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Integration of locating baseline-free nonlinear elements and identifying model-free nonlinear restoring forces in structures

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Abstract

Structural local nonlinearity often occurs when a structure is subject to strong excitation. Therefore, the identification of structural nonlinearity localizations and the characteristics of nonlinear restoring forces is of great significance in ensuring structural safety and reliability. Among the existing nonlinearity identification methods, locating structural nonlinear elements under seismic excitations is still a challenging problem and identifying model-free nonlinear restoring forces requires prior knowledge of nonlinearity position. To overcome these limitations, a novel two-step nonlinearity localization and identification algorithm is proposed in this paper. First, by considering the wavelet energy distribution in the nonlinear element become different from those of other linear elements, relative wavelet entropy which is able to quantify the difference or similarity between two wavelet energy distributions is employed to localize structural nonlinear elements based on the sparsity of structural nonlinearity. In the localization process, structural response data of the baseline linear structure are not required. Then, nonlinear restoring forces from nonlinear elements are regarded as ‘unknown virtual forces’ to the underlying linear structure. The generalized Kalman filter with unknown input, which was recently proposed by the authors, is used to identify the ‘unknown virtual forces’ and reconstruct the characteristics of nonlinear restoring forces without the models of nonlinear restoring forces. The proposed method is verified by numerical simulations of different types of nonlinear elements in different structures. Furthermore, it is tested by locating the MR damper and identifying its model-free nonlinear restoring forces in a laboratory four-story shear-type frame.

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Data availability

Data in this study are available from the corresponding author upon reasonable request.

References

  1. Chang, P.C., Flatau, A., Liu, S.C.: Review paper: health monitoring of civil infrastructure. Struct. Health Monit. 2(3), 257–267 (2003)

    Google Scholar 

  2. Ou, J.P., Li, H.: Structural health monitoring in mainland china: review and future trends. Struct. Health Monit. 9(3), 219–231 (2010)

    Google Scholar 

  3. Chen, H.P., Ni, Y.Q.: Structural Health Monitoring of Large Civil Engineering Structures. Wiley, Hoboken (2018)

    Google Scholar 

  4. Hou, R., Xia, Y.: Review on the new development of vibration-based damage identification for civil engineering structures: 2010–2019. J. Sound Vib. 491, 115741 (2021)

    Google Scholar 

  5. Yang, N., Lei, Y., Li, J., Hao, H., Huang, J.S.: A substructural and wavelet multiresolution approach for identifying time-varying physical parameters by partial measurements. J. Sound Vib. 523, 116737 (2022)

    Google Scholar 

  6. Brewick, P.T., Masri, S.F.: An evaluation of data-driven identification strategies for complex nonlinear dynamic systems. Nonlinear Dyn. 85(2), 1297–1318 (2016)

    MathSciNet  Google Scholar 

  7. Noël, J.P., Kerschen, G.: Nonlinear system identification in structural dynamics: 10 more years of progress. Mech. Syst. Signal Process. 83, 2–35 (2017)

    Google Scholar 

  8. Ying, Z.G., Ni, Y.Q.: A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters. J. Vib. Control 26, 1260–1272 (2019)

    MathSciNet  Google Scholar 

  9. Quaranta, G., Lacarbonara, W., Masri, S.F.: A review on computational intelligence for identification of nonlinear dynamical systems. Nonlinear Dyn. 99(2), 1709–1761 (2020)

    MATH  Google Scholar 

  10. Xu, B., He, J., Masri, S.F.: Data-based model-free hysteretic restoring force and mass identification for dynamic systems. Comput.-Aided Civil Infrastruct. Eng. 30(1), 2–18 (2015)

    Google Scholar 

  11. Li, Y.C., Jiang, R.N., Tapia, J., Wang, S.Q., Sun, W.: Structural damage identification based on short-time temporal coherence using free-vibration response signals. Measurement 151, 107209 (2019)

    Google Scholar 

  12. Liu, G., Mao, Z., Todd, M., Huang, Z.M.: Localization of nonlinear damage using state-space-based predictions under stochastic excitation. Smart Mater. Struct. 23(2), 025036 (2014)

    Google Scholar 

  13. Prawin, J., Rao, A.R.M.: Damage detection in nonlinear systems using an improved describing function approach with limited instrumentation. Nonlinear Dyn. 96, 1447–1470 (2019)

