基于有效参数的多源载荷位置识别及重构方法
MULTI-SOURCE LOAD POSITION IDENTIFICATION AND RECONSTRUCTION METHOD BASED ON EFFECTIVE PARAMETERS
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摘要: 载荷识别问题通常是病态的, 且结构常处在多个不同位置载荷的共同作用. 为了提升噪声环境下结构在多源载荷作用下位置的精确定位并提升冲击载荷的峰值识别精度, 本文提出了一种基于改进稀疏贝叶斯的多源载荷位置识别及重构方法. 通过引入独立精度的先验, 并提出了有效参数数量 \gamma 指导的参数更新策略, 可以自动识别载荷作用的位置并准确重构载荷. 有效参数数量可以连接先验分布与似然函数, 平衡残差范数和解范数的大小, 使得模型可以自适应调整正则化强度, 进而实现稀疏贝叶斯估计并准确估计噪声水平和重构载荷. 此外, 通过有效参数可以确定外部输入载荷的数量, 实现了多源载荷位置的识别与时间历程重构. 在悬臂梁试验中, 本文方法针对连续冲击载荷识别的平均峰值误差为0.39%, 优于传统贝叶斯方法和分数阶方法的6.17%和5.22%, 且在不同噪声水平下, 保持较高的载荷识别精度具有较好的抗噪性和鲁棒性. 该方法不仅在重构载荷精度和稳定性上优于传统正则化方法, 而且能够同时准确的识别多个外载荷的作用位置.Abstract: The load identification problem is usually ill-posed, and the structure is often subjected to the combined action of loads at multiple different positions. In order to improve the load positioning accuracy of the structure under multi-source load in the noise environment and improve the peak load identification accuracy of the impact load. In this paper, a multi-source load position identification and reconstruction method based on improved sparse Bayesian is proposed. By introducing a priori of independent accuracy and proposing a parameter update strategy guided by the number of effective parameters \gamma , the position of the load can be automatically identified and the load can be accurately reconstructed. The number of effective parameters can connect the prior distribution and the likelihood function, balance the size of the residual norm and the solution norm, so that the model can adaptively adjust the regularization intensity, thereby achieving sparse Bayesian estimation and accurately estimating the noise level and reconstruction load. In addition, the number of external input loads can be determined by the number of effective parameters, and the identification and time history reconstruction of multi-source load positions are realized. In the cantilever beam test, the average peak error of the proposed method for continuous impact load identification is 0.39 %, which is better than 6.17 % and 5.22 % of the traditional Bayesian method and the fractional order method. Under different noise levels, it still maintains high load identification accuracy and has good noise resistance and robustness. This method is not only superior to the traditional regularization method in the accuracy and stability of the reconstructed load, but also can accurately identify the position of multiple external loads.
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