A portable laminated rubber bearing nondestructive testing device and bearing damage identification method

Abstract

The application discloses a portable laminated rubber bearing nondestructive testing device and a bearing damage identification method. The testing device comprises a guide rail in the form of an I-shaped steel structure, which is provided with a plurality of bolt holes for mounting piezoelectric ceramic transducers; the piezoelectric ceramic transducers are arranged in the guide rail ring and used for generating and receiving elastic waves; customized bolts and nuts are used for fixing the piezoelectric ceramic transducers on the guide rail and exerting a certain pressure through pre-tightening force to ensure the propagation of elastic waves; and a circular ring type force sensor is attached to the nut of the customized bolt and used for monitoring the bolt pre-tightening force. The testing device provided by the application is suitable for all laminated rubber bearings without changing the bearing structure, realizes nondestructive testing of the bearing, and is simple to operate. The application also discloses a laminated rubber bearing damage identification method fusing a 1DCNN, an LSTM and an XGBoost algorithm, and high-precision identification of the damage type and degree of the laminated rubber bearing can be realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of rubber bearing health detection, and particularly relates to a portable laminated rubber bearing nondestructive testing device and a damage identification method. BACKGROUND

[0002] The laminated rubber bearing composed of multiple layers of rubber and steel plates has the advantages of simple structure, low cost, good isolation effect, etc., and has been widely used in bridge engineering, building engineering and other fields. However, factors such as temperature change and load duration cause the aging damage degree of the rubber bearing to develop continuously, which weakens the isolation performance of the bearing, thereby bringing risks to the safety of the structure.

[0003] At present, the main detection method is to judge by the experience of the detection personnel, which often faces the problem of low accuracy of the detection result. Therefore, the alternative method of combining piezoelectric wave method and machine learning technology for bearing aging damage degree detection has attracted attention. However, arranging piezoelectric ceramic transducers on the front side needs to change the structure of the bearing, on the other hand, it also faces the problems of difficulty in maintenance or replacement, increase in detection cost, and inability to be used for existing bearings. Arranging piezoelectric ceramic transducers on the side either connects the bearing and the transducer through an adhesive, or changes the structure of the bearing to fix the transducer by a bolt connection method. The former has problems such as inconvenient operation and inconsistent bonding strength, while the latter faces problems such as increased production process of the bearing, high production cost, and inapplicability to existing bearings.

[0004] In the prior art, a rectangular laminated rubber isolation bearing and a method for in-situ detection of aging damage thereof (CN118128208A) improves the structure of a common laminated rubber isolation bearing, as shown in Figure 1 arranges bolt holes to fix the transducer and the bearing together by a bolt connection method.

[0005] However, the existing technology has the following disadvantages: 1. The structure of the bearing needs to be changed to arrange bolt holes, which increases the production process and cost of the bearing, and is not applicable to existing bearings; 2. The steel plate layer is directly in contact with the air, which easily causes rust of the steel plate and reduces the mechanical properties of the bearing. SUMMARY

[0006] To solve the above technical problems, the present application provides a laminated rubber bearing nondestructive testing device which does not need to change the structure of the bearing and is applicable to all laminated rubber bearings, does not damage the bearing during detection, and is easy to operate, to solve the problems existing in the above prior art.

[0007] To achieve the above purpose, the present application provides a portable laminated rubber bearing nondestructive testing device, which comprises:

[0008] The rail is made of an I-shaped steel structure, and a circular ring and a plurality of bolt holes are arranged on the rail, for mounting a piezoelectric ceramic transducer;

[0009] The piezoelectric ceramic transducer is arranged in the circular ring of the rail and is used for generating and receiving elastic waves.

[0010] Customized bolts and nuts are used to fix the piezoelectric ceramic transducer on the rail and apply a certain pressure through pre-tightening force to ensure the propagation of the elastic waves.

[0011] The circular ring type force sensor is attached to the nut cap of the customized bolt and is used for monitoring the bolt pre-tightening force.

[0012] Preferably, the center line of the bolt hole is located on the symmetry plane of the rail.

