II ECCOMAS THEMATIC CONFERENCE ON SMART STRUCTURES AND MATERIALS C.A. Mota Soares et al. (Eds.) Lisbon, Portugal, July 18-21, 2005 DAMAGE ASSESSMENT OF REINFORCED CONCRETE USING ULTRASONIC WAVE PROPAGATION AND PATTERN RECOGNITION Chikako Kondo * and Akira Mita * Graduate Student, Department of System Design Engineering Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan e-mail: konchika@xd6.so-net.ne.jp, web page: http://mwww.mita.sd.keio.ac.jp/ Professor, Department of System Design Engineering Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan e-mail: mita@sd.keio.ac.jp, web page: http://mwww.mita.sd.keio.ac.jp/ Keywords: AE sensor, Wave Propagation, Pattern Recognition, Support Vector Machine Abstract. An active damage detection method using Support Vector Machine (SVM) is proposed. The SVM is known as a powerful pattern recognition tool that can be applied to complicated classification problems. A damage detection method using ultrasonic waves and SVM was adopted to characterize damages in concrete structures. AE sensors composed of stacked piezoelectric transducers (PZT) were used to predict damages by using differences of propagation wave signals recorded before and after damages. The wavelet transform was applied for a time-frequency analysis of the propagation waves to characterize the feature vectors for feeding to SVMs. This method can correctly estimate the location of damages. Applicability of proposed damage detection method was successfully demonstrated. 1 INTRODUCTION Damage assessment plays an important role in maintenance or understanding the condition of the structures. However, damage assessment methods currently available for concrete structures still have many problems associated with the variety of concrete material characteristics. Additionally, they require involvement of experts in most cases. Furthermore, the results of damage detection tests vary widely because of the persons who 1
conducted the experiments [1,2]. Thus, a new assessment method that resolves the problems is needed. The purpose of this study is to propose a damage detection method that can obtain the detailed information of the damage by creating feature vectors for pattern recognition. The SVM which is one of the pattern recognition tools is effectively utilized in the system to achieve this purpose. 2 WAVELET TRANSFORM AND SUPPORT VECTOR MACHINE 2.1 Wavelet Transform The Fourier transform decomposes a signal into its various frequency components. As it uses the sinusoidal basis functions that are localized in frequency only, it loses the transient feature of signals. Therefore, it is necessary to implement the time-frequency analysis for diagnostics of transient signals induced by damages. In time-frequency analysis, the short-time Fourier transform calculates the local spectral density using windowing techniques to analyze a small section of the signal at a time. However, it has a higher resolution in the frequency domain but a lower resolution in the time domain. Moreover, it is impossible to simultaneously achieve high resolution in time and frequency [3]. In order to overcome the limitations of harmonic analysis, it has been considered to use the alternative families of orthogonal basis functions called wavelets. The continuous wavelet transform (CWT) decomposes a signal into time and frequency domain by the dilatation of a wavelet ψ (t) given in the following equation, where continuous variables a and b are the scale and translation parameters, respectively [4]. 1 t b ( wf )( b, a) = x( t) ψ dt (1) a a 2.2 Support Vector Machine The Support Vector Machine (SVM) is a mechanical learning system that uses a hypothesis space of linear functions in a high dimensional feature space [5,6]. The simplest model is called Linear SVM (LSVM), and it works for data that are linearly separable in the original feature space only. In the early 1990s, nonlinear classification in the same procedure as LSVM became possible by introducing nonlinear functions called Kernel functions without being conscious of actual mapping space. This extended technique of nonlinear feature spaces is called Nonlinear SVM (NSVM) shown in figure 1. n Assume the training sample S consisting of vectors x i R with i = 1,..., N, and each vector x i belongs to either of two classes thus is given a label y i { 1,1 }. The pair of ( w, b) defines a separating hyper-plane of equation as follows: (( x 1 y ),..., ( x )) S =,, 1 N y N (2) 2
