The trajectory importance measure of the shaping machine under stochastic excitation

Two trajectory importance measures, the trajectory importance measure based on variance and the moment-independent trajectory importance measure, are proposed to represent the time-variant effects of input uncertainty on the output uncertainty of the shaping machine under stochastic excitation in its work stroke, respectively. At the same time, the trajectory importance measure based on the failure probability is proposed to reflect the contribution of the input uncertainty on the dynamic reliability of the mechanism. These three trajectory importance measures provide different references to improve the performance and reliability of the mechanism from the time-variant perspective. As the probability density evolution method (PDEM) is employed to solve the proposed trajectory importance measures, it can improve the computational efficiency largely without losing precision. Results of the shaping mechanism illustrate the feasibility of the proposed trajectory importance measures and the veracity of the PDEM in solving the lathe mechanism.