[0013] Preferably, an incompletely closed circular ring is fixed at the lower wing plate of the rail, the inner diameter of the circular ring is consistent with the outer diameter of the piezoelectric ceramic transducer, and the depth of the circular ring is lower than the height of the piezoelectric ceramic transducer.

[0014] Preferably, the width of the rail and the diameter of the nut cap of the customized bolt are not less than the outer diameter of the circular ring type force sensor, so that the circular ring type force sensor can accurately monitor the bolt pre-tightening force.

[0015] Preferably, during the detection process, the display value of the circular ring type force sensor is a constant value, so as to ensure that the stress of the transducer is uniformly distributed.

[0016] Preferably, the installation process of the detection device comprises:

[0017] The nut cap of the customized bolt is attached to the circular ring type force sensor, and the customized bolt is connected with the rail together.

[0018] The piezoelectric ceramic transducer is placed in the circular ring of the rail, the bottom surface of the piezoelectric ceramic transducer is attached to the side surface of the laminated rubber support, and the piezoelectric ceramic transducer is placed in the circular ring of the opposite rail and is attached to the side surface of the laminated rubber support through the customized bolt.

[0019] The two nuts are simultaneously and slowly tightened by a wrench, so as to ensure that the display value of the circular ring type force sensor is consistent, until a pre-set value is reached.

[0020] In order to achieve the above technical purpose, the application further provides a laminated rubber support damage identification method, characterized by comprising the following steps:

[0021] Based on the portable laminated rubber support non-destructive testing device, the laminated rubber supports with different damage types and different damage degrees are detected to obtain detection signals.

[0022] The detection signals are filtered to remove noise in the signals, and wavelet packet energy spectrum of the filtered detection signals is obtained by wavelet packet decomposition;

[0023] A multi-label classification model is established, wavelet packet energy spectrum of all detection signals is taken as input parameters, damage type and degree of the support are taken as output parameters, the multi-label classification model is trained, and a trained multi-label classification model is obtained; wherein the multi-label classification model adopts a model architecture that fuses one-dimensional convolutional neural network, long short-term memory neural network and extreme gradient boosting algorithm;

[0024] Based on the portable laminated rubber support nondestructive testing device, detection signals of a laminated rubber support to be detected are obtained;

[0025] The detection signals are filtered and decomposed by wavelet packet in sequence, and wavelet packet energy spectrum to be detected is obtained;

[0026] The wavelet packet energy spectrum to be detected is taken as input parameters and substituted into the trained multi-label classification model, and identification results of damage type and degree are obtained.

[0027] Preferably, the wavelet packet energy spectrum is:

[0028]

[0029] wherein i is the number of decomposition layers, j is the node number, n is the sampling point, W i,j (n) is the node coefficient, E i,j is the wavelet packet energy obtained by wavelet packet decomposition of the detection signal.

[0030] Preferably, the multi-label classification model is:

[0031] H 1DCNN =f 1DCNN (X;θ 1DCNN )

[0032] H LSTM =f LSTM (H 1DCNN ;θ LSTM )

[0033] Y Pre =f XGBoost (H LSTM ;θ XGBoost )

[0034] wherein H 1DCNN and H LSTM are output features of the 1DCNN model and the LSTM model respectively, θ 1DCNN , θ LSTM and θ XGBoostThe parameters of the 1DCNN model, the LSTM model and the XGBoost model respectively; X and Y are the wavelet packet energy spectrum and the model prediction result respectively.

[0035] Compared with the prior art, the present application has the following advantages and technical effects:

[0036] The present application provides a kind of laminated rubber support nondestructive testing device, comprising: guide rail, using I-shaped steel structure, it is provided with annular ring and multiple bolt holes on it, respectively for installing piezoelectric ceramic transducer and custom bolt;Piezoelectric ceramic transducer is set at the guide rail annular ring, for generating and receiving elastic wave;Custom bolt and nut are used to fix the piezoelectric ceramic transducer on the guide rail, and a certain pressure is applied by pre-tightening force to ensure the propagation of the elastic wave;Annular force sensor is attached to the screw cap of the custom bolt, for monitoring bolt pre-tightening force.The detection device provided by the present application does not need to change the support structure, is suitable for all laminated rubber supports, realizes the non-injury detection of support, and is easy to operate.

