Improving prediction capabilities of complex dynamic models via parameter selection and estimation

Chu, Ying‐Hao; Huang, Zuyi; Hahn, Juergen

doi:10.1016/j.ces.2009.06.057

Cited by 34 publications

(57 citation statements)

References 27 publications

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“…, n. The set of all feasible curves is denoted by X = X t 0 ,t 1 ,...,tn;x 0 ,x 1 ,...xn . Given also a nonempty set A of C 1 vector fields A on M , define J : (1) is the derivative of x with respect to t, and denotes the Riemannian norm. A minimizer (x, A) of J = J t 0 ,t 1 ,...,tn;x 0 ,x 1 ,...xn is said to be conditionally-optimal or just optimal.…”

Section: Optimalitymentioning

confidence: 99%

“…Because the x (1) [p] are uniformly bounded for p ≥ P , {y p : p ≥ P } ⊂ M is Cauchy, with limitȳ say. Using some coordinate chart containingȳ, represent each x…”

Section: First Order Necessary Conditionsmentioning

confidence: 99%

“…To do so requires knowledge about the nature of the supposed approximation, which in practice depends on context. We are going to assume x (1) is close to A(x) in the L 2 sense, namely x (1) (t) = A(x(t)) + g(t) where g : [t 0 , t n ] → E m is L 2 -small. Possibly g(t) = G(x(t)) where G is another vector field.…”

Section: Introductionmentioning

confidence: 99%

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Conditional extremals

Noakes

2012

Math. Control Signals Syst.

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Imagine that measurements are made at times t 0 and t 1 of the trajectory of a physical system whose governing laws are given approximately by a class A of so-called prior vector fields. Because the physical laws are not known precisely, the measurements might not be realised by the integral curve of any prior field. We want to estimate the behaviour of the physical system between times t 0 and t 1 . This is done by solving a variational problem, yielding so-called conditional extrema which satisfy an Euler-Lagrange equation. Then conservative prior fields on simply-connected Riemannian manifolds are characterised in terms of their conditional extrema. For specific prior fields on space forms, conditional extrema are obtained in terms of the Weierstrass elliptic function. Another class of examples comes from left-invariant prior fields on bi-invariant Lie groups, whose conditional extrema are shown to be right translations of pointwise-products of 1-parameter subgroups.

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Section: Optimalitymentioning

confidence: 99%

“…Because the x (1) [p] are uniformly bounded for p ≥ P , {y p : p ≥ P } ⊂ M is Cauchy, with limitȳ say. Using some coordinate chart containingȳ, represent each x…”

Section: First Order Necessary Conditionsmentioning

confidence: 99%

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Conditional extremals

Noakes

2012

Math. Control Signals Syst.

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“…For systems such as large chemical plants, for example, it is possible to collect large amount of information so that one can use techniques, such as developed by control theory for system identification, resulting in adequate model parameter estimation [26,56,57]. As system scale grows, information gathering opportunities decrease, and information about the system and its environment becomes sparse, consequently the validation of the model used for control decision making is running into difficulties.…”

Section: The Challenge Of Maintaining Sustainability and Viabilitymentioning

confidence: 99%

Enterprise engineering and management at the crossroads

Bernus

Goranson²,

Gøtze

et al. 2016

Computers in Industry

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“…A mean squared error (MSE) based approach combined with orthogonalization method was proposed by Wu et al to determine the number of parameters to estimate, 13 wherein the lowest corrected critical ratio is considered as a termination. In order to increase the robustness, an approach similar to the Monte Carlo simulation‐based method by Chu et al 14 was proposed by McLean et al 15 Instead of calculating the sensitivity matrix and considering the trade‐off between bias and variance at each step, a measurement based parameter estimation technique is used to rank the parameters. Since the modeler may be interested in making accurate predictions at different input settings from those corresponding to the current measurement, a revised criterion was developed by Eghtesadi et al 16 and also a parameter selection approach based on the revised criterion was proposed 17 .…”

Section: Introductionmentioning

confidence: 99%

Reduced Hessian based parameter selection and estimation with simultaneous collocation approach

Chen

Biegler

2020

AIChE Journal

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Parameter estimation is a critical step in the building of process models. Given the nonlinear structure and limited measurements, it is often difficult to correctly estimate all the parameters involved in the model. Linear dependence and low correlation among the parameters are the main problems to be handled in parameter estimation. The common approach is to estimate a subset of the parameters by fixing the others at reasonable values. However, it is a challenge to determine which parameters can be properly estimated. In this work, the ratio between standard deviation and estimated parameter value is introduced for evaluating the estimability. A Gauss‐Jordan elimination based approach is proposed for parameter estimability ranking. Combined with the proposed ranking approach and approximate ratio criterion, a reduced Hessian based approach is proposed for parameter selection and estimation under a simultaneous collocation framework. The proposed approach is at least as effective and more efficient than competing approaches based on multiple eigenvalue decompositions or orthogonalizations for larger problems. Three case studies with increasing complexity are presented to demonstrate the performance of the proposed approach.

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Improving prediction capabilities of complex dynamic models via parameter selection and estimation

Cited by 34 publications

References 27 publications

Conditional extremals

Conditional extremals

Enterprise engineering and management at the crossroads

Reduced Hessian based parameter selection and estimation with simultaneous collocation approach

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