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Structural Reliability Analysis by Using Non-Probabilistic Multi-Cluster Ellipsoidal Model.

Kun Li1,2, Hongwei Liu2

  • 1School of Mechatronics Engineering, Changsha University, Changsha 410083, China.

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|September 23, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a non-probabilistic multi-cluster ellipsoidal model for structural reliability analysis when sample data is limited. The new method improves accuracy for multi-cluster data, enhancing risk assessment in engineering design.

Keywords:
Gaussian cluster analysismulti-cluster ellipsoidal modelnon-probabilistic reliability analysissecond order approximation method

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Area of Science:

  • Engineering
  • Computational Mechanics
  • Reliability Engineering

Background:

  • Uncertainties are inherent in engineering practice and require consideration in structural design and optimization to mitigate risks.
  • Probabilistic models for uncertainties are often unavailable due to limited samples, and conventional non-probabilistic models lack precision for multi-cluster data distributions.

Purpose of the Study:

  • To propose an improved non-probabilistic multi-cluster ellipsoidal model (multi-CEM) for critical structural reliability analysis.
  • To enhance the accuracy and compactness of sample representation for better reliability analysis results.

Main Methods:

  • Constructing a Gaussian mixture model (GMM) for multi-cluster samples using the expectation maximization (EM) algorithm.
  • Developing the multi-CEM based on the GMM.
  • Computing non-probabilistic reliability (NPR) indexes using the Hasofer-Lind-Rackwitz-Fiessler (HL-RF) algorithm for intersected and non-intersected multi-CEM components.
  • Calculating multidimensional volume ratios of the safe domain to the total uncertainty domain to indicate structural NPR.

Main Results:

  • The proposed multi-CEM accurately and compactly describes multi-cluster sample distributions.
  • The method yields satisfactory structural reliability analysis results, validated by numerical examples and a practical application.
  • Non-probabilistic reliability indexes and overall structural NPR were effectively computed.

Conclusions:

  • The multi-CEM offers a superior approach for structural reliability analysis with limited, multi-cluster data compared to conventional methods.
  • The proposed method effectively addresses the challenge of unavailable probabilistic models in engineering design.
  • The study demonstrates the practical effectiveness and improved accuracy of the multi-CEM for critical structural reliability assessments.