[0037] The present application also provides a kind of laminated rubber support damage and its degree identification method, by the identification method provided by the present application, the high-precision identification of laminated rubber support damage type and its degree can be realized. BRIEF DESCRIPTION OF DRAWINGS

[0038] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and its description together with the drawings make an application and do not limit the application. In the drawings:

[0039] Figure 1 It is a schematic diagram of prior art detection device;

[0040] Figure 2 It is a schematic diagram of the detection device of the embodiment of the present application;

[0041] Figure 3 It is a schematic diagram of the guide rail of the embodiment of the present application;

[0042] Figure 4 It is a schematic diagram of the support damage and its degree detection method based on 1DCNN-LSTM-XGBoost algorithm of the embodiment of the present application;

[0043] Wherein, 1, custom bolt;2, annular force sensor;3, nut;4, guide rail;5, piezoelectric ceramic transducer;6, laminated rubber support;7, bolt hole;8, annular ring;9, upper flange;10, web;11, lower flange. DETAILED DESCRIPTION

[0044] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0045] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0046] Example 1

[0047] like Figures 2-3 As shown, this embodiment provides a non-destructive testing device for laminated rubber bearings. The testing device consists of a guide rail 4, a piezoelectric ceramic transducer 5, a custom bolt 1, a nut 3, and a ring-type force sensor 2.

[0048] The main body of the guide rail 4 adopts an I-beam structure to save steel and improve overall rigidity. Multiple bolt holes 7 are provided on the guide rail 4 to facilitate the installation of the detection device by moving the bolt positions according to the dimensions of the laminated rubber support 6. The bolt holes 7 are located at the center of the guide rail 4 and pass through the upper flange 9, web 10, and lower flange 11.

[0049] A partially closed ring 8 is fixed at the lower wing plate 11 of the guide rail for housing the piezoelectric ceramic transducer 5. The unclosed portion of the ring 8 is used to house the transmission line of the piezoelectric ceramic transducer 5. The inner diameter of the ring 8 must match the outer diameter of the piezoelectric ceramic transducer 5, and the depth of the ring 8 must be less than the height of the piezoelectric ceramic transducer 5 to apply a certain pressure to the piezoelectric ceramic transducer 5 through bolt preload, ensuring the propagation of elastic waves.

[0050] Based on the dimensions of the laminated rubber support 6, the bolt hole 7 on the guide rail 4, and the ring-type force sensor 2, the dimensions of the customized bolt 1 and nut 3 need to be obtained to ensure the smooth installation of the piezoelectric ceramic transducer 5.

[0051] The annular force sensor 2 is fitted together with the nut of the custom bolt 1 to monitor the bolt preload. The readings from the two force sensors should be completely identical and constant to ensure good contact between the piezoelectric ceramic transducer 5 and the surface of the laminated rubber support 6, thereby ensuring the propagation of elastic waves.

[0052] Example 2

[0053] This embodiment also provides a method for identifying damage to laminated rubber bearings, including two main steps: calibration experiment 1) and on-site inspection 2).

[0054] In calibration experiment 1), the general steps are as follows:

[0055] 1.1) Manufacture a batch of laminated rubber bearings with different damage types and different damage degrees, select the type of piezoelectric ceramic transducer, and manufacture the detection device according to the size of the bearing and the size of the transducer.

[0056] 1.2) Attach the custom bolt nut to the circular ring force sensor, and connect the custom bolt to the guide rail together.

[0057] 1.3) Place the piezoelectric ceramic transducer in the guide rail circular ring, and attach the transducer bottom surface to the bearing side surface. At the same time, place the upper transducer in the circular ring of the opposite guide rail, and attach it to the bearing side surface through the custom bolt. Tighten the nuts gently, and the detection device will not loosen.

[0058] 1.4) Slowly move the detection device to ensure that the guide rail is level with the horizontal plane, the two transducers are on the same axis, and the transducers are in the detection position.

[0059] 1.5) Slowly tighten the bolts with wrenches at the same time on both nuts, ensuring that the values displayed by the circular ring force sensor are consistent, until the pre-set value is reached.

