The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters

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Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method (2011, methodology): “method [19–21] and other types of stochastic methods [22,23] have been developed to analyze random structures.”
Probability density evolution analysis of engineering structures via cubature points (2012, methodology): “11 The CDFs over the time interval [0, 20]s (the nonlinear structure with 6 random variables)”
First order reliability method for time-variant problems using series expansions (2015, background): “Based on the fact that the time-variant reliability is determined by the global extreme values of the response, Chen and Li (2007) proposed an approach for the evaluation of the extreme value distribution of dynamic systems based on the probability density evolution method.”
A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis (2013, methodology): “They include the Monte Carlo simulation (MCS) [4], the Gamma process method [5], the Markov chain method [6], the extreme value distribution method [7,8], the upcrossing rate method [9,10], and the composite limit state method [1].”
Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation (2014, methodology): “There are two basic types of methods for time-dependent reliability: extreme value methods [31-35] and first-passage methods [30, 33, 36-42].”