Damage detection optimization using the wavelet entropy and genetic algorithm

Transcription

1 Southern Cross University 23rd Australasian Conference on the Mechanics of Structures and Materials 2014 Damage detection optimization using the wavelet entropy and genetic algorithm S A. Ravanfar H Abdul Razak Z Ismail S J S Hakim Publication details Ravanfar, SA, Abdul Razak, H, Ismail, Z, Hakim, SJS 2014, 'Damage detection optimization using the wavelet entropy and genetic algorithm', in ST Smith (ed.), 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23), vol. II, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, pp ISBN: epublications@scu is an electronic repository administered by Southern Cross University Library. Its goal is to capture and preserve the intellectual output of Southern Cross University authors and researchers, and to increase visibility and impact through open access to researchers around the world. For further information please contact epubs@scu.edu.au.

2 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23) Byron Bay, Australia, 9-12 December 2014, S.T. Smith (Ed.) DAMAGE DETECTION OPTIMIZATION USING THE WAVELET ENTROPY AND GENETIC ALGORITHM S.A. Ravanfar* StrucHMRS Group, Department of Civil Engineering, Faculty of Engineering,, Kuala Lumpur, Malaysia. (Corresponding Author) H. Abdul Razak StrucHMRS Group, Department of Civil Engineering, Faculty of Engineering,, Kuala Lumpur, Malaysia. Z. Ismail Department of Civil Engineering, Faculty of Engineering,, Kuala Lumpur, Malaysia. S.J.S. Hakim StrucHMRS Group, Department of Civil Engineering, Faculty of Engineering,, Kuala Lumpur, Malaysia. ABSTRACT This study presents an optimized damage identification algorithm using genetic algorithm (GA) to optimally determine the location and severity of damage in beam-like structures without baseline data. For this purpose, a vibration-based damage detection algorithm using a damage indicator called Relative Wavelet Packet Entropy (RWPE) was applied to determine the location and severity of damage. To improve the algorithm, GA was utilized to optimize the algorithm so as to identify the best choice of wavelet parameters. To examine the robustness and accuracy of the proposed method, numerical examples and experimental cases with different damage depths were considered and conducted. KEYWORDS Relative wavelet packet entropy, genetic algorithm, damage detection, beam-like structures. INTRODUCTION Structural monitoring and damage detection are areas of current interest in civil, mechanical and aerospace engineering. Most damage detection methods are visual or localized experimental procedures such as acoustic or ultrasonic methods, magnetic field methods, radiographs, eddy-current and thermal field methods. All these experimental techniques require that the location of damage be known a priori and that the portion of the structure under inspection be easily accessible. These limitations led to the development of global monitoring techniques based on changes in the vibration characteristics of the structure. Structural identification made on the basis of vibration data is an important research topic that has wide application for structural health monitoring, structural control, and response prediction (Farrar et al. 2001; Fan and Qiao 2011). This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit

3 Most of the vibration-based damage detection methods are often formulated as given changes of structural dynamic characteristics between the baseline and the current state to identify the location and severity of damage. However, due to absence of baseline data from undamaged states for most of the existing structures, these methods cannot be applied. To avoid this limitation, researchers have proposed several approaches for detecting structural damage without prior knowledge of the undamaged state. Ratcliffe (1997) proposed a damage identification method based on modified Laplacian operator for a beam, which operates only on data obtained from the damaged structure to locate variation in the structural stiffness. In this procedure, a cubic curve fit to modal data is performed and the difference between the curve fit and actual data is determined in order to locate the damage. Basically, the curve fit data serve as the baseline. The method was developed using a 1-D finite element model of beam, and demonstrated by experiment. The procedure was subsequently termed the 1-D gapped-smoothing method. Yoon et al. (2005) extended the 1-D gapped-smoothing method to the 2-D gapped-smoothing method to locate regions in a structure where the stiffness varies, in which baseline data and theoretical models of the presumably undamaged structure are not applied during the analysis. The procedure was conducted with a finite element model of a plate, and experiments on composite plates with deliberately induced multiple delaminations. Most of the proposed techniques for damage identification without the baseline modal parameters require the use of finite element models of the test structure to replace the baseline data from the intact structure. Therefore, an inaccurate finite element model may lead to large model errors which will consequently yield incorrect results in damage detection. Recently, wavelet analysis has become a widely used signal processing tool in the field of vibrationbased damage detection due to its potential characteristics such as singularity detection, good handling of noisy data and being very informative about damage location/time. Consequently, many studies on damage detection have focused on the wavelet transform scheme (Kim and Melhem 2004; Ovanesova and Suarez 2004; Umesha et al. 2009). Zhong and Oyadiji (2007) developed an approach based on the difference between two sets of detailed coefficients by using stationary wavelet transform (SWT) for crack detection in beam-like structures. The main limitation of the method is its applicability in symmetric beams. A new approach to measure acceleration response of a damaged beam was proposed by Mikami et al. (2011). This method was based on the variation between two sets of power spectrum density magnitudes calculated by means of wavelet packet decomposition components of two sets of dynamic data of the damaged beam. In the last two decades, genetic algorithms (GAs) (Haupt and Haupt 2004) have been recognized as promising intelligent search techniques for difficult optimization problems. A correct selection of the GA operators and parameters is crucial as they affect the solution and the algorithm running time (Elkamchouchi and Wagih 2003). Vakil-Baghmisheh et al. (2008) successfully applied the genetic algorithm to predict the size and location of a crack in a cantilever beam. In this study, a proposed algorithm for optimized damage detection in beam-like structures is investigated and applied to a damaged steel beam. This new approach is based on wavelet packet transform (WPT) combined with entropy analysis to determine an effective damage indicator, RWPE, for investigating the location and severity of damage. To improve the algorithm, GA was used to optimize the algorithm so as to identify the best choice of wavelet parameters. The proposed approach is verified through the numerical and experimental examples on damaged beam with different damage scenarios. It is shown that the present algorithm is able to identify the location and severity of damage precisely. WAVELET PACKET Wavelet Packet Decomposition (WPD) Wavelet analysis is multi-resolution analysis in the time and frequency domain of a non-stationary signal. It can be considered as an extension of the traditional Fourier transform with a modifiable window size and location (Neild et al. 2003). The wavelet packet function is defined as ACMSM

