An Enhanced Adaptive Chirp Mode Decomposition for Instantaneous Frequency Identification of Time-Varying Structures
Publication: Journal of Aerospace Engineering
Volume 36, Issue 5
Abstract
Adaptive chirp mode decomposition (ACMD) is a novel decomposition algorithm, which can decompose the multicomponent signals and identify its instantaneous frequencies (IFs) simultaneously. It is crucial for ACMD to predefine the decomposition parameter (i.e., the initial IF). However, the nonstationary signals with closely spaced frequency modes or heavy noise render it difficult to preset the initial IF based on the Fourier spectrum. To overcome the difficulty of predefining the initial IF of the ACMD, a tractable version of the ACMD, termed as the enhanced adaptive chirp mode decomposition (EACMD), is proposed in this study. The EACMD adopts an adaptive method based on the maximum entropy power spectrum to automatically determine the initial IF. A simulated dynamic signal is used to evaluate the characteristics and performance of the EACMD. Furthermore, the proposed EACMD is employed to identify the IFs of time-varying structures. The effectiveness of EACMD is illustrated and verified by using a 3-story shear building model and a cable with time-varying tension forces. The results show that the EACMD can overcome the difficulty of predefining the initial IF of the ACMD and is suitable for identifying the IFs of time-varying structures, providing more accurate results than the existing techniques.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant Nos. 52078486 and 51978263), the National Key Research and Development Program of China (Grant No. 2021YFE0105600), the Key Project for Scientific and Technological Cooperation Scheme of Jiangxi Province (Grant Nos. 20212BDH80022 and 20223BBH80002), and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2023ZZTS0154).
References
Auger, F., and P. Flandrin. 1995. “Improving the readability of time-frequency and time-scale representations by the reassignment method.” IEEE Trans. Signal Process. 43 (5): 1068–1089. https://doi.org/10.1109/78.382394.
Chen, G. D., and Z. C. Wang. 2012. “A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components.” Mech. Syst. Signal Process. 28 (Apr): 258–279. https://doi.org/10.1016/j.ymssp.2011.02.002.
Chen, Q., J. Chen, X. Lang, L. Xie, and S. Lu. 2020a. “Detection and diagnosis of oscillations in process control by fast adaptive chirp mode decomposition.” Control Eng. Practice 97 (Apr): 104307. https://doi.org/10.1016/j.conengprac.2020.104307.
Chen, S., X. Dong, Z. Peng, W. Zhang, and G. Meng. 2017. “Nonlinear chirp mode decomposition: A variational method.” IEEE Trans. Signal Process. 65 (22): 6024–6037. https://doi.org/10.1109/TSP.2017.2731300.
Chen, S., M. Du, Z. Peng, Z. Feng, and W. Zhang. 2020b. “Fault diagnosis of planetary gearbox under variable-speed conditions using an improved adaptive chirp mode decomposition.” J. Sound Vib. 468 (Mar): 115065. https://doi.org/10.1016/j.jsv.2019.115065.
Chen, S., K. Wang, C. Chang, B. Xie, and W. Zhai. 2021. “A two-level adaptive chirp mode decomposition method for the railway wheel flat detection under variable-speed conditions.” J. Sound Vib. 498 (Apr): 115963. https://doi.org/10.1016/j.jsv.2021.115963.
Chen, S., Y. Yang, Z. Peng, S. Wang, W. Zhang, and X. Chen. 2019. “Detection of rub-impact fault for rotor-stator systems: A novel method based on adaptive chirp mode decomposition.” J. Sound Vib. 440 (Feb): 83–99. https://doi.org/10.1016/j.jsv.2018.10.010.
Daubechies, I., J. Lu, and H. T. Wu. 2011. “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool.” Appl. Comput. Harmon. Anal. 30 (2): 243–261. https://doi.org/10.1016/j.acha.2010.08.002.
Dragomiretskiy, K., and D. Zosso. 2013. “Variational mode decomposition.” IEEE Trans. Signal Process. 62 (3): 531–544. https://doi.org/10.1109/TSP.2013.2288675.
Du, Z., X. Chen, H. Zhang, and R. Yan. 2015. “Sparse feature identification based on union of redundant dictionary for wind turbine gearbox fault diagnosis.” IEEE Trans. Ind. Electron. 62 (10): 6594–6605. https://doi.org/10.1109/TIE.2015.2464297.
