Development of a Deep Learning System for Predicting the Shape of Delamination in Rubber Dampers
2024 Volume 5 Issue 2 Pages 66-73
Details
2024 Volume 5 Issue 2 Pages 66-73
Since the 1995 Hyogo-ken Nanbu Earthquake, rubber dampers have been increasingly adopted to improve earthquake resistance. However, in recent years, a deterioration phenomenon has been reported in which the vulcanization bonding area between the bottom of the rubber damper laminate and the bottom steel plate peels off. Although this delamination causes a significant reduction in seismic performance, a method for accurately measuring the degree of delamination has not yet been established. Previous studies have shown that there is a relationship between the degree of rubber damper delamination and the shape of warpage. Therefore, in this study, we have learned this relationship by deep learning using a neural network and developed a system to estimate the degree of delamination from the shape of the rubber damper’s warpage. As a result, it was found that deep learning can be successfully used to estimate the degree of delamination from the shape of the warpage of a rubber damper.
(1) Research Background
Rubber dampers are widely used in bridge structures, primarily for seismic resistance and damping. They effectively absorb seismic energy, thereby reducing the damage caused by earthquakes to bridge structures. In Japan, the effectiveness of rubber dampers was fully demonstrated during the 1995 Hanshin-Awaji Earthquake. Following this event, the adoption rate of rubber dampers and related damping technologies in bridge engineering increased significantly1). Given Japan’s location in a seismically active zone, the seismic performance of bridges has become a crucial factor in engineering design, with rubber dampers playing a vital role in enhancing the seismic resilience of bridges.
In recent years, studies have reported that rubber dampers experience aging over time. Aging leads to the degradation of the rubber material’s properties, directly affecting the load-carrying capacity of the dampers. One notable sign of aging is the delamination of rubber dampers. Delamination is the deterioration of the vulcanized bonding area between the lower steel plate and the laminate, which is caused by the corrosion of the lower steel plate. When this delamination occurs, it has been confirmed that it is the starting point of rupture and lowers the ultimate bearing capacity2). Therefore, timely detection of the aging degree of rubber dampers, particularly the changes in delamination shape, is essential for ensuring the safe operation of bridges.
(2) Current Research Status
The existing methods for detecting deterioration of rubber dampers primarily rely on manual inspection and surface detection techniques, which make it difficult to accurately assess the internal delamination of the rubber dampers. To obtain detailed internal delamination information, it is often necessary to remove the dampers from the bridge and rupture them. However, this method is not only time-consuming and labor-intensive but also challenging to implement in practical engineering scenarios. Therefore, developing a method that can accurately predict the internal delamination shape of rubber dampers without disassembly is of paramount importance.
Previous studies have attempted to evaluate the position of delamination between the internal steel plate and rubber layer of rubber bearings caused by aging deterioration using the acoustic emission (AE) method, a nondestructive inspection technique3). The AE method has only been used to detect delamination near the center of the laminate, and it is not known if the AE method is effective for delamination that occurs in the adhesive layer between the bottom of the laminate and the lower steel plate. It has also been confirmed that steel plates affect the accuracy of damage location estimation.
In recent years, neural networks and deep learning technologies have made significant advancements, demonstrating powerful analysis, computation, and prediction capabilities, especially in fields such as image recognition, natural language processing, and autonomous driving. Deep learning, by mimicking the connection structure of human brain neurons, can automatically extract features and patterns from large amounts of data, greatly improving the efficiency of data processing and analysis. In predicting the delamination shape of bridge rubber dampers, deep learning has shown great potential. By using deep learning models, it is possible to predict the internal delamination shape based on the observable edge warping of the rubber dampers. This provides an efficient and feasible method for detecting rubber damper delamination without the need for disassembly.
(3) Research Objectives
This study aims to predict the internal delamination shape of rubber dampers using deep learning technology, combined with the observable edge warping of the rubber dampers. Research4) indicates that there is a certain relationship between the shear deformation shape of rubber dampers and their internal delamination shape. Based on this relationship, this study will employ deep learning algorithms to construct a predictive model, with the goal of accurately predicting the internal delamination shape of rubber dampers that has been sheared and deformed by elongation and contraction due to temperature changes in the girder.
This chapter describes the process of generating training data for deep learning. Training a deep learning model requires a large amount of data as a foundation. The adequacy and diversity of the data directly affect the model’s performance and generalization ability. Therefore, when predicting the delamination shape of rubber dampers, it is essential to collect and generate a substantial amount of reasonable and effective training data. However, it is not practical to collect a considerable amount of actual rubber dampers with delamination and to confirm the shear shape and delamination shape. Therefore, rubber damper models that reproduce a wide variety of delamination shapes were created by FEM analysis, and shear deformation shapes were obtained from the analysis results.
