非线性时域识别方程的不适定性与正则化方法研究

研究了非线性时域识别方程的不适定性及其正则化求解方法。雅可比矩阵的性态能够反映非线性识别方程的性态，因此雅可比矩阵的条件数是非线性识别方程的不适定性的度量。阻尼最小二乘法只是一种强迫正定的计算方法，其识别结果仍然对测试噪声很敏感，解决该问题的有效途径是将阻尼最小二乘法与正则化方法两者结合使用。算例表明，将先验的参数预估值引入Tikhonov镇定泛函可以得到稳定的参数解，且识别误差与原始数据的测试噪声基本保持在同一水平。

Research on Ⅲ-Condition and Regularization Method of Nonlinear Identification Equation in Time-Domain

The ill-condition and regularization method of structural parameter identification in time domain are studied. The property of nonlinear identification equations, can be described by Jacobi matrix, whose condition number is the index of ill-condition of the equation. Damping least square solution is not a real Tikhonov regularization solution, which is still sensitive to measurement noise. But taking the regularized function in the form of Tikhonov as the objective function, damping least squares algorithm can solve the nonlinear ill-posed problem effectively. The numerical example shows that the regularization method with parameter forecast constraint can result in a robust solution whose error level corresponds to the noise level of testing data in principle.