[1] Zimoch Z. Sensitivity analysis of vibrating systems. Journal of Sound & Vibration, 1987, 115(3): 447-58.
[2] Chang, K.C., Kim, et al. Modal-parameter identification and vibration-based damage detection of a damaged steel truss bridge. Engineering Structures, 2016, 122: 156-173.
[3] Farahani R.V., Penumadu D. Damage identification of a full-scale five-girder bridge using time-series analysis of vibration data. Engineering Structures, 2016, 115: 129-39.
[4] Yan Y.J., Cheng L., Wu Z.Y., et al. Development in Vibration-Based Structural Damage Detection Technique. Mechanical Systems & Signal Processing, 2007, 21(5): 2198-211.
[5] Li B., Li Z., Zhou J., et al. Damage localization in composite lattice truss core sandwich structures based on vibration characteristics. Composite Structures, 2015, 126: 34–51.
[6] Dawari V.B., Kamble P.P., Vesmawala G.R. Structural Damage Identification Using Modal Strain Energy Method. Advances in Structural Engineering, 2015, 2599-607.
[7] Shi Z.Y., Law S.S., Zhang L.M. Structural Damage Detection from Modal Strain Energy Change. American Society of Civil Engineers, 2014, 126(12): 1216-23.
[8] Kim J.T., Stubbs N. Crack detection in beam-type structures using frequency data. Journal of Sound & Vibration, 2003, 259(1): 145-60.
[9] Döhler M., Hille F., Mevel L., et al. Structural health monitoring with statistical methods during progressive damage test of S101 Bridge. Engineering Structures, 2014, 69(9): 183-93.
[10] Dutta A., Talukdar S. Damage detection in bridges using accurate modal parameters. Finite Elements in Analysis & Design, 2004, 40(3): 287-304.
[11] Hu C., Afzal M.T. A statistical algorithm for comparing mode shapes of vibration testing before and after damage in timbers. Journal of Wood Science, 2006, 52(4): 348-52.
[12] Wu S., Zhou J., Rui S., et al. Reformulation of elemental modal strain energy method based on strain modes for structural damage detection. Advances in Structural Engineering, 2016, 20(6): 896-905.
[13] Frans R., Arfiadi Y., Parung H. Comparative study of mode shapes curvature and damage locating vector methods for damage detection of structures. Procedia Engineering, 2017, 171: 1263-71.
[14] Ding Q., Zou C., Tang Y., et al. Damage Detection in Roads and Bridges Based on Modal Strain Energy Method. Proceedings of the International Conference on Transportation Engineering, 2013: 1753-1758.
[15] Kahl K., Sirkis J.S. Damage detection in beam structures using subspace rotation algorithm with strain data. AIAA Journal, 2015, 34(12): 2609-14.
[16] Abdel Wahab M.M., De Roeck G. Damage Detection in Bridges Using Modal Curvatures: Application to a Real Damage Scenario. Journal of Sound & Vibration, 1999, 226(2): 217-35.
[17] Liang Y.C., Hwu C. On-line identification of holes/cracks in composite structures. Smart Materials & Structures, 2001, 10(4): 599.
[18] Ndambi J.M., Vantomme J., Harri K. Damage assessment in reinforced concrete beams using eigenfrequencies and mode shape derivatives. Engineering Structures, 2002, 24(4): 501-15.
[19] Swamidas A.S.J., Chen Y. Monitoring crack growth through change of modal parameters. Journal of Sound and Vibration, 1995, 186(2): 325-43.
[20] Dackermann U., Smith W.A., Randall R.B. Damage identification based on response-only measurements using cepstrum analysis and artificial neural networks. Structural Health Monitoring, 2014, 13(4): 430-444.
[21] Liu Y.Y., Ju Y.F., Duan C.D., et al. Structure damage diagnosis using neural network and feature fusion. Engineering Applications of Artificial Intelligence, 2011, 24(1): 87-92.
