In this study, the discrete wavelet packet transform (DWPT) has been used for the single-step and iterative denoising methods for enhancing data with a high level of noise to identification of modal frequencies in ambient vibration tests on a petrochemical process tower in Shiraz, Iran. The ambient vibration test is performed by the wind load. All mechanical systems operated during the test; hence, different noise sources exist. Here, both high and low frequency ranges are decomposed effectively in the DWPT, and it provides a lot of global and localized information. The DWPT-based one-step denoising method fails to properly denoise the high-level noisy data with denoising thresholds obtained by different theoretical methods. For this reason, the so-called peeling approach achieved by an iterative denoising method is used to enhance the quality of the signal. For this iterative method, the parameters are obtained by the trial-and-error method. After the signal-enhancement stage, the signal processing step is performed by continuous wavelet transforms (CWTs) to detect the time-frequency information in the data. Furthermore, the modal frequencies are directly identified by the cross wavelet transform (XWT) and the corresponding spectral power density. Finally, the estimated frequencies by XWT are compared with the natural frequencies of a damaged model simulated by the finite element (FE) method.
Y. Tamura, Damping in buildings and estimation techniques, In: Y. Tamura, A. Kareem, editors. Advanced Structural Wind Engineering: Springer, (2013) 347-76.
L. Carassale, F. Percivale, editors. POD-based modal identification of wind-excited structures. Proceedings of the Twelfth International Conference on Wind Engineering, Cairns, Australia (2007).
T.-H. Le, Y. Tamura, editors. Modal identification of ambient vibration structure using frequency domain decomposition and wavelet transform, Proceedings of the 7th Asia-Pacific conference on wind engineering, Taipei, Taiwan (2009).
J. Lardies, S. Gouttebroze, Identification of modal parameters using the wavelet transform, International Journal of Mechanical Sciences, 44(11) (2002) 2263-83.
X. He, B. Moaveni, J.P. Conte, A. Elgamal, S. F. Masri, Modal identification study of Vincent Thomas bridge using simulated wind‐induced ambient vibration data, Computer-Aided Civil and Infrastructure Engineering, 23(5) (2008) 373-88.
X. H. He, X. G. Hua, Z. Q. Chen, F. L. Huang, EMD-based random decrement technique for modal parameter identification of an existing railway bridge, Engineering Structures, 33(4) (2011) 1348-56.
C. S. Huang, S. L. Hung, C. I. Lin, W. C. Su, A wavelet‐based approach to identifying structural modal parameters from seismic response and free vibration data, Computer-Aided Civil and Infrastructure Engineering, 20(6) (2005) 408-23.
K. K. Wijesundara, C. Negulescu, E. Foerster, D. Monfort Climent, Estimation of modal properties of structures through ambient excitation measurements using continuous wavelet transform, Engineering Structures (2012).
T. Kijewski, A. Kareem, Wavelet transforms for system identification in civil engineering, Computer-Aided Civil and Infrastructure Engineering, 18(5) (2003) 339-55.
J. Lin, L. Qu, Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis. Journal of Sound and Vibration, 234(1) (2000) 135-48.
K. F. Al-Raheem, A. Roy, K. P. Ramachandran, D. K. Harrison, S. Grainger, Rolling element bearing faults diagnosis based on autocorrelation of optimized: wavelet de-noising technique, International Journal of Advanced Manufacturing Technology, 40(3-4) (2009) 393-402.
B. Yan, A. Miyamoto, E. Brühwiler, Wavelet transform-based modal parameter identification considering uncertainty, Journal of Sound and Vibration, 291(1) (2006) 285-301.
X. Jiang, H. Adeli, Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings, International Journal for Numerical Methods in Engineering, 71(5) (2007) 606-29.
R. A. Osornio-Rios, J. P. Amezquita-Sanchez, R. J. Romero-Troncoso, A. Garcia-Perez, MUSIC-ANN analysis for locating structural damages in a truss-type structure by means of vibrations, Computer-Aided Civil and Infrastructure Engineering 27(9) (2012) 687-98.
M. Meo, G. Zumpano, X. Meng, E. Cosser, G. Roberts, A. Dodson, Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms, Mechanical Systems and Signal Processing, 20(5) (2006) 1112-33.
N. Kang, H. Kim, S. Choi, S. Jo, J. S. Hwang, E. Yu, Performance evaluation of TMD under typhoon using system identification and inverse wind load estimation, Computer-Aided Civil and Infrastructure Engineering, 27(6) (2012) 455-73.
C. S. Huang, W. C. Su, Identification of modal parameters of a time invariant linear system by continuous wavelet transformation, Mechanical Systems and Signal Processing, 21(4) (2007) 1642-64.
B. Yan, A. Miyamoto. A comparative study of modal parameter identification based on wavelet and Hilbert–Huang transforms, Computer-Aided Civil and Infrastructure Engineering, 21(1) (2006) 9-23.