4 (1) where a wavelet packet is a function of three indices with integers i, j and k, denoting the modulation, the scale and the translation parameter, respectively. Moreover, (t) = for i = 0 and (t) = (t) for i = 1. The wavelet is called the scaling function and (t) is called the mother wavelet function. The wavelets for i > 1 are obtained from the scaling function and the mother wavelet function as: (2) (3) where g(k) and h(k) are quadrature mirror filters associated with the mother wavelet function and the scaling function. The original signal can be expressed as a summation of WPD components as, (4) where t is time lag; is the WPD component signal that can be represented by a linear combination of wavelet packet functions as follows: (5) WPD offers good time resolution in the high-frequency range of a signal and good frequency resolution in the low-frequency range of the signal. DAMAGE IDENTIFICATION PROCEDURE The wavelet packet component energy is a suitable tool to identify and characterize a specific phenomenon of signal in the time-frequency domain. The wavelet packet energy of a signal is defined as (6) where and stand for decomposed wavelet components. The total signal energy can be expressed as the summation of wavelet packet component energies when the mother wavelet is orthogonal. The damage detection problem can be formulated through the changes in the wavelet packet entropy of damaged structures to detect the location and severity of damage. To identify the change of vibration signals of a structure, the fundamental fitness function at a location has been considered as: ( ) ( ) (7) where is the energy ratio of each wavelet coefficient, and denote locations where the data is measured. It is notable that accelerations measured in the same direction should be used in computations of RWPE. Numerical investigation Finite Element Method Analysis To verify the suitability of the proposed method in beam-like structures, numerical simulations were conducted on I-section steel beam with a span length of 3m and simulated damage elements, as shown in Figure 1. Damage was simulated in the form of a notch with a 3mm width located at locayion 5. Damage depth for all beams was increased gradually from 3mm up to 75mm as depicted in Figure 1a. The mass density and modulus of elasticity of the beam material were 7850 and 2.1 GPa, respectively, and the Poisson s ratio was ACMSM

5 RWPE (a) Cross section (b) Damage location Figure 1. Numerical model of tested beam To identify the characteristics of damage in the beam, the node acceleration responses of the beam under the impulse load were obtained from sixteen locations on the top flange as shown in Figure 1b at a sampling frequency of 2000 Hz. To simulate an impulse load, the force-time history was applied at location 14 on the beam. GA was employed to search for the optimal Daubechies order and decomposition level of the signals by maximizing the fitness function. The parameters of GA are: probability of crossover Pc is 0.7, probability of mutation Pm is 0.2, the selection function is Tournament, the maximum number of generation is 200, the fitness normalization is Rank and the population size pop is 30. In addition, Table 1 indicates the variables of the GA used in the research. Table 1. GA variables Variable name Range Optimized value in tested beam Daubechies order DB1-DB31 DB2 Decomposition level Results and Discussion To validate the proposed damage detection method, the simulated simply-supported beams with damage elements were considered. Figure 2 shows the values of damage indicators calculated according to Eq. 7. By running the GA, DB2 and level 5 were selected as the best values for the Daubechies order and decomposition level, respectively Locations Figure 2. Histograms of damage indictors in beam with DB2 Results have illustrated that the damage locations can be accurately determined from the measured time history acceleration responses through variation of damage indicators. In addition, the respective amplitude levels of the histograms can be used as a criterion to identify severity of damage, although not quantitatively Depth of damages (mm) ACMSM