    Google Scholar 

  14. Prawin, J., Rao, A.R.M.: Detection and quantification of non-linear structural behavior using frequency domain methods. Res. Nondestruct. Eval. 31, 69–106 (2019)

    Google Scholar 

  15. Peng, Z., Li, J., Hao, H., Li, C.: Nonlinear structural damage detection using output-only Volterra series model. Struct. Control. Health Monit. 28(9), e2802 (2021)

    Google Scholar 

  16. Kolluri, M.M., Allemang, R.J., Phillips, A.W.: Non-parametric detection and localization of structural nonlinearities using orthogonal projections. Mech. Syst. Signal Process. 123, 455–465 (2019)

    Google Scholar 

  17. Wang, X., Khodaparast, H.H., Shaw, A.D., Friswell, M.I., Zheng, G.T.: Localization of local nonlinearities in structural dynamics using spatially incomplete measured data. Mech. Syst. Signal Process. 99, 364–383 (2018)

    Google Scholar 

  18. Civera, M., Fragonara, L.Z., Surace, C.: A novel approach to damage localization based on bispectral analysis and neural network. Smart Struct. Syst. 20(6), 669–682 (2017)

    Google Scholar 

  19. Li, H., Tao, D.W., Huang, Y., Bao, Y.Q.: A data-driven approach for seismic damage detection of shear-type building structures using the fractal dimension of time-frequency features. Struct. Control. Health Monit. 20(9), 1191–1210 (2012)

    Google Scholar 

  20. Zhang, M.W., Peng, Z.K., Dong, X.J., Zhang, W.M., Meng, G.: Location identification of nonlinearities in MDOF systems through order determination of state-space models. Nonlinear Dyn. 84(3), 1837–1852 (2016)

    MathSciNet  MATH  Google Scholar 

  21. Josefsson, A., Magnevall, M., Ahlin, K., Broman, G.: Spatial location identification of structural nonlinearities from random data. Mech. Syst. Signal Process. 27, 410–418 (2012)

    Google Scholar 

  22. Peng, Z.K., Lang, Z.Q., Chu, F.L., Meng, G.: Locating nonlinear components in periodic structures using nonlinear effects. Struct. Health Monit. 9, 401–411 (2010)

    Google Scholar 

  23. Peng, Z.K., Lang, Z.Q.: Detecting the position of nonlinear component in periodic structures from the system responses to dual sinusoidal excitations. Int. J. Non-Linear Mech. 42, 1074–1083 (2007)

    Google Scholar 

  24. Lang, Z.Q., Park, G., Farrar, C.R., Todd, M.D., Mao, Z., Zhao, L., Worden, K.: Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems. Int. J. Non-Linear Mech. 46(6), 841–853 (2011)

    Google Scholar 

  25. Zhao, X.Y., Lang, Z.Q., Park, G., Farrar, C.R., Todd, M.D., Mao, Z., Worden, K.: A new transmissibility analysis method for detection and location of damage via nonlinear features in MDOF structural systems. IEEE/ASME Trans. Mechatron. 20(4), 1933–1947 (2015)

    Google Scholar 

  26. Ren, W.X., Sun, Z.S.: Structural damage identification by using wavelet entropy. Eng. Struct. 30(10), 2840–2849 (2008)

    Google Scholar 

  27. Ravanfar, S.A., Abdul, R.H., Ismail, Z., Monajemi, H.: An improved method of parameter identification and damage detection in beam structures under flexural vibration using wavelet multi-resolution analysis. Sensors 15(9), 22750–22775 (2015)

    Google Scholar 

  28. Lee, S.G., Yun, G.J., Shang, S.: Reference-free damage detection for truss bridge structures by continuous relative wavelet entropy method. Struct. Health Monit. 13(3), 307–320 (2014)

    Google Scholar 

  29. Ravanfar, S.A., Abdul, R.H., Ismail, Z., Hakim, S.: A hybrid wavelet based-approach and genetic algorithm to detect damage in beam-like structures without baseline data. Exp. Mech. 56(8), 1411–1426 (2016)

    Google Scholar 

  30. Zhou, C., Chase, J.G., Rodgers, G.W.: Efficient hysteresis loop analysis-based damage identification of a reinforced concrete frame structure over multiple events. J. Civ. Struct. Heal. Monit. 7(4), 541–556 (2017)

    Google Scholar 

  31. Xu, B., Zhao, Y., Deng, B.C., Du, Y.B., Wang, C., Ge, H.B.: Nonparametric nonlinear restoring force and excitation identification with Legendre polynomial model and data fusion. Struct. Health Monit. 21, 264–281 (2021)

