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An E Ective Approach to Structural Damage Localization in Exural Members Based on Generalized S-Transform

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An E Ective Approach to Structural Damage Localization in Exural Members Based on Generalized S-Transform Scientia Iranica A (2019) 26(6), 3125{3139 Sharif University of Technology Scientia Iranica Transactions A: Civil Engineering http://scientiairanica.sharif.edu An e ective approach to structural damage localization in exural members based on generalized S-transform H. Amini Tehrania, A. Bakhshia;, and M. Akhavatb a. Department of Civil Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9313 Tehran, Iran. b. School of Civil Engineering, Iran University of Science & Technology, Tehran, Iran. Received 7 February 2017; received in revised form 22 October 2017; accepted 23 December 2017 KEYWORDS Abstract. This paper presents a method for structural damage localization based on signal processing using generalized S-transform (S ). The S-transform is a combination Damage localization; GS of the properties of the Short-Time Fourier Transform (STFT) and Wavelet Transform Signal processing; (WT) that has been developed over the last few years in an attempt to overcome inherent Generalized limitations of the wavelet and short-time Fourier transform in time-frequency representation S-transform; of non-stationary signals. The generalized type of this transform is the S -transform Time-frequency GS that is characterized by an adjustable Gaussian window width in the time-frequency representation; representation of signals. In this research, the S -transform was employed due to its Non-stationary GS favorable performance in the detection of the structural damages. The performance of signals. the proposed method was veri ed by means of three numerical examples and, also, the experimental data obtained from the vibration test of 8-DOFs mass-sti ness system. By means of a comparison between damage location obtained by the proposed method and the simulation model, it was concluded that the method was sensitive to the damage existence and clearly demonstrated the damage location. © 2019 Sharif University of Technology. All rights reserved. 1. Introduction increased considerably due to the recent advances in the eld of sensors and other electronic technologies [1]. Structural health monitoring has become an evolving These advances provide a wide range of response area during the recent years with an increasing need signals such as velocity, acceleration, and displace- to ensure the safety and functionality of structures. It ment caused by low- to high-intensity earthquakes and can be stated that the importance of structural health environmental loads. Doubling et al. [2] provided a monitoring lies in the serviceability and safety of struc- comprehensive history of structural health monitoring tures during their service life; of course, appropriate methods together with eciencies and disadvantages of and timely actions are required for their maintenance each method. Sohn et al. [3] presented comprehensive and retro tting. In the past few decades, using signal literature reviews of vibration-based damage detection processing tools in structural health monitoring has and health monitoring methods for structural and mechanical systems. Signal-based methods investigate changes in the *. Corresponding author. Tel.: +98 21 66164243; features derived from the series or their corresponding E-mail addresses: aminitehrani [email protected] (H. Amini Tehrani); [email protected] (A. Bakhshi); spectra using proper signal processing tools. One of the [email protected] (M. Akhavat). most commonly used signal processing techniques is the Fast Fourier Transform (FFT), which transmits signals doi: 10.24200/sci.2017.20019 from the time domain into the frequency domain. In 3126 H. Amini Tehrani et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3125{3139 other words, the evaluation of the FFT of a signal considering the evolution of dynamic characteristics of results in a graph in the frequency domain by taking structures with time. Ditommaso et al. [23] recently into account the average size of each spectral amplitude developed a methodology for damage assessment and assessed on the entire length of the analyzed signal. localization of framed structures subjected to strong- It is evident that the transient phase of the signal, motion earthquakes. In this method, the information which appears to be a fraction of the whole signal, related to the evolution of the equivalent viscous is entirely distorted [4]. Therefore, the FFT is not damping factor and mode shape is extracted from the a proper tool for processing non-stationary signals. recorded signal using a band-variable lter and Stock- The non-stationarity of the recorded signals is not well Transform. Then, based on the fundamental mode merely due to the damage to structures; even the shapes evaluated before, during, and after the seismic non-stationarity of the input and the possible inter- event, the modal curvature variation is quanti ed, and action with the ground or adjacent structures can damage location is identi