Nonlinear system identification in structural dynamics: 10 more years of progress

[en] Nonlinear system identification is a vast research field, today attracting a great deal of attention in the structural dynamics community. Ten years ago, in an MSSP paper reviewing the progress achieved until then, it was concluded that the identification of simple continuous structures with localised nonlinearities was within reach. The past decade witnessed a shift in emphasis, accommodating the growing industrial need for a first generation of tools capable of addressing complex nonlinearities in larger-scale structures. The objective of the present paper is to survey the key developments which arose in the field since 2006, and to illustrate state-of-the-art techniques using a real-world satellite structure. Finally, a broader perspective to nonlinear system identification is provided by discussing the central role played by experimental models in the design cycle of engineering structures.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Noël, Jean-Philippe ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Kerschen, Gaëtan ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Nonlinear system identification in structural dynamics: 10 more years of progress

Publication date :

2017

Journal title :

Mechanical Systems and Signal Processing

ISSN :

0888-3270

eISSN :

1096-1216

Publisher :

Academic Press, London, United Kingdom

Volume :

Pages :

2-35

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 23 September 2016

Statistics

Number of views

159 (25 by ULiège)

Number of downloads

8 (5 by ULiège)

More statistics

Scopus citations^®

454

Scopus citations^®
without self-citations

437

OpenCitations

274

OpenAlex citations

443

Bibliography

[1] Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C., Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20 (2006), 505–592.
[2] Boechler, N., Theocharis, G., Daraio, C., Bifurcation-based acoustic switching and rectification. Nat. Mater. 10 (2011), 665–668.
[3] Antonio, D., Zanette, D.H., Lopez, D., Frequency stabilization in nonlinear micromechanical oscillators. Nat. Commun., 3, 2012, 806.
[4] Strachan, B.S., Shaw, S.W., Kogan, O., Subharmonic resonance cascades in a class of coupled resonators. J. Comput. Nonlinear Dyn., 8(4), 2013, 041015.
[5] Oueini, S., Neyfeh, A., Analysis and application of a nonlinear vibration absorber. J. Vib. Control 6 (2000), 999–1016.
[6] Vyas, A., Bajaj, A.K., Dynamics of autoparametric vibration absorbers using multiple pendulums. J. Sound Vib. 246 (2001), 115–135.
[7] Vakakis, A.F., Gendelman, O., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S., Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. 2008, Springer.
[8] Quinn, D.D., Triplett, A.L., Vakakis, A.F., Bergman, L.A., Energy harvesting from impulsive loads using intentional essential nonlinearities. J. Vib. Acoust., 133, 2011, 011004.
[9] Green, P.L., Worden, K., Atallah, K., Sims, N.D., The benefits of Duffing-type nonlinearities and electrical optimisation of a mono-stable energy harvester under white Gaussian excitations. J. Sound Vib. 331 (2012), 4504–4517.
[10] Karami, A., Inman, D.J., Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesting. Appl. Phys. Lett., 100, 2012, 042901.
[11] Ewins, D.J., Weekes, B., Delli Carri, A., Modal testing for model validation of structures with discrete nonlinearities. Philos. Trans. R. Soc. A, 373, 2015, 20140410.
[12] K. Carney, I. Yunis, K. Smith, C.Y. Peng, Nonlinear dynamic behavior in the Cassini spacecraft modal survey, in: Proceedings of the 15th International Modal Analysis Conference (IMAC), Orlando, FL, 1997.
[13] J.R. Ahlquist, J.M. Carreño, H. Climent, R. de Diego, J. de Alba, Assessment of nonlinear structural response in A400M GVT, in: Proceedings of the 28th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2010.
[14] D.E. Adams, R.J. Allemang, Survey of nonlinear detection and identification techniques for experimental vibrations structural dynamic model through feedback, in: Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 1998.
[15] K. Worden, Nonlinearity in structural dynamics: the last ten years, in: Proceedings of the European COST F3 Conference on System Identification and Structural Health Monitoring, Madrid, Spain, 2000.
[16] Worden, K., Tomlinson, G.R., Nonlinearity in Structural Dynamics: Detection, Identification and Modelling. 2001, Institute of Physics Publishing, Bristol, UK.
[17] P. Lubrina, S. Giclais, C. Stephan, M. Boeswald, Y. Govers, N. Botargues, AIRBUS A350 XWB GVT: State-of-the-art techniques to perform a faster and better GVT campaign, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[18] E. Menga, S. Hernandez, S. Moledo, C. Lopez, Nonlinear dynamic analysis of assembled aircraft structures with concentrated nonlinearities, in: Proceedings of the 16th International Forum on Aeroelasticity and Structural Dynamics (IFASD), Saint Petersburg, Russia, 2015.
[19] High Level Group on Aviation Research, ACARE Flightath 2050 – Europe's vision for aviation 〈 http://www.acare4europe.com/sites/acare4europe.org/files/document/Flightpath2050_Final.pdf〉, Visited on 1 October 2015.