    Google Scholar 

  32. Li, H., Mao, C.X., Ou, J.P.: Identification of hysteretic dynamic systems by using hybrid extended Kalman filter and wavelet multiresolution analysis with limited observation. J. Eng. Mech. 139(5), 547–558 (2013)

    Google Scholar 

  33. Xu, B., He, J., Shirley, J.D.: Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: approach and validation. Nonlinear Dyn. 82(3), 1507–1522 (2015)

    Google Scholar 

  34. Wang, L., Guo, J., Takewaki, I.: Real-time hysteresis identification in structures based on restoring force reconstruction and Kalman filter. Mech. Syst. Signal Process. 150, 107297 (2021)

    Google Scholar 

  35. Lei, Y., He, M.Y.: Identification of the nonlinear properties of rubber-bearings in base-isolated buildings with limited seismic response data. Sci. China Technol. Sci. 56(5), 1224–1231 (2013)

    Google Scholar 

  36. Liu, L.J., Lei, Y., He, M.Y.: Locating and identifying model-free structural nonlinearities and systems using incomplete measured structural responses. Smart Struct. Syst. 15(2), 409–424 (2015)

    Google Scholar 

  37. Su, H., Yang, X.J., Liu, L.J., Lei, Y.: Identifying nonlinear characteristics of model-free MR dampers in structures with partial response data. Measurement 130, 362–371 (2018)

    Google Scholar 

  38. Yang, X.J., Su, H., Liu, L.J., Lei, Y.: Identification of the nonlinear characteristics of rubber bearings in model-free base-isolated buildings using partial measurements of seismic responses. J. Low Freq. Noise Vib. Control 39(3), 690–703 (2020)

    Google Scholar 

  39. Lei, Y., Yang, X.J., Huang, J.S., Zhang, F.B., Liu, L.J.: Identification of model-free hysteretic forces of magnetorheological dampers embedded in buildings under unknown excitations using incomplete structural responses. Struct. Control. Health Monit. 28(5), e2715 (2021)

    Google Scholar 

  40. Li, J., Law, S.S.: Substructural response reconstruction in wavelet domain. J. Appl. Mech. 78(4), 041010 (2011)

    Google Scholar 

  41. Lei, Y., Zhang, Y.X., Mi, J.N., Liu, W.F., Liu, L.J.: Detecting structural damage under unknown seismic excitation by deep convolutional neural network with wavelet-based transmissibility data. Struct. Health Monit. 20(4), 1583–1596 (2020)

    Google Scholar 

  42. Valikhani, M., Younesian, D.: Bayesian framework for simultaneous input/state estimation in structural and mechanical systems. Struct. Control. Health Monit. 26(9), e2379 (2019)

    Google Scholar 

  43. Markou, A.A., Oliveto, G., Athanasiou, A.: Response simulation of hybrid base isolation systems under earthquake excitation. Soil Dyn. Earthq. Eng. 84, 120–133 (2016)

    Google Scholar 

  44. Xu, Z.D., Zhao, Y.L., Guo, Y.Q., Yang, X.L., Sarwar, W.: Shaking table tests of magnetorheological damped frame to mitigate the response under real-time online control. Smart Mater. Struct. 28(11), 115021 (2019)

    Google Scholar 

  45. Zhao, Y.L., Xu, Z.D.: A hysteretic model considering Stribeck effect for small-scale magnetorheological damper. Smart Mater. Struct. 27(6), 065021 (2018)

    Google Scholar 

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Acknowledgements

The authors also greatly appreciate the kind support from Prof. Zhaodong Xu at Southeast University, China, by providing the MR damper device in the experiment.

Funding

This research is sponsored by the National Natural Science Foundation of China via the key Grant No. 51838006.

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Authors and Affiliations

  1. Department of Civil Engineering, Xiamen University, Xiamen, China

    Ying Lei, Xiongjun Yang, Jianan Mi & Lijun Liu

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  1. Ying Lei
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  2. Xiongjun Yang
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Correspondence to Ying Lei.

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Lei, Y., Yang, X., Mi, J. et al. Integration of locating baseline-free nonlinear elements and identifying model-free nonlinear restoring forces in structures. Nonlinear Dyn 111, 12855–12869 (2023). https://doi.org/10.1007/s11071-023-08536-1

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