Local maximum-entropy based surrogate model and its application to structural reliability analysis


Structural reliability analysis encompasses the statistical nature of structural safety evaluation as well as design with a huge number of random variables. Many researchers have adopted the Monte-Carlo simulation in order to predict structural systems’ failure possibilities. This approach demands thousands of evaluations of the performance function of a structural system. These computations can be performed if the performance function y(x) is expressed as an explicit function form or as analytical form in terms of the random variables x.

In case the performance functions are in the implicit form, such computations call for extra effort and will consume more time. Implicit performance functions generally occur when expensive physical experiments or when comprehensive numerical analyses are adopted for mechanical analysis of a structural system. The steep computational cost of operating high fidelity and complicated simulations renders this impractical.

Therefore, there is a quest for an approach to replace the steep-cost simulation models by surrogate models, which are also known as response surface models or metamodels, in the process of reliability analysis. However, surrogate models have been used in the structural reliability analysis. For instance, the Polynomial Regression is a form of surrogate model that has been widely adopted in the structural reliability analysis.

Several researchers have tried to enhance the performance of the Polynomial Regression surrogate models. Unfortunately, the performance of this model is limited in applications with non-linear functions. Higher order polynomials have been adopted to address this difficulty, but instabilities occur. Moreover, it is quite challenging to provide adequate sampling data for the analysis of the coefficients in high-order polynomials.

For this reason, alternative surrogate models have been introduced to address the challenges of Polynomial Regression surrogate models. Bo Li and Hao Wang at Case Western Reserve University in collaboration with Jiang Fan, Huming Liao, Junheng Hu, Zhiying Chen at Beihang University also Jian Lu at Guangdong Institute of Aeronautics and Astronautics Equipment & Technology proposed a surrogate model based on Local Maximum-Entropy approximation in a bid to blend the benefits of both global and local approximation schemes. By changing the degree of locality, this model was constructed consistent with the local behavior of the response function at the prediction points. Their research work is published in journal, Structural Multidisciplinary Optimization.

The authors systematically analyzed the performance of the proposed Local Maximum-Entropy approximation surrogate model by comparing to the typical surrogate models in three forms of problems. The robustness and the efficiency of the Local Maximum Entropy-based surrogate model was demonstrated in the application of the turbine disk reliability evaluation. Finally, the authors performed a model-based Uncertainty Quantification analysis to quantify the uncertainty of the system.

The Local Maximum entropy-based surrogate model was found to be accurate and robust in all the test cases and in the engineering problem. The model also excelled in high order nonlinearity problems with a smaller number of sample points. This attribute was derived from the computation of the Local Maximum Entropy shape functions that demanded lesser sampling points and could be carried out effectively and robustly in any spatial dimensions.

The derivatives of the shape functions were auxiliary outputs of the calculation without any extra computation cost. This further increased the transparency of the model. In general, the Local Maximum Entropy-based surrogate model developed in the study enable a seamless bridge between global and local approximation schemes.


Jiang Fan, Huming Liao, Hao Wang, Junheng Hu, Zhiying Chen, Jian Lu and Bo Li. Local maximum-entropy based surrogate model and its application to structural reliability analysis. Structural Multidisciplinary Optimization.


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