(1) Generation of delamination shapes
Fig.1 shows the specific process of generating the peeling curve data used to train the deep learning model. The generation of initial curve data is mainly divided into six stages: Shape Initialization Stage, Shape Generation Stage, Shape Detection Stage, Shape Extraction Stage, Shape Processing Stage, and Shape Output Stage. Each stage is interconnected, collectively determining the generation of the initial training data.
First, the parameters used in this process are initialized in the Shape Initialization stage.
In the shape generation stage, a random number of points are placed at random locations on the edges where delamination begins. Then, ellipses of random sizes are generated centered on the placed points. Here, to avoid too unrealistic delamination shapes, the aspect ratio of the ellipse is restricted not to exceed 3:1. In the shape detection stage, the ellipse shape is verified, and if the limit is exceeded, the parameters (number of ellipses, ellipse center position, and ellipse size) are determined again.
Next, the shape extraction stage extracts only the outermost edges of the generated multiple ellipses. However, since the data as it is contains sharp areas of high curvature, a Savitzky-Golay filter is used to smooth the data in the shape processing stage. In addition, the curve is approximated as a staircase so that it follows the elemental partitioning of the structural analysis model.
Finally, at the Shape Output stage, the necessary delamination shapes are output after confirming that the required number of delamination shapes has been generated as training data. This time, 250 different delamination shapes were generated by following this process.
Fig.2 shows an example of the above process used to generate delamination shapes.
(2) FEM analysis
This chapter describes the finite element analysis performed during the study phase. The analysis uses the general-purpose structural analysis program ABAQUS ver.6.14 as a static analysis in which shear displacement is applied to a rubber damper model. The created rubber damper model is shown in Fig.3. The steel mesh is defined as an 8-node solid element type (C3D8R), and the rubber mesh is defined as an 8-node solid element type of hybrid element (C3D8RH) since the behavior of the rubber material is similar to incompressibility.
In the analysis of this study, it is necessary to represent the delamination shape generated by the method described in the previous section in the model. Therefore, delamination was represented by fully bonding the bonded areas and uncoupling the delaminated areas in the contact area between the lower steel plate and the laminate in the analytical model, following the delamination shape. It is assumed here that delamination does not progress due to the shear of the rubber damper.
As boundary conditions, the bottom of the lower steel plate is completely fixed, and the top of the upper steel plate is subjected to forced displacement in the direction that causes delamination to open up, for static analysis. A maximum shear displacement of 39.2 mm is used for forced displacement, which corresponds to 70% of the allowable shear strain at normal conditions as described in the Road Bridge Bearing Handbook5). Shear strain is the ratio of shear displacement to the rubber layer’s total thickness excluding the rubber damper’s steel plate.
The Ogden model shown in equation (1) was adopted as the strain energy density function for the material constitutive law of rubber materials. However, a volume change term was added to account for the micro-compressibility of rubber.
λ̅j (j = 1,2,3) and J are deviation elongation ratio in each direction and elastic volume ratio, respectively. The material properties of the Ogden model are shown in Table 1. The material property values for isotropic change are those for rubber materials provided by the Association for Nonlinear CAE6).
Fig.4 shows an example of a deformation diagram obtained from the analysis results. Shear deformation of the delaminated rubber damper results in warping of the bottom surface of the laminate. The vertical displacement of the four outer edges of the bottom of the laminate (red arrows in Fig.4) was extracted as an index to evaluate the shear deformation shape, which is referred to as the amount of warpage.
In this chapter, we describe the organization of deep learning models and the training process. The Python pandas and numpy libraries are mainly used for data organization in this chapter, and the Pytorch library is used to construct the deep learning model.
(1) Data Processing and Format Conversion
Based on the results from the aforementioned FEM analysis, we obtained the amount of warpage values corresponding to a series of randomly generated rubber damper delamination models under 14 different shear strains ranging from 5%, 10%, 15%, ..., to 70%. In addition, to increase the number of training data, the amount of warpage values of the analyzed cases and the cases where the delamination shape was reversed from left to right were generated by rearranging the order of the warpage values of the analysis results. Table 2 shows the number of training data at each shear strain. Basically, the total number of cases is 500, consisting of 250 cases of structural analysis results and 250 cases with delamination shapes reversed from left to right. The number of cases at some shear strains is less than 500, but this is because there are some cases where the solution of the structural analysis does not converge and no results are obtained for large shear strains.
