Abstract
Due to the great challenges of measuring forces directly, identifying dynamic loads based on accessible responses is a crucial problem in engineering, helping ensure integrity and reliability of mechanical structures. Dynamic load identification is a difficult inverse problem due to matrix ill-posedness, noise-sensitivity and computational scale, especially in uncertain structures. Unexpected inaccurate or non-unique solutions may be found if these problems are not well addressed. During the past decades, many methods have been proposed to deal with these problems. This paper tries to provide a comprehensive review of techniques for dynamic load identification, including under ill-posedness and uncertain parameter processing; with an emphasis on the statistical, data science, machine learning, and artificial intelligence aspects. Classical physics-based dynamic load identification theories in frequency and time domain are also introduced. Research challenges and prospects of dynamic load identification in mechanical systems are discussed finally. This review may offer guidelines for dynamic load identification in practical complex structures, as well as possibilities for further researches. Some methods could have broader applicability to other inverse problems.
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References
Sanchez J, Benaroya H (2014) Review of force reconstruction techniques. J Sound Vib 333(14):2999
Wu S, Law S (2011) Vehicle axle load identification on bridge deck with irregular road surface profile. Eng Struct 33(2):591
Zheng S, Zhou L, Lian X, Li K (2011) Coherence analysis of the transfer function for dynamic force identification. Mech Syst Signal Process 25(6):2229
Acosta M, Kanarachos S (2018) Tire lateral force estimation and grip potential identification using Neural Networks. Ext Kalman Filter Recurs Least Squares Neu Comput Appl 30(11):3445
Trivailo P, Carn C (2006) The inverse determination of aerodynamic loading from structural response data using neural networks. Inv Prob Sci Eng 14(4):379
Nakamura T, Igawa H, Kanda A (2012) Inverse identification of continuously distributed loads using strain data. Aerosp Sci Technol 23(1):75
Ertveldt J, Pintelon R, Vanlanduit S (2016) Identification of unsteady aerodynamic forces from forced motion wind tunnel experiments, AIAA Journal pp. 3265–3273
Maes K, Van Nimmen K, Gillijns S, Lombaert G (2017) Validation of time-delayed recursive force identification in structural dynamics. Procedia Eng 199:2154
Amiri AK, Bucher C (2017) A procedure for in situ wind load reconstruction from structural response only based on field testing data. J Wind Eng Ind Aerodyn 167:75
Li Y, Luo Y, Wan HP, Yun CB, Shen Y (2020) Identification of earthquake ground motion based on limited acceleration measurements of structure using Kalman filtering technique. Struct Cont Health Monit 27(1):e2464
Hollkamp JJ, Gordon RW (2008) Reduced-order models for nonlinear response prediction: implicit condensation and expansion. J Sound Vib 318(4–5):1139
He Z, Zhang Z, Li E (2019) Multi-source random excitation identification for stochastic structures based on matrix perturbation and modified regularization method. Mech Syst Signal Process 119:266
Hwang Js, Kareem A, Kim Wj (2009) Estimation of modal loads using structural response. J Sound Vib 326(3–5):522
Lai T, Yi TH, Li HN (2016) Parametric study on sequential deconvolution for force identification. J Sound Vib 377:76
Bartlett F, Flannelly W (1979) Model verification of force determination for measuring vibratory loads. J Am Helicopter Soc 24(2):10
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction. Springer Science & Business Media
Dobson B, Rider E (1990) A review of the indirect calculation of excitation forces from measured structural response data. Proc Instit Mech Eng Part C: Mech Eng Sci 204(2):69
