Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Reliability-based design optimization using kriging surrogates and subset simulation (1104.3667v1)

Published 19 Apr 2011 in stat.ME and stat.ML

Abstract: The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. The surrogate error onto the limit-state surfaces is propagated to the failure probabilities estimates in order to provide an empirical error measure. This error is then sequentially reduced by means of a population-based adaptive refinement technique until the kriging surrogates are accurate enough for reliability analysis. This original refinement strategy makes it possible to add several observations in the design of experiments at the same time. Reliability and reliability sensitivity analyses are performed by means of the subset simulation technique for the sake of numerical efficiency. The adaptive surrogate-based strategy for reliability estimation is finally involved into a classical gradient-based optimization algorithm in order to solve the RBDO problem. The kriging surrogates are built in a so-called augmented reliability space thus making them reusable from one nested RBDO iteration to the other. The strategy is compared to other approaches available in the literature on three academic examples in the field of structural mechanics.

Citations (413)

Summary

  • The paper demonstrates that combining kriging surrogates with subset simulation accurately estimates reliability while significantly cutting computational effort.
  • The authors implement a sequential adaptive refinement procedure to enhance surrogate accuracy near critical limit-state surfaces.
  • The strategy integrates with gradient-based optimization, providing a robust framework for engineering design under uncertainty.

Analyzing Reliability-Based Design Optimization Using Kriging Surrogates and Subset Simulation

This paper presents a comprehensive strategy for addressing reliability-based design optimization (RBDO) problems, emphasizing kriging surrogate modeling combined with subset simulation techniques. The research gravitates toward scenarios where performance models, typically nonlinear finite element models, demand significant computational resources, rendering traditional simulation-based reliability assessments infeasible.

Core Methodology

The authors propose a hybrid approach utilizing both metamodels and advanced simulation techniques to efficiently solve RBDO problems. Central to this method is the use of kriging as a surrogate modeling tool. Kriging is favored due to its ability to provide not only predictions but also a quantifiable measure of uncertainty, which is crucial for both reliability analysis and its optimization.

The methodology follows a sequentially adaptive refinement procedure to ensure the surrogate model's accuracy near the limit-state surface by iteratively reducing surrogate errors through additional design of experiment (DOE) iterations. By employing this adaptive refinement, the performance function's surrogate becomes sufficiently accurate for reliability analysis without requiring it to be exact across the entire input space.

Additionally, the authors apply subset simulation, a powerful variance reduction technique, for reliability and reliability sensitivity analyses, ensuring numerical efficiency.

Numerical Implementation and Comparative Evaluation

The proposed strategy is embedded within a traditional gradient-based optimization framework, allowing for integration with reliability estimates directly derived from kriging surrogates. The strategy is benchmarked against established methods across multiple example problems, including the elastic buckling of a column, a short column subjected to axial and bending loads, and a bracket structure under multiple failure modes.

Key results demonstrated that the kriging-based surrogate approach can achieve similar performance with significantly reduced computational effort compared to direct simulation-based approaches, achieving convergence with only a few dozen evaluations of the expensive performance functions. The adaptive refinement ensures the surrogate's reliability more robustly than most-probable-failure-point-based approaches.

Implications and Future Directions

This research offers significant insights into the practical application of RBDO in situations where computational resources are a limiting factor. The method provides a pathway to leverage surrogate modeling's strengths to articulate reliability constraints within design optimization studies, reducing the computational burden traditional methods would incur.

In terms of future development, further paper is encouraged to explore the application of this approach to real-world engineering problems involving higher-dimensional input spaces and more complex performance models. Investigating the scalability of the proposed method when handling cases with over a few thousand variables or evaluations is recommended. Additionally, extending the methodology to incorporate multiple failure modes more inherently linked with real-world applications could be a promising avenue.

In conclusion, the integration of kriging surrogates and subset simulation within a reliability-based optimization framework demonstrates a viable path towards efficient and practical RBDO in engineering design, aligning with evolving computational capabilities and industrial applications.