分数阶FGM(p,1,t^(α))模型及其应用

FGM(p,1,t^(α))Model with Fractional Order and Its Application

针对传统GM(1,1)模型预测局限性,以灰色GM(1,1,t^(α))模型为基础,构建了分数阶灰色FGM(p,1,t^(α))预测模型.在已有经典GM(1,1,t^(α))模型的基础上,将一阶累加灰生成拓展为分数阶累加灰生成,使得构建的模型更加符合新信息优先原理.另外,依据分数阶微积分理论,将整数阶导数灰色模型推广到分数阶导数灰色模型,并对模型进行求解.其次,讨论了参数几种特殊取值下的该模型的性质及适用范围.以平均相对误差为目标函数,利用粒子群优化算法求解模型最优参数.实际案例结果表明,所建立的模型能够较好的模拟常见振荡数据序列的波动趋势和特征,具有较强的适应性和拟合性能.

To overcome the prediction limitations of the traditional GM(1,1)model,a fractional order FGM(p,1,t^(α))model with time powers based on the GM(1,1,t^(α))model is proposed.Firstly,On the basis of classical GM(1,1,t^(α))model,on the one hand,it is extended to the fractional order cumulative grey generation,which makes the constructed model more consitent with the new information priority principle.on the other hand,generalize the integer derivative grey model to the fractional derivative grey model based on the fractional calculus theory.Secondly,the properties and application scope of this proposed model are analyzed under the circumstance of known parameter values.Moreover,the optimal cumulative order r,the fractional derivative p and the power exponentαare determined by utilizing the Particle Swarm Optimization based on the target function of minimizing the average relative error.The experimental results show that the model established can better simulate the fluctuation trends and characteristics of common oscillation data sequences,and has strong adaptability and fitting performance.