Gilles, J. 2013. “Empirical wavelet transform.” IEEE Trans. Signal Process. 61 (16): 3999–4010. https://doi.org/10.1109/TSP.2013.2265222.
Hou, T. Y., and Z. Shi. 2016. “Sparse time-frequency decomposition based on dictionary adaptation.” Philos. Trans. R. Soc. London, Ser. A 374 (2065): 20150192. https://doi.org/10.1098/rsta.2015.0192.
Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu. 1998. “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proc. R. Soc. London, Ser. A 454 (1971): 903–995. https://doi.org/10.1098/rspa.1998.0193.
Huang, T. L., M. L. Lou, H. P. Chen, and N. B. Wang. 2018. “An orthogonal Hilbert-Huang transform and its application in the spectral representation of earthquake accelerograms.” Soil Dyn. Earthquake Eng. 104 (Jan): 378–389. https://doi.org/10.1016/j.soildyn.2017.11.005.
Huang, Z., J. Zhang, T. Zhao, and Y. Sun. 2015. “Synchrosqueezing S-transform and its application in seismic spectral decomposition.” IEEE Trans. Geosci. Remote Sens. 54 (2): 817–825. https://doi.org/10.1109/TGRS.2015.2466660.
Li, H., Z. Li, and W. Mo. 2017. “A time varying filter approach for empirical mode decomposition.” Signal Process. 138 (Sep): 146–158. https://doi.org/10.1016/j.sigpro.2017.03.019.
Liu, J. L., J. Y. Zheng, X. J. Wei, W. X. Ren, and I. Laory. 2019. “A combined method for instantaneous frequency identification in low frequency structures.” Eng. Struct. 194 (Sep): 370–383. https://doi.org/10.1016/j.engstruct.2019.05.057.
Lu, L., W. X. Ren, and S. D. Wang. 2022. “Fractional Fourier transform: Time-frequency representation and structural instantaneous frequency identification.” Mech. Syst. Signal Process. 178 (Oct): 109305. https://doi.org/10.1016/j.ymssp.2022.109305.
Luo, Z. J., T. Liu, S. Z. Yan, and M. B. Qian. 2018. “Revised empirical wavelet transform based on auto-regressive power spectrum and its application to the mode decomposition of deployable structure.” J. Sound Vib. 431 (Sep): 70–87. https://doi.org/10.1016/j.jsv.2018.06.001.
Mateo, C., and J. A. Talavera. 2018. “Short-time Fourier transform with the window size fixed in the frequency domain.” Digital Signal Process. 77 (Jun): 13–21. https://doi.org/10.1016/j.dsp.2017.11.003.
Mika, B., D. Komorowski, and E. Tkacz. 2018. “Assessment of slow wave propagation in multichannel electrogastrography by using noise-assisted multivariate empirical mode decomposition and cross-covariance analysis.” Comput. Biol. Med. 100 (Sep): 305–315. https://doi.org/10.1016/j.compbiomed.2017.12.021.
Qu, H. Y., T. Y. Li, and G. D. Chen. 2018. “Multiple analytical mode decompositions for nonlinear system identification from forced vibration.” Eng. Struct. 173 (Oct): 979–986. https://doi.org/10.1016/j.engstruct.2018.07.037.
Ren, W., G. Chen, and W. Hu. 2005. “Empirical formulas to estimate cable tension by cable fundamental frequency.” Struct. Eng. Mech. 20 (3): 363–380. https://doi.org/10.12989/sem.2005.20.3.363.
Shang, X. Q., T. L. Huang, H. P. Chen, W. X. Ren, and M. L. Lou. 2023. “Recursive variational mode decomposition enhanced by orthogonalization algorithm for accurate structural modal identification.” Mech. Syst. Signal Process. 197 (Aug): 110358. https://doi.org/10.1016/j.ymssp.2023.110358.
Thakur, G., and H. T. Wu. 2011. “Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples.” SIAM J. Math. Anal. 43 (5): 2078–2095. https://doi.org/10.1137/100798818.
Ulrych, T. J., and T. N. Bishop. 1975. “Maximum entropy spectral analysis and autoregressive decomposition.” Rev. Geophys. 13 (1): 183–200. https://doi.org/10.1029/RG013i001p00183.
Wang, C., W. X. Ren, Z. C. Wang, and H. P. Zhu. 2013. “Instantaneous frequency identification of time-varying structures by continuous wavelet transform.” Eng. Struct. 52 (Jul): 17–25. https://doi.org/10.1016/j.engstruct.2013.02.006.
