# Automobile Rear Axle Health Monitoring Technology Based on Deep Learning

Authors: Quanyu Zhang; Zhenzhong Zhang; Fengqin Ke; Yanan Gao; Yi Chen
Journal: Mobile Information Systems
 (2022)

---

## Abstract

The rear axle is prone to fatigue fracture due to the complicated load impact throughout the vehicle’s service procedure. Real-time suspension health monitoring during operation is an excellent strategy for avoiding such situations. This paper takes the automobile rear axle as the research object and uses the deep learning model to study the rear axle health monitoring technology. A damage prediction model combining multi-Gaussian fitting and long-term and short-term memory neural network is proposed for automobile rear axle health monitoring. The feature extraction method based on multi-Gaussian fitting can obtain comprehensive power spectral density information with fewer feature parameters, which is conducive to improve the calculation efficiency. The LSTM model can accurately identify the fatigue damage value of the rear axle from the extracted characteristic information and ensure the high precision of the damage prediction results. Several deep learning-based comparison models are used to demonstrate that the GAPSD LSTM model has good prediction accuracy and computation efficiency at the same time. It has been proven that the GAPSD LSTM model can efficiently and accurately forecast the fatigue damage of the rear axle by comparing the damage prediction results of all deep learning models.


---

## Body

## 1. Introduction

Due to the complex structure and bad operating conditions, the key components of the vehicle, such as the rear axle, will bear severe loads in the service process making it easy to cause fatigue fracture of the structure. According to the statistics [1], more than 90% of the damage to auto parts belongs to fatigue fracture. In recent years, although the level of automobile design and manufacturing has been continuously improved, accidents caused by fatigue fracture of automobile parts are still common. The occurrence of these accidents seriously endangers the personal safety and property safety of passengers and has aroused great social attention to the structural safety of vehicles. It may include the fracture of the steering knuckle of the front suspension of Ford Yihu off-road vehicle, the fracture of the coil spring of the front suspension of Nissan Qida car, and the fracture of the torsion beam rear suspension of Volkswagen Suteng car. We have counted the large-scale recall events caused by the hidden danger of fatigue fracture of auto parts in recent years. We know that almost all brands of cars have the hidden danger of fatigue fracture of auto parts. As an important bearing mechanism of the automobile, the rear axle of the automobile is subjected to complex load in the process of automobile service. It is one of the main structures with hidden dangers of fatigue fracture. Nearly half of the recalls were caused by the hidden danger of fatigue fracture in the suspension structure. In order to avoid fatigue fracture of automobile parts in the service cycle, the main method used in the automobile industry is structural fatigue damage analysis in the automobile design stage. At present, the semianalytical technique is the most widely utilized fatigue damage analysis method for automobile structures. This approach verifies the simulation model of an automobile structure using measured data from a durability test and then estimates its real service life based on the simulation analysis findings of an automobile structure. The results predicted by the semianalysis method will be different from the actual service life because the semianalysis method does not consider the real load condition of each vehicle in the actual service process, and there will be model errors and simulation analysis errors in the simulation analysis process. The statistical results show that using semianalytical method to predict fatigue damage cannot ensure the safety of automobile structure in the actual use process. Therefore, solving the fatigue fracture problem of automobile parts needs more effective theory and technology support. To ensure the safety of automobile structure in the normal service cycle, real-time monitoring of the fatigue damage state of automobile structure is a desirable solution. Structural health monitoring technology can predict the damage state of the structure in real time through effective data analysis methods according to a variety of operating parameters in the service process of the structure. Applying this technology to the key components of automobile can accurately predict the fatigue damage state of key components in the service process of automobile. It provides massive and real analysis data for the durability design of automobile structure, which is helpful to improve the safety and structural design level of automobile.The data gathered in the development of rear axle health monitoring technology will be quite vast and have high dynamic characteristics due to the complicated operating circumstances and strong nonlinear features. As a kind of mass consumption, the economy, reliability, and practicability must be considered when studying the rear axle health monitoring technology. Based on the above two factors, the rear axle health monitoring technology needs to meet the following requirements:Try to select sensors that have been widely used in mass-produced vehicles. To address the key issues, this study conducted research on damage prediction and test data collection, which provides a strong theoretical foundation for the future application of structural health monitoring technology in automobile structures and is critical for improving automobile safety.


