Gradient-based iterative parameter estimation for Box-Jenkins systems with finite measurement data

2009 ◽  
Author(s):  
Dongqing Wang ◽  
Jiyang Dai ◽  
Feng Ding
Keyword(s):  
Parameter Estimation ◽  
Measurement Data ◽  
Gradient Based

Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Pileun Kim ◽  
Jonathan Rogers ◽  
Jie Sun ◽  
Erik Bollt
Keyword(s):  
Parameter Estimation ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Measurement Data ◽  
Relative Magnitude ◽  
Initial Guess ◽  
Series Data ◽  
System Parameters ◽  
Estimation Problems ◽  
System States

Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.

scholarly journals Efficient gradient-based parameter estimation for dynamic models using qualitative data

2021 ◽  
Author(s):  
Leonard Schmiester ◽  
Daniel Weindl ◽  
Jan Hasenauer
Keyword(s):  
Parameter Estimation ◽  
Qualitative Data ◽  
Dynamic Models ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Gradient Calculation ◽  
Order Of Magnitude ◽  
Gradient Based ◽  
Objective Function Values

AbstractMotivationUnknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.ResultsHere, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. Additionally, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.AvailabilityThe proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

Ridge estimation iterative algorithm to ill-posed uncertainty adjustment model

2020 ◽  
Author(s):  
tieding lu
Keyword(s):  
Parameter Estimation ◽  
Iterative Algorithm ◽  
Measurement Data ◽  
Estimation Method ◽  
Coefficient Matrix ◽  
Observation Equation ◽  
Validity And Reliability ◽  
Ridge Estimation ◽  
Adjustment Model ◽  
Ill Posed

<p> Uncertainties usually exist in the process of acquisition of measurement data, which affect the results of the parameter estimation. The solution of the uncertainty adjustment model can effectively improve the validity and reliability of parameter estimation. When the coefficient matrix of the observation equation has a singular value close to zero, i.e., the coefficient matrix is ill-posed, the ridge estimation can effectively suppress the influence of the ill-posed problem of the observation equation on the parameter estimation. When the uncertainty adjustment model is ill-posed, it is more seriously affected by the error of the coefficient matrix and observation vector. In this paper, the ridge estimation method is applied to ill-posed uncertainty adjustment model, deriving an iterative algorithm to improve the stability and reliability of the results. The derived algorithm is verified by two examples, and the results show that the new method is effective and feasible.</p>

Battery State of Health and Charge Estimation Using Polynomial Chaos Theory

2013 ◽  
Author(s):  
Saeid Bashash ◽  
Hosam K. Fathy
Keyword(s):  
Parameter Estimation ◽  
Chaos Theory ◽  
Polynomial Chaos ◽  
Search Algorithm ◽  
Estimation Method ◽  
Experimental Tests ◽  
Internal Resistance ◽  
Battery State Of Charge ◽  
Gradient Based ◽  
Polynomial Chaos Theory

In this effort, we use the generalized Polynomial Chaos theory (gPC) for the real-time state and parameter estimation of electrochemical batteries. We use an equivalent circuit battery model, comprising two states and five parameters, and formulate the online parameter estimation problem using battery current and voltage measurements. Using a combination of the conventional recursive gradient-based search algorithm and gPC framework, we propose a novel battery parameter estimation strategy capable of estimating both battery state-of-charge (SOC) and parameters related to battery health, e.g., battery charge capacity, internal resistance, and relaxation time constant. Using a combination of experimental tests and numerical simulations, we examine and demonstrate the effectiveness of the proposed battery estimation method.

scholarly journals Parameter estimation in stock assessment modelling: caveats with gradient-based algorithms

2018 ◽  
Vol 75 (5) ◽  
pp. 1553-1559 ◽  
Author(s):  
Sam Subbey
Keyword(s):  
Parameter Estimation ◽  
State Of The Art ◽  
Stock Assessment ◽  
The State ◽  
Cautionary Note ◽  
Machine Precision ◽  
Fisheries Science ◽  
Increasing Trend ◽  
Gradient Based ◽  
Blind Faith

Abstract Using simple illustrative examples, this note highlights some of the caveats with gradient-based algorithms. This class of algorithms underpins the state-of-the-art modelling platform in fisheries science. The goal is to sound a cautionary note about an increasing trend in fisheries science, where blind faith is being invested in results obtained from algorithms that are fast, and proven to have machine precision.

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