[20] D. Di Maio, A. delli Carri, F. Magi, I.A. Sever, Detection of nonlinear behaviour of composite components before and after endurance trials, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[21] D. Di Maio, P. Bennett, C. Schwingshackl, D.J. Ewins, Experimental non-linear modal testing of an aircraft engine casing assembly, in: Proceedings of the 31st International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2013.
[22] M. Boeswald, M. Link, C. Schedlinksi, Computational model updating and validation of aero-engine finite element models based on vibration test data, in: Proceedings of the 11th International Forum on Aeroelasticity and Structural Dynamics (IFASD), Munich, Germany, 2005.
[23] Noël, J.P., Renson, L., Kerschen, G., Complex dynamics of a nonlinear aerospace structure: experimental identification and modal interactions. J. Sound Vib. 333 (2014), 2588–2607.
[24] M. Link, M. Boeswald, S. Laborde, M. Weiland, A. Calvi, An approach to non-linear experimental modal analysis, in: Proceedings of the 28th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2010.
[25] Carrella, A., Ewins, D.J., Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions. Mech. Syst. Signal Process. 25 (2011), 1011–1027.
[26] N.E. Wierschem, S.A. Hubbard, J. Luo, L.A. Fahnestock, B.F. Spencer, D.D. Quinn, D.M. McFarland, A.F. Vakakis, L.A. Bergman, Experimental blast testing of a large 9-story structure equipped with a system of nonlinear energy sinks, in: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Portland, OR, USA, 2013.
[27] Nayfeh, A.H., Mook, D.T., Nonlinear Oscillations. 1979, John Wiley & Sons, New York, NY, USA.
[28] Guckenheimer, J., Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. 1983, Springer-Verlag, New York, NY, USA.
[29] Kuznetsov, Y.A., Elements of Applied Bifurcation Theory. 2004, Springer-Verlag, New York, NY, USA.
[30] Sharma, S., Coetzee, E., Lowenberg, M., Neild, S.A., Krauskopf, B., Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective. Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci., 373, 2015, 20140406.
[31] Gatti, G., Uncovering inner detached resonance curves in coupled oscillators with nonlinearity. J. Sound Vib. 372 (2016), 239–254.
[32] Rosenberg, R.M., The normal modes of nonlinear n-degree-of-freedom systems. J. Appl. Mech. 29 (1962), 7–14.
[33] Vakakis, A.F., Manevitch, L.I., Mikhlin, Y.V., Pilipchuk, V.N., Zevin, A.A., Normal Modes and Localization in Nonlinear Systems. 1996, John Wiley & Sons, New York, NY.
[34] Shaw, S.W., Pierre, C., Normal modes for non-linear vibratory systems. J. Sound Vib. 164:1 (1993), 85–124.
[35] Dhooge, A., Govaerts, W., Kuznetsov, Y.A., MATCONT: A Matlab package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29:2 (2003), 141–164.
[36] E. Doedel, AUTO, Software for Continuation and Bifurcation Problems in Ordinary Differential Equations 〈 http://indy.cs.concordia.ca/auto, Visited on 1 October 2015.
[37] Karkar, S., Cochelin, B., Vergez, C., A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems. J. Sound Vib. 333:12 (2014), 2554–2567.
[38] Laxalde, D., Thouverez, F., Complex non-linear modal analysis of mechanical systems: application to turbomachinery bladings with friction interfaces. J. Sound Vib. 322 (2009), 1009–1025.
[39] Schilder, F., Vogt, W., Schreiber, S., Osinga, H.M., Fourier methods for quasi-periodic oscillations. Int. J. Numer. Methods Eng. 67 (2006), 629–671.
[40] Eason, R.P., Dick, A.J., A parallelized multi-degrees-of-freedom cell mapping method. Nonlinear Dyn. 77 (2014), 467–479.
[41] Belardinelli, P., Lenci, S., A first parallel programming approach in basins of attraction computation. Automatica 80 (2016), 76–81.
[42] Detroux, T., Renson, L., Masset, L., Kerschen, G., The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput. Methods Appl. Mech. Eng. 296 (2015), 18–38.
[43] M.S. Allen, R.J. Kuether, Substructuring with nonlinear subcomponents: a nonlinear normal mode perspective, in: Proceedings of the 30th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2012.
[44] F. Wenneker, P. Tiso, A substructuring method for geometrically nonlinear structures, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[45] D.A. Ehrhardt, M.S. Allen, T.J. Beberniss, Measurement of nonlinear normal modes using mono-harmonic force appropriation: experimental investigation, in: Proceedings of the 33rd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2015.
[46] Cusumano, J.P., Kimble, B.W., A stochastic interrogation method for experimental measurements of global dynamics and basin evolution: application to a two-well oscillator. Nonlinear Dyn. 8 (1995), 213–235.
[47] Waite, J.J., Virgin, L.N., Wiebe, R., Competing responses in a discrete mechanical system. Int. J. Bifurc. Chaos, 24(1), 2014, 1430003.
[48] Wiebe, R., Virgin, L.N., Spottswood, S.M., Stochastic interrogation of competing responses in a nonlinear distributed system. Nonlinear Dyn. 79:1 (2010), 607–615.
[49] Bureau, E., Schilder, F., Elmegard, M., Santos, I.F., Thomsen, J.J., Starke, J., Experimental bifurcation analysis of an impact oscillator – determining stability. J. Sound Vib. 333:21 (2014), 5464–5474.
[50] Beck, J.L., Katafygiotis, L.S., Updating models and their uncertainties. I: Bayesian statistical framework. J. Eng. Mech. 124 (1998), 455–461.
[51] Muto, M., Beck, J.L., Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J. Vib. Control 14:1–2 (2008), 7–34.