## 2. Related Work

Reference [2] gives a review of the deep learning-based SHM of civil infrastructures with the main content including a summary of the history of the development of deep learning, the applications of deep learning-based data processing approaches in the SHM of many kinds of civil infrastructures, and the key challenges and future trends of the strategy of deep learning-based SHM. A real-time sow behavior detection algorithm based on deep learning (SBDA-DL) is proposed [3]. Wearable smart-log patch with the Internet of Things (IoT) sensors has been designed and developed with multimedia technology [4]. Therefore, it is required to develop an effective, low-cost technology to ascertain vehicle loads in relation to spatiotemporal load distribution on long-span bridges. Reference [5] proposed a noncontact vehicle identification methodology to distinguish a vehicle from its load based on machine vision technology and deep learning algorithms. In contrast to this, several cutting-edge technology-based solutions are being employed in developed countries to enhance the crop yield with the optimal use of resources. To this end, Reference [6] proposes an integrated approach for monitoring crop health using IoT, machine learning, and drone technology. While there have been multiple review studies published on vibration-based structural damage detection, there has not been a study where the transition from traditional methods to ML and DL methods is described and discussed. Reference [7] aims to fulfill this gap by presenting the highlights of the traditional methods and providing a comprehensive review of the most recent applications of ML and DL algorithms utilized for vibration-based structural damage detection in civil structures. Reference [8]emphasizes the need for machine learning in designing HAR systems that combine inertial sensors with physiological and environmental sensors. A comprehensive review is performed, primarily on the applications of AI models for SHM to maintain the sustainability of diverse civil infrastructures [9]. Reference [10] focuses on the enormous potential of speech technology for revolutionizing the healthcare domain. The diagnosis of the monitoring platform is usually manual, which is challenging to ensure that there are enough doctors online to provide a timely, efficient, and accurate diagnosis. To address these issues, Reference [11] proposes a 5G-enabled real-time cardiovascular monitoring system for COVID-19 patients using deep learning.


## 3. Methodology

### 3.1. Theory and Model of Suspension Structure Damage Prediction

#### 3.1.1. Rear Axle Damage Prediction Theory

The fundamental difficulty in estimating the fatigue damage of the rear axle structure determines the relevant link between vehicle vibration characteristic characteristics and torsion beam fatigue damage. The relationship between the vibration characteristic parameterq (t) and the fatigue damage di of the rear axle structure can be expressed as follows [11, 12]:(1)Hd−qt=diqt=diεtεtFbtFbtqt=Hd−εtHε−FbtHFb−qt,where Hd−qt represents the transfer function of the whole vehicle, εt represents the strain response at the dangerous position of fatigue damage of torsion beam, Fbt represents the boundary load of the suspension structure, Hd−εt represents the transfer function composed of the strain life calculation method, Hε−Fbt represents the transfer function of the suspension, and HFb−qt represents the transfer function of the vehicle body. It can be seen from (1) that the corresponding relationship between q (t) and di is affected by the dynamic response characteristics of vehicle body, suspension, and structural fatigue damage. Because the automobile is a complex nonlinear system, it is very difficult to establish the corresponding relationship between q (t) and di directly using mathematical formulas. The deep learning model has a strong nonlinear mapping ability through multilayer nonlinear calculation. Therefore, when the dynamic response characteristics of the whole vehicle are unknown, the damage prediction model based on deep learning can accurately establish the corresponding relationship between q (t) and di.


