Tikhonov regularization-based operational transfer path analysis

Abstract To overcome ill-posed problems in operational transfer path analysis (OTPA), and improve the stability of solutions, this paper proposes a novel OTPA based on Tikhonov regularization, which considers both fitting degrees and stability of solutions. Firstly, fundamental theory of Tikhonov regularization-based OTPA is presented, and comparative studies are provided to validate the effectiveness on ill-posed problems. Secondly, transfer path analysis and source contribution evaluations for numerical cases studies on spherical radiating acoustical sources are comparatively studied. Finally, transfer path analysis and source contribution evaluations for experimental case studies on a test bed with thin shell structures are provided. This study provides more accurate transfer path analysis for mechanical systems, which can benefit for vibration reduction by structural path optimization. Furthermore, with accurate evaluation of source contributions, vibration monitoring and control by active controlling vibration sources can be effectively carried out.

[1]  Amit Bhaya,et al.  Adaptive choice of the Tikhonov regularization parameter to solve ill-posed linear algebraic equations via Liapunov Optimizing Control , 2015, J. Comput. Appl. Math..

[2]  Patrick Paultre,et al.  Consistent regularization of nonlinear model updating for damage identification , 2009 .

[3]  Lothar Reichel,et al.  Tikhonov regularization based on generalized Krylov subspace methods , 2012 .

[4]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[5]  Seungchul Lee,et al.  Source Contribution Evaluation of Mechanical Vibration Signals via Enhanced Independent Component Analysis , 2012 .

[6]  Ryan Wen Liu,et al.  A predictor-corrector iterated Tikhonov regularization for linear ill-posed inverse problems , 2013, Appl. Math. Comput..

[7]  Sandris Ručevskis,et al.  Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection , 2015 .

[8]  Christof Devriendt,et al.  Operational transfer path analysis , 2010 .

[9]  Tao Qian,et al.  Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem , 2014, Appl. Math. Comput..

[10]  L. Reichel,et al.  Large-scale Tikhonov regularization via reduction by orthogonal projection , 2012 .

[11]  Judith C. Hill,et al.  Regularization of soft-X-ray imaging in the DIII-D tokamak , 2015, J. Comput. Phys..

[12]  J. Antoni,et al.  Empirical Bayesian regularization of the inverse acoustic problem , 2015 .

[13]  R. Pourgholi,et al.  A numerical technique for solving IHCPs using Tikhonov regularization method , 2010 .

[14]  Quentin Leclere,et al.  On the use of artificial excitation in operational transfer path analysis , 2013 .

[15]  Thai Doan Chuong,et al.  Tikhonov-type regularization method for efficient solutions in vector optimization , 2010, J. Comput. Appl. Math..

[16]  Wim Desmet,et al.  Application of the transmissibility concept in transfer path analysis , 2010 .

[17]  Vikram Khipple Mulligan,et al.  Analyzing complicated protein folding kinetics rapidly by analytical Laplace inversion using a Tikhonov regularization variant. , 2012, Analytical biochemistry.

[18]  Mathieu Aucejo,et al.  Structural source identification using a generalized Tikhonov regularization , 2014 .

[19]  Seungchul Lee,et al.  Investigations of denoising source separation technique and its application to source separation and identification of mechanical vibration signals , 2014 .

[20]  Lijun Zhao,et al.  Neural network for constrained nonsmooth optimization using Tikhonov regularization , 2015, Neural Networks.

[21]  X. Y. Li,et al.  Adaptive Tikhonov regularization for damage detection based on nonlinear model updating , 2010 .

[22]  Juan Luis Fernández-Martínez,et al.  The effect of noise and Tikhonov's regularization in inverse problems. Part I: The linear case , 2014 .

[23]  Wim Desmet,et al.  OPAX: A new transfer path analysis method based on parametric load models , 2011 .

[24]  Ferit Küçükay,et al.  Hybrid acoustic synthesis – Assessment of rear final drives in an early stage of development, on the basis of transfer path analyses and test bench measurements , 2014 .

[25]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[26]  Zhengjia He,et al.  Independent component analysis based source number estimation and its comparison for mechanical systems , 2012 .

[27]  Abderrahman Bouhamidi,et al.  Conditional gradient Tikhonov method for a convex optimization problem in image restoration , 2014, J. Comput. Appl. Math..

[28]  Xiangtuan Xiong,et al.  A Tikhonov-type method for solving a multidimensional inverse heat source problem in an unbounded domain , 2012, J. Comput. Appl. Math..

[29]  W. Choe,et al.  Modified Phillips–Tikhonov regularization for plasma tomography , 2010 .

[30]  P. Hansen.  The discrete picard condition for discrete ill-posed problems , 1990 .

[31]  Wei Liu,et al.  A V-curve criterion for the parameter optimization of the Tikhonov regularization inversion algorithm for particle sizing , 2012 .

[32]  J. Beck,et al.  Estimation metrics and optimal regularization in a Tikhonov digital filter for the inverse heat conduction problem , 2013 .

[33]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[34]  Patrick Guillaume,et al.  Decoupling of mechanical systems based on in-situ frequency response functions: The link-preserving, decoupling method , 2015 .

[35]  Wei Cheng,et al.  A Comprehensive Study of Vibration Signals for a Thin Shell Structure Using Enhanced Independent Component Analysis and Experimental Validation , 2014 .

[36]  Li Yan,et al.  Research on the procedure for analyzing the sound quality contribution of sound sources and its application , 2014 .

[37]  Yu-Bin Zhou,et al.  Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation , 2015, J. Comput. Appl. Math..

[38]  Glaucio H. Paulino,et al.  An operator splitting algorithm for Tikhonov-regularized topology optimization , 2013 .

[39]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[40]  Oriol Guasch,et al.  Experimental validation of the direct transmissibility approach to classical transfer path analysis on a mechanical setup , 2013 .

[41]  Paolo Novati,et al.  Automatic parameter setting for Arnoldi-Tikhonov methods , 2014, J. Comput. Appl. Math..

[42]  D. de Klerk,et al.  Operational transfer path analysis: Theory, guidelines and tire noise application , 2010 .