[0060] 1.6) Operate the instrument to obtain the detection signal that penetrates the entire bearing.

[0061] 1.7) Slowly loosen both nuts with wrenches at the same time until the nuts are completely removed. First remove the guide rail and piezoelectric ceramic transducer on the side without the circular ring force sensor, then remove the piezoelectric ceramic transducer, custom bolt, and circular ring force sensor on the other side in order.

[0062] 1.8) Repeat steps 1.2)-1.6) to obtain detection signals for laminated rubber bearings with different damage types and different damage degrees. Filter all detection signals to remove noise in the signals, and ensure that the detection signal frequency is consistent with the excitation signal frequency. Determine the wavelet packet basis and the number of decomposition layers, and use wavelet packet decomposition to obtain the wavelet packet energy spectrum of the detection signal.

[0063] 1.9) Use the wavelet packet energy spectrum of all detection signals as input parameters, and the damage type and its degree of the bearing as output parameters. Use a model architecture that combines one-dimensional convolutional neural networks, long short-term memory neural networks, and extreme gradient boosting algorithms to establish a multi-label classification model.

[0064] The specific steps include:

[0065] S1. Preparation before experiment;

[0066] Suitable piezoelectric ceramic transducer (determine the type of transducer according to the size of the bearing to be detected, ensure that the wave signal can penetrate the entire bearing), circular ring force sensor (select the model of force sensor according to the bolt pre-tightening force and the size of each part of the detection device) and guide rail (the specific size should be determined according to the size of the bearing, the model of the force sensor, etc.) are selected to ensure the smooth installation of the detection device. Select appropriate excitation signal, excitation frequency, excitation time and other parameters. In addition, check whether the related instruments are working properly, check whether the required materials and tools are complete, clean the transducer and the impurities on the side of the bearing body to ensure smooth and flat surface.

[0067] In this embodiment, the piezoelectric ceramic transducer uses a longitudinal wave transducer (the resonant frequency is 58 kHz, the diameter is 38 mm, and the height is 30 mm), and the circular ring force sensor uses a hydraulic circular ring force sensor F6116 (the maximum acting force is 120 kN). During the test, the force sensor value is set to 1.5 kN and remains unchanged. The excitation signal uses a sweep signal, the frequency range is 10-100 kHz, the duration is 2 s, and the amplitude is ±10 V. Check whether the related equipment is normal, and whether the surface of the bearing and the surface of the transducer are flat. In addition, as long as the size of each part of the detection device can ensure the smooth installation of the transducer and the application of a certain pressure, the specific size is not required.

[0068] S2. Aging test;

[0069] Put M bearings identical to the bearing to be detected into the aging oven for aging test, the aging temperature is W℃, the aging time is S days each time (determined according to the detection frequency and bearing replacement requirements during actual detection), and the total number of aging tests is D. During the test, the bearing needs to be subjected to a certain interval of tool shaft pressure by using tooling, and the pressure remains unchanged. In addition, there should be multiple bearings under the same tool shaft pressure to consider the differences in the production process of the bearing. In order to cover the bearing working shaft pressure and aging degree as much as possible and improve the application range of the model, the aging time should be as short as possible each time and the number of aging tests should be as many as possible.

[0070] In this embodiment, 100 bearings are put into the aging oven for aging test, the aging temperature is 80℃, the aging time is 24 hours each time, and the total number of aging tests is 15. During the test, the bearing needs to be subjected to different tool shaft pressures, i.e. 1-20 MPa, with an interval of 1 MPa. In addition, there are 5 bearings under the same tool shaft pressure, which have different degrees of peeling damage to consider the peeling damage type.

[0071] S3. Mechanical property test and wave method test;

[0072] After each aging test, the support needs to be placed in a room temperature condition of 23±2℃ for 48 hours, and then the mechanical property test (according to the specification “Rubber bearing Part 1: Test methods for isolation rubber bearings” (GBT 20688.1-2007)) and the wave method test are carried out. The piezoelectric ceramic transducer is placed in the ring on the detection bracket, and the ring type force sensor is placed on the side of the nut on the bolt. When the pre-tightening force is applied, the nut needs to be tightened step by step to ensure that the forces borne by the two ring type force sensors are consistent or have a small difference at all times, so as to avoid the formation of an angle between the bottom surface of the piezoelectric ceramic transducer and the surface of the support, which affects the transmission and collection of signals.

