Polynomial chaos expansion approximation for dimension-reduction model-based reliability analysis method and application to industrial robots

Polynomial chaos expansion (PCE) is considered an excellent method for accurately and efficiently reliability analysis in various engineering problems. However, it becomes practically infeasible in scenarios characterized by high-dimensional input random variables and thousands of training data. To solve this problem, this paper proposes a new PCE-based surrogate-assisted method. To start with, the interacting variables are screened out from original high-dimensional input random variables by contribution-degree analysis (CDA). The original high-dimensional performance function is decomposed into a lower-dimensional component function composed of the interacting variables and multiple one-dimensional component function containing only one non-interacting variable. Then, PCE combined with a sample points selection strategy is used to fit the lower-dimensional component function, and a full PCE is utilized for fitting each one-dimensional component function. Three methods, namely the Hadamard's inequality of the design matrix, the rank revealing QR factorization of the design matrix and the maximum entropy, are implemented to realize sample point selection. Four examples are investigated to demonstrated the effectiveness of the proposed method.