基于交替方向乘子法的冲击载荷识别

Impact force identification based on alternating direction method of multipliers

针对冲击载荷识别矩阵大型化、病态性严重的问题,提出了一种基于交替方向乘子法的新型迭代正则化方法并成功应用于冲击载荷识别。建立了冲击载荷识别等式,并通过正则化处理转化为具有可分离结构凸优化问题;其次,将交替方向乘子法应用于冲击载荷识别中,并基于L曲线准则给出了算法获取最优解时的收敛条件;以悬臂梁和高速压力机的冲击载荷识别为例进行了数值研究,验证了该方法的可行性及有效性。分析结果表明提出的冲击载荷识别方法较正则最小二乘法具有更高的精度,识别的高速压力机冲击力更接近于实验值。

For the problems of large-size equation, and severe ill-posed matrix in the impact force identification, a new iterative regularization method was proposed by alternating direction method of multipliers （ADMM） and successfully applied to the impact force identification. Firstly, the impact force identification equation was established and converted into a convex optimization problem with separate structure through regularization. Then, the ADMM method was applied to the impact force identification, and convergence condition of optimal solution was given by L curve criterion. Finally, numerical researches were carried out with cantilever beam and high-speed press suffering from impact forces, which verified the feasibility and effectiveness of the method. The analysis results indicate that the impact force identification method has a higher accuracy than regularized least squares, and the value of the identified impact force under high-speed press is closer to the experimental result.