Tikhonov方法在不适定模型修正中的应用

邱飞力,张立民,张卫华

振动与冲击 ›› 2015, Vol. 34 ›› Issue (12) : 121-126.

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PDF(1357 KB)
振动与冲击 ›› 2015, Vol. 34 ›› Issue (12) : 121-126.
论文

Tikhonov方法在不适定模型修正中的应用

  • 邱飞力,张立民,张卫华
作者信息 +

The parameters updating of simulations models with ill-posed characteristics

  • Feili Qiu, Limin Zhang, Weihua Zhang
Author information +
文章历史 +

摘要

数值建模和分析在结构动态设计中应用广泛,为获取准确的计算模型,基于参数灵敏度有限元修正技术得到迅速发展。然而,参数灵敏度矩阵病态性和修正目标函数方程组的不适定性,造成最小二乘直接法难以得到稳定的物理解。为此,对灵敏度矩阵的病态和模型优化方程组的不适定性进行研究,以铁道车辆6自由度离散模型和有限元支架模型为载体,采用Tikhonov正则化方法分别完成了超定系统和欠定系统仿真模型的参数修正。从而,解决了病态不适定系统中最小二乘直接法无稳定物理解的缺陷。参数修正后的模型准确反应了实际结构的尺寸差别和质量,这表明该方法具有实际的应用价值。

Abstract

With the numerical analysis and modeling wildly application and correct simulating model urgent requirement ,the parameter-sensitivity updating method has been developed rapidly. The direct least square method always can’t get the real parameter solution as the ill-posed system targets equations and the ill-conditioned sensitivity matrixes. The ill characteristics of the sensitivity matrixes and targets equations were researched. Then a six-dof discrete vehicle and the frame finite element model were updated with the Tikhonov regulation method, as the over determination and under determination simulation model separately. The problem of the direct least square method was solved. The updated models show mass of the real structure and the error between the components exactly, it’s proved that the method can be applied in engineering practice. 
 

关键词

模型修正 / 参数灵敏度 / 不适定系统 / 正则化方法

Key words

model updating / parameter-sensitivity / ill-posed system / regulation method

引用本文

导出引用
邱飞力,张立民,张卫华. Tikhonov方法在不适定模型修正中的应用[J]. 振动与冲击, 2015, 34(12): 121-126
Feili Qiu, Limin Zhang, Weihua Zhang. The parameters updating of simulations models with ill-posed characteristics[J]. Journal of Vibration and Shock, 2015, 34(12): 121-126

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