A new method for solving multiple definite integrals using multiple sets of correlation extreme learning machines

Abstract

PurposeThis paper aims to develop a novel method and apply it to solve multiple definite integrals. The proposed method is constructed based on multiple sets of correlation extreme learning machines (MCELM).Design/methodology/approachThe authors present a novel method for solving multiple definite integrals. By using an extreme learning machine (ELM) to learn the integrand function, the primitive function is analytically derived based on the functional expression of the trained ELM and expressed by another ELM, while the correlations between the two ELMs are established. Solutions of multiple definite integrals can be realized by applying this process repeatedly.FindingsTo verify the validity and effectiveness of the proposed method, various examples are selected and its numerical solutions are obtained by using the proposed method. The proposed method has high computational accuracy and efficiency, and the superiority is illustrated by comparing with some other existing methods.Originality/valueMCELM method is proposed for solving multiple definite integrals. The method can be applied for solving multiple definite integrals appearing in applications, the strong applicability of the method in engineering problems is demonstrated in structural system reliability analysis of a cantilever beam.