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A Novel Method for Uncertainty Inverse Problems and Application to Material Characterization of Composites

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Abstract

A novel method is suggested to deal with so-called uncertainty inverse problems (UIPs) which are a class of inverse problems with uncertainty in the system parameters of the forward model. Interval which represents a closed bounded set of real numbers is used to model and characterize the uncertainty in our formulation, and hence only the bounds of the uncertainty of the system parameters are needed. For a specific input vector, the possible values of the outputs form an interval vector because of the uncertainty. An error function is defined using the measured interval vector of the outputs and those computed using a forward model. The UIP is then formulated as an optimization problem which minimizes the error function. To improve the optimization efficiency, an interval forward model is constructed based on the interval analysis method which can calculate very efficiently the bounds of the outputs caused by the uncertainty of the system parameters. The present method is applied to a complex inverse problem, namely material characterization of composite laminates using elastic waves. Uncertainty of load is considered, and the hybrid numerical method (HNM) is used to compute the transient displacement responses. The engineering constants of two kinds of laminates are successfully identified using the simulated measurements of the outputs.

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Acknowledgements

This work is supported by the national 973 program under the Grant No. 2004CB719402, the program for Century Excellent Talents in University (NCET-04-0766), the National Natural Science Foundation of China (10572048) and the National Science Fund for Distinguished Young Scholars (50625519).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    C. Jiang & X. Han

  2. Centre for Advanced Computations in Engineering Science, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260, Singapore

    G. R. Liu

  3. Singapore–MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore, 117576, Singapore

    G. R. Liu

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  1. C. Jiang
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  2. G. R. Liu
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  3. X. Han
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Correspondence to G. R. Liu.

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Jiang, C., Liu, G.R. & Han, X. A Novel Method for Uncertainty Inverse Problems and Application to Material Characterization of Composites. Exp Mech 48, 539–548 (2008). https://doi.org/10.1007/s11340-007-9081-5

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  • DOI: https://doi.org/10.1007/s11340-007-9081-5

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