[0073] In order to cover the working axial pressure of the support as much as possible, the axial pressure interval should be as small as possible during the wave method test, and the range is 1-20 MPa with an interval of 1 MPa. The monitoring signals of the support at different aging times t and different axial pressures F l are obtained through the wave method experiment. The signal matrix is as follows:

[0074]

[0075] Wherein, i represents the working axial pressure of the support in the aging test, j represents different degrees of peeling damage, T represents the total aging time (the row represents different aging times), and F represents the maximum axial pressure (the column represents different axial pressures of the support during the wave method test).

[0076] S4. Detection signal processing;

[0077] All detection signals are filtered to remove noise in the signals (the frequency is controlled within the range of 10-100 kHz), and the wavelet packet energy spectrum of the detection signal is obtained by wavelet packet decomposition (the wavelet packet basis is db5, and the decomposition layer is 8 layers).

[0078] S5. Establishing a machine learning model;

[0079] Taking the wavelet packet energy spectrum as the input parameter and the aging damage degree of the support as the output parameter, a network framework based on the fusion of one-dimensional convolutional neural network, long short-term memory neural network and extreme gradient boosting algorithm (1DCNN-LSTM-XGBoost) is used to establish the aging damage degree prediction model of the support. In 1DCNN-LSTM-XGBoost, the 1DCNN algorithm is used to extract the high-level local features in the wavelet packet energy spectrum of the detection signal, the LSTM algorithm is used to extract the time-dependent relationship in the high-level local features, and the XGBoost algorithm is further used to establish a high-precision prediction model. The support damage and its degree detection method based on the 1DCNN-LSTM-XGBoost algorithm is as shown in Figure 4 . The specific framework is as follows:

[0080] S501. The database (wavelet packet energy spectrum of all detection signals) is randomly divided into three parts in the ratio of 7:2:1: training set, validation set and test set, which are used for model training, validation and testing, respectively. Local features are extracted through six 1DCNN layers, with a kernel size of 3 and an L2 regularization factor of 0.001. The number of filters in these layers is 128, 256, 512, 1024, 2048 and 4096, respectively. After each convolutional layer, there is a batch normalization layer, a max pooling layer (pool size 2) and a Dropout layer (dropout rate 0.1), which are used to extract local features, reduce data dimension and enhance the generalization ability of the model, respectively.

[0081] S502. After extracting local features through 1DCNN layers, the data is flattened using the Flatten layer, and then reshaped using the Reshape layer with parameters (2, 4096) to adjust the shape of the data suitable for input into the LSTM network for further extraction of temporal features. The LSTM layer consists of 4 layers with unit numbers of 2048, 1024, 512 and 256, respectively. All LSTM layers use the ReLU activation function followed by a Dropout layer with a dropout rate of 0.1.

[0082] S503. Three fully connected layers with unit numbers of 512, 256 and 128, respectively, and an L2 regularization factor of 0.001 for each layer. Each layer is followed by a Dropout layer with a dropout rate of 0.1 to further prevent overfitting. The output layer of the model is a Softmax layer with 6 units corresponding to 6 classification labels. In addition, the 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).

[0083] S504. Save the 1DCNN-LSTM model with the highest prediction accuracy on the test set, and use the output of the last fully connected layer (i.e., the fully connected layer with 128 units) as the input parameter of the XGBoost model, with the corresponding degrees of aging damage and peeling damage as the output parameters (multi-label classification model). The values of hyperparameters such as the number of trees and the maximum depth of each tree are adjusted continuously using a trial-and-error strategy until the prediction accuracy of the model on the training set, validation set and test set meets the requirements.

[0084] In the field detection 2), specifically:

[0085] S1. Obtain the detection signal of the laminated rubber support to be detected through the detection device and method. It is worth noting that the parameters of the instrument and equipment used for detection should be consistent with those used in the calibration experiment to ensure the accuracy of the detection results.

