A New Fibonacci-based Algorithm for Locating Peak Intensity Measure of IDA Curves

Abstract

Although incremental dynamic analysis (IDA) can be regarded as an accurate tool for evaluating seismic capacity of structures, it is very time intensive. Generating IDA curves requires performing multiple nonlinear time-history analyses (NTHA) for given earthquake records. In this paper, a new algorithm based on Fibonacci sequence is developed for finding the maximum intensity measure (IM) under which the structure’s dynamic response is numerically stable. It is shown that, by performing a very limited number of evaluations, the method can locate this point with the desired accuracy even if the IDA curve is not unimodal. Once the maximum IM is found, the whole IDA curve can be obtained by performing a few more NTHAs. Since the proposed method can be regarded as an optimal approach for establishing the IDA curves, it can be efficiently used in optimization problems in which objective functions or the constraints are related to IDA analyses.