[52] Namdeo, V., Manohar, C.S., Nonlinear structural dynamical system identification using adaptive particle filters. J. Sound Vib. 306 (2007), 524–563.
[53] Green, P.L., Worden, K., Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty. Philos. Trans. R. Soc. A, 373, 2015, 2051.
[54] Ebrahimian, H., Astroza, R., Conte, J.P., Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method. Earthq. Eng. Struct. Dyn. 44 (2015), 1495–1522.
[55] Kerschen, G., Golinval, J.C., Hemez, F.M., Bayesian model screening for the identification of nonlinear mechanical structures. J. Vib. Acoust. 125 (2003), 389–397.
[56] Ritto, T.G., Soize, C., Sampaio, R., Probabilistic model identification of the bit-rock-interaction-model uncertainties in nonlinear dynamics of a drill-string. Mech. Res. Commun. 37:6 (2010), 584–589.
[57] Y. Ben-Haim, S. Cogan, Linear bounds on an uncertain non-linear oscillator: an info-gap approach, in: Proceedings of the IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties, Saint Petersburg, Russia, 2009.
[58] Pintelon, R., Schoukens, J., System Identification: A Frequency Domain Approach. 2001, IEEE Press, Piscataway, NJ, USA.
[59] Ewins, D.J., Modal Testing: Theory, Practice and Application. 2000, Research Studies Press, Baldock, UK.
[60] Maia, N.M.M., Silva, J.M.M., Theoretical and Experimental Modal Analysis. 1997, Research Studies Press, Baldock, UK.
[61] Ljung, L., System Identification – Theory for the User. 1999, Prentice Hall, Upper Saddle River, NY, USA.
[62] A. Calvi, N. Roy, Spacecraft Mechanical Loads Analysis Handbook, ESA Requirements and Standards Division, Noordwijk, The Netherlands, 2013.
[63] Schoukens, J., Vaes, M., Pintelon, R., Linear system identification in a nonlinear setting: nonparametric analysis of the nonlinear distortions and their impact on the best linear approximation. IEEE Control Syst. 36:3 (2016), 38–69.
[64] Zhang, E., Antoni, J., Pintelon, R., Schoukens, J., Fast detection of system nonlinearity using nonstationary signals. Mech. Syst. Signal Process. 24 (2010), 2065–2075.
[65] Widanage, W.D., Stoev, J., Van Mulders, A., Schoukens, J., Pinte, G., Nonlinear system identification of the filling phase of a wet-clutch system. Control Eng. Pract. 19 (2011), 1506–1516.
[66] M. Vaes, J. Schoukens, B. Peeters, J. Debille, T. Dossogne, J.P. Noël, G. Kerschen, Nonlinear ground vibration identification of an F-16 aircraft. Part I: fast nonparametric analysis of distortions in FRF measurements, in: Proceedings of the 16th International Forum on Aeroelasticity and Structural Dynamics (IFASD), Saint Petersburg, Russia, 2015.
[67] Grange, P., Clair, D., Baillet, L., Fogli, M., Brake squeal analysis by coupling spectral linearization and modal identification methods. Mech. Syst. Signal Process. 23 (2009), 2575–2589.
[68] M.B. Özer, H.N. Özgüven, A new method for localization and identification of non-linearities in structures, in: Proceedings of the 6th ASME Biennial Conference on Engineering Systems Design and Analysis (ESDA), Istanbul, Turkey, 2002.
[69] Özer, M.B., Özgüven, H.N., Royston, T.J., Identification of structural non-linearities using describing functions and the Sherman–Morrison method. Mech. Syst. Signal Process. 23 (2009), 30–44.
[70] Aykan, M., Özgüven, H.N., Parametric identification of nonlinearity in structural systems using describing function inversion. Mech. Syst. Signal Process. 40 (2013), 356–376.
[71] Wang, X., Zheng, G.T., Equivalent Dynamic Stiffness Mapping technique for identifying nonlinear structural elements from frequency response functions. Mech. Syst. Signal Process. 68–69 (2016), 394–415.
[72] Sracic, M.W., Allen, M.S., Method for identifying models of nonlinear systems using linear time periodic approximations. Mech. Syst. Signal Process. 25 (2011), 2705–2721.
[73] Sracic, M.W., Allen, M.S., Identifying parameters of multi-degree-of-freedom nonlinear structural dynamic systems using linear time periodic approximations. Mech. Syst. Signal Process. 46 (2014), 325–343.
[74] Moaveni, B., Asgarieh, E., Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems. Mech. Syst. Signal Process. 31 (2012), 40–55.
[75] Chen, Q., Worden, K., Peng, P., Leung, A.Y.T., Genetic algorithm with an improved fitness function for (N)ARX modelling. Mech. Syst. Signal Process. 21 (2007), 994–1007.
[76] Peng, Z.K., Lang, Z.Q., Wolters, C., Billings, S.A., Worden, K., Feasibility study of structural damage detection using NARMAX modelling and Nonlinear Output Frequency Response Function based analysis. Mech. Syst. Signal Process. 25 (2011), 1045–1061.
[77] K. Worden, R.J. Barthorpe, Identification of hysteretic systems using NARX models, part I: evolutionary identification, in: Proceedings of the 30th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2012.
[78] K. Worden, R.J. Barthorpe, Identification of hysteretic systems using NARX models, part 2: a Bayesian approach, in: Proceedings of the 30th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2012.
[79] Masri, S.F., Caughey, T.K., A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46 (1979), 433–447.
[80] T. Dossogne, J.P. Noël, C. Grappasonni, G. Kerschen, B. Peeters, J. Debille, M. Vaes, J. Schoukens, Nonlinear ground vibration identification of an F-16 aircraft. Part II: understanding nonlinear behaviour in aerospace structures using sine-sweep testing, in: Proceedings of the 16th International Forum on Aeroelasticity and Structural Dynamics (IFASD), Saint Petersburg, Russia, 2015.