ed. show the ine ectiveness of classic techniques [5]. A With all the advantages over all other transforms, large number of researchers have developed methods such as wavelet and short-time Fourier transform, for overcoming the above-mentioned problems of the the S-transform also has some disadvantages one of FFT in processing non-stationary signals. The short- which is an invariable window that has no parameter time Fourier transform [6,7], the complex demodulation for allowing its width to be adjusted in the time or technique [8], and the Generalized Time-Frequency frequency domain. To overcome this problem, the Distribution (GTFD) as proposed by Cohen [9] are generalized S-transform is introduced with adjustable examples of these methods. time and frequency resolution. In recent years, extensive research has been car- In this paper, the generalized S-transform is pre- ried out in the eld of structural health monitoring sented to detect the presence and location of damage by utilizing the decomposing features of wavelet and in structures. Herein, the rst wavelet transform and wavelet packet transforms. Ovanesova and Suarez [10] S-transform are presented; then, their di erences in used the wavelet transform to detect cracks in a the time-frequency representation signal are expressed one-story plane frame. They investigated the e ec- in the form of a simple example. Afterward, the tiveness of wavelet analysis in detecting cracks by generalized S-transform is introduced, and the damage using numerical examples. Ren and Sun [11] used a detection procedure is explained by taking advantage combination of wavelet transform and Shannon entropy of this transform. The eciency of the proposed to detect structural damage from vibrational signals. method for damage detection is examined with respect They used wavelet entropy, relative wavelet entropy, to three di erent numerical examples. Furthermore, and time-wavelet entropy as damage-sensitive features the experimental data from the vibration test of a for the detection and determination of the damage mass-sti ness system are used to verify the proposed location. Several recent studies investigating wavelet- approach. The results reveal that the proposed method based methods can be found in [12-15]. is robust and ecient for the detection and localization Wavelet and wavelet packet transforms have some of damage. imperfections such as unavailability of the width of time-frequency window for all frequencies, which is in- 2. Signal processing tools evitable for having windows with adjustable width [16]. These transformations present more advantages than 2.1. Wavelet transform the FFT and the STFT, yet do not allow for a fair The wavelet transform is a method for converting a assessment of the local spectrum. In other words, signal into another form, which either makes certain these instruments are incapable to perform a correct features of the original signal more amenable to study evaluation of the spectral characteristics, considering or enables the original dataset to be described more the instantaneous variations [4]. succinctly. There are, in fact, a large number of Stockwell et al. [17] introduced a new trans- wavelets to choose from for data analysis. The best one form (S-transform) that combines the characteris- for a particular application depends on both the nature tics of Short-Time Fourier Transform (STFT) and of the signal and what we require from the analysis [24]. wavelet transform. Unlike the wavelet transform, the The wavelet transform of a continuous signal, f(t), can S-transform preserves phase-referenced information. be expressed as follows [25]: This transform has been used by some researchers in Z various elds such as seismology [18,19]. In structural 1 +1 t b W (a; b) = p f(t) dt; (1) health monitoring, for the rst time, Pakrashi and jaj 1 a Ghosh [20] used the S-transform to detect cracks in beams. Ditommaso et al. [21,22] introduced a lter where a and b are the scale and the transformation based on S-transform to process the response signals, parameter, respectively. a;b is the complex conjugate H. Amini Tehrani et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3125{3139 3127 of a;b. Function a;b(t) is obtained from Function (t) The width of the Gaussian window changes with (mother wavelet) by scale a and transformation in the 1=jfj. This change creates distributions with di erent time domain using b. time-frequency resolutions. However, the value of 1=jfj is constant, and the width of the window cannot be 2.2. S-Transform adaptively adjusted to the frequency distribution of the The S-transform produces a time-frequency representa- signal. tion of a time series. It uniquely combines a frequency- The S-transform uses a window with variable dependent resolution with simultaneous localization of widths so that the time window can be wider at the the real and imaginary spectra. This transform was low-frequency band to gain higher frequency resolution. introduced by Stockwell et al. [17]. On the contrary, the time window is narrower at the The continuous S-transform of function h(t) with high-frequency band to obtain higher time resolution.
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