#### 3.1.2. Damage Prediction Model Based on Deep Learning

At present, the deep neural network model is represented by DCNN and LSTM that is widely used in the research of structural health monitoring technology [13–16]. Among them, two kinds of damage prediction models based on deep learning have been proved to achieve relatively higher damage prediction accuracy. The first is the damage prediction model combining DCNN and LSTM (simply called as DCLSTM model). The second type of damage prediction model is the joint time-frequency prediction model of DWTM and DWT-DCT (for short, the joint time-frequency prediction model of DWTM and DWT-DCT). The DCT converts the picture into different pixels. The pixel of the image is then transmuted to compress form. The compressed picture is then converted into a quantization process. Dwt is used to separate the image into a pixel. These studies show that the damage prediction model based on deep learning has a flexible structural form. It can not only combine different types of deep neural network models but also combine the deep neural network model with other structural health monitoring technologies [17]. Its deep learning structure is shown in Figure 1.Figure 1
Deep learning structure for the damage prediction model.For structural health monitoring technology, the computational efficiency of the deep learning model will affect its development cycle and long-term prediction accuracy. Despite the fact that the deep learning model has been shown in several experiments to attain great prediction accuracy, the structural health monitoring technology based on deep learning still faces the problem of how to have high prediction accuracy and computational efficiency at the same time. Different depth learning models use various feature extraction methods and damage identification models, resulting in variations in prediction accuracy and computation efficiency. It is required to build an adequate feature extraction approach and utilize a reliable damage identification model to properly acquire the related link between feature parameters and structural damage to effectively anticipate structural damage. Based on this idea, a damage prediction model established on multi-Gaussian fitting and LSTM is proposed, which is called GAPSD-LSTM model for short. To prove that the GAPSD-LSTM model has high prediction accuracy and calculation efficiency at the same time, several groups of comparison models based on deep learning are established. These groups include the DTCWT-LSTM model, DTCWT-DCNN model, DCLSTM model, DTCWT-DCLSTM model, and PSD-LSTM model [18–21].The specific steps are as follows:Step 1: collect sample data through a vehicle durability test. The key problems to be solved in this step include selecting appropriate sensors, determining the number and installation location of sensors, and performing appropriate preprocessing operations on data.Step 2: extract feature information from the test data. Each vibration response signal’s power spectral density distribution information is acquired using a feature extraction approach based on multi-Gaussian fitting, and the appropriate feature parameters are selected as the input parameters of the LSTM model by using the PCA-RCDFS feature selection method.Step 3: the LSTM model predicts the local fatigue damage value by first performing data fusion in the input layer and then using the LSTM layer and the entire connection layer. To establish the complicated nonlinear connection between vibration characteristic parameters and local fatigue damage values with precision, it is necessary to reasonably determine several key parameters of the LSTM model such as the number of LSTM layers and the number of neurons in each LSTM layer, and the learning rate of the training process.Step 4: estimate the damage state of the rear axle. The trained LSTM model is used to predict the local fatigue damage value of the rear axle in each time series, and the damage state and residual fatigue life of the rear axle are calculated. According to the linear fatigue damage accumulation calculation method, the real-time damage state Dc and the remaining driving mileage Mr of the structure can be obtained by the following formulas, respectively:(2)Dc=∑iΔDi,(3)Mr=DTD−1∗Mi,where ΔDi represents the local fatigue damage value of the structure in the i-th time series predicted by the GAPSD LSTM model; DT represents the cumulative fatigue damage value when the structure is damaged; Mi represents the cumulative mileage of the vehicle at the i-th time series step.


### 3.2. Contrast Model Based on Deep Learning

To prove that the GAPSD LSTM model has high prediction accuracy and computational efficiency at the same time, several comparison models based on deep learning are established. Recent studies have pointed out that the DTCWT model can effectively extract multiscale subband signals from measurement data; the DCNN model can automatically extract useful feature information from complex data; the LSTM model can efficiently deal with time series prediction. The combined use of the above models also shows that more accurate prediction results can be obtained. According to these studies, the DTCWT-LSTM model, DTCWT-DCNN model, DCLSTM model, and DTCWT-CLSTM model are established as comparison models. To prove that the feature extraction method based on multi-Gaussian fitting can obtain comprehensive frequency domain feature information, the PSD-LSTM model is also established as the comparison model. The power spectral inertia of the model is to extract the power spectral density distribution information of each section of measured data.


