-Body Open Systems

Science.gov (United States)

Beau, M.; del Campo, A.

2017-07-01

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

Energy Technology Data Exchange (ETDEWEB)

Eldred, Michael Scott; Vigil, Dena M.; Dalbey, Keith R.; Bohnhoff, William J.; Adams, Brian M.; Swiler, Laura Painton; Lefantzi, Sophia (Sandia National Laboratories, Livermore, CA); Hough, Patricia Diane (Sandia National Laboratories, Livermore, CA); Eddy, John P.

2011-12-01

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.

Identifyability measures to select the parameters to be estimated in a solid-state fermentation distributed parameter model.

Science.gov (United States)

da Silveira, Christian L; Mazutti, Marcio A; Salau, Nina P G

2016-07-08

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid-state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905-917, 2016. © 2016 American Institute of Chemical Engineers.

Automated detection of sleep apnea from electrocardiogram signals using nonlinear parameters

International Nuclear Information System (INIS)

Acharya, U Rajendra; Faust, Oliver; Chua, Eric Chern-Pin; Lim, Teik-Cheng; Lim, Liang Feng Benjamin

2011-01-01

Sleep apnoea is a very common sleep disorder which can cause symptoms such as daytime sleepiness, irritability and poor concentration. To monitor patients with this sleeping disorder we measured the electrical activity of the heart. The resulting electrocardiography (ECG) signals are both non-stationary and nonlinear. Therefore, we used nonlinear parameters such as approximate entropy, fractal dimension, correlation dimension, largest Lyapunov exponent and Hurst exponent to extract physiological information. This information was used to train an artificial neural network (ANN) classifier to categorize ECG signal segments into one of the following groups: apnoea, hypopnoea and normal breathing. ANN classification tests produced an average classification accuracy of 90%; specificity and sensitivity were 100% and 95%, respectively. We have also proposed unique recurrence plots for the normal, hypopnea and apnea classes. Detecting sleep apnea with this level of accuracy can potentially reduce the need of polysomnography (PSG). This brings advantages to patients, because the proposed system is less cumbersome when compared to PSG

Effect of nonlinear void reactivity on bifurcation characteristics of a lumped-parameter model of a BWR: A study relevant to RBMK

Energy Technology Data Exchange (ETDEWEB)

Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)

2017-04-15

Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

Science.gov (United States)

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.