Hillary B, Ewins D (1984) The use of strain gauges in force determination and frequency response function measurements In: Proceedings of IMAC
Turco E (2005) A strategy to identify exciting forces acting on structures. Int J Numer Meth Eng 64(11):1483
Qiu B, Zhang M, Li X, Qu X, Tong F (2020) Unknown impact force localisation and reconstruction in experimental plate structure using time-series analysis and pattern recognition. Int J Mech Sci 166:105231
Holzdeppe D, Öry H (1988) Reconstruction of instationary wind load distribution on structures from measured structural response time histories. J Wind Eng Ind Aerodyn 28(1–3):231
Hollandsworth P, Busby H (1989) Reconstruction of instationary wind load distribution on structures from measured structural response time histories. Int J Impact Eng 8(4):315
Inoue H, Harrigan JJ, Reid SR (2001) Review of inverse analysis for indirect measurement of impact force. Appl Mech Rev 54(6):503
Liu J, Sun X, Han X, Jiang C, Yu D (2015) Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method. Mech Syst Signal Process 56:35
Lage Y, Maia N, Neves M, Ribeiro A (2013) Force identification using the concept of displacement transmissibility. J Sound Vib 332(7):1674
Inoue H, Ikeda N, Kishimoto K, Shibuya T, Koizumi T (1995) Inverse analysis of the magnitude and direction of impact force. JSME Int J Ser A, Mech Mat Eng 38(1):84
Uhl T (2007) The inverse identification problem and its technical application. Arch Appl Mech 77(5):325
Wei Y, Xie P, Zhang L (2016) Tikhonov regularization and randomized GSVD. SIAM J Matrix Analy Appl 37(2):649
Chen Z, Qin L, Zhao S, Chan TH, Nguyen A (2019) Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification. Adv Struct Eng 22(12):2687
Wensong J, Zhongyu W, Jing L (2018) A fractional-order accumulative regularization filter for force reconstruction. Mech Syst Signal Process 101:405
Wang L, Liu J, Lu ZR (2020) Bandlimited force identification based on sinc-dictionaries and Tikhonov regularization. J Sound Vib 464:114988
Wang L, Han X, Xie Y (2013) A new conjugate gradient method for solving multi-source dynamic load identification problem. Int J Mech Mater Des 9(3):191
Chen Z, Chan TH, Nguyen A (2018) Moving force identification based on modified preconditioned conjugate gradient method. J Sound Vib 423:100
Li Z, Feng Z, Chu F (2014) A load identification method based on wavelet multi-resolution analysis. J Sound Vib 333(2):381
Park Y, Reichel L, Rodriguez G, Yu X (2018) Parameter determination for Tikhonov regularization problems in general form. J Comput Appl Math 343:12
Chen Z, Chan TH (2017) A truncated generalized singular value decomposition algorithm for moving force identification with ill-posed problems. J Sound Vib 401:297
Aucejo M, De Smet O (2018) A space-frequency multiplicative regularization for force reconstruction problems. Mech Syst Signal Process 104:1
Aucejo M, De Smet O, De JF (2019) On a space-time regularization for force reconstruction problems. Mech Syst Signal Process 118:549
Wang L, Liu Y (2020) A novel method of distributed dynamic load identification for aircraft structure considering multi-source uncertainties, Structural and Multidisciplinary Optimization pp. 1–24
Liu J, Meng X, Xu C, Zhang D, Jiang C (2018) Forward and inverse structural uncertainty propagations under stochastic variables with arbitrary probability distributions. Comput Methods Appl Mech Eng 342:287
Liu J, Han X, Jiang C, Ning H, Bai Y (2011) Dynamic load identification for uncertain structures based on interval analysis and regularization method. Int J Comput Methods 8(04):667
Vigsø M, Brincker R, Georgakis C (2019) Evaluating the Effect of Modelling Errors in Load Identification Using Classical Identification Methods, Shock and Vibration 2019
Zhang E, Antoni J, Feissel P (2012) Bayesian force reconstruction with an uncertain model. J Sound Vib 331(4):798
