Data-driven polynomial chaos-interval metamodel for dynamics and reliability analysis under hybrid uncertainty

As the complexity of engineering systems increases, the probability distribution information of model parameters becomes limited owing to the influence of environmental or natural phenomena. To solve this problem, a data-driven polynomial chaos-interval metamodel (DDPCIM) is proposed herein to quantify random and interval uncertainties in an engineering system. The orthogonal polynomial basis corresponding to each dimensional random variable was based on the statistical moments of the random variable. The multidimensional orthogonal polynomial basis was obtained by performing a tensor-product operation on a one-dimensional orthogonal polynomial basis. Legendre (or Chebyshev) polynomials can be selected as the polynomial basis functions corresponding to the interval variables. In addition, the interval sampling technique was improved to make the bounds of the output response closer to realistic results. The proposed DDPCIM has higher computational accuracy and efficiency than traditional methods, such as the polynomial Chaos–Legendre metamodel (PCLM) and the method combining Monte Carlo and scanning tests (CMCST). Finally, the DDPCIM was applied to achieve the desired level of reliability for engineering systems with hybrid uncertainty. Numerical examples show that the DDPCIM is a robust and efficient method for analysing the reliability of engineering structures with hybrid uncertainty.