Volterra模型参数灰色辨识的变步长Simpson数值积分法

针对观测数据的非等间隔性及波动性严重影响参数辨识精度问题,基于拉格朗日插值公式,推导出了变步长Simpson数值积分公式,并结合灰色系统理论,提出了一种模型参数灰色辨识的改进方法.用此方法对Volterra模型中的参数进行了辨识仿真,与以往的曲线拟合方法进行了对比分析,并简要分析了模型的初值问题.计算研究表明,基于变步长Simpson数值积分公式的灰色辨识方法在处理非等时间间隔以及数据波动性较大的参数辨识问题时稳定性较好,可满足高精度辨识模型参数的要求.

Parameter grey estimation of Volterra model based onSimpson formula with different steps

Based o n Lag rang e interpolat ion formula, Simpson formula w ith different steps w as deduced todeal w ith the influence of unequal interval and most f luctuating data on parameter est imat ion w ith highpr ecision. Accor ding to g rey system theory , an improved method of parameter grey est imation w as putfo rw ard. Parameters of Vol terra model w er e est imated and simulated by this metho d, and compared w iththe resul ts o f former curv e f it ting methods. The issue of init ial values w as also analyzed. T he analyses indicatethat the impr oved method w ith Simpso n formula is superior to the former o nes w hen the data observedare unequal interval and mo st f luctuat ing , and parameter est imat io n can be fulfilled with hig h precision.