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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.
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［1］Inoue H, Ikeda N, Nishimoto K, et al. Inverse analysis of the magnitude and direction of impact force[J]. JSME International Journal. Series A, Mechanics and Material Engineering,1995, 38(1): 84-91.
［2］Wu E, Tsai C, Tseng L. A deconvolution method for force reconstruction in rods under axial impact[J]. The Journal of the Acoustical Society of America,1998, 104(3): 1418-1426.
［3］Wang B. Prediction of impact and harmonic forces acting on arbitrary structures: theoretical formulation[J]. Mechanical Systems and Signal Processing,2002, 16(6): 935-953.
［4］He P, Jia F. Reconstruction of impact force of mechanical press in time domain[J]. Journal of Southeast University,2011, 27(4): 400-404.
［5］Boukria Z, Perrotin P, Bennani A. Experimental impact force location and identification using inverse problems: application for a circular plate[J]. International Journal of Mechanics,2011, 5(1): 48-55.
［6］La V, Zem cík R, Kroupa T, et al. Reconstruction of impact force on curved panel using piezoelectric sensors[J]. Procedia Engineering, 2012, 48: 367-374.
［7］Gunawan F E, Homma H, Kanto Y. Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction[J]. Journal of Sound and Vibration,2006, 297(1): 200-214.
［8］Hansen P C. Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems[J]. Numerical algorithms,1994, 6(1): 1-35.
［9］Bauer F, Lukas M A. Comparingparameter choice methods for regularization of ill-posed problems[J].Mathematics and Computers in Simulation. 2011, 81(9): 1795-1841.
［10］Peaceman D W, Rachford J H H. The numerical solution of parabolic and elliptic differential equations[J]. Journal of the Society for Industrial & Applied Mathematics,1955, 3(1): 28-41.
［11］Douglas J, Gunn J E. A general formulation of alternating direction methods[J]. Numerische Mathematik,1964, 6(1): 428-453.
［12］Gabay D, Mercier B. A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J]. Computers & Mathematics with Applications, 1976, 2(1): 17-40.
［13］李玉华. 求解凸规划问题的松弛交替方向乘子法[D]. 郑州：郑州大学, 2009.Li Y H. A relaxed Alternating Directions of Multipliers Method for Convex Programming[D]. Zhengzhou: Zhengzhou University, 2009.
［14］Chan R H, Tao M, Yuan X. Linearized alternating direction method of multipliers for constrained linear least-squares problem[J]. East Asian Journal on Applied Mathematics,2012, 4(2): 326-341.
［15］石然然，李名尧，张报建，等. 基于LabVIEW的螺旋压力机打击力测量系统简[J]. 锻压技术, 2013,38(5):123-126.Shi R R, Li M Y, Zhang B J, et al. Strike force measuring system of screw press based on LabVIEW[J]. Forging & Stamping Technology, 2013, 38(5): 123-126.
［16］傅志方，华宏星. 模态分析理论及应用[M]. 上海: 上海交通大学出版社, 2000.Fu Z F, Hua H X. Modal Analysis Theory and Its Application[M]. Shanghai: Shanghai Jiaotong University Press, 2000.
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