Parameter set selection for estimation of nonlinear dynamic systems

Chu, Ying‐Hao; Hahn, Juergen

doi:10.1002/aic.11295

Cited by 67 publications

(64 citation statements)

References 32 publications

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“…However, the selection of practically unidentifiable parameters is a rough procedure. Therefore, a more elaborated analysis should be applied to determine the identifiable parameters (for instance, SsS in section 2.2.1., or see also Chu and Hahn (2007), (2012) and Kravaris, et. al., (2013) for more advanced methods).…”

Section: Is Well-conditioned?mentioning

confidence: 92%

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Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

López

Barz

Körkel

et al. 2015

Computers & Chemical Engineering

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Section: Is Well-conditioned?mentioning

confidence: 92%

“…(18) with respect to the complete parameter variance ‫ߠ‪ሺ‬ݎܽݒ‬ ሻ (i.e., ߨ ൌ ‫ݎܽݒ‬ చ ሺߠ ሻ/‫ݎܽݒ‬ሺߠ ሻ) a variance decomposition can be conducted (Belsley et al, 1980). The variance decomposition proportion ߨ quantifies the contribution of each singular value ߫ to the variance ‫ߠ‪ሺ‬ݎܽݒ‬ ሻ.…”

mentioning

confidence: 99%

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

López

Barz

Körkel

et al. 2015

Computers & Chemical Engineering

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“…Among the large number of parameters shown in Table 2, some are easier to estimate than the others. According to the analysis obtained by Chu et al, 21 the fluid density q and the pre-exponential factor k 0 have larger sensitivities where as activation energy E/R has smaller sensitivity. In the following simulations, both easier-to-estimate and harder-to-estimate sets of parameters are tested using the proposed method.…”

Section: Cstr With Jacket Dynamicsmentioning

confidence: 94%

Constrained receding‐horizon experiment design and parameter estimation in the presence of poor initial conditions

Zhu

Huang

2010

AIChE Journal

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An optimal experiment design assumes the existence of an initial or nominal process model. The efficiency of this procedure depends on how the initial model is chosen. This creates a practical dilemma as estimating the model is precisely what the experiment tries to achieve. A novel approach to experiment design for identification of nonlinear systems is developed, with the purpose of reducing the influence of poor initial values. The experiment design and the parameter estimation are conducted iteratively under a receding-horizon framework. By taking steady-state prior knowledge into account, constraints on the parameters can be derived. Such constraints help reduce influence of poor initial models. The proposed algorithm is illustrated through examples to demonstrate its efficiency. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: [2808][2809][2810][2811][2812][2813][2814][2815][2816][2817][2818][2819][2820] 2011 Keywords: receding-horizon design, optimal experiment design, constrained EKF IntroductionOptimal experiment design aims at determining optimal experiment conditions to achieve a specific set of objectives. Experiment design is a broad subject that includes aspects such as input design, operating point design, and sampling time design. Although a significant amount of literature on optimal experiment design for linear systems has been published since the 1970s, 1,2 the optimal experiment design concerning nonlinear systems has remained largely unexplored.One significant challenge for nonlinear experiment design as well as parameters identification is that the sensitivity functions used to search for optimal conditions depend on the unknown model parameters. Three existing methods have been proposed to address this challenge: minimax experiment design, ED (expectation of determinant)/EID (expectation of the inverse of determinant)-optimal design, and adaptive experiment design.Minimax experiment design attempts to achieve robust experiment by minimizing the largest possible modeling error. This approach needs no prior information about parameter distributions. There are two recent representative publications on this topic. Rojas et al.3 developed a method of optimizing the worst case of modeling error over the parameter set, while a convex optimization algorithm is implemented on a linear system. In conjunction, Welsh and Rojas 4 proposed an algorithm to solve a robust optimal experiment design problem by scenario approach. To construct convex or semidefinite convex problems, both techniques formulate the identification problem in frequency domain, but neither of the methods can be used for identification in nonlinear system. Moreover, the optimality objective function for nonlinear identification is generally difficult to be formulated as a convex or semidefinite convex problem.Another group of methods (especially popular in bioscience fields) are experiment designs by optimizing over the expected determinant of a Fisher information matrix Correspondence concerning this article ...

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“…where x i is the i-th state variable in the model, p j is the j-th model parameter in the vector p, and t is the time at which the partial derivative is evaluated [2,3,32]. The local sensitivity coefficient represents the change in a model state with respect to a change in the value of a parameter, and is a function of time and the parameter vector.…”

Section: Optimal Experimental Designmentioning

confidence: 99%

“…where x is the column vector of state variables, p is the column vector of model parameters, and f is the column vector of functions defining the model, as in Equation (1) [32]. To calculate the D-optimality criterion value for a given experiment design, the model ODEs (Equation (1)) are solved simultaneously with the sensitivity equations (Equation (6)), the FIM is constructed (Equations (4) and (5)), and the determinant can then be computed.…”

Section: Optimal Experimental Designmentioning

confidence: 99%

Optimal Experimental Design for Parameter Estimation of an IL-6 Signaling Model

Sinkoe

Hahn

2017

Processes

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IL-6 signaling plays an important role in inflammatory processes in the body. While a number of models for IL-6 signaling are available, the parameters associated with these models vary from case to case as they are non-trivial to determine. In this study, optimal experimental design is utilized to reduce the parameter uncertainty of an IL-6 signaling model consisting of ordinary differential equations, thereby increasing the accuracy of the estimated parameter values and, potentially, the model itself. The D-optimality criterion, operating on the Fisher information matrix and, separately, on a sensitivity matrix computed from the Morris method, was used as the objective function for the optimal experimental design problem. Optimal input functions for model parameter estimation were identified by solving the optimal experimental design problem, and the resulting input functions were shown to significantly decrease parameter uncertainty in simulated experiments. Interestingly, the determined optimal input functions took on the shape of PRBS signals even though there were no restrictions on their nature. Future work should corroborate these findings by applying the determined optimal experimental design on a real experiment.

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Parameter set selection for estimation of nonlinear dynamic systems

Cited by 67 publications

References 32 publications

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

Constrained receding‐horizon experiment design and parameter estimation in the presence of poor initial conditions

Optimal Experimental Design for Parameter Estimation of an IL-6 Signaling Model

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