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This article proposes two strategies for time-dependent probabilistic fatigue analysis considering stochastic loadings and strength degradation based on the failure transformation and multi-dimensional kernel density estimation method. The time-dependent safety margin function is first established to describe the limit state of the time-dependent failure probability for mechatronics equipment with stochastic loadings and strength degradation. Considering the effective safety margin points and the corresponding number of the load cycles, two strategies for transforming the time-dependent failure probability calculation to the static reliability calculation are then proposed. Multi-dimensional kernel density estimation method is finally employed to build the probability density functions and the reliability is estimated based on the probability density functions. An engineering case of a filtering gear reducer is presented to validate the effectiveness of the proposed methods both in computational efficiency and accuracy.

A time-dependent probabilistic fatigue analysis method considering stochastic loadings and strength degradation