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A generalized moving least square–based response surface method for efficient reliability analysis of structure

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Abstract

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Sounak Kabasi

  2. Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, India

    Sounak Kabasi, Atin Roy & Subrata Chakraborty

Authors
  1. Sounak Kabasi
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  2. Atin Roy
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  3. Subrata Chakraborty
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Correspondence to Subrata Chakraborty.

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The authors declare that they have no conflict of interest.

Replication of results

All the necessary information for generating the data sets for the problems are presented in the manuscript. The first author of this manuscript is pursuing his doctoral study and the codes can be available from the first author on request.

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Responsible Editor: Byeng D Youn

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Kabasi, S., Roy, A. & Chakraborty, S. A generalized moving least square–based response surface method for efficient reliability analysis of structure. Struct Multidisc Optim 63, 1085–1097 (2021). https://doi.org/10.1007/s00158-020-02743-9

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  • DOI: https://doi.org/10.1007/s00158-020-02743-9

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