Vol.112 (Architecture and Civil Engineering 215), pp.68-73 http://dx.doi.org/1.14257/astl.215.112.14 Damage detection using output-only measurement by indirect approach Young-Jun Ahn 1, Seung-Guk Lee 1, Dong-Ho Cho 1, Hee-Chang Eun 1, Taek-Sun Kang 1 1 Department of Architectural Engineering, Kangwon National University, Chuncheon 2-71, Gangwon-Do, Korea v2zone@naver.com, angangyo@naver.com, woolima79@hanmail.net, heechang@kangwon.ac.kr, gaisungpa@kepco.co.kr Abstract. Indirect measurement method doesn t require a number of sensors and a large amount of labor. It is necessary to evaluate the comparable applicability to the direct measurement approach. This study investigates the validity of damage detection method using output-only measurement by indirect approach. The damage is detected using the curvature of power spectral density evaluation and proper orthogonal modes (POMs) of the responses data collected by experiments. The sensitivity of damage detection using time response and frequency response is compared through the beam test. It is illustrated in experiments that the indirect method can be widely utilized despite of the existence of external noise. Keywords: damage detection, indirect approach, truss, measurement, sensor, noise. 1 Introduction The direct method directly collects response data from measurement sensors attached on test structure and the indirect approach indirectly from the structure to install the sensors rather than the test structure. The direct method requires a number of sensors and a large amount of labor to attach the sensors and measure data. Such difficulties can be overcome by the indirect method. The existing damage detection methods are performed using measurement data in the time-domain or frequency-domain. The time-domain methods usually go through stochastic processes. Cattarius and Inman [1] provided a non-destructive time-domain approach to examine structural damage using time histories of the vibration response of the structure. Majumder and Manohar [2] developed a time-domain approach to detect damage in bridge structures by analyzing the combined system of the bridge and vehicle. Sandesh and Shankar [3] presented a time-domain damage detection scheme based on a substructure system identification method using Genetic Algorithms and Particle Swarm Optimization to filter out the updated parameters. Lu Corresponding author ISSN: 2287-1233 ASTL Copyright 215 SERSC
Vol.112 (Architecture and Civil Engineering 215) and Gao [4] presented a time series model for the diagnosis of structural damage considering a damage sensitive feature without input excitation. The POMs constitute a set of optimal basis functions with respect to energy content of the signal. The POM obtained from the PODs effectively extracts the principal component of a large DOF system or complex physical phenomena. The POD is used in utilizing the context of turbulence to extract coherent structures [5], detecting the number of signals in a multichannel time-series [6], capturing the modes of a reaction-diffusion chemical process [7] and describing quantitative changes in spatial complexity during extended episodes of ventricular fibrillation [8]. And the method can be applied in obtaining reduced-order models of unsteady viscous flows [9], forecasting in meteorology [8] and classifying speech data [1]. This work investigates the applicability of damage detection by the indirect measurement approach comparable to the direct measurement approach. Measurement raw data in the time-domain and frequency-domain are modified in the process of power spectral density evaluation (PSE) and proper orthogonal decomposition (POD), respectively. The effectiveness of the indirect approach depending on the collected data in the time-domain and frequency-domain is compared in beam test. The validity of the proposed method is illustrated in a beam test. 2 Beam test The action of an impact force at a position on a damaged member leads to a variation in vibration at the damaged region. A steel beam in Fig. 1 was tested to detect the damage location by the responses of an accelerometer bonded on a rubber eraser under the action of impact hammer. The measurement data are indirectly collected by the accelerometer through the eraser. The beam is 12mm in length, and its gross cross-section is 5 mm 9 mm. The damage is located at 93mm between nodes 15 and 16 from the left end, and its cross-section is 5 mm 6 mm. The experiment was carried out with the roving of accelerometer bonded on an eraser. The hammer has been impacted at a single reference point to excite the beam, whereas a uniaxial accelerometer roved around. The measurement data of the vibration signals in the time-domain and frequency-domain are collected by the accelerometer under the hammer excitation at a fixed point. Nineteen measurement points are positioned at intervals of 6 mm. An acceleration response data set in the time-domain and another frequency response function (FRF) data set in the frequency-domain were collected. The experiment was conducted using a DYTRAN model 355B1 uniaxial accelerometer along with a miniature transducer hammer (Brüel & Kjaer model 824) to excite the system. The data acquisition system was a DEWETRON model DEWE-43. Copyright 215 SERSC 69
Vol.112 (Architecture and Civil Engineering 215) Fig. 1. A beam structure model for detecting damage by indirect measurement approach Two data sets were collected in the time-domain and frequency-domain. The acceleration response data at all nodes of the beam structure during the first two seconds due to the action of the impact hammer at node 1 are transformed to the power spectral density evaluation in the frequency-domain. Power spectral density (PSD), defined as the squared value of the signal, describes the power of a signal or time series distributed over different frequencies. The PSD is the 8.6 6.5 Acceleration response(g) 4 2-2 Power Spectral Density.4.3.2-4.1-6.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time(sec.) (a) 5 1 15 2 25 3 35 4 45 5 Frequency(Hz/sample) (b).4 4 x 1-3.35 3.3 Max. of PSD.25.2.15 Curvature of PSD Max. 2 1.1.5-1 2 4 6 8 1 12 14 16 18 2-2 2 4 6 8 1 12 14 16 18 2 (c) (d) Fig. 2. Experimental results extracted from accelerometer responses: (a) acceleration responses, (b) power spectral density, (c) maximum PSD nearby the first resonance frequency, (d) curvature of maximum PSD 7 Copyright 215 SERSC
