Gear remaining useful life prediction using generalized polynomial chaos collocation method

A method of using generalized polynomial chaos technique to deal with uncertainty quantification in gear life prediction is presented in this paper. The uncertain material parameters in Paris' law are modeled as random variables and the crack propagation process based on Paris' law is treated as stochastic. The failure time of a cracked gear is expressed as the summation of a series of orthogonal polynomials with random variables. The stochastic collocation algorithm is employed to obtain the numerical solution of the stochastic equation. Comparing to Monte Carlo simulation, generalized polynomial chaos technique is capable of considering multi-dimensional uncertainty space with faster convergence rate, which allows the equipment health prognostics to be implemented in a practical and much more efficient way.