Reliability analysis of structures using polynomial chaos expansions

Practical engineering issues such as design optimization, design space exploration, sensitivity analyses, and reliability analyses need many simulations. If a single simulation is very time-consuming, engineers cannot perform the thousands or even millions of simulations needed for such analyses. The polynomial chaos expansion (PCE) method is an effective method that allows analyses of complex problems. This paper introduces the mathematical theory of the PCE method and presents a structural reliability analysis example. The performance response function for the structural reliability analysis is expressed as a PCE using Hermite polynomials. A general form of the Hermite polynomial, which is suitable for use in a computer program, is used to generalize the PCE analysis program and the adaptive selection of the polynomial order. Then, the accuracy and applicability of the surrogate model are verified using structural reliability analysis examples with explicit performance functions. The results show that the model has an excellent convergence rate with higher order PCE giving higher accuracy. The examples also show that the direct use of explicit performance functions is the easiest way to investigate PCE surrogate models.