[81] Saad, P., Al Majid, A., Thouverez, F., Dufour, R., Equivalent rheological and restoring force models for predicting the harmonic response of elastomer specimens. J. Sound Vib. 290 (2006), 619–639.
[82] Bonisoli, E., Vigliani, A., Identification techniques applied to a passive elasto-magnetic suspension. Mech. Syst. Signal Process. 21 (2007), 1479–1488.
[83] Rizos, D., Feltrin, G., Motavalli, M., Structural identification of a prototype pre-stressable leaf-spring based adaptive tuned mass damper: nonlinear characterization and classification. Mech. Syst. Signal Process. 25 (2011), 205–221.
[84] Goege, D., Sinapius, J.M., Experiences with dynamic load simulation by means of modal forces in the presence of structural non-linearities. Aerosp. Sci. Technol. 10 (2006), 411–419.
[85] Allen, M.S., Sumali, H., Epp, D.S., Piecewise-linear restoring force surfaces for semi-nonparametric identification of nonlinear systems. Nonlinear Dyn. 54 (2008), 123–155.
[86] Worden, K., Hickey, D., Haroon, M., Adams, D.E., Nonlinear system identification of automotive dampers: a time and frequency-domain analysis. Mech. Syst. Signal Process. 23 (2009), 104–126.
[87] Ceravolo, R., Erlicher, S., Zanotti Fragonara, L., Comparison of restoring force models for the identification of structures with hysteresis and degradation. J. Sound Vib. 332 (2013), 6982–6999.
[88] Xu, B., He, J., Dyke, S.J., Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: approach and validation. Nonlinear Dyn. 82:3 (2015), 1507–1522.
[89] Ahmadian, H., Jalali, H., Pourahmadian, F., Nonlinear model identification of a frictional contact support. Mech. Syst. Signal Process. 24 (2010), 2844–2854.
[90] Tasbihgoo, F., Caffrey, J.P., Masri, S.F., Development of data-based model-free representation of non-conservative dissipative systems. Int. J. Non-linear Mech. 42 (2007), 99–117.
[91] Wang, J., Wierschem, N., Spencer, B.F. Jr., Lu, X., Experimental study of track nonlinear energy sinks for dynamic response reduction. Eng. Struct. 94 (2015), 9–15.
[92] Lacy, S.L., Bernstein, D.S., Subspace identification for non-linear systems with measured-input non-linearities. Int. J. Control 78 (2005), 906–926.
[93] Marchesiello, S., Garibaldi, L., A time domain approach for identifying nonlinear vibrating structures by subspace methods. Mech. Syst. Signal Process. 22 (2008), 81–101.
[94] Van Overschee, P., De Moor, B., Subspace Identification for Linear Systems: Theory, Implementation and Applications. 1996, Kluwer Academic Publishers, Dordrecht, The Netherlands.
[95] Adams, D.E., Allemang, R.J., A new derivation of the frequency response function matrix for vibrating non-linear systems. J. Sound Vib. 227 (1999), 1083–1108.
[96] Adams, D.E., Allemang, R.J., A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback. Mech. Syst. Signal Process. 14 (2000), 637–656.
[97] Richards, C.M., Singh, R., Identification of multi-degree-of-freedom non-linear systems under random excitations by the “reverse path” spectral method. J. Sound Vib. 213 (1998), 673–708.
[98] Marchesiello, S., Garibaldi, L., Identification of clearance-type nonlinearities. Mech. Syst. Signal Process. 22 (2008), 1133–1145.
[99] Noël, J.P., Marchesiello, S., Kerschen, G., Subspace-based identification of a nonlinear spacecraft in the time and frequency domains. Mech. Syst. Signal Process. 43 (2014), 217–236.
[100] Marchesiello, S., Fasana, A., Garibaldi, L., Modal contributions and effects of spurious poles in nonlinear subspace identification. Mech. Syst. Signal Process. 74 (2016), 111–132.
[101] Haroon, M., Adams, D.E., A modified H2 algorithm for improved frequency response function and nonlinear parameter estimation. J. Sound Vib. 320 (2009), 822–837.
[102] Spottswood, S.M., Allemang, R.J., Identification of nonlinear parameters for reduced order models. J. Sound Vib. 295 (2006), 226–245.
[103] Magnevall, M., Josefsson, A., Ahlin, K., Broman, G., Nonlinear structural identification by the “Reverse Path” spectral method. J. Sound Vib. 331 (2012), 938–946.
[104] Josefsson, A., Magnevall, M., Ahlin, K., Broman, G., Spatial location identification of structural nonlinearities from random data. Mech. Syst. Signal Process. 27 (2012), 410–418.
[105] A. delli Carri, B. Weekes, D. Di Maio, D.J. Ewins, Extending modal testing technology for model validation of engineering structures with sparse nonlinearities: a first case study, Mech. Syst. Signal Process., in press.
[106] Narayanan, M.D., Narayanan, S., Padmanabhan, C., Multiharmonic excitation for nonlinear system identification. J. Sound Vib. 311 (2008), 707–728.
[107] Narayanan, M.D., Narayanan, S., Padmanabhan, C., Parametric identification of nonlinear systems using multiple trials. Nonlinear Dyn. 48 (2007), 341–360.
[108] Schetzen, M., The Volterra and Wiener Theories of Nonlinear Systems. 1980, John Wiley & Sons, New York, NY, USA.
[109] da Silva, S., Cogan, S., Foltête, E., Nonlinear identification in structural dynamics based on Wiener series and Kautz filters. Mech. Syst. Signal Process. 24 (2010), 52–58.
[110] Chatterjee, A., Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions. J. Sound Vib. 329 (2010), 3325–3334.
[111] Lang, Z.Q., Billings, S.A., Energy transfer properties of non-linear systems in the frequency domain. Int. J. Control 78 (2005), 345–362.