[22] Li Z., Park H.S., Adeli H. New method for modal identification of super high‐rise building structures using discretized synchrosqueezed wavelet and Hilbert transforms. The Structural Design of Tall and Special Buildings, 2017, 26(3): 1-16.
[23] Gomes G.F., Chaves J.A.S., Almeida F.A.D. An inverse damage location problem applied to AS-350 rotor blades using bat optimization algorithm and multiaxial vibration data. Mechanical Systems and Signal Processing, 2020, 145: 106932.
[24] Gomes G.F., Pereira J.V.P. Sensor placement optimization and damage identification in a fuselage structure using inverse modal problem and firefly algorithm. Evolutionary Intelligence, 2020, 13: 571–591.
[25] Ferreira G.G., Alves D.A.F., Simes D.C.S., et al. An estimate of the location of multiple delaminations on aeronautical CFRP plates using modal data inverse problem. International Journal of Advanced Manufacturing Technology, 2018, 99: 1155–1174.
[26] Zhong K., Teng S., Liu G., et al. Structural Damage Features Extracted by Convolutional Neural Networks from Mode Shapes. Applied Sciences, 2020, 10(12): 4247.
[27] Teng S., Chen G., Gong P., et al. Structural damage detection using convolutional neural networks combining strain energy and dynamic response. Meccanica, 2020, 55: 945–959.
[28] Doebling S.W., Farrar C.R., Prime M.B. A Summary Review of Vibration-Based Damage Identification Methods. Shock & Vibration Digest, 1998, 30(2): 91-105.
[29] Saltelli A., Chan K., Scott E.M. Sensitivity Analysis. John Wiley and Sons, New York, 2000.
[30] Aloisio A., Battista L.D., Alaggio R., et al. Sensitivity analysis of subspace-based damage indicators under changes in ambient excitation covariance, severity and location of damage. Engineering Structures, 2020, 208: 110235.
[31] Morassi A., Vestroni F. Dynamic methods for damage detection in structures. Lectures of the CISM Course, 2008.
[32] Stubbs N., Kim J.T. Damage localization in structures without baseline modal parameters. AIAA Journal, 2012, 34(8): 1644-9.
[33] Nelson R.B. Simplified calculation of eigenvector derivatives. AIAA Journal, 1976, 14(9): 1201-5.
[34] Lee I., Jung G. An efficient algebraic method for the computation of natural frequency and mode shape sensitivities—Part I. Distinct natural frequencies. Computers & Structures, 1997, 62(3): 429-435
[35] Lee I.-W., Jung G.-H. An efficient algebraic method for the computation of natural frequency and mode shape sensitivities—Part II. Multiple natural frequencies. Computers & Structures, 1997, 62(3): 437-43.
[36] Friswell M.I., Adhikari S. Derivatives of complex eigenvectors using Nelson's method. AIAA Journal, 2000, 38: 2355-2357.
[37] Adhikari S. Rates of Change of Eigenvalues and Eigenvectors in Damped Dynamic System. AIAA Journal, 1999, 37(11): 1452-8.
[38] Chen G., Gong P.P., Liang P. Sensitivity analyses of resonant frequencies and modal strain energy of damaged beams by perturbation method. Journal of Vibroengineering, 2019, 21(1): 40-51.
[39] Li L., Hu Y., Wang X., et al. Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues. Finite Elements in Analysis & Design, 2013, 72: 21-34.
[40] Li L., Hu Y., Wang X. Numerical methods for evaluating the sensitivity of element modal strain energy. Finite Elements in Analysis & Design, 2013, 64: 13-23.
[41] He J., Fu Z.-F. Modal analysis. Oxford, Boston: Butterworth-Heinemann, 2001.
[42] Guan H., Karbhari V.M. Improved damage detection method based on Element Modal Strain Damage Index using sparse measurement. Journal of Sound & Vibration, 2008, 309(3-5): 465-94.