A Multimodal Time‐Variant Reliability Analysis Method With Application to Morphing Wing Mechanism

ABSTRACT A time‐varying reliability analysis method is proposed through uncertainty propagation and first‐order reliability method (FORM) under the influence of multimodal distributions. First, a novel theoretical model is established considering both multimodal distributions and time‐varying reliability. The modeling consists of Gaussian mixture models and a process discretization model, both of which are mixed to characterize the uncertainty parameters. Second, the time‐varying multimodal analysis method is proposed based on the adaptive sparse mesh and process discretization. Third, the probability density function (PDF) of response is calculated by the adaptive sparse grid numerical integration method, and the FORM is used to calculate the probability of failure. To improve the accuracy of the PDF, a convergence mechanism is used to increase the order of the statistical moments and reduce the entropy of the response. Moreover, the adaptive sparse grid method is able to improve computational efficiency in solving response moments, which adjusts the grid density according to the importance of the influencing factors. Finally, the time‐varying reliability method is applied to the reliability analysis of the morphing wings mechanism, which operates in environments where external loads exhibit multimodal distribution. The effectiveness is verified by three numerical examples and a morphing wing example.