Quantification of Structural Damage with Self-Organizing Maps

Chapter 5 Quantification of Structural Damage with Self-Organizing Maps Osama Abdeljaber, Onur Avci, Ngoan Tien Do, Mustafa Gul, Ozan Celik, and F. Necati Catbas Abstract One of the main tasks in structural health monitoring process is to create reliable algorithms that are capable of translating the measured response into meaningful information reflecting the actual condition of the monitored structure. The authors have recently introduced a novel unsupervised vibration-based damage detection algorithm that utilizes selforganizing maps to quantify structural damage and assess the overall condition of structures. Previously, this algorithm had been tested using the experimental data of Phase II Experimental Benchmark Problem of Structural Health Monitoring, introduced by the IASC (International Association for Structural Control) and ASCE (American Society of Civil Engineers). In this paper, the ability of this algorithm to quantify structural damage is tested analytically using an experimentally validated finite element model of a laboratory structure constructed at Qatar University. Keywords Self organizing maps • Damage detection • Damage identification • Structural health monitoring • Modal testing 5.1 Introduction Engineering structures are subjected to environmental and human-induced factors that reduce reliability and life cycle performance regardless of their design quality. Structural damage due to deterioration, fatigue, corrosion, creep, shrinkage and scour are commonly encountered especially in countries with extreme climate. The traditional approaches of damage assessment which basically rely on visual inspection and human judgment are no longer effective due to economical and practical reasons. Therefore, it is of utmost importance to develop automated and smart structural damage detection systems with the ability to assess the structural condition in the real-time. In general, damage detection techniques are classified into local and global methods. Local damage detection methods are developed to detect and quantify damage in a relatively small scale, whereas global techniques are implemented to track the overall behavior of structures. Due to the large size and complexity of civil infrastructures, local damage assessment methods are not sufficient for health monitoring of such structures. Consequently, local damage detection techniques should be incorporated with global techniques (i.e., vibration-based techniques) to develop an efficient structural health monitoring system that provides a complete understanding of the structural condition. Vibration-based damage assessment methods use the vibration response of the structure measured by a relatively small set of accelerometers for damage identification and quantification. Vibration-based damage assessment approaches are divided into parametric and nonparametric methods. Parametric methods use structural system identification algorithms to identify the modal parameters of the monitored structure, such as modal frequencies and damping ratios, according to the measured vibration response. Nonparametric methods employ statistical approaches to process raw acceleration signals and extract damage indicators. Nonparametric algorithms demonstrate damage features that cannot be easily attributed to physical changes of the monitored structure [1]. Therefore, nonparametric methods have attracted the attention of researchers in the field of structural health monitoring [2]. O. Abdeljaber • O. Avci (*) Department of Civil and Architectural Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar e-mail: onur.avci@qu.edu.qa N.T. Do • M. Gul Department of Civil and Environmental Engineering, University of Alberta, 7-203 Donadeo Innovation Centre for Engineering, 9211-116 Street NW, Edmonton, AB, Canada, T6G 2R3 O. Celik • F.N. Catbas Department of Civil, Environmental and Construction Engineering, University of Central Florida, Central Florida Blvd, Orlando, FL 32816-2450, USA # The Society for Experimental Mechanics, Inc. 2016 A. Wicks, C. Niezrecki (eds.), Structural Health Monitoring, Damage Detection & Mechatronics, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29956-3_5 47 48 O. Abdeljaber et al. Artificial neural networks (ANNs) have been used by several researchers in an attempt to develop nonparametric damage detection algorithms. Many types ANNs have been implemented for this purpose such as nonlinear autoregressive with exogenous inputs (NARX) neural networks [3], probabilistic resource allocation networks [4], pattern recognition neural networks [5], and Bayesian neural networks [6]. Self-organizing maps (SOMs) are another important type of neural networks that can be used