2.1.1. Smart Bearing Construction

As shown in Figure 2, the smart bearing used in this study mainly consists of eight transducers, eight cover plates, two protective steel plates, and a laminated rubber bearing. To ensure that the placement of the transducers does not affect the axial and horizontal stiffness of the bearing, the transducers are symmetrically arranged on the upper and lower sides of the bearing. The upper transducers are used to generate the excitation signal (exciters), while the lower transducers are used to collect the detection signal (sensors). The purpose of placing a cover plate is to apply a certain pressure to the transducer, ensuring the effectiveness of wave transmission. The primary purpose of placing protective steel plates on the upper and lower sides of the bearing is to ensure that the transducers do not come into direct contact with the upper and lower structures (as the transducers can withstand only limited axial pressure), thereby allowing them to function properly. Each protective steel plate is designed with four measurement holes (to accommodate the transducers), four wire ducts (to house the connecting wires), and multiple bolt holes.

As shown in Figure 2(a), there are four exciters (G1–G4) and four sensors (S1–S4) arranged on the upper and lower sides of the bearing, respectively. In this study, the transducers used are longitudinal wave transducers with a diameter of 38 mm and a height of 30 mm. The specific parameters are shown in Table 1.

As shown in Figure 2(a), the transducer is placed between the cover plate and the bearing, and a certain amount of pressure (with a torque value of 2.5 N·m each) is applied to the cover plate using a bolted connection, thereby fixing the transducer to the surface of the bearing. The bolts connecting the transducers and the bearing are cup head hex socket bolts with a diameter of 4 mm and a length of 40 mm, with a strength grade of 12.9 (tensile strength of 1200 MPa and yield strength of 1080 MPa). As shown in Figure 3, the cover plate has a diameter of 54 mm and a thickness of 5 mm, with a groove of 38 mm in diameter and 1 mm in depth (used for mounting the transducers and maintaining its relative position to the cover plate). The three bolt holes are evenly spaced, with each located 46 mm from the center of the cover plate.

As shown in Figure 4, the protective steel plate has dimensions of 270 mm (length) × 270 mm (width) × 50 mm (height). The internal measurement hole has a diameter of 60 mm, with a distance of 50 mm between its center and the center of the protective steel plate.

As shown in Figure 5, the square laminated rubber bearing has dimensions of 200 mm (length) × 200 mm (width) × 60 mm (height). It is composed of five layers of thin steel plates (190 mm × 190 mm × 2 mm), two layers of thick steel plates (190 mm × 190 mm × 10 mm), and six layers of rubber (190 mm × 190 mm × 5 mm). The surface of the bearing is equipped with multiple bolt holes, which are categorized into two types based on the diameter: 4 and 8 mm. The 4 mm bolt holes are used to fix the transducers to the surface of the bearing, while the 8 mm bolt holes are used to connect the protective steel plates to the bearing.

2.1.2. Rupture Damage Creation

Due to the inability to obtain bearings with multiple damage degrees using the compression-shear testing machine, and the operational difficulties and uncontrollable damage degrees encountered when using cutting tools, this study creates rupture damage by separating the rubber and steel plate layers with cellophane, as shown in Figure 6. During the production process of laminated rubber bearing, a vulcanizing adhesive is applied to the overlapping areas of the steel plate and rubber layers. The vulcanized adhesive undergoes a chemical reaction at high temperatures, thereby firmly bonding the rubber and steel plate layers together. In this study, a strip of cellophane was placed around the outer edge of the contact area between the central steel plate and the rubber layer, without using the vulcanizing adhesive (as shown in Figure 6(d)). As a result, in the areas with cellophane, the rubber and steel plates are separated. Depending on the width of the outer area, the bearing’s rupture damage degrees are classified as Degree 0 (0 mm), Degree 1 (10 mm), Degree 2 (20 mm), Degree 3 (30 mm), Degree 4 (40 mm), and Degree 5 (50 mm), as shown in Figure 6(e). Degree 0 signifies that the bearing has no rupture damage (i.e., the bearing is healthy). Two bearings were fabricated for each rupture damage degree, resulting in a total of 12 laminated rubber bearings.

It is worth noting that there are certain differences between the rupture damage of the laminated rubber bearings designed in this study and actual conditions. Therefore, in future research, in addition to developing methods with higher detection accuracy, it will be necessary to obtain detection signals from bearings that more closely resemble or even match actual rupture damage conditions to improve the generalization capability of the prediction model.