Vol.112 (Architecture and Civil Engineering 215) Fourier transform of the autocorrelation function, which provides the transformation from the time-domain to the frequency-domain. Figures 2(a) and (b) represent the acceleration responses and their PSD curves, respectively. This work estimates the Welch PSD by dividing the response into eight segments in length. The PSD are obtained by the rectangular window function, sample overlapping of 5%, and frequency resolution of.5. The first resonance is located at 13.9 Hz / sample by Fig. 2(b). Taking the maximum PSDs in the neighborhood of the first resonance frequency, the resulting curve is given in Fig. 2(c). It is observed that the location to represent the abrupt change of the curve coincides with the damage location and the damage can be detected by the PSD curve. Considering that the beam is a flexural member, the curvature estimated by the second order finite difference method also indicates the damage region as shown in Fig. 2(d). It can be mentioned from this analysis that the PSD evaluation method starting from the acceleration response in the time-domain measured by the indirect approach provides explicit damage information despite of the existence of external noise. The measured data are collected as FRFs in the frequency-domain, which is defined as the ratio of the response mode of a system to its excitation force. The FRF response data can be experimentally obtained by the roving of measurement sensors or the 5 4.5 4 3.5 3 FRF 2.5 2 1.5 1.5 5 1 15 2 25 3 35 4 45 5 Frequency(Hz) (a).4 2 x 1-3.35.3-2 POM.25.2 POM curvature -4-6 -8.15-1.1-12.5 5 1 15 2-14 2 4 6 8 1 12 14 16 18 2 (b) (c) Fig. 3. Experimental results in the frequency domain: (a) FRF curves, (b) POM nearby the first resonance frequency, (c) POM curvature impact hammer. The FRF can be expressed as a function of the cross and auto spectra, which can readily be obtained from most multi-channel data acquisition systems. Copyright 215 SERSC 71
Vol.112 (Architecture and Civil Engineering 215) Figure 3(a) exhibits the FRF curves at all nodes measured by the indirect approach. It is displayed that the first resonance is located at 13.9 Hz. The POD extracts a basis to decompose the data so that the projection of the data contains as much energy as possible. Extracting the FRFs in the range of 13.62 14.893 Hz including the firsr resonance frequency, the POMs are derived. The POM curve shown in Fig. 3(b) corresponds to the first proper orthogonal value (POV). It takes the same form of the first vibration mode but doesn t provide the information on the damage. The POM curvature plot using the second order finite difference method is shown in Fig. 3(c). The abrupt variation of the curvature curve is found at several locations due to the existence of external noise. The damage location is explicitly not detected based on the plot. From this experiment, the time response is less sensitive to the external noise than the frequency response. It is concluded that the damage detection method based on the measurement data in the time-domain by the indirect approach provides more accurate damage information than the one in the frequency-domain. 3 Conclusions This work evaluated the validity of the indirect approach to detect damage by the data from sensor bonded on the eraser rather than on the test structure. Two different measurement data sets in the time-domain and the frequency-domain are utilized in this indirect approach. From this experimental work, it is concluded that the indirect method can be utilized in detecting damage despite of the presence of external noise. And the damage detection method based on the measurement data in the time-domain by the indirect approach provides more accurate damage information than the one in the frequency-domain. Acknowledgment. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (213R1A1A257431). References 1. Cattarius, J., Inman, D.J.: Time domain analysis for damage detection in smart structures, Mechanical Systems and Signal Processing 11(3), 49-423 (1997) 2. Majumder, L., Manohar, C.S.: A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source, Journal of Sound and Vibration 268, 699-716 (23) 3. Sandesh, S., Shankar, K.: Damage identification of a thin plate in the time-domain with substructuring-an application of inverse problem, International Journal of Applied Science and Engineering 7, 79-93 (29) 4. Lu, Y., Gao, F.: A novel time-domain auto-regressive model for structural damage diagnosis, Journal of Sound and Vibration 283, 131-149 (25) 5. Alampalli, S., Fu, G., Dillon, E.E.: Signal versus noise in damage detection of experimental 72 Copyright 215 SERSC
Vol.112 (Architecture and Civil Engineering 215) modal analysis, Journal of Structural Engineering 123, 237-245 (1997) 6. Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H., Wu, C.G.: Proper orthogonal decomposition and its applications- Part 1: Theory, Journal of Sound and Vibration 252, 527-544 (22) 7. Wu, C.G., Liang, Y.C., Lin, W.Z., Lee, H.P., Lim, S.P.:A note on equivalence of proper orthogonal decomposition methods, Journal of Sound and Vibration 265 113-111. (23) 8. Kerschen, G., Golinval, J.C., Vakakis, A.F., Bergman, L.A.: The method proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: An overview, Nonlinear Dynamics 41 147-169. (25) 9. Tumer, I.Y., Wood, K.L., Busch-Vishniac, I.J.: Monitoring of signals from manufacturing process using the Karhunen-Loeve transform, Mechanical Systems and Signal Processing 14, 111-126 (2) 1. Holmes, P., Lumley, J.L., Berkooz, G.:Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge, New York, 1996 Copyright 215 SERSC 73