[0086] S2. The detection signal is sequentially filtered and wavelet packet decomposed to obtain a corresponding wavelet packet energy spectrum;

[0087] S3. The wavelet packet energy spectrum is substituted into a trained multi-label classification model to obtain a recognition result of the damage type and its degree.

[0088] S4. If the support is seriously aged (the mechanical performance obviously decreases), a measure such as replacing the support should be taken to ensure the safety of the structure.

[0089] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any change or replacement easily thought of by those skilled in the art within the technical range disclosed by the present application should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A portable non-destructive testing device for laminated rubber bearings, characterized in that, It comprises: a guide rail in the shape of an I-beam, with a circular ring and a plurality of bolt holes for mounting a piezoelectric ceramic transducer; a piezoelectric ceramic transducer arranged in the circular ring of the guide rail for generating and receiving elastic waves; customized bolts and nuts for fixing the piezoelectric ceramic transducer on the guide rail and exerting a certain pressure through pre-tightening force to ensure the propagation of the elastic waves; a circular ring force sensor in contact with the nut of the customized bolt for monitoring the bolt pre-tightening force; the width of the guide rail and the diameter of the nut of the customized bolt are not less than the outer diameter of the circular ring force sensor to ensure accurate monitoring of the bolt pre-tightening force by the circular ring force sensor; the installation process of the detection device comprises: contacting the nut of the customized bolt with the circular ring force sensor and connecting the customized bolt with the guide rail together; placing the piezoelectric ceramic transducer in the circular ring of the guide rail, contacting the bottom surface of the piezoelectric ceramic transducer with the side surface of the laminated rubber support, and placing the piezoelectric ceramic transducer in the circular ring of the opposite guide rail and contacting the side surface of the laminated rubber support together through the customized bolt; simultaneously tightening the two nuts slowly with a wrench to ensure that the values displayed by the circular ring force sensor are consistent until the pre-set value is reached; the center line of the bolt hole is located on the symmetry plane of the guide rail; an incompletely closed circular ring is fixed at the lower flange plate of the guide rail, the inner diameter of the circular ring is consistent with the outer diameter of the piezoelectric ceramic transducer, and the depth of the circular ring is lower than the height of the piezoelectric ceramic transducer; during the detection process, the display value of the circular ring force sensor is a constant value to ensure uniform distribution of the force on the transducer.

2. A method for identifying damage of a laminated rubber bearing, characterized by, It comprises the following steps: based on the portable laminated rubber support non-destructive testing device of claim 1, detecting laminated rubber supports with different damage types and different damage degrees to obtain detection signals; filtering all detection signals to remove noise in the signals, and using wavelet packet decomposition to obtain the wavelet packet energy spectrum of the filtered detection signals; establishing a multi-label classification model, taking the wavelet packet energy spectrum of all detection signals as input parameters and the damage type and degree of the support as output parameters, training the multi-label classification model to obtain a trained multi-label classification model; wherein the multi-label classification model adopts a model architecture that integrates one-dimensional convolutional neural network, long short-term memory neural network and extreme gradient boosting algorithm; based on the portable laminated rubber support non-destructive testing device of claim 1, obtaining the to-be-detected signal of the laminated rubber support to be detected; sequentially filtering and wavelet packet decomposing the to-be-detected signal to obtain the to-be-detected wavelet packet energy spectrum; inputting the to-be-detected wavelet packet energy spectrum into the trained multi-label classification model as input parameters to obtain the identification result of the damage type and degree.

3. The damage identification method of a laminated rubber bearing according to claim 2, characterized in that, The wavelet packet energy spectrum is: In the formula, i is the number of decomposition layers; j is the node number; and n is the sampling point. is the node coefficient; is the wavelet packet energy of the detection signal obtained through wavelet packet decomposition.

4. The damage identification method of a laminated rubber bearing according to claim 2, characterized in that, The multi-label classification model is: In the formula, H 1DCNN and H LSTM are the output features of the 1D CNN model and the LSTM model, respectively; θ 1DCNN , θ LSTM and θ XGBoost are parameters of 1D CNN model, LSTM model and XGBoost model, respectively; X and Y Pre are wavelet packet energy spectrum and model prediction results, respectively.

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