<i>T</i>-Optimum Designs for Discrimination Between Two Multiresponse Dynamic Models

Uciński, Dariusz; Bogacka, D. Barbara

doi:10.1111/j.1467-9868.2005.00485.x

Cited by 75 publications

(53 citation statements)

References 35 publications

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“…Uciński and Bogacka [42] used a SIP based algorithm to find T-optimal designs for dynamic models. The SIP procedure relies on the relaxation paradigm proposed by Shimizu and Aiyoshi [38] for minimax problems.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

Duarte

Wong

Atkinson

2015

Journal of Multivariate Analysis

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T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

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Section: Introductionmentioning

confidence: 99%

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

Duarte

Wong

Atkinson

2015

Journal of Multivariate Analysis

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“…Exceptions to this naive approach constitute the works originating in statistical optimum experimental design (Fedorov and Hackl, 1997;Pázman, 1986;Pukelsheim, 1993;Walter and Pronzato, 1997;Atkinson and Donev, 1992;Uciński and Bogacka, 2005;Uciński and Atkinson, 2004) and its extensions to models for dynamic systems, especially in the context of the optimal choice of sampling instants and input signals (Goodwin and Payne, 1977;Titterington, 1980;Ljung, 1999;Gevers, 2005;Hjalmarsson, 2005). In this vein, various computational schemes have been developed to attack directly the original problem or its convenient approximation.…”

Section: Optimal Sensor Location For Parameter Identificationmentioning

confidence: 99%

Sensor network scheduling for identification of spatially distributed processes

Uciński

2010

2010 Conference on Control and Fault-Tolerant Systems (SysTol)

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The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.

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“…In the context of parameter estimation, exceptions to this naive approach constitute the works originating in statistical optimum experimental design (Fedorov and Hackl, 1997;Walter and Pronzato, 1997;Uciński and Bogacka, 2005;Uciński and Atkinson, 2004), and its extensions to models for dynamic systems, especially in the context of the optimal choice of sampling instants and input signals (Ljung, 1999;Gevers, 2005;Hjalmarsson, 2005). In this vein, various computational schemes have been developed to directly attack the original problem or its convenient approximation.…”

Section: Problem Formulation In Terms Ofmentioning

confidence: 99%

Sensor network design for the estimation of spatially distributed processes

Uciński¹,

Patan²

2010

International Journal of Applied Mathematics and Computer Science

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In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum-likelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.

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T-Optimum Designs for Discrimination Between Two Multiresponse Dynamic Models

Cited by 75 publications

References 35 publications

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

Sensor network scheduling for identification of spatially distributed processes

Sensor network design for the estimation of spatially distributed processes

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