Aucejo M, De Smet O (2018) On a full Bayesian inference for force reconstruction problems. Mech Syst Signal Process 104:36
Lourens E, Reynders E, De Roeck G, Degrande G, Lombaert G (2012) An augmented Kalman filter for force identification in structural dynamics. Mech Syst Signal Process 27:446
Azam SE, Chatzi E, Papadimitriou C (2015) A dual Kalman filter approach for state estimation via output-only acceleration measurements. Mech Syst Signal Process 60:866
Jang T, Baek H, Han S, Kinoshita T (2010) Indirect measurement of the impulsive load to a nonlinear system from dynamic responses: inverse problem formulation. Mech Syst Signal Process 24(6):1665
Jang T, Baek H, Choi HS, Lee SG (2011) A new method for measuring nonharmonic periodic excitation forces in nonlinear damped systems. Mech Syst Signal Process 25(6):2219
Jang T (2013) A method for simultaneous identification of the full nonlinear damping and the phase shift and amplitude of the external harmonic excitation in a forced nonlinear oscillator. Comput Struct 120:77
Lei Y, Wu Y, Li T (2012) Identification of non-linear structural parameters under limited input and output measurements. Int J Non-Linear Mech 47(10):1141
Ma CK, Ho CC (2004) An inverse method for the estimation of input forces acting on non-linear structural systems. J Sound Vib 275(3–5):953
Guo L, Ding Y, Wang Z, Xu G, Wu B (2018) A dynamic load estimation method for nonlinear structures with unscented Kalman filter. Mech Syst Signal Process 101:254
Lourens E, Papadimitriou C, Gillijns S, Reynders E, De Roeck G, Lombaert G (2012) Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors. Mech Syst Signal Process 29:310
Cao X, Sugiyama Y, Mitsui Y (1998) Application of artificial neural networks to load identification. Comput Struct 69(1):63
Staszewski WJ, Worden K, Wardle R, Tomlinson GR (2000) Fail-safe sensor distributions for impact detection in composite materials. Smart Mater Struct 9(3):298
Qiu B, Zhang M, Xie Y, Qu X, Li X (2019) Localisation of unknown impact loads on a steel plate using a pattern recognition method combined with the similarity metric via structural stress responses in the time domain. Mech Syst Signal Process 128:429
Prawin J, Rao ARM (2018) An online input force time history reconstruction algorithm using dynamic principal component analysis. Mech Syst Signal Process 99:516
Ghajari M, Sharif-Khodaei Z, Aliabadi M, Apicella A (2013) Identification of impact force for smart composite stiffened panels. Smart Mater Struct 22(8):085014
Bangji Z, Shouyu Z, Qingxi X, Nong Z (2017) Load identification of virtual iteration based on Tikhonov regularization and model reduction, Hong Kong Load identification of virtual iteration based on Tikhonov regularization and model reduction. J Soc Sci 44(2)
Kay SM (1993) Fundamentals of statistical signal processing. Prentice Hall PTR
Body CY (2014) Load identifcation for BEV based on power spectrum decomposition under road excitation, SAE Technical Paper 2014-01-2044. https://doi.org/10.4271/2014-01-2044
Meriam JL, Kraige LG (2012) Engineering mechanics: dynamics, vol 2. Wiley
Williams Jr JH (2019) Fundamentals of applied dynamics . MIT Press
Lu Z, Law S (2007) Identification of system parameters and input force from output only. Mech Syst Signal Process 21(5):2099
Strang G, Introduction to linear algebra, vol. 3 Wellesley, MA: Wellesley-Cambridge Press
Hildebrand FB (1987) Introduction to numerical analysis. Courier Corporation
Jia Y, Yang Z, Guo N, Wang L (2015) Random dynamic load identification based on error analysis and weighted total least squares method. J Sound Vib 358:111
Jia Y, Yang Z, Song Q (2015) Experimental study of random dynamic loads identification based on weighted regularization method. J Sound Vib 342:113
Casella G, Berger RL (2002) Statistical inference, vol 2. Duxbury Pacific Grove, CA
Lehmann EL, Casella G (2006) Theory of point estimation. Springer Science & Business Media
