State-of-the-art non-stationary hypersurface reliability methodology, accounting for memory effects

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.