中文摘要：

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。

英文摘要：

Firstly, a variable scale integral function was formed based on the idea of the integral moving average, and a weighted integral moving average optimal approximate response function model was proposed under least squares conditions. Secondly, a shape function method was used to construct optimal approximate load model. The real Duhamel integral equation can be obtained with the combination of approximate load and response. The discretization of Duhamel integral results in a systematically discretized equation, which can be used for load identification. Thirdly, the regularization method was used for load identification, by using the least squares solution of the regularization method to construct a function of the regularization parameter. A new method was proposed for choosing the optimal regularization parameter. Finally, numerical examples and experimental verification illustrated that the new method can obtain a stable solution with better accuracy and noise resistance.