to generate a two-dimensional map that describes the topology of the input data. In other words, SOMs are utilized to cluster highdimensional data set into a number of groups. SOMs are trained using unsupervised learning rules, which means that the training process of SOMs relies only on the internal properties between the inputs and does not require input–output samples [7]. Recently, the authors have introduced a novel nonparametric damage detection algorithm that relies on SOMs to extract damage indices from the acceleration data in the time domain measured under random excitation. In a previous study [8], the authors have demonstrated the ability of this algorithm to quantify structural damage under five damage scenarios included in Phase II Experimental Benchmark Problem of Structural Health Monitoring [9]. These scenarios include removing braces and/or loosening bolts of an experimental four-story steel frame. The results have shown that this algorithm is accurate, robust, and reliable for damage quantification. In the study presented herein, the SOM-based damage detection algorithm is tested analytically on a finite element model of a recently constructed lab structure. As will be explained in Sect. 5.2, this lab structure represents the first phase of the construction of a grandstand simulator at Qatar University (QU). The accuracy of the finite element model used in this study has been experimentally validated by comparing the finite element modal properties to the actual properties of the lab structure which were measured using experimental modal testing. The five damage cases considered in this study are created analytically either by introducing damage to a number of connections or by slightly reducing the stiffness of particular beams. 5.2 Qatar University Grandstand Simulator The authors are currently conducting comprehensive analytical and laboratory studies related to structural health monitoring and vibrations serviceability of stadia. These studies aim at developing new structural damage detection methods optimized for monitoring of modern stadia as well as investigating the effects of human-environment-structure interaction on the dynamic response of such structures. A grandstand simulator is currently under construction at Qatar University to serve as a test bed for the aforementioned studies. QU grandstand simulator is still in the initial phase of construction. So far, as shown in Fig. 5.1, only the main steel frame has been constructed. Non-structural elements such as the risers, treads, handrails, and seats will be installed in the next stage of construction. However, before proceeding with the construction of the complete structure, the authors have decided to utilize the test structure in its current form to conduct a series of studies related to modal testing and structural damage detection. Fig. 5.1 QU grandstand simulator under construction 5 Quantification of Structural Damage with Self-Organizing Maps 49 The main steel frame of QU grandstand simulator consists of 8 main beams and 25 filler beams supported on 4 columns. The eight main beams are 4.6 m long, while the length of the five filler beams in the lower portion is about 1 m and the length of the remaining filler beams is 77 cm. The main girders as well as the secondary beams were assigned by slender steel sections (IPE120). The 25 filler beams are removable and interchangeable which makes this test structure ideal for damage detection studies since many damage scenarios can be simulated either by loosening the bolts at beams to girder connections or by replacing some of the filler beams with damaged ones. 5.3 Verification of the Finite Element Model Based on the design calculation and CAD drawings, a detailed three-dimensional finite element model of the main steel frame of QU grandstand was created using Abaqus 6-14 [10]. This FE model is shown in Fig. 5.2. All members within the steel deck were modeled as C3D20R elements (20-node quadratic brick, reduced integration). A very fine mesh was used to model the members in order to enhance the accuracy of the FE model. The connections between the main and secondary beams were modeled in Abaqus as tie constraints. The steel deck was assumed to be pin-supported over the locations of the four columns. All elements in the FE model were assigned by 210 GPa Young’s modulus, 0.3125 Poisson’s ratio, and 7850 Kg/m3 density. Lanczos eigensolver was used to identify the natural frequencies and the mode shapes of the first four bending modes of the FE model. The results of this numerical modal analysis are provided in Fig. 5.3 and Table 5.1. Dynamic impact test was carried out in order to experimentally measure the actual natural frequency, mode shapes, and damping ratios of the steel frame. In order to verify the accuracy of the finite element model, a comparison between the finite element and experimental modal frequencies is presented in Table 5.1. This comparison indicates an excellent agreement between the actual frequencies measured experimentally by impact testing and those predicted analytically by finite element analysis especially for the first two bending modes. Therefore, it can be concluded that the finite element model represents the fundamental modes of the structure accurately even without applying finite element model updating techniques. 