## 3.1. Theory and Model of Suspension Structure Damage Prediction

### 3.1.1. Rear Axle Damage Prediction Theory

The fundamental difficulty in estimating the fatigue damage of the rear axle structure determines the relevant link between vehicle vibration characteristic characteristics and torsion beam fatigue damage. The relationship between the vibration characteristic parameterq (t) and the fatigue damage di of the rear axle structure can be expressed as follows [11, 12]:(1)Hd−qt=diqt=diεtεtFbtFbtqt=Hd−εtHε−FbtHFb−qt,where Hd−qt represents the transfer function of the whole vehicle, εt represents the strain response at the dangerous position of fatigue damage of torsion beam, Fbt represents the boundary load of the suspension structure, Hd−εt represents the transfer function composed of the strain life calculation method, Hε−Fbt represents the transfer function of the suspension, and HFb−qt represents the transfer function of the vehicle body. It can be seen from (1) that the corresponding relationship between q (t) and di is affected by the dynamic response characteristics of vehicle body, suspension, and structural fatigue damage. Because the automobile is a complex nonlinear system, it is very difficult to establish the corresponding relationship between q (t) and di directly using mathematical formulas. The deep learning model has a strong nonlinear mapping ability through multilayer nonlinear calculation. Therefore, when the dynamic response characteristics of the whole vehicle are unknown, the damage prediction model based on deep learning can accurately establish the corresponding relationship between q (t) and di.


### 3.1.2. Damage Prediction Model Based on Deep Learning

At present, the deep neural network model is represented by DCNN and LSTM that is widely used in the research of structural health monitoring technology [13–16]. Among them, two kinds of damage prediction models based on deep learning have been proved to achieve relatively higher damage prediction accuracy. The first is the damage prediction model combining DCNN and LSTM (simply called as DCLSTM model). The second type of damage prediction model is the joint time-frequency prediction model of DWTM and DWT-DCT (for short, the joint time-frequency prediction model of DWTM and DWT-DCT). The DCT converts the picture into different pixels. The pixel of the image is then transmuted to compress form. The compressed picture is then converted into a quantization process. Dwt is used to separate the image into a pixel. These studies show that the damage prediction model based on deep learning has a flexible structural form. It can not only combine different types of deep neural network models but also combine the deep neural network model with other structural health monitoring technologies [17]. Its deep learning structure is shown in Figure 1.Figure 1
Deep learning structure for the damage prediction model.For structural health monitoring technology, the computational efficiency of the deep learning model will affect its development cycle and long-term prediction accuracy. Despite the fact that the deep learning model has been shown in several experiments to attain great prediction accuracy, the structural health monitoring technology based on deep learning still faces the problem of how to have high prediction accuracy and computational efficiency at the same time. Different depth learning models use various feature extraction methods and damage identification models, resulting in variations in prediction accuracy and computation efficiency. It is required to build an adequate feature extraction approach and utilize a reliable damage identification model to properly acquire the related link between feature parameters and structural damage to effectively anticipate structural damage. Based on this idea, a damage prediction model established on multi-Gaussian fitting and LSTM is proposed, which is called GAPSD-LSTM model for short. To prove that the GAPSD-LSTM model has high prediction accuracy and calculation efficiency at the same time, several groups of comparison models based on deep learning are established. These groups include the DTCWT-LSTM model, DTCWT-DCNN model, DCLSTM model, DTCWT-DCLSTM model, and PSD-LSTM model [18–21].The specific steps are as follows:Step 1: collect sample data through a vehicle durability test. The key problems to be solved in this step include selecting appropriate sensors, determining the number and installation location of sensors, and performing appropriate preprocessing operations on data.Step 2: extract feature information from the test data. Each vibration response signal’s power spectral density distribution information is acquired using a feature extraction approach based on multi-Gaussian fitting, and the appropriate feature parameters are selected as the input parameters of the LSTM model by using the PCA-RCDFS feature selection method.Step 3: the LSTM model predicts the local fatigue damage value by first performing data fusion in the input layer and then using the LSTM layer and the entire connection layer. To establish the complicated nonlinear connection between vibration characteristic parameters and local fatigue damage values with precision, it is necessary to reasonably determine several key parameters of the LSTM model such as the number of LSTM layers and the number of neurons in each LSTM layer, and the learning rate of the training process.Step 4: estimate the damage state of the rear axle. The trained LSTM model is used to predict the local fatigue damage value of the rear axle in each time series, and the damage state and residual fatigue life of the rear axle are calculated. According to the linear fatigue damage accumulation calculation method, the real-time damage state Dc and the remaining driving mileage Mr of the structure can be obtained by the following formulas, respectively:(2)Dc=∑iΔDi,(3)Mr=DTD−1∗Mi,where ΔDi represents the local fatigue damage value of the structure in the i-th time series predicted by the GAPSD LSTM model; DT represents the cumulative fatigue damage value when the structure is damaged; Mi represents the cumulative mileage of the vehicle at the i-th time series step.


