非线性振动系统参数识别的迭代离散变分方法
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自然科学基金重点项目(10632030),973项目(2006CB705403)的资助


An iterative parameter identification method for nonlinear vibration systems based on discrete variational principle
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    摘要:

    针对存在干扰的非线性振动系统,本文提出了一种识别模型参数的时域迭代方法.首先,对于每一组包含随机干扰的测量数据样本,将待辨识参数对时间的导数引入到系统代价函数中,进而利用离散变分原理导出关于待辨识参数的差分方程,并与修改后的系统约束方程一同求解;通过迭代计算使待识别参数从给定的初始值收敛到稳定的真值.然后,对通过n组干扰样本得到的参数识别结果取平均值,并作为最终辨识结果.最后,利用本方法对一个四自由度非线性振动系统的模型参数进行了识别仿真,数值结果证明了该方法的有效性.

    Abstract:

    An iterative system identification scheme for the nonlinear vibration systems with random noise was presented. Firstly, for each sample of measured data with random disturbance, the derivative with respect to the unknown parameters was introduced into the cost function; then the difference equations for the unknown parameters were obtained by means of the discrete variational principle, and solved simultaneously with the revised constraint equations; thus, the tobeidentified parameters were guided from given initial conditions to their true numerical values with an iterative procedure. Secondly, for many data samples with random disturbance, the mean value of the tobeidentified parameters was obtained as the identification results. Finally, simulations for parameter identification of nonlinear vibration systems with fourdegreeoffreedom were presented so as to verify the proposed algorithm. Numerical results demonstrate that the parameter identification technology is effective.

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刘正山,吴志刚.非线性振动系统参数识别的迭代离散变分方法[J].动力学与控制学报,2009,7(3):200~204; Liu Zhengshan, Wu Zhigang. An iterative parameter identification method for nonlinear vibration systems based on discrete variational principle[J]. Journal of Dynamics and Control,2009,7(3):200-204.

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  • 收稿日期:2009-01-14
  • 最后修改日期:2009-03-11
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