( w x) + b = 0 However, Eq.(3) can possibly separate any part of the feature space, therefore one needs to establish an optimal separating hyper-plane (OSH) that divides S leaving all. (3) Original feature space xr n High dimensional space Original feature space xr n Figure 1: Non-linear SVM. The points of the same class on the same side, while maximizing the margin which is the distance of the closest point of S. The closest vector x i is called support vector and the OSH ( w ', b' ) can be determined by solving an optimization problem. The resulting SVM is called Hard Margin SVM. In order to relax the situation, Hard Margin SVM is generalized by introducing non-negative slack variables ξ = ξ, ξ, K, ξ ) as follows: minimize subject to margin y i 1 = + C ξ, d( w' ) ( w' w' ) 2 (( w' x ) + b' ) 1 ξ, i i ( 1 2 N i i = 1, 2,...,N, ξ 0. The purpose of the extra term of the C ξ i, where the sum of i = 1,..., N is to keep under control the number of misclassified vectors. The parameter C can be regarded as a regularization parameter. The OSH tends to maximize the minimum distance of 1 w with small C, and minimize the number of misclassified vectors with large C. To solve the case of nonlinear decision surfaces, the OSH is carried out by nonlinearly transforming a set of original feature vectors x i into a high-dimensional feature space by mapping Φ : x i a zi and then performing the linear separation. However, it requires an enormous computation of inner products ( Φ( x) Φ( xi )) in the high-dimensional feature space. Therefore, using a Kernel function which satisfies the Mercer s theorem given in Eq.(5) is required to significantly reduce the calculations to solve the nonlinear problems. In this study, we used the Gaussian kernel given in Eq.(6) as the kernel function. (4) ( Φ(x) Φ(x )) = ( x, ) i K x i (5) 3
K( x, x i exp( x ) = σ x i 2 ) (6) 3 DAMAGE DETECTION FOR REINFORCED CONCRETE This study's objectives are to know where the broken point of reinforcing bar is by observing wave propagation and to classify robust or damage automatically by using pattern recognition. The method of this study can resolve at least two problems; involvement of experts and preliminary survey. 3.1 Experiment set up 5cm Robust bar1 bar2 bar3 10cm Damage Broken point slit 2cm 3cm 3cm 2cm 25cm 50cm Figure 1: Specimen The specimens used in the experiment are shown in Figure 1. In this study, two specimens, ROBUST and DAMAGE were tested. There are 3 reinforcing bars, and in the middle of specimen, there is a slit. From this slit, the central reinforcing bar of damage specimen was cut. For a signal generation, a two-peak narrow-band, modulated sinusoidal burst waveform was selected for the actuator signal to simulate a transient wave. This signal vibrates the AE sensor as an actuator, and propagating wave was acquired by the other AE sensors as the sensors. The signal generation, signal filtering, A/D signal conversion were done using an Acellent Technologies Inc. SMART Suitcase [7]. Data acquisition was done by oscilloscope. 3.2 Choice of Frequency Before testing, it is needed to choose frequency of input wave. In the concrete specimen, high frequency wave is scattering easily and it has strong decay, on the other hand, low frequency wave doesn t have a good directivity, because concrete is not homogeneous. The experiments were conducted as follow. 4
One sensor and one actuator are put on the middle of the specimen just above reinforcing bars. The distance between the two AE sensors is 4cm. 3 points in each specimen, 6 points in all were measured.the frequencies of input wave were examined by 50 khz, 100 khz, 200 khz, 500 khz, 1 MHz. Figure 2 shows output waveform of robust specimen. Big amplitude is recognized when input wave is 50 khz, 100 khz, so we focus on 50 khz and 100 khz. Figure 3 shows power spectrum densities (PSD) of output waves. It is recognized PSD of 100 khz is bigger than PSD of 50 khz. Figure 4 shows cross spectrum densities (CSD) of 100 khz has opposite phase at damage specimen. Therefore, 100 khz was chosen as the input wave. bar1 bar2 bar3 p Figure 2: Choice of frequency 5
bar1 bar2 bar3 Figure 3: PSD Figure 4: CSD bar1 bar2 bar3 3.2 Damage Detection To obtain the information of the specimen that has damage or not, the experiment of damage detection was done. Figure 5 shows sensor arrangement. One sensor and one actuator are put on the middle of the specimen. The distance between the two AE sensors is 4cm. When a1 actuator is shaken, the data were acquired from s1 to s5 sensors. In this way, 25 points in each specimen, 50 points in all were measured. The output waveforms when the sensor arrangement were (a1,s1), (a3,s3), (a5,s5), were shown in Figure 6. The Red line in the middle of Figure 6 means the wave that passed the 6
