Kinnear, Hugh Jonathan; (2025) Niching Strategies for Multimodal Rare-event Simulation. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Reliability analysis focuses on estimating the small probability of failure of physical sys- tems, that is, the probability that demand exceeds their capacity. There are many modern techniques capable of solving this problem, such as subset simulation, sequential impor- tance sampling and improved cross entropy. Unfortunately, significant challenges arise for these methods when dealing with problems that have a high-dimensional input, a com- putationally expensive performance function, and crucially, some form of multimodality. This thesis proposes strategies to address multimodality inspired by niching techniques from the field of evolutionary multimodal optimisation. The thesis also introduces several novel methods that combine niching techniques with concepts from reliability analysis. The foundational component is the niching initial sampling, a robust algorithm that is able to consistently populate all the high density regions of a multimodal reliability problem’s failure region. This procedure is then used to develop two novel frameworks. Firstly, niching decomposition subset simulation, suit- able for very high-dimensional reliability problems, uses a hill valley test to explicitly decompose the problem into simpler components, demonstrating improved performance over standard existing methods on difficult benchmarks found in the literature including the meatball function counterexample and black swan reliability problems. Secondly the niching model framework, suitable for relatively low-dimensional reliability problems, in- tegrates niching initial sampling with modelling techniques and methods for estimating normalisation constants such as importance sampling, bridge sampling and line sampling. in particular the use of bridge sampling allows for a novel approach to using classifica- tion algorithms for reliability analysis. These successful developments and applications demonstrate the power of niching techniques, particularly in high dimensions, and move toward the eventual goal of a meta-algorithm for black-box problems that can determine the most appropriate reliability method based on problem characteristics.

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