5.4 The SOM-Based Damage Detection Algorithm As previously mentioned, the authors have recently developed and tested an SOM-based nonparametric damage detection algorithm [8]. In this algorithm, SOMs are utilized to process the signals acquired by the accelerometers in the time domain measured under random excitation in order to generate a topology map for the random response at each node. The topology maps generated for the undamaged structure are considered as the structural signature. The algorithm requires dividing the accelerometers into groups of two. For each group, a self-organized map is trained and used to extract features from the relative response between its two accelerometers for the undamaged structure. These features (in the form of two-dimensional maps) constitute the baseline of the proposed damage assessment technique. When damage assessment is conducted, the same feature extraction procedure is applied. By comparing the baseline and the measured two-dimensional maps, damage can be quantified by measuring the extent to which the relative response between the two accelerometers in each group has changed with respect to the undamaged condition. The training and implementation processes of the SOM-based damage detection algorithm are explained in the following two subsections. Fig. 5.2 Abaqus finite element model of the test structure 50 O. Abdeljaber et al. Fig. 5.3 The first four bending modes of the test structure Table 5.1 Comparison between the finite element and the experimental natural frequencies Bending mode 1 2 3 4 5.4.1 Finite element frequency (Hz) 16.00 16.58 24.48 48.34 Experimental frequency (Hz) 15.7 16.4 25.2 50.6 Error (%) 1.91 1.10 2.86 4.47 Training of the SOMs Training of the SOMs is conducted according to the following steps: Step 1: The vibration response of the undamaged structure under random excitation signal is measured for n time steps using a set of accelerometers.
Step 2: The accelerometers are divided into k groups Gi¼1 , Gi¼2 , . . . , Gi¼k . Each group is assigned by two accelerometers G1i and G2i . Step 3: The relative acceleration signal between the two accelerometers in each group i is computed as Si ¼ G2i G1i ð5:1Þ Step 4: For each relative acceleration signal Si, at each
time step t, the acceleration  value at this time step as well as the values at d time steps behind Sti d , Sti dþ1 , . . . , Sti 1 are stored in a vector Vti ¼ Sti d Sti dþ1 . . . Sti 1 Sti . Therefore, at the end of this step a total of n vectors are stored for each acceleration signal. This process is illustrated in Fig. 5.4. Step 5: All vectors generated in the previous step are normalized by dividing each one by its maximum absolute value according to the following equation. VNti ¼ Vti max Vti ð5:2Þ 5 Quantification of Structural Damage with Self-Organizing Maps 51 Fig. 5.4 Signals processing and computation of vectors Acceleration Relative Acceleration Signal Time Step (T) Step 6: The normalized vectors corresponding to each relative accelerometer signal Si are arranged in a matrix  t i i i . The number of matrices generated in this step equals to the total number of groups k. VNt¼2 . . . VNt¼n Mi ¼ VNt¼1 Step 7: A self-organizing map SOMi is trained to cluster the normalized vectors in each matrix Mi corresponding to the relative acceleration signal Si into a two dimensional topology map Tui with a dimension of ðl  lÞ. In other words, the self-organizing map SOMi is trained to classify the n normalized vectors in the matrix Mi into ðl  lÞ groups according to the similarity between the vectors. Therefore, each element in the topology map generated after the training of SOMi will be assigned by an integer which describes how many vectors in the matrix Mi are assigned to the group represented by this element. The training of the SOMs is carried out using batch unsupervised weight/bias training algorithm. At the end of this step, a total of k SOMs corresponding to the total number of accelerometers groups are trained. Also, a total of k topology maps are obtained. The trained SOMs are stored in order to be used for damage assessment. The procedure described in this step is explained in Fig. 5.5.
