Volterra series is powerful for nonlinear system modeling and has gained great interest of scientists across many disciplines for its theory foundation, brief formulation, and precise physics.The main difficulty of engineering application of Volterra series is the identification of Volterra kernels because the number of parameters need to identify increases exponentially with the order of the kernel.To reduce the number of estimated parameters, this paper expands the first kernel and the second kernel with piecewise quadratic multiwavelet basis function and turns the problem into the solution of a few expansion coefficients.The result of the demonstration on a prototypical nonlinear oscillator is shown that the identified kernels match with the analytical kernels very well and they can accurately predict the responses of the system to different inputs.Besides, for the common input cannot include the nonlinear effect of the interaction of different frequency in a nonlinear system, the paper designs input called two dimension chirp suited for identification of the second order Volterra kernel.Compared with the commonly used chirp inputs, numerical experiment verifies that this input can excite the nonlinear characteristics of the system better.%Volterra级数作为一种非线性系统模型,因其具有坚实的理论基础、简洁的表示形式和明确的物理意义,在许多领域引起了广泛的研究兴趣.Volterra级数实际应用的难点在于Volterra核的辨识,随着核阶次的增加待辨识参数的数量呈指数增长.为了减少待辨识参数,文章以分段二次多小波为基函数将Volterra一阶核和二阶核展开,将问题转化为少数展开系数的估计问题.通过典型的非线性振荡器进行验证,结果表明Volterra核的辨识结果非常接近于理论值,同时由Volterra级数能准确计算系统在不同输入下的响应.此外,针对常用的输入信号无法反映非线性系统中不同频率相互作用产生的非线性影响,文中设计了一种适合于二阶核辨识的输入,称为二维扫频,与常用扫频信号相比,试验结果表明这种输入明显能更好地激励系统的非线性特性.
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