W. C. Su, C. S. Huang, C. H. Chen, C. Y. Liu, H. C. Huang, Q. T. Le, Identifying the modal parameters of a structure from ambient vibration data via the stationary wavelet packet, Computer-Aided Civil and Infrastructure Engineering, 29(10) (2014) 738-57.
W. C. Su, C. Y. Liu, Huang CS. Identification of instantaneous modal parameter of time‐varying systems via a wavelet‐based approach and its application, Computer-Aided Civil and Infrastructure Engineering, 29(4) (2014) 279-98.
S.-L. Chen, J.-J. Liu, H.-C. Lai, Wavelet analysis for identification of damping ratios and natural frequencies, Journal of Sound and Vibration, 323(1) (2009) 130-47.
R. X. Gao, R. Yan, Wavelets: Theory and Applications for Manufacturing: Springer Science & Business Media (2010).
N. E. Huang, Introduction to the Hilbert Huang transform and its related mathematical problems, In: N. E. Huang, S. S. P. Shen, editors. Hilbert-Huang Transform and its Applications: World Scientific, (2011) p. 1-26.
A. Teolis, Computational Signal Processing with Wavelets: Springer Science & Business Media (2012).
M. Misiti, Y. Misiti, G. Oppenheim, J.-M. Poggi, Wavelets and Their Applications: John Wiley & Sons, 2013.
S. Mallat, A Wavelet Tour of Signal Processing, (Wavelet Analysis & Its Applications): Academic Press, 1999.
P. Van Fleet, Discrete Wavelet Transformations: An Elementary Approach with Applications: John Wiley & Sons, 2008.
M. Jansen, Noise Reduction by Wavelet Thresholding: Springer Science & Business Media (2012).
K. P. Soman, Insight into Wavelets: From Theory to Practice: PHI Learning Pvt. Ltd. (2010).
R. R. Coifman, M. V. Wickerhauser, Adapted waveform “de-Noising” for medical signals and images, IEEE Engineering in Medicine and Biology Magazine, 14(5) (1995) 578-86.
R. R. Coifman, M. V. Wickerhauser, Experiments with adapted wavelet de-noising for medical signals and images. In: Akay M, editor. Time Frequency and Wavelets in Biomedical Signal Processing: IEEE press series in Biomedical Engineering (1998).
L. J. Hadjileontiadis, S. M. Panas, Separation of discontinuous adventitious sounds from vesicular sounds using a wavelet-based filter, IEEE Transactions on Biomedical Engineering, 44(12) (1997) 1269-81.
L. J. Hadjileontiadis, C. N. Liatsos, C. C. Mavrogiannis, T. A. Rokkas, S. M. Panas, Enhancement of bowel sounds by wavelet-based filtering, IEEE Transactions on Biomedical Engineering, 47(7) (2000) 876-86.
R. Ranta, C. Heinrich, V. Louis-Dorr, D. Wolf, Interpretation and improvement of an iterative wavelet-based denoising method. IEEE Signal Processing Letters, 10(8) (2003) 239-41.
R. Ranta, V. Louis-Dorr, C . Heinrich, D. Wolf, Iterative wavelet-based denoising methods and robust outlier detection. IEEE Signal Processing Letters, 12(8) (2005) 557-60.
J.-L. Starck, A. Bijaoui. Filtering and deconvolution by the wavelet transform, Signal Process, 35(3) (1994) 195-211.
A. Grinsted, J. C. Moore, S. Jevrejeva, Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes Geophys, 11(5/6) (2004) 561-6.
W. J. Staszewski, Identification of damping in MDOF systems using time-scale decomposition, Journal of Sound and Vibration, 203(2) (1997) 283-305.
J. Guo, G. Wei, X. Li, D. Jin, F. Liu, Modal identification of structures with closely spaced modes based on improved empirical wavelet transform, Journal of Vibration Engineering & Technologies, 10(7) (2022) 2625-2640.
Zh. Bai, J. Wei, K. Chen, Kaiyan Wang, ICEEMDAN and improved wavelet threshold for vibration signal joint denoising in OPAX, Journal of Mechanical Science and Technology, 38 (2024) 1-11.
K. C. Raath, K. B. Ensor, A. Crivello, D. W. Scott, Denoising non-stationary signals via dynamic multivariate complex wavelet thresholding, Entropy 25(11) (2023) 1546.
A. Silik, M. Noori, W.A. Altabey, J. Dang, R. Ghiasi, A new denoising technique via wavelet analysis of structural vibration response for structural health monitoring applications, Lifelines (2022) 691-706.
A. Silik, M. Noori, Z. Wu, W.A. Altabey, J. Dang, N. S. Farhan, Wavelet-based vibration denoising for structural health monitoring, Urban Lifeline, 2024 2(1), 1-14.
Q. Liao, Z. Sheng, P. Guo, Research on the Wavelet Denoising Algorithm for Thorpe Analysis Based on the Radiosonde Data, Remote Sensing, 17(1) 2025,114-126.