Anderson T (2003) An introduction to multivariate statistical analysis. Wiley, New York
Lin J, Zhang Y, Zhao Y (2011) Pseudo excitation method and some recent developments. Proc Eng 14:2453
Lin J, Guo X, Zhi H, Howson WP, Williams FW (2001) Computer simulation of structural random loading identification. Comput Struct 79(4):375
Bühlmann P, Van De Geer S (2011) Statistics for high-dimensional data: methods, theory and applications. Springer Science & Business Media
Newland D (2013) Mechanical Vibration Analysis and Computation. Courier Corporation
Benaroya H, Nagurka M, Han S (2017) Mechanical vibration: analysis, uncertainties, and control. CRC Press
Den Hartog JP (1985) Mechanical vibrations. Courier Corporation
Lalanne C (2002) Mechanical vibration & shock. Wiley Online Library
Law SS, Bu JQ, Zhu X (2005) Time-varying wind load identification from structural responses. Eng Struct 27(10):1586
Callier FM, Desoer CA (2012) Linear system theory. Springer Science & Business Media
Baake SU (2011) Michael, The Peano-Baker series. Proc Steklov Instit Math 275:155–159. https://doi.org/10.1134/S0081543811080098
Dacunha JJ (2005) Transition matrix and generalized matrix exponential via the Peano-Baker series. J Diff Equ Appl 11(15):1245
Liu J, Sun X, Han X, Jiang C, Yu D (2014) A novel computational inverse technique for load identification using the shape function method of moving least square fitting. Comput Struct 144:127
Anil BM, Chopra K (2005) Dynamics of Structures, Pearson Education India
Meirovitch L (1986) Elements of vibration analysis. McGraw-Hill
Allison TC, Miller AK, Inman DJ (2008) A deconvolution-based approach to structural dynamics system identification and response prediction. J vibration and acoustics 130(3)
Liu J, Meng X, Jiang C, Han X, Zhang D (2016) Time-domain Galerkin method for dynamic load identification. Int J Numer Meth Eng 105(8):620
Wang T, Wan Z, Wang X, Hu Y (2015) A novel state space method for force identification based on the Galerkin weak formulation. Comput Struct 157:132
Liu J, Li B (2018) A novel strategy for response and force reconstruction under impact excitation. J Mech Sci Technol 32(8):3581
Li X, Zhao H, Chen Z, Wang Q, Chen Ja, Duan D (2018) Force identification based on a comprehensive approach combining Taylor formula and acceleration transmissibility. Inverse Problems in Science and Engineering 26(11):1612
Lai T, Yi TH, Li HN, Fu X (2017) An explicit fourth-order Runge-Kutta method for dynamic force identification. Int J Struct Stab Dyn 17(10):1750120
Li Q, Lu Q (2018) A hierarchical Bayesian method for vibration-based time domain force reconstruction problems. J Sound Vib 421:190
Jacquelin E, Bennani A, Hamelin P (2003) Force reconstruction: analysis and regularization of a deconvolution problem. J Sound Vib 265(1):81
Yu L, Chan TH (2003) Moving force identification based on the frequency-time domain method. J Sound Vib 261(2):329
Khoo S, Ismail Z, Kong K, Ong Z, Noroozi S, Chong W, Rahman A (2014) Impact force identification with pseudo-inverse method on a lightweight structure for under-determined, even-determined and over-determined cases. Int J Impact Eng 63:52
Liu J, Meng X, Zhang D, Jiang C, Han X (2017) An efficient method to reduce ill-posedness for structural dynamic load identification. Mech Syst Signal Process 95:273
Zhu T, Xiao Sn, Yang Gw (2014) Force identification in time domain based on dynamic programming. Appl Math Comput 235:226
Aucejo M (2014) Structural source identification using a generalized Tikhonov regularization. J Sound Vib 333(22):5693
Qiao B, Mao Z, Liu J, Zhao Z, Chen X (2019) Group sparse regularization for impact force identification in time domain. J Sound Vib 445:44
Huang C, Wang L, Fu M, Lu ZR, Chen Y (2020) A novel iterative integration regularization method for ill-posed inverse problems. Eng Comput pp. 1–21
