High-dimensional reliability analysis based on the improved number-theoretical method

Abstract

Different stochastic analysis methods have been employed for the reliability analysis of a structural system. However, the lack of a high-dimensional point selection method limits their application to capture the reliability of complex structures with high-dimensional variables. A novel high-dimensional uniform point selection method based on the number-theoretical method is proposed to address this problem. A new generating vector is proposed to form the high-dimensional point set with its components written as linear multiples of the primitive root of prime number in the number-theoretical method. This is different from the current practice where exponent calculation is needed to form the vector. The components in higher dimensions are mappings of that in last lower dimensions. The uniformity of the generated point set is the same as that from the traditional number-theoretical method but with dramatically reduced computation. The probability density evolution method is then employed for the reliability analysis with the generated high-dimensional point set. Performance and accuracy of the proposed method are verified via three numerical examples. Results show that the failure probability and reliability obtained by the proposed method have similar accuracy to those from the reference Monte Carlo method but with much reduced computation compared to those from reference and other existing traditional methods.