[112] Peng, Z.K., Lang, Z.Q., Billings, S.A., Non-linear output frequency response functions of mdof systems with multiple non-linear components. Int. J. Non-linear Mech. 42 (2007), 941–958.
[113] Peng, Z.K., Lang, Z.Q., Billings, S.A., Linear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency-response functions. Mech. Syst. Signal Process. 21 (2007), 3108–3122.
[114] Peng, Z.K., Lang, Z.Q., Billings, S.A., Nonlinear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency-response functions. Mech. Syst. Signal Process. 22 (2008), 1582–1594.
[115] Vazquez Feijoo, J.A., Worden, K., Montes Garcia, P., Lagunez Rivera, L., Juarez Rodriguez, N., Pech P'erez, A., Analysis of mdof nonlinear systems using associated linear equations. Mech. Syst. Signal Process. 24 (2010), 2824–2843.
[116] Vazquez Feijoo, J.A., Worden, K., Stanway, R., System identification using associated linear equations. Mech. Syst. Signal Process. 18 (2004), 431–455.
[117] Noël, J.P., Kerschen, G., Frequency-domain subspace identification for nonlinear mechanical systems. Mech. Syst. Signal Process. 40 (2013), 701–717.
[118] McKelvey, T., Akcay, H., Ljung, L., Subspace-based multivariable system identification from frequency response data. IEEE Trans. Autom. Control 41:7 (1996), 960–979.
[119] Van Overschee, P., De Moor, B., Continuous-time frequency domain subspace system identification. Signal Process. 52:7 (1996), 179–194.
[120] A. delli Carri, D.J. Ewins, Nonlinear identification of a numerical benchmark structure: from measurements to FE model updating, in: Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 2014.
[121] Noël, J.P., Kerschen, G., Foltête, E., Cogan, S., Grey-box identification of a nonlinear solar array structure using cubic splines. Int. J. Non-linear Mech. 67 (2014), 106–119.
[122] R. Porwal, N.S. Vyas, Nonlinear damping estimation of self-excited system using wavelet transform, in: Proceedings of the 27th International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2009.
[123] Heller, L., Foltête, E., Piranda, J., Experimental identification of nonlinear dynamics properties of built-up structures. J. Sound Vib. 327 (2009), 183–196.
[124] Demarie, G.V., Ceravolo, R., Sabia, D., Argoul, P., Experimental identification of beams with localized nonlinearities. J. Vib. Control 17 (2011), 1721–1732.
[125] Feldman, M., Hilbert Transform Applications in Mechanical Vibration. 2011, John Wiley & Sons, Chichester, UK.
[126] Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454 (1998), 903–995.
[127] Feldman, M., Time-varying vibration decomposition and analysis based on the Hilbert transform. J. Sound Vib. 295 (2006), 518–530.
[128] Feldman, M., Considering high harmonics for identification of non-linear system by Hilbert transform. Mech. Syst. Signal Process. 21 (2007), 943–958.
[129] Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M., Bergman, L.A., Toward a fundamental understanding of the Hilbert–Huang transform in nonlinear dynamics. J. Vib. Control 14 (2008), 77–105.
[130] Lee, Y.S., Tsakirtzis, S., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Physics-based foundation for empirical model decomposition: correspondence between intrinsic mode functions and slow flows. AIAA J. 47 (2009), 2938–2963.
[131] Pai, P.F., Palazotto, A.N., Detection and identification of nonlinearities by amplitude and frequency modulation analysis. Mech. Syst. Signal Process. 22 (2008), 1107–1132.
[132] Feldman, M., Identification of weakly nonlinearities in multiple coupled oscillators. J. Sound Vib. 303 (2007), 357–370.
[133] Gendelman, O.V., Starosvetsky, Y., Feldman, M., Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: description of response regimes. Nonlinear Dyn. 51 (2008), 31–46.
[134] M. Bertha, J.C. Golinval, Identification of a time-varying beam using Hilbert Vibration Decomposition, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[135] Feldman, M., Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems. Mech. Syst. Signal Process. 47 (2014), 66–77.
[136] Braun, S., Feldman, M., Decomposition of non-stationary signals into varying time scales: some aspects of the EMD and HVD methods. Mech. Syst. Signal Process. 25:7 (2011), 2608–2630.
[137] Y. Huang, C.J. Yan, Q. Xu, On the difference between empirical mode decomposition and Hilbert vibration decomposition for earthquake motion records, in: Proceedings of the 15th World Conference of Earthquake Engineering (WCEE), Lisbon, Portugal, 2012.
[138] D.J. Ewins, A future for experimental structural dynamics, in: Proceedings of the International Conference on Noise and Vibration Engineering (ISMA), Leuven, Belgium, 2006.
[139] Renson, L., Kerschen, G., Cochelin, B., Numerical computation of nonlinear normal modes in mechanical engineering. J. Sound Vib. 364 (2016), 177–206.
[140] Carrella, A., Nonlinear identifications using transmissibility: dynamic characterisation of Anti Vibration Mounts (AVMs) with standard approach. Int. J. Mech. Sci. 63 (2012), 74–85.
[141] J.R. Wright, M.F. Platten, J.E. Cooper, M. Sarmast, Identification of multi-degree-of-freedom weakly non-linear systems using a model based in modal space, in: Proceedings of the International Conference on Structural System Identification, Kassel, Germany, 2001.