X. An, C. Li, F. Zhang, Application of adaptive local iterative filtering and approximate entropy to vibration signal denoising of hydropower unit, Journal of Vibroengineering, 2016 18(7), 4299-4311.
H. Yousefi, A. Taghavi Kani, I. Mahmoudzadeh Kani, S. Mohammadi, Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran, Frontiers of Structural and Civil Engineering, 14 (2020)446-472.
H. Yousefi, , S. S. Ghorashi, T. Rabczuk, Directly simulation of second order hyperbolic systems in second order form via the regularization concept, Communications in Computational Physics, 20(1) (2016) 86-135.
J. Samadi, Seismic Behavior of Structure-Equipment in a Petrochemical Complex to Evaluate Vulnerability Assessment: a Case Study, University of Tehran (2010).
Shin, K. and Hammond, J., Fundamentals of Signal Processing for Sound and Vibration Engineers, (2008) John Wiley & Sons.
S. Mallat, A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way, Academic Press, Inc., 2008.
P. Van Fleet, Discrete Wavelet Transformations: An Elementary Approach with Applications, John Wiley & Sons, (2019).
M. Jansen, Noise Reduction by Wavelet Thresholding, Springer Science & Business Media, 2001.
K. M. Jeevan, S. Krishnakumar, An algorithm for wavelet thresholding based image denoising by representing images in hexagonal lattice, Journal of Applied Research and Technology, 16(2) (2018) 103-114.
A. Mansi, L. Dunai, M. Cao, Wavelet-based denoising of structural health monitoring strain measurements, Measurement: Sensors, 42 (2025) 101974.
S. A. Malik, S. A. Parah, H. Aljuaid, B. A. Malik, An iterative filtering based ECG denoising using lifting wavelet transform technique, Electronics, 12(2) (2023) 387.
F. M. Bayer, A. J. Kozakevicius, R. J. Cintra. An iterative wavelet threshold for signal denoising, Signal Processing162 (2019) 10-20.
A. Silik, M. Noori, W. A. Altabey, J. Dang, R. Ghiasi, and Zh. Wu, Optimum wavelet selection for nonparametric analysis toward structural health monitoring for processing big data from sensor network: A comparative study, Structural Health Monitoring,21(3) (2022) 803-825.
X. Jiang, Q. Lang, Q. Jing, H. Wang, J. Chen, and Q. Ai, An improved wavelet threshold denoising method for health monitoring data: A case study of the Hong Kong-Zhuhai-Macao Bridge immersed tunnel, Applied Sciences,12(13) (2022) 6743.
G. Jia, J. Yang, and H. Liang, A Combined Denoising Method of Adaptive VMD and Wavelet Threshold for Gear Health Monitoring, Structural Durability & Health Monitoring19(4) (2025).
A. Silik, M. Noori, W. A. Altabey, R. Ghiasi, and Zh. Wu, Comparative analysis of wavelet transform for time-frequency analysis and transient localization in structural health monitoring, Structural Durability & Health Monitoring,15(1) (2021) 1.
Ahangar Ebrahimi, E. , Yousefi, H. , Mahmoudzadeh Kani, I. and Taghavi Kani, A. (2025). Iterative Data Enhancement of Ambient Vibration Tests for the Nitrate-Prilling Tower in Shiraz Petrochemical Complex. AUT Journal of Civil Engineering, 9(3), 253-278. doi: 10.22060/ajce.2025.23610.5889
MLA
Ahangar Ebrahimi, E. , , Yousefi, H. , , Mahmoudzadeh Kani, I. , and Taghavi Kani, A. . "Iterative Data Enhancement of Ambient Vibration Tests for the Nitrate-Prilling Tower in Shiraz Petrochemical Complex", AUT Journal of Civil Engineering, 9, 3, 2025, 253-278. doi: 10.22060/ajce.2025.23610.5889
HARVARD
Ahangar Ebrahimi, E., Yousefi, H., Mahmoudzadeh Kani, I., Taghavi Kani, A. (2025). 'Iterative Data Enhancement of Ambient Vibration Tests for the Nitrate-Prilling Tower in Shiraz Petrochemical Complex', AUT Journal of Civil Engineering, 9(3), pp. 253-278. doi: 10.22060/ajce.2025.23610.5889
CHICAGO
E. Ahangar Ebrahimi , H. Yousefi , I. Mahmoudzadeh Kani and A. Taghavi Kani, "Iterative Data Enhancement of Ambient Vibration Tests for the Nitrate-Prilling Tower in Shiraz Petrochemical Complex," AUT Journal of Civil Engineering, 9 3 (2025): 253-278, doi: 10.22060/ajce.2025.23610.5889
VANCOUVER
Ahangar Ebrahimi, E., Yousefi, H., Mahmoudzadeh Kani, I., Taghavi Kani, A. Iterative Data Enhancement of Ambient Vibration Tests for the Nitrate-Prilling Tower in Shiraz Petrochemical Complex. AUT Journal of Civil Engineering, 2025; 9(3): 253-278. doi: 10.22060/ajce.2025.23610.5889