Extreme Value Theory, or univariate EVT, is widely used to assess structural risks of failure or damage, brought on by excessive environmental stressors in structural design. In engineering practice, a combination of multiple cross-correlated system components and covariates, rather than a single, univariate load, is what causes failure or damage. A multimodal state-of-the-art reliability-based approach for the multivariate structural design is presented. State-of-the-art pre-asymptotic multivariate methodology in combination with an accurate extrapolation scheme was utilized to model the Joint Probability Distribution Function (JPDF) tail of an M-dimensional random/stochastic process. The primary aim of this study was to envisage a generic, state-of-the-art multivariate reliability approach for assessing the failure or damage risks of high-dimensional dynamic systems. Note that for a multidimensional series-type system, its failure is given by a first passage event, and any parallel-type system can be equivalently reformulated as a series-type one. Novelty: The advocated multidimensional structural reliability approach would enable the extraction of relevant excessive dynamics information from time histories that had been physically recorded or numerically simulated. A variety of multimodal nonlinear dynamic systems can have their failure (damage) risks accurately and efficiently predicted using the proposed multimodal hypersurface Gaidai reliability methodology, which considers non-stationarity and memory (clustering) effects. High-dimensional, big data, deep-sea, ocean engineering and aerospace applications can benefit from the advocated multidimensional reliability approach.
Gaidai et al. (Mon,) studied this question.