Step 8: The topology maps for the undamaged case generated by each SOM Tui¼1 , Tui¼2 , . . . , Tui¼k are normalized by dividing each map by the total number of normalized vectors in the corresponding matrix Mi (i.e. the number of time steps n in the recorded acceleration signals). TNui ¼ Tui n ð5:3Þ
i¼2 i¼k are stored in order to be used Step 9: The normalized topology maps for the undamaged case TNi¼1 u , TNu , . . . , TNu for damage assessment. 52 O. Abdeljaber et al. Fig. 5.5 Training of selforganizing maps and generation of topology maps 5.4.2 Structural Damage Assessment Here, the SOMs as well as the normalized topology maps for the undamaged case obtained by the previous procedure are used to evaluate the condition of the monitored structure by comparing the measured topology maps to the topology maps generated for the undamaged case (i.e. the structural signature). This is explained in the following steps. Step 1: The response of the monitored structure under random excitation is measured for n time steps using a set of accelerometers. Step 2: The steps 2–6 explained in the previous section are followed in order to create the matrices
Mi¼1 , Mi¼2 , . . . , Mi¼k that contain the normalized vectors for each relative accelerometer signal. Step 3: For each relative accelerometer signal Si, the corresponding self-organizing map SOMi trained according to the undamaged response in the previous section is used to generate a topology map Tmi. At the end of this step, a total of k topology maps are generated.
i¼2 i¼k Step 4: The measured topology maps for the current case Ti¼1 are normalized by dividing each map by m , Tm , . . . , Tm the total number of normalized vectors in the corresponding matrix Mi (i.e. the number of time steps n in the recorded acceleration signals). TNmi ¼ Tmi n ð5:4Þ Step 5: Each measured normalized topology map TNmi is compared to the corresponding undamaged normalized topology map TNui generated in the previous section. This is done by computing the root mean square (rms) value of the difference between the measured and the undamaged maps according Eq. (5.5). The computed value is called the damage index for the accelerometer group i. At the end of this step, the damage indices at each node are computed ðDI i¼1 , DI i¼2 , . . . , DI i¼k Þ. The damage indices can be scaled by a constant C. Steps 3, 4 and 5 are illustrated in Fig. 5.6. DI i ¼ C  rms TNui TNmi
ð5:5Þ Step 6: The damage indices are summed to evaluate the overall condition of the structure according to the following equation. D¼ k X DI i ð5:6Þ i¼1 High values of D indicate a considerable change in the structural signature, which can be used to evaluate the severity of damage. On the other hand, low values of D (closer to zeros) indicate that the monitored structure is undamaged. 5 Quantification of Structural Damage with Self-Organizing Maps 53 Fig. 5.6 Computation of damage indices 5.5 Numerical Demonstration of the Damage Detection Algorithm In this section, the finite element model of the lab structure created and verified in Sect. 5.3 is utilized to demonstrate the ability of the damage detection algorithm to assess the overall structural condition. As shown in Fig. 5.7, the structure is assumed to be equipped with a total of 15 accelerometers. The accelerometers are grouped in 10 groups as explained in Table 5.2. The five damage cases illustrated in Figs. 5.8 and 5.9 are considered in this study. For the first four cases, damage is simulated by reducing the stiffness at a number of beam-beam connections by 50 %. For the Case 5, further damage is introduced by slightly reducing the stiffness of a main girder (by 10 %). The five damage scenarios are arranged to the damage severity, from almost undamaged to (Case 1) to extremely damaged (Case 5). The procedure explained in Sect. 5.4.1 was followed to train the SOMs required for damage detection. Abaqus software was used to simulate the response of the undamaged structure under a randomly-generated white noise base excitation. The dynamic response was computed for 20 s at a time increment of 0.001 s. This analysis resulted in 15 acceleration signals, each consisting of 15  103 time steps. Based on these signals, a total of 10 SOMs (corresponding to the number of accelerometers groups) were generated and trained. Also, the resulting topology maps were stored in order to be used damage assessment. A Matlab [11] code has been written to carry out the SOM training process. This code employs the batch unsupervised weight/bias training algorithm available in Matlab Neural Network Toolbox under “trainbu” subroutine. The parameters of the damage detection algorithm were selected based on trial-and-error. The size of SOMs was selected as l  l ¼ 12  12, and the number of past acceleration values in vectors Vti was taken as d ¼ 20. Similarly, the acceleration response of the structure under the five damage cases was simulated using Abaqus for the same duration and time increment. Again, the responses were computed under randomly-generated white noise excitation signals. The damage assessment process described in Sect. 5.4.2 was programmed using Matlab and applied to compute the 10 damage indices and the overall damage index under each damage case. The results of this process are given in Table 5.3. Also, the total damage values for the five cases are graphically presented in Fig. 5.10. 