[142] Z. Yang, G. Dimitriadis, G.A. Vio, J.E. Cooper, J.R. Wright, Identification of structural free-play non-linearities using the non-linear resonant decay method, in: Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 2006.
[143] Platten, M.F., Wright, J.R., Dimitriadis, G., Cooper, J.E., Identification of multi-degree of freedom non-linear system using an extended modal space model. Mech. Syst. Signal Process. 23 (2009), 8–29.
[144] Platten, M.F., Wright, J.R., Cooper, J.E., Dimitriadis, G., Identification of a nonlinear wing structure using an extended modal model. AIAA J. Aircr. 46:5 (2009), 1614–1626.
[145] J.M. Londono, J.E. Cooper, Experimental identification of a system containing geometric nonlinearities, in: Proceedings of the 32th International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[146] Fuellekrug, U., Goege, D., Identification of weak non-linearities within complex aerospace structures. Aerosp. Sci. Technol. 23 (2012), 53–62.
[147] Wright, J.R., Cooper, J.E., Desforges, M., Normal mode force appropriation – theory and application. Mech. Syst. Signal Process. 13 (1999), 217–240.
[148] Peeters, M., Kerschen, G., Golinval, J.C., Dynamic testing of nonlinear vibrating structures using nonlinear normal modes. J. Sound Vib. 330 (2011), 486–509.
[149] Peeters, M., Kerschen, G., Golinval, J.C., Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech. Syst. Signal Process. 25 (2011), 1227–1247.
[150] Zapico-Valle, J.L., Garcia-Dieguez, M., Alonso-Camblor, R., Nonlinear modal identification of a steel frame. Eng. Struct. 56 (2013), 246–259.
[151] D.A. Ehrhardt, R.B. Harris, M.S. Allen, Numerical and experimental determination of nonlinear normal modes of a circular perforated plate, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[152] Ehrhardt, D.A., Allen, M.S., Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay. Mech. Syst. Signal Process. 76–77 (2016), 612–633.
[153] Londono, J.M., Neild, S.A., Cooper, J.E., Identification of backbone curves of nonlinear systems from resonance decay responses. J. Sound Vib. 348 (2015), 224–238.
[154] Renson, L., Gonzalez-Buelga, A., Barton, D.A.W., Neild, S.A., Robust identification of backbone curves using control-based continuation. J. Sound Vib. 367 (2016), 145–158.
[155] Stephan, C., Festjens, H., Renaud, F., Dion, J.L., Poles tracking of weakly nonlinear structures using a Bayesian smoothing method. Mech. Syst. Signal Process., 2015 in press.
[156] Hill, T.L., Cammarano, A., Neild, S.A., Wagg, D.J., Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. J. Sound Vib. 349 (2015), 276–288.
[157] S. Peter, R. Riethmüller, R.I. Leine, Tracking of backbone curves of nonlinear systems using Phase‐Locked‐Loops, in: Proceedings of the 34th International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2016.
[158] Ahmadian, H., Zamani, A., Identification of nonlinear boundary effects using nonlinear normal modes. Mech. Syst. Signal Process. 23 (2009), 2008–2018.
[159] Giannini, O., Casini, P., Vestroni, F., Nonlinear harmonic identification of breathing crack in beams. Comput. Struct. 129 (2013), 166–177.
[160] Rébillat, M., Hajrya, R., Mechbal, N., Nonlinear structural damage detection based on cascade of Hammerstein models. Mech. Syst. Signal Process. 62–63 (2015), 129–148.
[161] Bovsunovsky, A., Surace, C., Non-linearities in the vibrations of elastic structures with a closing crack: a state of the art review. Mech. Syst. Signal Process. 62–63 (2015), 129–148.
[162] Noël, J.P., Renson, L., Grappasonni, C., Kerschen, G., Identification of nonlinear normal modes of engineering structures under broadband forcing. Mech. Syst. Signal Process. 74 (2016), 95–110.
[163] Peeters, B., Van der Auweraer, H., Guillaume, P., Leuridan, J., The PolyMAX frequency-domain method: a new standard for modal parameter estimation?. Shock Vib. 11:3–4 (2004), 395–409.
[164] Lee, Y.S., Tsakirtzis, S., Vakakis, A.F., Bergman, L.A., McFarland, D.M., A time-domain nonlinear system identification method based on multiscale dynamic partitions. Meccanica 46 (2011), 625–649.
[165] Lee, Y.S., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Non-linear system identification of the dynamics of aeroelastic instability suppression based on targeted energy transfers. Aeronaut. J. 114 (2010), 61–82.
[166] Eriten, M., Kurt, M., Luo, G., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Nonlinear system identification of frictional effects in a beam with a bolted joint connection. Mech. Syst. Signal Process. 39 (2013), 245–264.
[167] Chen, H., Kurt, M., Lee, Y.S., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection. Mech. Syst. Signal Process. 46 (2014), 91–113.
[168] Poon, C.W., Chang, C.C., Identification of nonlinear elastic structures using empirical mode decomposition and nonlinear normal modes. Smart Struct. Syst. 3 (2007), 423–437.
[169] M.W. Sracic, M.S. Allen, H. Sumali, Identifying the modal properties of nonlinear structures using measured free response time histories from scanning laser Doppler vibrometer, in: Proceedings of the 30th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2012.
[170] Pai, P.F., Time–frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems. Mech. Syst. Signal Process. 25 (2011), 2358–2374.
[171] Bellizzi, S., Sampaio, R., The Smooth Decomposition as a nonlinear modal analysis tool. Mech. Syst. Signal Process. 64-65 (2015), 245–256.
