PSO-GM(1,1,N,p,ξ)模型在变形预测中的应用

Application of PSO-GM(1,1,N,p,ξ) Model to Prediction of Deformation

通过对传统GM(1,1)缺陷分析和改进的基于权的PGM(1,1)建模机理描述,顾及PGM(1,1)中背景值构造时取相同的参数不能充分降低模型的预测误差,对不同的时刻引入不同的参数来改进GM(1,1)背景值序列的计算公式,将这种背景值构造方法和灰元N引入GM(1,1)建立了新的白化方程。在建立的新的白化方程基础上,用龙格-库塔法以修正的初始值计算累加值的模拟序列。针对引入的参数较多问题,采用粒子群算法寻找满足相对误差均值最优的参数,从而建立了基于粒子群优化算法和加权灰色组合的PSO-GM模型。工程实例应用表明,新模型的拟合精度高,预测效果好,相对其他两种原有模型预测精度有明显提高。

Through defect analysis on traditional GM（1,1） and the mechanism description of improved base on the weight of PGM（1,1）, we consider that if the same parameters are taken in GM（1,1） whenconstructing background values, then the prediction error of the model cannot be sufficiently reduced. Differ- ent parameters are applied at different times to improve the GM（1,1） background value sequence formula. This kind of background value construction method and grey element N are applied to the GM（1,1） to build a new albino equation. On the basis of the establishment of the new albino equation, the modified initial value through the Runge-Kutta method is applied to calculate the accumulated value of the simulation sequence. To resolve the introduction of many parameters, the particle swarm optimization algorithm is used to find optimal parameters which satisfy the relative error, so the PSD-GM model based on the particle swarm optimization algorithm and the weighted grey combination is established. The application of an engineering example shows that fitting precision of the new model is high, the predictive effect is good, and the predictive accuracy of the new model is improved significantly compared with the other two models.