54 O. Abdeljaber et al. Fig. 5.7 Accelerometers distribution and IDs Table 5.2 Accelerometers groups 5.6 Group number 1 2 3 4 5 6 7 8 9 10 First accelerometer AC01 AC02 AC03 AC04 AC05 AC06 AC07 AC08 AC09 AC10 Second accelerometer AC06 AC07 AC08 AC09 AC10 AC11 AC12 AC13 AC14 AC15 Discussion The damage assessment results shown in Table 5.3 demonstrate the ability of the damage detection algorithm to quantify structural damage. Starting from the slightest damage case (i.e. Case 1), damaging one connection only has resulted in a relatively low overall damage value of 15.4. When further damage is introduced in Case 2 by damaging two more critical connections, the total damage value computed by the algorithm has increased dramatically to 105.3 (by about 580 % compared to Case 1). For Case 3, two additional beam-beam connections were damaged, however, the total damage amount increased by only 35 % to a value of 142.7. This is totally expected since the two additional connections damaged in Case 3 correspond to a non-critical filler beam. Therefore, introducing damage to these connections didn’t affect the structural 5 Quantification of Structural Damage with Self-Organizing Maps Fig. 5.8 Damage cases 1–4 (highlighted connections represent damaged connections) Fig. 5.9 Damage case 5 (highlighted connections represent damaged connections, and red beam represents a damaged beam) 55 56 O. Abdeljaber et al. Table 5.3 Damage indices computed for the five damage cases Damage case 1 2 3 4 5 DI1 1.56 4.64 6.01 12.68 16.62 DI2 1.21 17.71 23.23 19.98 17.35 DI3 1.52 4.23 5.45 12.92 26.50 DI4 1.78 4.42 5.43 12.85 26.23 DI5 1.84 12.74 19.63 32.33 56.21 DI6 1.81 5.41 6.33 11.06 17.00 DI7 1.57 10.34 15.16 30.93 25.65 DI8 2.19 11.71 15.11 31.42 67.66 DI9 0.75 13.31 23.04 19.66 25.23 DI10 1.19 16.74 23.32 19.73 27.61 Total damage 15.41 105.27 142.72 203.58 306.07 Fig. 5.10 Total damage values of the five damage cases performance significantly. Again, damaging several additional non-critical connections in Case 4 increased the total damage only by 43 % to a value of 203.6. In Case 5, the algorithm is tested against another damage scenario in which one of the stiffness of one of the main beam is slightly reduced (by 10 %) in addition to the connections damaged in the previous four cases. The total damage for this case increased by 50 % with respect to the previous damage case which shows that the algorithm is able to detect and quantify damage due to slight loss of stiffness. Overall, the algorithm has shown great sensitivity to damage. Additionally, the total damage value D computed for each damage case is found to be proportional to the actual damage amount. 5.7 Conclusion A novel nonparametric vibration-based damage detection algorithm has been previously introduced by the authors. In the study presented in this paper, the ability of this algorithm to assess the overall structural condition was numerically demonstrated. A detailed three-dimensional finite element model of a test structure was utilized for this purpose. The accuracy of the FE model was verified experimentally by comparing the FE modal characteristics to the actual properties measured experimentally. The performance of the algorithm was tested against five simulated damage cases. It was concluded that the algorithm is sensitive to structural damage. Moreover, the total damage value computed using the proposed algorithm is representative the actual amount of damage in each damage scenario. Therefore, this algorithm is useful as an indicator to the overall structural health. It is highly recommended to conduct further studies to understand the relationship between the distribution of the damage indices and the location of damage. Such studies will allow the algorithm to identify the location of damaged members/ connections. Additionally, it is recommended to conduct extensive experimental studies in order to verify the findings of the numerical analysis presented in this paper. Acknowledgements The financial support for this research was provided by Qatar National Research Fund, QNRF (a member of Qatar Foundation) via the National Priorities Research Program (NPRP), Project Number: NPRP 6-526-2-218. 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