Wang L, Xu L, Xie Y, Du Y, Han X (2019) A new hybrid conjugate gradient method for dynamic force reconstruction. Adv Mech Eng 11(1):1687814018822360
Strang G, Linear algebra and learning from data, Wellesley-Cambridge Press
Hansen PC (1990) Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM J Sci Stat Comput 11(3):503
Hansen PC (2005) Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion, vol 4. Siam
Xu P (1998) Truncated SVD methods for discrete linear ill-posed problems. Geophys J Int 135(2):505
He Z, Lin X, Li E (2019) A non-contact acoustic pressure-based method for load identification in acoustic-structural interaction system with non-probabilistic uncertainty. Appl Acoust 148:223
Reichel L, Sadok H (2008) A new L-curve for ill-posed problems. J Comput Appl Math 219(2):493
Hansen PC, Mosegaard K (1996) Piecewise polynomial solutions without a priori break points. Num Linear Algebra With Applications 3(6):513
Hansen PC (1989) Regularization GSVD and truncatedGSVD. BIT Num Math 29(3):491
Dykes L, Reichel L (2014) Simplified GSVD computations for the solution of linear discrete ill-posed problems. J Comput Appl Math 255:15
Gunawan FE (2012) Levenberg-Marquardt iterative regularization for the pulse-type impact-force reconstruction. J Sound Vib 331(25):5424
Nordberg TP, Gustafsson I (2006) Using QR factorization and SVD to solve input estimation problems in structural dynamics. Comput Methods Appl Mech Eng 195(44–47):5891
Morigi S, Reichel L, Sgallari F (2006) A truncated projected SVD method for linear discrete ill-posed problems. Num Algor 43(3):197
Kilmer ME, Hansen PC, Espanol MI (2007) A projection-based approach to general-form Tikhonov regularization. SIAM J Sci Comput 29(1):315
González A, Rowley C, OBrien EJ (2008) A general solution to the identification of moving vehicle forces on a bridge. Int J Numer Meth Eng 75(3):335
Noschese S, Reichel L (2016) Some matrix nearness problems suggested by Tikhonov regularization. Linear Algebra Appl 502:366
Aucejo M, De Smet O (2017) A multiplicative regularization for force reconstruction. Mech Syst Signal Process 85:730
Mao Y, Guo X, Zhao Y (2010) A state space force identification method based on Markov parameters precise computation and regularization technique. J Sound Vib 329(15):3008
Nikolova M (2004) A variational approach to remove outliers and impulse noise. J Math Imaging Vision 20(1–2):99
Aucejo M, De Smet O (2016) Bayesian source identification using local priors. Mech Syst Signal Process 66:120
Hochstenbach ME, Reichel L, Rodriguez G (2015) Regularization parameter determination for discrete ill-posed problems. J Comput Appl Math 273:132
Hansen PC, Jensen TK, Rodriguez G (2007) An adaptive pruning algorithm for the discrete L-curve criterion. J Comput Appl Math 198(2):483
Reichel L, Rodriguez G (2013) Old and new parameter choice rules for discrete ill-posed problems. Num Algor 63(1):65
Hansen PC (2007) Regularization tools version 4.0 for Matlab 7.3. Numerical algorithms 46(2):189
Liu Y, Shepard WS Jr (2005) Dynamic force identification based on enhanced least squares and total least-squares schemes in the frequency domain. J Sound Vib 282(1–2):37
Antoni J (2012) A Bayesian approach to sound source reconstruction: optimal basis, regularization, and focusing. J Acoustical Soc Am 131(4):2873
He Z, Zhang Z, Li E (2020) Random dynamic load identification for stochastic structural-acoustic system using an adaptive regularization parameter and evidence theory, Journal of Sound and Vibration p. 115188
Wang L, Liu J, Xie Y, Gu Y (2018) A new regularization method for the dynamic load identification of stochastic structure. Comput Math Appl 76(4):741
Wang L, Cao H, Xie Y (2015) An improved iterative Tikhonov regularization method for solving the dynamic load identification problem. Int J Comput Methods Eng Sci Mech 16(5):292
Wang L, Xie Y, Wu Z, Du Y, He K (2019) A new fast convergent iteration regularization method. Eng Comput 35(1):127