## 3.1.1. Rear Axle Damage Prediction Theory

The fundamental difficulty in estimating the fatigue damage of the rear axle structure determines the relevant link between vehicle vibration characteristic characteristics and torsion beam fatigue damage. The relationship between the vibration characteristic parameterq (t) and the fatigue damage di of the rear axle structure can be expressed as follows [11, 12]:(1)Hd−qt=diqt=diεtεtFbtFbtqt=Hd−εtHε−FbtHFb−qt,where Hd−qt represents the transfer function of the whole vehicle, εt represents the strain response at the dangerous position of fatigue damage of torsion beam, Fbt represents the boundary load of the suspension structure, Hd−εt represents the transfer function composed of the strain life calculation method, Hε−Fbt represents the transfer function of the suspension, and HFb−qt represents the transfer function of the vehicle body. It can be seen from (1) that the corresponding relationship between q (t) and di is affected by the dynamic response characteristics of vehicle body, suspension, and structural fatigue damage. Because the automobile is a complex nonlinear system, it is very difficult to establish the corresponding relationship between q (t) and di directly using mathematical formulas. The deep learning model has a strong nonlinear mapping ability through multilayer nonlinear calculation. Therefore, when the dynamic response characteristics of the whole vehicle are unknown, the damage prediction model based on deep learning can accurately establish the corresponding relationship between q (t) and di.


