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首先,基于积分滑动平均思想构造了变尺度加权积分函数,提出了最小二乘意义下加权积分滑动平均最佳近似响应函数模型。其次,利用形函数方法构造最佳近似载荷模型,组合近似载荷及响应得到实际情况下的Duhamel积分方程,对Duhamel积分离散化得到用于载荷识别的离散线性系统方程。再次,使用正则化方法进行载荷识别。利用正则化方法中最小二乘解构造以正则化参数为自变量的函数,提出了一种选取最优正则化参数的新方法。最后,数值仿真及试验验证将该文提出方法与传统方法进行了比较,结果说明新方法能够得到精度较好的近似稳定解,并且具有较好的抗噪性。
First of all, based on the idea of integral sliding averages, a variable scale weighted integral function is constructed, and a weighted average integral sliding average best approximation response function model in the least square sense is proposed. Secondly, the best approximation load model is constructed by using the shape function method, the Duhamel integral equation is obtained by combining the approximate load and response, and the discrete linear system equations for load identification are obtained by discretization of Duhamel integrals. Thirdly, the regularization method is used for load identification. A new method to select the optimal regularization parameter is proposed by using the least squares solution of the regularization method to construct the regularization parameter as a function of the independent variable. Finally, numerical simulation and experimental verification compare the proposed method with the traditional one. The results show that the new method can obtain the approximate stable solution with good accuracy and has good noise immunity.