Life prediction of mechanical products of GM(1,1) based on particle swarm optimization

Abstract

When GM(1,1) is used in the life prediction of mechanical products, the experiment cost is saved and the experimental period is shortened. The research on the whitening differential equation of GM(1,1) indicates that both the background value and the initial value of GM(1,1) have important effect on the prediction accuracy. In this paper, a new PSO-GM(1,1, lambda, b ) optimization model has been proposed to improve the prediction accuracy of GM(1,1). Firstly GM(1,1) has been improved with the difference scheme and made use of the parameter lambda to correct the background value; secondly the parameter b has been used to correct the initial value; lastly because of the nonlinear traits between the parameters lambda , b and the prediction errors, particle swarm optimization(PSO) has been used to solve the best value of lambda, b according to the criterion of minimizing the absolute value of mean relative error, then a new PSO-GM(1,1, lambda, b ) optimization model has been constructed. The correction deduction and PSO calculation lambda , b show that the prediction accuracy of the PSO-GM (1,1, lambda, b) is much higher than that of the GM (1, 1). The two practical examples about the life prediction of mechanical products show that the optimization method of PSO-GM(1,1, lambda, b ) is remarkable.