2.2.1. Detection Process

During the detection process, one excitation and one reception strategy are employed. When an exciter is activated, the sensor on the same vertical axis collects the vibration signal.

The general process for detecting rupture damage in laminated rubber bearings based on the active sensing method is shown in Figure 7. The detecting system mainly consists of the NI DAQ system (NI PXIe-1071), piezoelectric transducers, and charge amplifier (YE5853). The NI DAQ system serves a dual purpose of generating excitation signals and acquiring detection signals. In this study, the excitation signal was a swept frequency signal with a duration of 1 s, an amplitude of ±10 V, and a frequency range of 1–100 kHz. In addition, the sampling frequency was 1 MHz, and the acquisition time was 1.5 s, starting 0.2 s early to fully capture the vibration signal. The exciter converts the excitation signal into a vibration signal, while the sensor converts the received vibration signal, which penetrates the entire laminated rubber bearing, into a charge signal. The charge amplifier converts the charge signal into a voltage signal and amplifies it simultaneously. In this study, the charge amplifier had a gain of 30, a sensitivity of 2.4, and allowed signals with frequencies below 100 kHz to pass through.

2.2.2. Loading Scheme

To obtain detection signals from the bearings under different axial pressures and improve the model’s applicability, this study designed the loading scheme shown in Figure 8. As illustrated in Figure 8, a total of 10 levels of axial pressure (i.e., 0, 1, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, and 20 MPa) were designed. Once the axial pressure stabilized, the active sensing method testing was conducted. Among them, the setting of 1 MPa is used to simulate a scenario where there is an axial force acting on the bearing, but its magnitude can be almost negligible. In this experiment, a microcomputer-controlled electrohydraulic servo compression–shear testing machine was used to apply pressure to the laminated rubber bearing, with a maximum loading pressure of up to 2000 kN (as shown in Figure 9). The loading scheme was carried out three times in total. Before each loading, the transducers needed to be reinstalled to ensure that the proposed machine learning model takes into account the impact of installation errors on the detection signals.

According to the Chinese code standard for seismic isolation design of the building (GB/T 51408-2021) [16], for standard fortified buildings, the maximum design axial pressure of laminated rubber bearings under gravity loads and rare earthquakes are 15 and 30 MPa, respectively. In addition, the axial pressure limit of the bearings used in this study is not less than 90 MPa. Therefore, it is reasonable to set the maximum axial pressure loading value at 20 MPa. This ensures that the bearings will not experience cumulative damage during the experiment and covers the axial pressure values encountered by most bearings in use. Given that the excitation of the exciters and the collection of detection signals require a certain amount of time, it is necessary to uphold the stability of axial pressure during this duration.

4.2.1. 1DCNN–LSTM Part

1DCNN is a variant of CNNs specifically designed for processing one-dimensional data, such as time series, signal processing, and sequential data. It offers advantages such as local feature learning, parameter sharing, translation invariance, and high computational efficiency [17, 18]. Unlike two-dimensional CNNs, which handle 2D images, 1DCNN slide convolutional kernels over a one-dimensional space, capturing local patterns in the data and effectively extracting features while maintaining computational efficiency [19].

The LSTM algorithm is a special form of RNN specifically designed for processing and predicting time series data [11]. Traditional RNNs, with their inherent recurrent structure, can capture temporal dependencies in sequential data. However, they often face issues such as vanishing or exploding gradients when dealing with long sequences, making it difficult for the network to remember long-term dependencies. LSTM addresses this problem by introducing a specially designed unit structure, the LSTM cell, which enables the network to better capture and retain long-term dependencies.

Therefore, this study utilizes a 1DCNN to extract local high-level features from the wavelet packet energy spectra of detection signals, and an LSTM to further extract their temporal features. The 1DCNN–LSTM part mainly consists of a database, 1DCNN layers, LSTM layers, and fully connected layers. First, the detection signals received by the sensors undergo filtering and WPD to obtain the wavelet packet energy spectra (i.e., the database in Figure 14). The database is randomly divided into three parts in a 7:2:1 ratio: training, validation, and test sets, which are used for model training, validation, and testing, respectively.