(2) Neural Network Configuration
Fig.5 shows the simplified architecture of the Multi-Layer Perceptron Regression (MLP) model used in this study. The structure consists of four hidden layers, and the nodes in each layer are fully connected. ReLU is used for the activation function and mean square error (MSE) for the loss function.
(3) K-Fold Cross Validation
In the typical approach to training neural networks, the dataset is divided into two parts: a training set and a validation set. However, this one-time split strategy has some limitations. For example, the evaluation results are sensitive to data splitting and some of the data is not used for training, which can lead to unstable evaluation results.
In this study, a K-Fold Cross Validation scheme7) is employed to improve the general neural network training approach. In this scheme, the dataset is divided into K subsets. Each time, one subset is chosen as the validation set, while the remaining K-1 subsets are used as the training set for deep learning model training. After the training is completed, a different subset is used as the validation set, and the process is repeated K times. For example, in the case of this study, with K=10, the data set is divided into 10 subsets as shown in Fig.6, one as the validation set each time, and the training and evaluation are repeated 10 times. This scheme allows us to take advantage of all the data, reduce the variability of the evaluation, and improve the generalizability of the model.
Fig.7 shows the line graph of the deep learning training loss at 70% shear strain. Each background color represents a phase of K-Fold cross-validation. As shown, in the first training session, there are more training cycles and higher loss values. As training continues, the loss value decreases, and the model’s accuracy improves. The loss values in subsequent K-Fold validation stages remain within a smaller range, further ensuring the detection accuracy and generalization performance of the obtained deep learning model.
In this study, the accuracy of the constructed deep learning model is verified using the delamination shape obtained by shear rupturing a rubber damper that was actually in service, as shown in Fig.8. Fig.9 shows the delamination shape for accuracy verification. The delamination shape in (a) simulates the actual delamination shape shown in Fig.8. In addition, the delamination shapes in Fig.9(b) and (c) are randomly generated peel shapes. These three delamination shapes are not included in the training data of the deep learning model, and they are generated in a different way from the delamination shape generation method described in Chapter 2.
Fig.10 compares the predicted delamination shape with the actual delamination shape. For reasons of space limitation, the representative results are shown at 5%, 35%, and 70% shear strain. The amount of warpage input to the deep learning model is the result of the structural analysis model that reflects the delamination shape shown in Figure 8. It can be seen that the predicted delamination shape shows the similar trend with the correct shape.
It is considered effective to use the area of the delamination shape to evaluate the scale of delamination. Therefore, the area ratio defined by Equation (2) is introduced as an index to evaluate the prediction accuracy.
Equation (2) states that the closer the area ratio is to 1, the closer the predicted delamination shape area is to the actual delamination shape area. Fig.11 shows the area ratio for each shear strain. Fig.11 shows that the area ratio is within the range of 100 to ±25% for all shear strains.
As a result, it was confirmed that the predicted delamination shape closely matches the correct shape at all shear strains. Since the purpose of this study is to use the delamination boundary as an index to confirm the seismic performance of delaminated rubber dampers, it is not necessary to predict the delamination boundary completely, and we believe that the prediction accuracy shown in this study is sufficient. In this study, the number of training data varied depending on the shear strain, but since the prediction accuracy was not dependent on shear strain, the effect of the variation in the number of training data was considered to be small.
This study proposes a deep learning approach for nondestructive inspection of delamination shapes on rubber dampers. First, a variety of delamination shapes were generated, and FEM analysis was performed using a rubber damper model that reflected the delamination. Next, the accuracy of the proposed method was verified by deep learning using the training data set generated from the analysis results. The results obtained from this study can be summarized as follows:
(1) Preparing a large amount of training data by FEM analysis is time-consuming. Therefore, the number of FEM analyses was successfully reduced by only using data organization to generate results when the delamination shape is reversed from left to right, and by adopting the Cross Validation scheme, which allows efficient use of training data without waste.
(2) When the trained deep learning model was asked to predict three different peel shapes, which were not used in training, the correct and predicted peel shapes showed good correspondence at all shear strains. The area ratios were calculated to be within the range of 100 to ±25% in all cases. The proposed method was confirmed to be effective as a nondestructive inspection method for rubber dampers.
In order to put the delamination shape prediction system proposed in this study into practical use, it is necessary to actually measure the amount of warpage. Image processing technology is expected using a camera can be used for this purpose.
In addition, in this study, rubber dampers have been treated as the target, but deterioration due to delamination has also been observed in rubber bearings. Therefore, it can be used that the same detection method can be applied to rubber bearings by modifying the conditions of the structural analysis and creating a data set.