## 3.1.2. Damage Prediction Model Based on Deep Learning

At present, the deep neural network model is represented by DCNN and LSTM that is widely used in the research of structural health monitoring technology [13–16]. Among them, two kinds of damage prediction models based on deep learning have been proved to achieve relatively higher damage prediction accuracy. The first is the damage prediction model combining DCNN and LSTM (simply called as DCLSTM model). The second type of damage prediction model is the joint time-frequency prediction model of DWTM and DWT-DCT (for short, the joint time-frequency prediction model of DWTM and DWT-DCT). The DCT converts the picture into different pixels. The pixel of the image is then transmuted to compress form. The compressed picture is then converted into a quantization process. Dwt is used to separate the image into a pixel. These studies show that the damage prediction model based on deep learning has a flexible structural form. It can not only combine different types of deep neural network models but also combine the deep neural network model with other structural health monitoring technologies [17]. Its deep learning structure is shown in Figure 1.Figure 1
Deep learning structure for the damage prediction model.For structural health monitoring technology, the computational efficiency of the deep learning model will affect its development cycle and long-term prediction accuracy. Despite the fact that the deep learning model has been shown in several experiments to attain great prediction accuracy, the structural health monitoring technology based on deep learning still faces the problem of how to have high prediction accuracy and computational efficiency at the same time. Different depth learning models use various feature extraction methods and damage identification models, resulting in variations in prediction accuracy and computation efficiency. It is required to build an adequate feature extraction approach and utilize a reliable damage identification model to properly acquire the related link between feature parameters and structural damage to effectively anticipate structural damage. Based on this idea, a damage prediction model established on multi-Gaussian fitting and LSTM is proposed, which is called GAPSD-LSTM model for short. To prove that the GAPSD-LSTM model has high prediction accuracy and calculation efficiency at the same time, several groups of comparison models based on deep learning are established. These groups include the DTCWT-LSTM model, DTCWT-DCNN model, DCLSTM model, DTCWT-DCLSTM model, and PSD-LSTM model [18–21].The specific steps are as follows:Step 1: collect sample data through a vehicle durability test. The key problems to be solved in this step include selecting appropriate sensors, determining the number and installation location of sensors, and performing appropriate preprocessing operations on data.Step 2: extract feature information from the test data. Each vibration response signal’s power spectral density distribution information is acquired using a feature extraction approach based on multi-Gaussian fitting, and the appropriate feature parameters are selected as the input parameters of the LSTM model by using the PCA-RCDFS feature selection method.Step 3: the LSTM model predicts the local fatigue damage value by first performing data fusion in the input layer and then using the LSTM layer and the entire connection layer. To establish the complicated nonlinear connection between vibration characteristic parameters and local fatigue damage values with precision, it is necessary to reasonably determine several key parameters of the LSTM model such as the number of LSTM layers and the number of neurons in each LSTM layer, and the learning rate of the training process.Step 4: estimate the damage state of the rear axle. The trained LSTM model is used to predict the local fatigue damage value of the rear axle in each time series, and the damage state and residual fatigue life of the rear axle are calculated. According to the linear fatigue damage accumulation calculation method, the real-time damage state Dc and the remaining driving mileage Mr of the structure can be obtained by the following formulas, respectively:(2)Dc=∑iΔDi,(3)Mr=DTD−1∗Mi,where ΔDi represents the local fatigue damage value of the structure in the i-th time series predicted by the GAPSD LSTM model; DT represents the cumulative fatigue damage value when the structure is damaged; Mi represents the cumulative mileage of the vehicle at the i-th time series step.


## 3.2. Contrast Model Based on Deep Learning

To prove that the GAPSD LSTM model has high prediction accuracy and computational efficiency at the same time, several comparison models based on deep learning are established. Recent studies have pointed out that the DTCWT model can effectively extract multiscale subband signals from measurement data; the DCNN model can automatically extract useful feature information from complex data; the LSTM model can efficiently deal with time series prediction. The combined use of the above models also shows that more accurate prediction results can be obtained. According to these studies, the DTCWT-LSTM model, DTCWT-DCNN model, DCLSTM model, and DTCWT-CLSTM model are established as comparison models. To prove that the feature extraction method based on multi-Gaussian fitting can obtain comprehensive frequency domain feature information, the PSD-LSTM model is also established as the comparison model. The power spectral inertia of the model is to extract the power spectral density distribution information of each section of measured data.