Wang, Y., Z. He, and Y. Zi. 2009. “A demodulation method based on improved local mean decomposition and its application in rub-impact fault diagnosis.” Meas. Sci. Technol. 20 (2): 025704. https://doi.org/10.1088/0957-0233/20/2/025704.
Wang, Z. C., and G. D. Chen. 2013. “Analytical mode decomposition of time series with decaying amplitudes and overlapping instantaneous frequencies.” Smart Mater. Struct. 22 (9): 095003. https://doi.org/10.1088/0964-1726/22/9/095003.
Wen, Q., X. G. Hua, Z. Q. Chen, H. W. Niu, and X. Y. Wang. 2018. “AMD-based random decrement technique for modal identification of structures with close modes.” J. Aerosp. Eng. 31 (5): 04018057. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000882.
Wu, Z., and N. E. Huang. 2009. “Ensemble empirical mode decomposition: A noise-assisted data analysis method.” Adv. Adapt. Data Anal. 1 (1): 1–41. https://doi.org/10.1142/S1793536909000047.
Xin, Y., H. Hao, and J. Li. 2019. “Operational modal identification of structures based on improved empirical wavelet transform.” Struct. Control Health Monit. 26 (3): e2323. https://doi.org/10.1002/stc.2323.
Yan, W. J., and W. X. Ren. 2013. “Use of continuous-wavelet transmissibility for structural operational modal analysis.” J. Struct. Eng. 139 (9): 1444–1456. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000711.
Yang, J. N., Y. Lei, and N. E. Huang. 2004. “Identification of natural frequencies and damping of in situ tall buildings using ambient wind vibration data.” J. Eng. Mech. 130 (5): 570e577. https://doi.org/10.1061/(ASCE)EM.0733-9399(2004)130:5(570.
Yang, N., Y. Lei, J. Li, H. Hao, and J. S. Huang. 2022. “A substructural and wavelet multiresolution approach for identifying time-varying physical parameters by partial measurements.” J. Sound Vib. 523 (Apr): 116737. https://doi.org/10.1016/j.jsv.2021.116737.
Yang, Q., J. Ruan, and Z. Zhuang. 2020. “Fault diagnosis for circuit-breakers using adaptive chirp mode decomposition and attractor’s morphological characteristics.” Mech. Syst. Signal Process. 145 (Nov): 106921. https://doi.org/10.1016/j.ymssp.2020.106921.
Yao, X. J., T. H. Yi, and C. X. Qu. 2022. “Autoregressive spectrum-guided variational mode decomposition for time-varying modal identification under nonstationary conditions.” Eng. Struct. 251 (Jan): 113543. https://doi.org/10.1016/j.engstruct.2021.113543.
Yeh, J. R., J. S. Shieh, and N. E. Huang. 2010. “Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method.” Adv. Adapt. Data Anal. 2 (2): 135–156. https://doi.org/10.1142/S1793536910000422.
Yin, J. C., A. N. Perakis, and N. Wang. 2018. “A real-time ship roll motion prediction using wavelet transform and variable RBF network.” Ocean Eng. 160 (Jul): 10–19. https://doi.org/10.1016/j.oceaneng.2018.04.058.
Yu, G., T. Lin, Z. Wang, and Y. Li. 2020. “Time-reassigned multisynchrosqueezing transform for bearing fault diagnosis of rotating machinery.” IEEE Trans. Ind. Electron. 68 (2): 1486–1496. https://doi.org/10.1109/TIE.2020.2970571.
Yu, G., Z. Wang, and P. Zhao. 2018. “Multisynchrosqueezing transform.” IEEE Trans. Ind. Electron. 66 (7): 5441–5455. https://doi.org/10.1109/TIE.2018.2868296.
Yu, K., H. Ma, H. Han, J. Zeng, H. Li, X. Li, Z. Xue, and B. Wen. 2019. “Second order multi-synchrosqueezing transform for rub-impact detection of rotor systems.” Mech. Mach. Theory 140 (Oct): 321–349. https://doi.org/10.1016/j.mechmachtheory.2019.06.007.
Zheng, J., M. Su, W. Ying, J. Tong, and Z. Pan. 2021. “Improved uniform phase empirical mode decomposition and its application in machinery fault diagnosis.” Measurement 179 (Jul): 109425. https://doi.org/10.1016/j.measurement.2021.109425.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 36 • Issue 5 • September 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Sep 7, 2022
Accepted: Apr 7, 2023
Published online: Jun 22, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 22, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.