6 RWPE EXPERIMENTAL VERIFICATION Most modal-based damage features such as natural frequencies, mode shapes, modal strain energy and modal flexibility are sensitive to noise and measurement errors, which results in difficulties for practical applications. Therefore, the proposed damage detection method should be verified with real measurement data from dynamic tests on structures where noise and measurement errors are present. To illustrate the proposed algorithm, the vibration tests were performed on the steel beam with a span length and different damage scenarios, as shown in Figure 3. Sixteen accelerometers were mounted on the top flange along the beam to measure the acceleration response with a sampling frequency of 2000 Hz for all signals. (a) Damage locations of tested beams (b) data acquisition system Figure 3. Beam tested in the laboratory Experimental Results From the results, the following observations can be made based on the structural response signal of damaged beam. By running the GA, Daubechies order 2 and decomposition level 6 were chosen as the best parameters for the adjustment of the algorithm for differentiating the damages, as shown in Figure 4. The damage location at position 5 could be precisely identified with the significant change in values of damage indicators Locations Figure 4. Histograms of RWPE Depth of damages (mm) The results have demonstrated that for different wavelet-based methods, the choice of the mother wavelet function is of paramount importance to improve the performance of the algorithm. CONCLUSIONS An intelligent damage identification algorithm to detect damage in beam-like structures using vibration signal was developed and implemented. To verify the efficiency and practicability of the ACMSM

7 method proposed in the current research, both numerical simulation and experimental tests were carried out. The damage indicator was obtained from an optimized wavelet packet transform which was combined with the information entropy to gain the advantages of both techniques. Also, all the results show that the optimal damage indicator can be successfully used to identify the damage locations as well as damage severity from the response data of the damaged beam using an effective comparative approach. REFERENCES Elkamchouchi, H. M., & Wagih, M. M. (2003). Genetic algorithm operators effect in optimizing the antenna array pattern synthesis. Paper presented at the Radio Science Conference, NRSC Proceedings of the Twentieth National. Fan, W., & Qiao, P. (2011). Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring, SAGE, Vol. 10, No. 1, pp Farrar, C. R., Doebling, S. W., & Nix, D. A. (2001). Vibration based structural damage identification. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Royal society publishing, Vol. 359, No. 1778, pp Haupt, R. L., & Haupt, S. E. (2004). Practical genetic algorithms: John Wiley & Sons. Kim, H., & Melhem, H. (2004). Damage detection of structures by wavelet analysis. Engineering Structures, Elsevier, Vol. 26, No. 3, pp Mikami, S., Beskhyroun, S., & Oshima, T. (2011). Wavelet packet based damage detection in beamlike structures without baseline modal parameters. Structure and Infrastructure Engineering, Taylor & Francis, Vol. 7, No. 3, pp Neild, S., McFadden, P., & Williams, M. (2003). A review of time-frequency methods for structural vibration analysis. Engineering Structures, Elsevier, Vol. 25, No. 6, pp Ovanesova, A., & Suarez, L. (2004). Applications of wavelet transforms to damage detection in frame structures. Engineering Structures, Elsevier,Vol. 26, No. 1, pp Ratcliffe, C. P. (1997). Damage detection using a modified Laplacian operator on mode shape data. Journal of Sound and Vibration, Elsevier, Vol. 204, No. 3, pp Umesha, P., Ravichandran, R., & Sivasubramanian, K. (2009). Crack detection and quantification in beams using wavelets. Computer Aided Civil and Infrastructure Engineering, Blackwell Publishing, Vol. 24, No. 8, pp Vakil-Baghmisheh, M.-T., Peimani, M., Sadeghi, M. H., & Ettefagh, M. M. (2008). Crack detection in beam-like structures using genetic algorithms. Applied Soft Computing, Elsevier, Vol. 8, No. 2, pp Yoon, M., Heider, D., Gillespie Jr, J., Ratcliffe, C., & Crane, R. (2005). Local damage detection using the two-dimensional gapped smoothing method. Journal of Sound and Vibration, Elsevier, Vol. 279, No. 1, pp Zhong, S., & Oyadiji, S. O. (2007). Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform. Mechanical Systems and Signal Processing, Elsevier, Vol. 21, No. 4, pp ACMSM