In structural vibration tests, one of the main factors which disturb the reliability and accuracy of the results are the noise signals encountered. To overcome this deficiency, this paper presents a discrete wavelet transform (DWT) approach to denoise the measured signals. The denoising performance of DWT is discussed by several processing parameters, including the type of wavelet, decomposition level, thresholding method, and threshold selection rules. To overcome the disadvantages of the traditional hard- and soft-thresholding methods, an improved thresholding technique called the sigmoid function-based thresholding scheme is presented. The procedure is validated by using four benchmarks signals with three degrees of degradation as well as a real measured signal obtained from a three-story reinforced concrete scale model shaking table experiment. The performance of the proposed method is evaluated by computing the signal-to-noise ratio (SNR) and the root-mean-square error (RMSE) after denoising. Results reveal that the proposed method offers superior performance than the traditional methods no matter whether the signals have heavy or light noises embedded.
References
[1]
Li, H.N.; Li, D.S.; Song, G.B. Recent applications of fiber optic sensors to health monitoring in civil engineering. Eng. Struct. 2004, 26, 1647–1657.
[2]
Ahn, D.; Park, J.S.; Kim, C.S.; Kim, J.; Qian, Y.X.; Itoh, T.A. Design of the low-pass filter using the novel microstrip defected ground structure. IEEE Tran. Microw. Theory Tech. 2001, 49, 86–93.
[3]
Jwo, D.J.; Cho, T.S. Critical remarks on the linearised and extended Kalman filters with geodetic navigation examples. Measurement 2010, 43, 1077–1089.
[4]
Wang, G.H.; Li, D.H.; Pan, W.M.; Zang, Z.X. Modified switching median filter for impulse noise removal. Signal Process 2010, 90, 3213–3218.
[5]
Baykal, B.; Constantinides, A.G. A neural approach to the underdetermined-order recursive least-squares adaptive filtering. Neural Netw. 1997, 10, 1523–1531.
[6]
Han, M.; Liu, Y.; Xi, J.; Guo, W. Noise smoothing for nonlinear time series using wavelet soft threshold. IEEE Signal Process. Lett. 2007, 14, 62–65.
[7]
Baili, J.; Lahouar, S.; Hergli, M.; Al-Qadi, I.L.; Besbes, K. GPR signal de-noising by discrete wavelet transform. NDT E. Int. 2009, 42, 696–703.
[8]
Donoho, D.L.; Johnstone, I.M. Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Assoc. 1995, 90, 1200–1224.
Gao, H.Y. Wavelet shrinkage denoising using the non-negative garrote. J. Comput. Graph. Statist. 1998, 7, 469–488.
[11]
Yoon, B.J.; Vaidyanathan, P.P. Wavelet-Based Denoising by Customized Thresholding. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, QC, Canada, 17– 21 May 2004; pp. 925–928.
[12]
Song, G.X.; Zhao, R.Z. Three novel models of threshold estimator for wavelet coefficients. Lect. Notes Comput. Sci. 2001, 2251, 145–150.
[13]
Leite, F.E.A.; Montagne, R.; Corso, G.; Vasconcelos, G.L.; Lucena, L.S. Optimal wavelet filter for suppression of coherent noise with an application to seismic data. Physica A. 2008, 387, 1439–1445.
[14]
Zhang, J.X.; Zhong, Q.H.; Dai, Y.P. The Determination of the Threshold and the Decomposition Order in Thereshold De-Nosing Method Based on Wavelet Transform. Proceedings of the Chinese Society for Electrical Engineering, Beijing, China, February 2004; pp. 118–122.
[15]
Baussard, A.; Nicolier, F.; Truchetet, F. Rational multiresolution analysis and fast wavelet transform: Application to wavelet shrinkage denoising. Signal Process 2004, 84, 1735–1747.