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An adaptive dimension decomposition and reselection method for reliability analysis

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Abstract

Recently, the research community in reliability analysis has seen a strong surge of interest in the dimension decomposition approach, which typically decomposes a multi-dimensional system response into a finite set of low-order component functions for more efficient reliability analysis. However, commonly used dimension decomposition methods suffer from two limitations. Firstly, it is often difficult or impractical to predetermine the decomposition level to achieve sufficient accuracy. Secondly, without an adaptive decomposition scheme, these methods may unnecessarily assign sample points to unimportant component functions. This paper presents an adaptive dimension decomposition and reselection (ADDR) method to resolve the difficulties of existing dimension decomposition methods for reliability analysis. The proposed method consists of three major components: (i) an adaptive dimension decomposition and reselection scheme to automatically detect the potentially important component functions and adaptively reselect the truly important ones, (ii) a test error indicator to quantify the importance of potentially important component functions for dimension reselection, and (iii) an integration of the newly developed asymmetric dimension-adaptive tensor-product (ADATP) method into the adaptive scheme to approximate the reselected component functions. The merits of the proposed method for reliability analysis are three-fold: (a) automatically detecting and adaptively representing important component functions, (b) greatly alleviating the curse of dimensionality, and (c) no need of response sensitivities. Several mathematical and engineering high-dimensional problems are used to demonstrate the effectiveness of the ADDR method.

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Acknowledgments

This work was partially supported by a grant from the Energy Technology Development Program (2010101010027B) and International Collaborative R&D Program (0420-2011-0161) of Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korean government’s Ministry of Knowledge Economy, the National Research Foundation of Korea (NRF) grant (No. 2011-0022051) funded by the Korea government, the Basic Research Project of Korea Institute of Machinery and Materials (Project Code: SC0830) supported by a grant from Korea Research Council for Industrial Science & Technology, and the Institute of Advanced Machinery and Design at Seoul National University (SNU-IAMD).

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  1. Chao Hu

    Present address: Medtronic, Inc., 6700 Shingle Creek Parkway Brooklyn Center, MN, 55430, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Maryland at College Park, College Park, MD, 20742, USA

    Chao Hu

  2. School of Mechanical and Aerospace Engineering, The Seoul National University, Seoul, Republic of Korea

    Byeng D. Youn & Heonjun Yoon

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  1. Chao Hu
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Correspondence to Byeng D. Youn.

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Hu, C., Youn, B.D. & Yoon, H. An adaptive dimension decomposition and reselection method for reliability analysis. Struct Multidisc Optim 47, 423–440 (2013). https://doi.org/10.1007/s00158-012-0834-0

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