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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016016845
pages 175-193

SEQUENTIAL SPARSITY ITERATIVE OPTIMAL DESIGN MODEL FOR CALIBRATION OF COMPLEX SYSTEMS WITH EPISTEMIC UNCERTAINTY

Weifeng Li
Institution of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong, 264001, People's Republic of China
Xiaojun Duan
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
Chang Li
College of Science, National University of Defense Technology, Changsha, Hunan, 410073, People's Republic of China

RÉSUMÉ

As for the experimental optimal design of some complex systems, it is difficult to obtain the accurate response model between the performance index and influence factors. But in some cases the prior information could provide a clue to construct the possible response model. An effective model calibration method is presented here based on the typical uncertainty quantification framework. In order to solve this epistemic uncertainty, some kinds of prior information about the system are utilized to obtain model-oriented basis functions, then a corresponding redundant regression model is designed to describe the internal response relationship. Through analyzing the influences of experimental costs, sampling sequences, and spatial positions of different experiment points, we define a sequential sparsity iterative optimal design model integrated with costs and spatio-temporal weights for experimental design. Based on sparse component analysis theory, calibration of a regression model with different stages is transformed into a sparse reconstruction problem. The conclusions from theoretical inferences as well as simulation results of the combined trigonometric polynomial function model and radar measurement model show that the parameter estimation error of the regression model is smaller, which demonstrates that the above-mentioned model is more efficient and comprehensive for its consideration of the weights for different influence factors and its consistence with practical experimental regulations.


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