Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method

• A multiplicative dimensional reduction method is proposed to represent a high-dimensional model function.
• An efficient computational method is developed for fractional moment computation.
• The complete output distribution is determined by using the principle of maximum entropy (MaxEnt) with fractional moments.
• A non-intrusive numerical method is proposed for structural reliability analysis.
• Example analysis shows that the proposed approach is highly accurate and efficient.

The structural reliability analysis is typically based on a model that describes the response, such as maximum deformation or stress, as a function of several random variables. In principle, reliability can be evaluated once the probability distribution of the response becomes available. The paper presents a new method to derive the probability distribution of a function of random variables representing the structural response. The derivation is based on the maximum entropy principle in which constraints are specified in terms of the fractional moments, in place of commonly used integer moments. In order to compute the fractional moments of the response function, a multiplicative form of dimensional reduction method (M-DRM) is presented. Several examples presented in the paper illustrate the numerical accuracy and efficiency of the proposed method in comparison to the Monte Carlo simulation method.