Iterative Equation Solver for Bridge Analysis Using Neural Networks

Abstract

A technique for enhancing finite‐element analysis equation solvers for particular problem domains, i.e., particular classes of structures such as highway bridges, is presented. The technique involves merging artificial neural networks, used as a domain knowledge‐encoding mechanism, together with a preconditioned conjugate gradient iterative equation‐solving algorithm. In the algorithm, neural networks are used to seed the initial solution vector and to precondition the matrix system using customizable and trainable neural networks. A case study is presented in which the technique is applied to the particular domain of flat‐slab highway bridge analysis. In the case study, neural networks are trained to encode the load‐displacement relationships for concrete flat‐slab highway bridges. Analytical load‐displacement data are generated using finite‐element analyses and subsequently used to train neural networks. Acting collectively, the neural networks predict approximate displacement patterns for flat‐slab bridges under arbitrary loading conditions.