Qiao B, Liu J, Liu J, Yang Z, Chen X (2019) An enhanced sparse regularization method for impact force identification. Mech Syst Signal Process 126:341
Donoho DL (2006) For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Commun Pure Appl Math A J Issued Courant Instit Math Sci 59(6):797
Koh K, Kim SJ, Boyd S (2007) An interior-point method for large-scale l1-regularized logistic regression. J Machine Learn Res 8(Jul):1519
Qiao B, Zhang X, Gao J, Liu R, Chen X (2017) Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction. Mech Syst Signal Process 83:93
Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math A J Issued by the Courant Instit Mathem Sci 57(11):1413
Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183
Qiao B, Zhang X, Gao J, Chen X (2016) Impact-force sparse reconstruction from highly incomplete and inaccurate measurements. J Sound Vib 376:72
Pan CD, Yu L, Liu HL, Chen ZP, Luo WF (2018) Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization. Mech Syst Signal Process 98:32
Bruckstein AM, Donoho DL, Elad M (2009) From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review 51(1):34
Tropp JA, Wright SJ (2010) Computational methods for sparse solution of linear inverse problems. Proc IEEE 98(6):948
Figueiredo MA, Nowak RD, Wright SJ (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Selected Top Signal Proces 1(4):586
Qiao B, Zhang X, Wang C, Zhang H, Chen X (2016) Sparse regularization for force identification using dictionaries. J Sound Vib 368:71
Wright SJ, Nowak RD, Figueiredo MA (2009) Sparse reconstruction by separable approximation. IEEE Trans Signal Process 57(7):2479
Rezayat A, Nassiri V, De Pauw B, Ertveldt J, Vanlanduit S, Guillaume P (2016) Identification of dynamic forces using group-sparsity in frequency domain. Mech Syst Signal Process 70:756
Wambacq J, Maes K, Rezayat A, Guillaume P, Lombaert G (2019) Localization of dynamic forces on structures with an interior point method using group sparsity. Mech Syst Signal Process 115:593
Chang X, Yan Y, Wu Y (2019) Study on solving the ill-posed problem of force load reconstruction. J Sound Vib 440:186
Lu Z, Chen X (2018) Generalized conjugate gradient methods for l1 regularized convex quadratic programming with finite convergence. Math Operat Res 43(1):275
Wei Z, Yao S, Liu L (2006) The convergence properties of some new conjugate gradient methods. Appl Math Comput 183(2):1341
Wang L, Cao H, Han X, Liu J, Xie Y (2015) An efficient conjugate gradient method and application to dynamic force reconstruction. J comput Sci 8:101
Samagassi S, Khamlichi A, Driouach A, Jacquelin E (2015) Reconstruction of multiple impact forces by wavelet relevance vector machine approach. J Sound Vib 359:56
Tran H, Inoue H (2018) Impact force reconstruction using wavelet deconvolution technique. ASEAN Eng. J. 8(1):53
Gunawan FE, Homma H, Kanto Y (2006) Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction. J Sound Vib 297(1–2):200
Qiao B, Chen X, Xue X, Luo X, Liu R (2015) The application of cubic B-spline collocation method in impact force identification. Mech Syst Signal Process 64:413
Hu N, Fukunaga H, Matsumoto S, Yan B, Peng X (2007) An efficient approach for identifying impact force using embedded piezoelectric sensors. Int J Impact Eng 34(7):1258
Sun R, Chen G, He H, Zhang B (2014) The impact force identification of composite stiffened panels under material uncertainty. Finite Elem Anal Des 81:38
Yan G, Zhou L (2009) Impact load identification of composite structure using genetic algorithms. J Sound Vib 319(3–5):869
Zhou J, Dong L, Guan W, Yan J (2019) Impact load identification of nonlinear structures using deep Recurrent Neural Network. Mech Syst Signal Process 133:106292
Lu K, Jin Y, Chen Y, Yang Y, Hou L, Zhang Z, Li Z, Fu C (2019) Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. Mech Syst Signal Process 123:264
