Time-dependent reliability analysis of flapping-wing mechanism considering truncated random variables

Time-dependent reliability evaluation is an advantageous approach to estimate the failure probability of a mechanism in its motion period. Truncated random variables exist in most mechanisms, and considering this factor can extra precisely consider the time-dependent reliability of mechanisms. This article proposes an established approach for time-dependent reliability evaluation of mechanisms thinking about truncated random variables. Firstly, the motion error function is established, and the input parameters are transformed from truncated variables to truncated standard normal variables. Then, the envelope function approach for remodeling time-dependent reliability troubles into time-independent reliability troubles hassle at a couple of time enlargement points. On this basis, the saddle point approximation method is used to calculate the failure likelihood at the expansion point, and the Gaussian-copula function is used to calculate the joint failure probability. Finally, the higher and decrease bounds of the complete failure chance are obtained through the second-order narrow reliability bounds. The application results on the flapping-wing mechanism show that the method can accurately and efficiently evaluate the time-dependent reliability of the mechanism thinking about the truncated random variables.