基于改进函数拟合法的冲击载荷识别研究

Research on Impact Force Reconstruction Based on Improved Function Fitting Method

冲击载荷识别在结构设计、振动控制、健康监测等领域具有重要作用。基于经典Tikhonov正则化的冲击载荷识别方法存在识别精度、稳定性等方面存在一定的局限,近年来兴起的函数拟合法为冲击载荷识别提供了新的思路。根据冲击载荷的稀疏性质以及考虑冲击载荷的加载、卸载过程,提出基于半余弦函数拟合的冲击载荷识别方法,通过遗传算法优化半余弦基函数的区间参数,建立基于半余弦函数拟合的冲击载荷识别正则化模型,解决基于函数拟合的冲击载荷识别方法的稳定性问题。将基于半余弦函数拟合的冲击载荷识别方法、经典Tikhonov正则化方法和正交多项式拟合法分别对梁结构、桁架结构与薄板结构的有限元模型进行冲击载荷识别计算,对悬臂梁结构进行试验验证。结果表明:基于半余弦函数拟合的冲击载荷识别方法能够得到时域上的稀疏信号,识别精度高,抗噪性能好。

Impact load identification plays an important role in the fields of structural design,vibration control,and structural health monitoring.The reconstruction method based on classic Tikhonov regularization has some limitations in identification accuracy and stability,and the function fitting method that has emerged in recent years provides new ideas for impact force reconstruction.According to the impact force is sparse in time domain and considering the loading and unloading process in the impact history,an impact force identification method based on semi-cosine function fitting is proposed.The interval parameters of the semi-cosine basis functions are optimized by genetic algorithm,and the regularization model of impact reconstruction based on semi-cosine function fitting is established,solving the stability problem of the impact inversion method based on function fitting.Here,the impact identification method based on semi-cosine function fitting,the classic Tikhonov regularization method and orthogonal polynomial fitting method are used to perform the impact inversion calculation on the finite element model of a beam structure,a truss structure and a thin plate structure,and the cantilever beam structure is examined and verified.The results show that:the proposed method based on semi-cosine function fitting can obtain sparse signals in time domain,having great advantages to obtain accurate inversion results and it has good robustness.