[172] Clement, S., Bellizzi, S., Cochelin, B., Ricciardi, G., Sliding window proper orthogonal decomposition: application to linear and nonlinear modal identification. J. Sound Vib. 333 (2014), 5312–5323.
[173] K. Worden, P.L. Green, A machine learning approach to nonlinear modal analysis, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[174] Worden, K., Wong, C.X., Parlitz, U., Hornstein, A., Engster, D., Tjahjowidodo, T., Al-Bender, F., Rizos, D.D., Fassois, S.D., Identification of per-sliding and sliding friction dynamics: grey box and black-box models. Mech. Syst. Signal Process. 21 (2007), 514–534.
[175] Worden, K., Staszewski, W.J., Hensman, J.J., Natural computing for mechanical systems research: a tutorial overview. Mech. Syst. Signal Process. 25 (2011), 4–111.
[176] Rouss, V., Charon, W., Cirrincione, G., Neural model of the dynamic behaviour of a non-linear mechanical systems. Mech. Syst. Signal Process. 23 (2009), 1145–1159.
[177] dos Santos Coelho, L., Pessoa, M.W., Nonlinear identification using a B-spline neural network and chaotic immune approaches. Mech. Syst. Signal Process. 23 (2009), 2418–2434.
[178] Pei, J., Mai, E.C., Wright, J.P., Masri, S.F., Mapping some basic functions and operations to multilayer feedforward neural networks for modeling nonlinear dynamical systems and beyond. Nonlinear Dyn. 71 (2013), 371–399.
[179] Pei, J., Masri, S.F., Demonstration and validation of constructive initialization method for neural networks to approximate nonlinear functions in engineering mechanics applications. Nonlinear Dyn. 79 (2015), 2099–2119.
[180] Witters, M., Swevers, J., Black-box model identification for a continuously variable, electro-hydraulic semi-active damper. Mech. Syst. Signal Process. 24 (2010), 4–18.
[181] Metered, H., Bonello, P., Oyadiji, S.O., The experimental identification of magnetorheological dampers and evaluation of their controllers. Mech. Syst. Signal Process. 24 (2010), 976–994.
[182] Ayala, H.V.H., dos Santos Coelho, L., Cascaded evolutionary algorithm for nonlinear system identification based on correlation functions and radial basis functions neural networks. Mech. Syst. Signal Process. 68-69 (2016), 378–393.
[183] Tavakolpour-Saleh, A.R., Nasib, S.A.R., Sepaqyan, A., Hashemi, S.M., Parametric and nonparametric system identification of an experimental turbojet engine. Aerosp. Sci. Technol. 43 (2015), 21–29.
[184] Paduart, J., Lauwers, L., Swevers, J., Smolders, K., Schoukens, J., Pintelon, R., Identification of nonlinear systems using Polynomial Nonlinear State Space models. Automatica 46 (2010), 647–656.
[185] R. Relan, L. Vanbeylen, Y. Firouz, J. Schoukens, Characterization and nonlinear modelling of Li-Ion battery, in: Proceedings of the 34th Benelux Meeting on Systems and Control, Lommel, Belgium, 2015.
[186] Dreesen, P., Ishteva, M., Schoukens, J., Decoupling multivariate polynomials using first-order information and tensor decompositions. SIAM J. Matrix Anal. Appl. 36:2 (2015), 864–879.
[187] Meyer, S., Link, M., Modelling and updating of local non-linearities using frequency response residuals. Mech. Syst. Signal Process. 17 (2003), 219–226.
[188] Isasa, I., Hot, A., Cogan, S., Sadoulet-Reboul, E., Model updating of locally non-linear systems based on multi-harmonic extended constitutive relation error. Mech. Syst. Signal Process. 25 (2011), 2413–2425.
[189] S. da Silva, S. Cogan, E. Foltête, F. Buffe, Metrics for non-linear model updating in mechanical systems, in: Proceedings of the 26th International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2008.
[190] Claeys, M., Sinou, J.J., Lambelin, J.P., Alcoverro, B., Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 19 (2014), 4196–4212.
[191] M.W. Sracic, S. Yang, M.S. Allen, Comparing measured and computed nonlinear frequency responses to calibrate nonlinear system models, in: Proceedings of the 30th International Modal Analysis Conference (IMAC), Jacksonville, FL, USA, 2012.
[192] da Silva, S., Non-linear model updating of a three-dimensional portal frame based on Wiener series. Int. J. Non-linear Mech. 46 (2011), 312–320.
[193] Lenaerts, V., Kerschen, G., Golinval, J.C., Proper orthogonal decomposition for model updating of non-linear mechanical systems. Mech. Syst. Signal Process. 15 (2001), 31–43.
[194] Kerschen, G., Golinval, J.C., A model updating strategy of non-linear vibrating structures. Int. J. Numer. Methods Eng. 60 (2004), 2147–2164.
[195] Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Methodology for model updating of mechanical components with local nonlinearities. J. Sound Vib. 357 (2015), 331–348.
[196] S. Peter, A. Grundler, P. Reuss, L. Gaul, R.I. Leine, Towards finite element model updating based on nonlinear normal modes, in: Proceedings of the 33rd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2015.
[197] Song, W., Dyke, S., Harmon, T., Application of nonlinear model updating for a reinforced concrete shear wall. J. Eng. Mech. 139 (2013), 639–649.
[198] Asgarieh, E., Moaveni, B., Stavridis, A., Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake. J. Sound Vib. 333 (2014), 6057–6073.
[199] Schueller, G.I., Jensen, H.A., Computational methods in optimization considering uncertainties – an overview. Comput. Methods Appl. Mech. Eng. 198 (2008), 2–13.
[200] Soize, C., A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics. J. Sound Vib. 288 (2005), 623–652.
