A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds

Arora, Nikhil; Biegler, Lorenz T.

doi:10.1023/b:coap.0000018879.40214.11

Cited by 29 publications

(31 citation statements)

References 36 publications

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“…In the braking process, this tire prints left [1,2,3] , which reflects the driving status and track of the vehicle under pre-braking, on the other hand, reflects driving speed of the vehicle under the pre-braking. Therefore, the braking imprint is an objective record in the accident process, which is based on analyzing the process of traffic accidents, reason and responsibilities identified.…”

Section: Introductionmentioning

confidence: 99%

Notice of Retraction: Study of vehicle braking model and simulation

Zhan-qing

Shi-yong

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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In order to accurate calculation vehicle pre-braking speed by the regression analysis data of vehicle braking speed, comparing and analyzing with LS estimation algorithm, instrumental variable estimation algorithm, generalized least squares estimation algorithm and Cor-LS algorithm, LS estimation algorithms is used to study on parameter estimation of the vehicle braking model, introducing multiple linear regression theory, building the pre-brake speed regression model. By using the simulation data, to calculate the braking system dynamic growth factor, to gain pre-braking speed regression model. Solved the problem of calculating vehicle brake speed. In the end, through the high-precision vehicle dynamics simulation model (veDYNA) platform to simulation, comparing the speed model and original model to verify the model speed validity and accuracy, the simulation results show good results

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Section: Introductionmentioning

confidence: 99%

Notice of Retraction: Study of vehicle braking model and simulation

Zhan-qing

Shi-yong

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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“…As a second example, in a number of current iterative methods for constrained optimization [1,16,24,35], a so-called normal step s is computed to try to improve constraint infeasibility by approximately solving the subproblem minimize s∈IR n J(x k )s + c(x k ) subject to s ≤ ∆ k .…”

Section: Motivationmentioning

confidence: 99%

Trust-region and other regularisations of linear least-squares problems

2009

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We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound x ≤ ∆ is imposed on the size of the solution, and in which the least value of linear combinations of Ax−b q 2 and a regularisation term x p 2 for various p and q = 1, 2 is sought. In each case, one of more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library.Subject classifications: AMS(MOS): 65F22, 65H05, 65K05, 90C25.

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“…1 The actual reduction is just the difference in the merit function at two successive iterates, i.e.…”

Section: Predicted and Actualmentioning

confidence: 99%

“…This requires a combination of well-formulated models and a robust nonlinear programming algorithm. Therefore, in this study, our goals are five-fold: (1) to analyze the DAE model and formulate an index-1 system from a high-index DAE, (2) to apply NTREST to the simultaneous parameter estimation of a DAE-constrained model of a reaction occurring in a CSTR, (3) to demonstrate robustness of NTREST on ill-conditioned discretized DAE parameter estimation problems, (4) to distinguish between the information contents of different measurements and to develop a way to obtain a minimum set of informative measurements, and (5) to demonstrate a general estimation EVM estimation problem.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for a Polymerization Reactor Model with a Composite-Step Trust-Region NLP Algorithm

Arora

Biegler

2003

Ind. Eng. Chem. Res.

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We consider an application of the trust-region SQP algorithm described by Arora and Biegler (Comput. Optim. Appl., in press) to the parameter estimation for a polymerization reactor. In particular, we are interested in the robustness of this algorithm in solving ill-conditioned optimization problems with differential algebraic (DAE) models. For this system, it is possible to measure a variety of states, such as production and concentrations. Some of these states contain more information and lead to more reliable parameter estimates than would be obtained if the states were not measured. To minimize sensor costs, it is thus beneficial to select the smallest combination of state measurements that contains the most information. Because the polymer process model is nonlinear, we decide to test the information content of measurements by analyzing properties of the reduced Hessian and constructing joint-confidence regions. This approach is related to the observability analysis (Albuquerque, J. S.; Biegler, L. T. AIChE J. 1996, 42, 2841. Narasimhan, S.; Jordache, C. Data Reconciliation and Gross Error Detection; Gulf Publishing Company: Houston, TX, 2000. Crowe, C. M. Chem. Eng. Sci. 1989, 44, 2909. However, for nonlinear problems, a reliable and efficient parameter estimation algorithm is essential for the measurement selection procedure. Finally, whereas inputs to the process are often held constant in parameter estimation problems, these inputs often contain noise. It is therefore necessary to reconcile inputs along with states in a simultaneous optimization framework. This problem becomes an errors in variables model (EVM) and can be considerably larger and more difficult to solve. In this study, we also consider the related EVM problem and compare results to the standard parameter estimation problem.

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A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds

Cited by 29 publications

References 36 publications

Notice of Retraction: Study of vehicle braking model and simulation

Notice of Retraction: Study of vehicle braking model and simulation

Trust-region and other regularisations of linear least-squares problems

Parameter Estimation for a Polymerization Reactor Model with a Composite-Step Trust-Region NLP Algorithm

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