Pan C, Yu L (2019) Identification of external forces via truncated response sparse decomposition under unknown initial conditions. Adv Struct Eng 22(15):3161
Zhou K, Zhang S, Huang Z, Zhang J (2019) An improved TSVD-GCV inversion algorithm of pore size distribution in time-domain induced polarization using migration Hankel matrix. J Petrol Sci Eng 183:106368
Cheng W, Hu Q, Li D (2019) A fast conjugate gradient algorithm with active set prediction for l1 optimization. Optim Meth Software 34(6):1277
Wipf D, Nagarajan S (2010) Iterative reweighted l1 and l2 methods for finding sparse solutions. IEEE J Select Topics Signal Proces 4(2):317
Liu J, Sun X, Li K, Jiang C, Han X (2015) A probability density function discretization and approximation method for the dynamic load identification of stochastic structures. J Sound Vib 357:74
Wang L, Liu Y, Liu Y (2019) An inverse method for distributed dynamic load identification of structures with interval uncertainties. Adv Eng Softw 131:77
Liu J, Sun X, Meng X, Li K, Zeng G, Wang X (2016) A novel shape function approach of dynamic load identification for the structures with interval uncertainty. Int J Mech Mater Des 12(3):375
Xu M, Huang J, Wang C, Li Y (2020) Fuzzy identification of dynamic loads in presence of structural epistemic uncertainties. Comput Methods Appl Mech Eng 360:112718
Zhang FL, Ni YC, Au SK, Lam HF (2016) Fast Bayesian approach for modal identification using free vibration data. Part I-Most probable value, Mech Syst Signal Proces 70:209
Ni YC, Zhang FL, Lam HF, Au SK (2016) Fast Bayesian approach for modal identification using free vibration data, Part II-Posterior uncertainty and application. Mech Syst Signal Process 70:221
Sun X, Liu J, Ding F, Wang X (2014) Identification method of dynamic loads for stochastic structures based on matrix perturbation theory. J Mech Eng 50(13):148
Zhang G, Song M, Liu M (2015) Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations. Appl Math Comput 258:12
Xu M, Du J, Wang C, Li Y, Chen J (2019) A dual-layer dimension-wise fuzzy finite element method (DwFFEM) for the structural-acoustic analysis with epistemic uncertainties. Mech Syst Signal Process 128:617
Faure C, Ablitzer F, Antoni J, Pezerat C (2017) Empirical and fully Bayesian approaches for the identification of vibration sources from transverse displacement measurements. Mech Syst Signal Process 94:180
Aucejo M, De Smet O (2019) An optimal Bayesian regularization for force reconstruction problems. Mech Syst Signal Process 126:98
Nadarajah S (2005) A generalized normal distribution. J Appl Statisti 32(7):685
Li Q, Lu Q (2019) A revised time domain force identification method based on Bayesian formulation. Int J Numer Meth Eng 118(7):411
Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2013) Bayesian data analysis. CRC Press
Møller J (2013) Spatial statistics and computational methods, vol 173. Springer Science & Business Media
Brooks S, Gelman A, Jones G, Meng XL (2011) Handbook of markov chain monte carlo. CRC Press
Ching J, Beck JL, Porter KA (2006) Bayesian state and parameter estimation of uncertain dynamical systems. Probab Eng Mech 21(1):81
Liu JJ, Ma CK, Kung IC, Lin DC (2000) Input force estimation of a cantilever plate by using a system identification technique. Comput Methods Appl Mech Eng 190(11–12):1309
Cumbo R, Tamarozzi T, Janssens K, Desmet W (2019) Kalman-based load identification and full-field estimation analysis on industrial test case. Mech Syst Signal Process 117:771
Risaliti E, Van Cauteren J, Tamarozzi T, Cornelis B, Desmet W (2016) In international conference on noise and vibration engineering (ISMA2016). Belgium, Leuven
Azam SE, Chatzi E, Papadimitriou C, Smyth A (2017) Experimental validation of the Kalman-type filters for online and real-time state and input estimation. J Vib Control 23(15):2494
Naets F, Cuadrado J, Desmet W (2015) Stable force identification in structural dynamics using Kalman filtering and dummy-measurements. Mech Syst Signal Process 50:235