broken point. It is recognized that the wave which passes the broken point is slow propagation and small amplitude. Therefore, these features are considered high correlation with damage. 2cm2cm Broken point 2cm 2cm s1 s2 s3 s4 s5 a1 a2 a3 a4 a5 s1 s2 s3 s4 s5 a1 a2 a3 a4 a5 4cm (a) robust specimen 4cm (b) damage specimen Figure 5: Sensor Arrangement a1s1 a3s3 a5s5 robust damage Figure 6: Output waveforms 7
4 PATTERN RECOGNITION USING SUPPORT VECTOR MACHINE 4.1 Creation of Feature Vectors For the damage detection using pattern recognition methods, creation of the feature vectors is needed. It was found that the waves which propagate on broken point of steel bar tend to propagate slowly and to have small amplitude by damage detection experiment. In order to take into account of these characteristics, feature vectors are created using the information of amplitude of per unit time. The procedures for creation of feature vectors are as follows. First, the raw data of output waveforms were applied wavelet transform to take out 100 khz component and then obtained the average of absolute amplitude value of per unit time. Feature vectors were created by the absolute amplitude value of first unit time as first dimension of feature vector, the absolute amplitude value of second unit time as second dimension, and so on. In this study, it was considered that time unit was 0.005ms, 0.01ms, and 0.02ms. In order to easy calculation, feature vectors were created in low dimension. Figure 7 shows creation of feature vectors. Robust Damage Robust Damage (a) raw data (b) applied WT First Dimension Second Dimension Robust Damage Second Dimension First Dimension (c) absolute value of amplitude (d) feature vectors Figure 7: creation of feature vectors (ex. 2 dimensions) 8
4.2 Build SVM In this study, SVMs were built in 3 cases shown in Figure 8. In the case 1, the sensor arrangements are parallel to reinforcing bar so that 10 points of the data were considered. In this case, the data of (a3,s3) in the damage specimen were assumed damage class. When feature vectors were created as 2 dimensions by using the data between 0 to 0.04ms dividing 0.02ms time units, it could classify the damage fairly. In the case 2, the data of all sensor arrangement, 50 points of the data were considered. The accuracy is similar to case 1. In the case 3, 12 points of data was considered. Two data (a2,s4) and (a4,s2) of damage specimen that passed the broken point were assumed damage class. In this case, it is hard to classify in all of the data. However, there is a possibility of classification robust or damage with accuracy in the case 3 when the feature vectors are created by higher dimension or shorter time unit. Figure 9 shows the distribution of feature vectors in case 1 and case 2. s1 s2 s3 s4 s5 a1 a2 a3 a4 a5 s1 s2 s3 s4 s5 a1 a2 a3 a4 a5 s1 s2 s3 s4 s5 a1 a2 a3 a4 a5 (a) case 1 (b) case 2 (c) case 3 Figure 8: SVM cases (pink line is damage class) Averages of abs in 0.020.04ms Damage class Averages of abs in 00.02ms Averages of abs in 0.020.04ms Damage class Averages of abs in 00.02ms (a) case 1 (b) case 2 Figure 9: Feature vectors distribution in case1 and case 2 9
5 CONCLUSIONS In this paper, a damage detection method for concrete structures using ultrasonic waves and pattern recognition techniques is proposed. The ultrasonic waves propagated through the damaged point of reinforcing bars were observed that have slow propagation and small amplitude. The feature vectors which were created by absolute values of amplitude of per unit time from the sensor signals applied wavelet transform were successfully used to build SVM. The waves which propagate just above the reinforcing bar were classified with high accuracy. However, to improve the proposed method for practical use, the proposal of the index of the better feature vectors that improve accuracy of discernment and the use of simulation data for creating the training data may be necessary. REFERENCES [1] H.Ikenaga, Review and Trend of Non-Destructive Tests on Concrete Structures, The Japanese Society for Non-Destructive Inspection, Vol50, No.7, 413-415 (2001). [2] T.Uomoto, K.Kato and S.Hirono, The Nondestructive Test for Concrete Structures, Kyoritsu Shuppan (1995). [3] Dae-Un Sung, Chun-Gon Kim, and Chang-Sun Hong, Monitoring impact damages in composite laminates using wavelet transform, Composites, Part B 33:35-43 (2002). [4] H.Jeong, and Y.Jang., Wavelet analysis of plate wave propagation in composite laminates, Composite Structures, 49:443-450 (2000). [5] Vapnik, V.N., The Nature of Statistical Learning Theory, Springer (1995). [6] Nello Christianini and John Shawe-Taylor, An Introduction to Support Vector Machines, (2000). [7] Mark Lin, Smart Layer and Smart Suitcase for Structural Health Monitoring Applications, Acellent Technologies,Inc. (2001). 10