First, local features are extracted through six 1DCNN layers, all with a kernel size of 3 and an L2 regularization factor of 0.001. The number of filters in these layers, in sequence, are 128, 256, 512, 1024, 2048, and 4096. Each convolutional layer is followed by a batch normalization layer, a max-pooling layer (with a pool size of 2), and a dropout layer (with a dropout rate of 0.1), which serve to extract the local features, reduce the dimensionality of the data, and enhance the generalization ability of the model, respectively. After extracting local features through the 1DCNN layers, a flatten layer is used to flatten the data, followed by a reshape layer, configured with the parameters (2, 4096), to adjust the data into a shape suitable for input into the LSTM network to further extract temporal features. The LSTM layers consist of four layers, with the number of units in the sequence being 2048, 1024, 512, and 256. All LSTM layers use the ReLU activation function and are followed by dropout layers with a dropout rate of 0.1. Finally, there are three fully connected layers (Dense) with the number of units in the sequence being 512, 256, and 128, each with an L2 regularization factor of 0.001. Each layer is followed by a dropout layer with a dropout rate of 0.1 to further prevent overfitting. The model’s output layer is a softmax layer with 6 units, corresponding to the 6 classification labels. In addition, the model’s optimizer is Adam, with an initial learning rate set to 1e − 4. The loss function used is categorical cross-entropy, and the evaluation metric is accuracy. The stopping criterion is when the iteration count reaches the set value (1000).

After multiple iterations of training, the 1DCNN–LSTM model with the best predictive performance is saved, and the output (one-dimensional vector) from the last fully connected layer (i.e., the layer with 128 units) is extracted as input features for the BO–XGB model.

4.2.2. BO–XGB Part

The BO algorithm is a global optimization method designed for optimizing black-box functions with high computational costs [20]. This approach involves constructing a probabilistic model of the objective function (typically a Gaussian process) and using an acquisition function to intelligently select the next evaluation point, thereby balancing exploration and exploitation to gradually approach the optimal solution. Unlike traditional grid search and random search, the BO algorithm excels in applications such as hyperparameter tuning, where it can find better solutions with fewer iterations. Its primary advantages lie in its efficiency and global optimization capabilities, making it particularly suitable for complex optimization problems with nonanalytic expressions and high computational costs [21, 22].

In 2016, Chen and Guestrin introduced the XGB algorithm based on the traditional gradient boosting trees (GBTs) algorithm [23]. Compared to traditional GBT, the XGB algorithm integrates pioneering techniques and optimization strategies, including the incorporation of regularization terms, parallel computing, Taylor expansion, and approximate algorithms. As a result, XGB demonstrates significant advantages in computational efficiency, overfitting prevention, missing value handling, model flexibility, robustness, interpretability, and early stopping mechanisms. The core idea of the XGB algorithm is to iteratively build new trees to correct the prediction errors of the previous trees, thereby continuously improving the model’s prediction accuracy.

Therefore, based on the deep features extracted from the 1DCNN–LSTM part, this study establishes a high-precision rupture damage degree prediction model using the XGB algorithm. The BO algorithm is employed to optimize the key hyperparameters of the XGB model, aiming to find the global optimal values of the hyperparameters with as few iterations as possible, thereby improving training efficiency and prediction accuracy. The deep features extracted from the 1DCNN–LSTM part are randomly divided into training, validation, and test sets in a 7:2:1 ratio. First, a reasonable search range for the hyperparameters in the XGB model is set based on experience. In this study, the hyperparameters being optimized are the number of trees and the maximum depth of each tree, with search ranges of 100–2000 and 1–20, respectively. During each iteration of the BO algorithm, the potential performance of new hyperparameter combinations is first predicted using a surrogate model, specifically Gaussian process regression (GPR), based on the existing hyperparameter combinations and their corresponding performance. The BO algorithm then optimizes the acquisition function, specifically expected improvement (EI), based on these predictions to select a new hyperparameter combination, which is subsequently used to train the XGB model. After training, the XGB model is evaluated on the validation set to record its performance. These performance results are fed back into the BO algorithm, which further updates the surrogate model and reoptimizes the acquisition function to select new hyperparameter combinations, repeating the process. This process continues until a predefined stopping criterion is met. In this study, the stopping criteria are when the iteration count of the BO algorithm reaches 200. After 200 iterations, the model with the highest test set accuracy, where the difference in accuracy between the training and test sets is within 0.05, is selected as the final model.

It is important to note that the parameter values in the above algorithm were determined through a trial-and-error strategy. When addressing different problems, these parameters may need to be adjusted based on the model’s prediction results.