## 4. Data Acquisition and Model Validation

This study conducted vehicle durability tests under various operating situations to establish that the rear axle health monitoring technology based on the GAPSD LSTM model has good prediction accuracy and calculation efficiency. In this paper, the vehicle durability test is described, and the fatigue damage prediction results of different depth learning models are compared and analyzed.To ensure the smooth bench test of the whole vehicle, the test process must be carried out in an orderly manner according to the test specifications.The bench test in this study includes the following five main steps:Step 1: check whether the whole vehicle and all test equipment are in good condition.Step 2: accurately install the strain sensor, inertial navigator, and stay wire displacement sensor at the specified position. The installation of strain sensors shall be carried out in strict accordance with the processes of cleaning, gluing, pasting, bridging, and inspection.Step 3: hinge the four wheels of the whole vehicle to the end of the actuator group strut of mts329 axle coupled road simulator and counterweight the vehicle.Step 4: start the test, input the specified road roughness data and vehicle driving speed, drive the actuator group to excite the vibration of the whole vehicle, and record the measurement data of each sensor during the test.Step 5: save all test measurement data, close the test equipment, and end the test.For the measured data obtained in the vehicle bench test, four steps of preprocessing are carried out in this study.First, the collected data are processed by eliminating trend items, deburring, and filtering. Then, the typical test data under each working condition are extracted according to the similar power spectral density method. However, the frequency of data gathered by the sensor throughout the test is as high as 500 Hz, resulting in very huge measurement data. The frequency of the measured data is lowered using the minimum sampling frequency determination approach given by foulard et al. to further minimize the measured data. The idea of the minimum sampling frequency determination method is to compare the relative error of fatigue damage value and of the fatigue damage dangerous position of torsion beam under the highest speed and the lowest speed operating conditions with different sampling frequencies. It can be seen from Table1that when the sampling frequency is not less than 100 Hz, the error of fatigue damage value is less than 10%. Therefore, selecting a value for every five sampling time steps will not have a significant impact on the accuracy of fatigue damage prediction. The data length after the above preprocessing operation on the measured data of the whole vehicle bench test is 160000. Some sample data are shown in Figure 2.Table 1
The strain response at the dangerous position of fatigue damage.
(Hz)Cp1Cp2Cp1Cp2Highest speedLowest speedHighest speedLowest speedHighest speedLowest speedHighest speedLowest speed5005.2E − 97.5E − 74.1E − 96.7E − 75.6E − 98.4E − 73.7E − 97.2E − 7200−1.4%−4.7%−1.9%−3.6%−2.4%−3.3%−3.2%−4.3%100−5.3%−9.1%−5.5%−8.9%−5.7%−7.6%−6.3%−8.7%50−16.3%−22.6%−15.3%−18.7%−15.5%−20.6%−15.9%−19.5%20−38.0%−48.0%−34.7%−42.3%−39.5%−57.2%−36.4%−46.6%Figure 2
The fatigue damage prediction value of GAPSD LSTM model: (a) CP1. (b) CP 2. (c) CP3. (d) CP4.
(a)(b)(c)(d)The data preprocessed in the above two steps are processed in segments. Considering that if each segment of data is too long, some local features of the data will not be clearly obtained in the process of feature extraction. Likewise, if each segment of data is too short, the information at the connection of each two segments of data will be truncated which will cause information distortion. Therefore, the length of each data segment should not be too long or too short. By comparing the effects of different segment lengths on the cumulative fatigue damage value—if the segment lengthd = 400—there are 400 samples in the training data.Finally, for each training sample, the local fatigue damage value is calculated using the strain life module in the fatigue damage calculation software nCode/GlyphWorks. These local fatigue damage values are taken as the logarithm value with the base of 10. The logarithmic calculation result is standardized to 0-1 using the following formula:(4)XN=Xt−XminXmin−Xmax.The rear axle health monitoring technology based on the GAPSD LSTM model can obtain high damage prediction accuracy and calculation efficiency at the same time. In the research of automobile rear axle health monitoring technology, the GAPSD-LSTM model can obtain the prediction accuracy close to that of the DTCWT-DCLSTM model. The calculation time of the model is very short which proves that the model can predict the fatigue damage of the rear axle efficiently and accurately. Their benchmark chart and mean absolute error are shown in Figures3 and 4.Figure 3
Benchmark chart for three kinds of encoder networks.Figure 4
Mean Absolute error.
(a)(b)


## 5. Conclusions

Fatigue fracture of automobile parts is an important factor affecting driving safety and automobile quality. As an effective means to prevent fatigue fracture in automobiles, structural health monitoring technology is of great significance. It improves the safety performance of the automobile. Although there is much research on structural health monitoring technology at home and abroad, there are still many problems to be resolved. The fatigue damage of suspension structure is predicted by combining the feature extraction method based on multi-Gaussian fitting and the LSTM model. First, the feature extraction method based on multi-Gaussian fitting is used to obtain the power spectral density distribution information of each vibration response signal. Then, the PCA-RCDFS feature selection method is used to select the Gaussian fitting feature parameters which are most related to fatigue damage. The LSTM beam’s fatigue damage position is then predicted using the LSTM beam’s fatigue damage risk value. Several deep learning comparison models are used to prove that the GAPSD LSTM model can achieve excellent prediction accuracy and computational efficiency.



---

*Source: 1419671-2022-08-11.xml*