[201] Ben-Haim, Y., Info-Gap Theory: Decisions Under Severe Uncertainty. 2006, Academic Press, London, UK.
[202] Beck, J.L., Au, S.K., Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation. J. Eng. Mech. 128 (2002), 380–391.
[203] Ching, J., Chen, Y., Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133 (2007), 816–832.
[204] Yuen, K.V., Beck, J.L., Updating properties of nonlinear dynamical systems with uncertain input. J. Eng. Mech. 129 (2003), 9–20.
[205] Corigliano, A., Mariani, S., Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Comput. Methods Appl. Mech. Eng. 193 (2004), 3807–3835.
[206] Wu, M., Smyth, A.W., Application of the unscented Kalman filter for real-time nonlinear structural system identification. Struct. Control Health Monit. 14 (2007), 971–990.
[207] Ching, J., Beck, J.L., Porter, K.A., Bayesian state and parameter estimation of uncertain dynamical systems. Probab. Eng. Mech. 21 (2006), 81–96.
[208] Ghosh, S., Manohar, C.S., Roy, D., Sequential importance sampling filters with a new proposal distribution for parameter identification of structural systems. Proc. R. Soc. Lond. A 464 (2008), 25–47.
[209] Nasrellah, H.A., Manohar, C.S., Finite element method based Monte Carlo filters for structural system identification. Probab. Eng. Mech. 26 (2011), 294–307.
[210] Chatzi, E.N., Smyth, A.W., The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing. Struct. Control Health Monit. 16 (2008), 99–123.
[211] Becker, W., Oakley, J.E., Surace, C., Gili, P., Rowson, J., Worden, K., Bayesian sensitivity analysis of a nonlinear finite element model. Mech. Syst. Signal Process. 32 (2012), 18–31.
[212] Beck, J.L., Zuev, K.M., Asymptotically independent Markov sampling: a new Markov chain Monte Carlo scheme for Bayesian inference. Int. J. Uncertain. Quantif. 3 (2013), 445–474.
[213] Green, P.L., Bayesian system identification of a nonlinear dynamical system using a novel variant of simulated annealing. Mech. Syst. Signal Process. 52–53 (2015), 133–146.
[214] Green, P.L., Bayesian system identification of a nonlinear dynamical system using a novel variant of simulated annealing. Mech. Syst. Signal Process. 52–53 (2015), 133–146.
[215] Chatzi, E., Smyth, A.W., Masri, S.F., Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty. Struct. Saf. 32 (2010), 326–337.
[216] Behmanesh, I., Moaveni, B., Lombaert, G., Papadimitriou, C., Hierarchical Bayesian model updating for structural identification. Mech. Syst. Signal Process. 64-65 (2015), 360–376.
[217] Hadjidoukas, P.E., Angelikopoulos, P., Papadimitriou, C., Koumoutsakos, P., A high performance computing framework for Bayesian uncertainty quantification of complex models. J. Comput. Phys. 284 (2015), 1–21.
[218] Gloth, G., Sinapsius, M., Analysis of swept-sine runs during modal identification. Mech. Syst. Signal Process. 18 (2004), 1421–1441.
[219] Bampton, M.C.C., Craig, J.R.R., Coupling of substructures for dynamic analyses. AIAA J. 6:7 (1968), 1313–1319.
[220] Renson, L., Noël, J.P., Kerschen, G., Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes. Nonlinear Dyn. 79 (2014), 1293–1309.
[221] Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F., Nonlinear normal modes. Part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23:1 (2009), 170–194.
[222] Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.C., Nonlinear normal modes. Part II: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23:1 (2009), 195–216.
[223] Gatti, G., Brennan, M.J., Kovacic, I., On the interactions of the responses at the resonance frequencies of a nonlinear two degrees-of-freedom system. Physica D 239 (2010), 591–599.
[224] J. Griffin, D.J. Ewins, Workshop on Benchmark Experiments in Contact Mechanics as Applied to Gas Turbine Engines, Technical report, Air Force Office of Scientific Research, 2002.
[225] ASME, Research committee on mechanics of jointed structures 〈 https://community.asme.org/research_committee_mechanics_jointed_structures/w/wiki/3795.activities.aspx, Visited on 1 October 2015.
[226] M.J. Starr, M.R. Brake, D.J. Segalman, L.A. Bergman, D.J. Ewins, in: Proceedings of the Third International Workshop on Jointed Structures, Technical Report, Sandia National Laboratories, 2013.
[227] D.J. Segalman, D.L. Gregory, M.J. Starr, B.R. Resor, M.D. Jew, J.P. Lauffer, N.M. Ames, Handbook on Dynamics of Jointed Structures, Sandia National Laboratories, Albuquerque, NM, USA, 2009.
[228] Gaul, L., Nitsche, R., The role of friction in mechanical joints. Appl. Mech. Rev. 54 (2001), 93–106.
[229] Segalman, D.J., A four-parameter Iwan model for lap-type joints. J. Appl. Mech. 72 (2005), 752–760.
[230] D.J. Segalman, A Modal Approach to Modeling Spatially Distributed Vibration Energy Dissipation, Technical Report, Sandia National Laboratories, 2010.
[231] M.R. Brake, P. Reuss, D.J. Segalman, L. Gaul, Variability and repeatability of jointed structures with frictional interfaces, in: Proceedings of the 32nd International Modal Analysis Conference (IMAC), Orlando, FL, USA, 2014.
[232] Gevers, M., A personal view on the development of system identification: a 30-year journey through an exciting field. IEEE Control Syst. Mag. 26:6 (2006), 93–105.
[233] Rasmussen, C.E., Williams, C.K.I., Gaussian Processes for Machine Learning. 2006, The MIT Press, Cambridge, MA, USA.