Hanke M, Neubauer A, Scherzer O (1995) A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer Math 72(1):21
Li L, Han B, Wang W (2007) RK type Landweber method for nonlinear ill-posed problems. J Comput Appl Math 206(1):341
Wang W, Han B (2009) An implicit Landweber method for nonlinear ill-posed operator equations. J Comput Appl Math 230(2):607
Yang JN, Lin S (2004) On-line identification of non-linear hysteretic structures using an adaptive tracking technique. Int J Non-Linear Mech 39(9):1481
Wu M, Smyth A (2008) Real-time parameter estimation for degrading and pinching hysteretic models. Int J Non-Linear Mech 43(9):822
Chatzi EN, Smyth AW (2008) The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing. Struct Cont Health Monit 16(1):99
Radhika B, Manohar C (2013) Dynamic state estimation for identifying earthquake support motions in instrumented structures. Earthquakes Struct 5(3):359
Ching J, Beck JL, Porter KA, Shaikhutdinov R (2006) Bayesian state estimation method for nonlinear systems and its application to recorded seismic response. J Eng Mech 132(4):396
Han J, Pei J, Kamber M (2011) Data mining: concepts and techniques. Elsevier
Lee D, Ahn TS, Kim HS (2018) A metric on the similarity between two frequency response functions. J Sound Vib 436:32. https://doi.org/10.1016/j.jsv.2018.08.051
Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289
Candès EJ (2008) The restricted isometry property and its implications for compressed sensing. CR Math 346(9):589. https://doi.org/10.1016/j.crma.2008.03.014
Haykin S (2010) Neural networks and learning machines. Pearson Education India
Wang J, Wang C, Lai X (2015) MIMO SVM based uncorrelated multi-source dynamic random load identification algorithm in frequency domain. J Comput Inform Syst 11(22):8165
Kozukue W, Hagiwara I, Miyaji H (2007) Input load identification using a holographic neural network. Int J Veh Des 43(1–4):173
Liu R, Hou Z, Wang S, Sheng D (2020) Dynamic bolt load identification for battery pack based on machine learning, Dynamic bolt load identification for battery pack based on machine learning. Tech. rep., SAE Technical Paper 2020-01-0865
Platt JC (1998) Sequential minimal optimization: A fast algorithm for training support vector machines
Alpaydin E (2020) Introduction to machine learning MIT press.
Bishop CM (2006) Pattern recognition and machine learning (information science and statistics). Springer-Verlag, New York Inc
Roseiro L, Alcobia C, Ferreira P, Baïri A, Laraqi N, Alilat N (2013) Identification of the forces in the suspension system of a race car using artificial neural networks, In: Computational Intelligence and Decision Making (Springer), pp. 469–477
Yann L, Yoshua B, Geoffrey H (2015) Deep learning. Nature 521:436–444. https://doi.org/10.1038/nature14539
Sekuła K, Cezary G, Jan HS (2013) On-line impact load identification. Shock and Vibration 20:123
Zhang C, Xu Y (2016) Optimal multi-type sensor placement for response and excitation reconstruction. J Sound Vib 360:112
Gupta DK, Dhingra AK (2013) Input load identification from optimally placed strain gages using D-optimal design and model reduction. Mech Syst Signal Process 40(2):556
Wang J, Law SS, Yang QS (2013) Sensor placement methods for an improved force identification in state space. Mech Syst Signal Process 41(s 1–2):254–267
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The authors gratefully acknowledge the support of National Natural Science foundation of China (Grant No. 51975312).
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Liu, R., Dobriban, E., Hou, Z. et al. Dynamic Load Identification for Mechanical Systems: A Review. Arch Computat Methods Eng 29, 831–863 (2022). https://doi.org/10.1007/s11831-021-09594-7
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DOI: https://doi.org/10.1007/s11831-021-09594-7