Modeling empirical judgments via Topological Structure and Optimization

Abstract

In this study, we introduce mathematical methods to supplement conventional maintenance practices that rely on empirical rules, with the aim of accelerating the digitization of maintenance processes. We present logically rigorous mathematical models addressing issues such as the selection of inspection methods. By applying abstract topological theory, we propose a framework for method selection that is independent of specific technologies. To bridge the gap between abstract mathematics and practical applications, we demonstrate a data-driven procedure for deriving optimal solutions through multi-objective optimization, illustrated using actual inspection method selection problems. Furthermore, we propose an algorithm incorporating step functions based on binary decisions as a practical approach to handling discontinuous mappings. The algorithm is validated through comparisons with actual post-earthquake inspection cases.