Dynamic analysis of railroad track faults based on neural network algorithms

The main contact relationships and motion characteristics of rolling bearings are the basis for the following assumptions:

Balls in rolling bearings are distributed equidistantly between the inner and outer raceways.

The inner ring of the rolling bearing rotates with the shaft and the outer ring is fixed in the housing.

There is pure rolling between the balls and the raceways.

Neglect the influence of oil film lubrication, friction heat effect.

Neglect bearing raceway surface corrugation degree, rotational inertia.

Only damage and elastic contact are considered between rolling body and raceway, other geometric errors are not considered.

According to the model assumption, in the process of bearing operation, bearing clearance, nonlinear contact force will produce variable flexibility VC vibration, so that the bearing in the process of operation, the total stiffness will show a cyclic change, Figure 1 for the rolling bearing motion model schematic diagram.

Figure 1.

Schematic diagram of rolling bearing motion model

As shown in Fig. 1, let the radius of inner ring of rolling bearing be R_n, the linear velocity of contact point of rolling body and inner raceway be v_n, the angular velocity of inner ring be ω_n, the radius of outer ring be R_w, the linear velocity of contact point of ball and outer raceway be v_w, the angular velocity of outer ring be ω_w, and the number of ball beings be N_b. According to kinematics relationship, it can be known: (1) { vn=ωn×Rnvw=ωw×Rw $\left\{ \begin{array}{*{35}{l}} {{v}_{n}}={{\omega }_{n}}\times {{R}_{n}} \\ {{v}_{w}}={{\omega }_{w}}\times {{R}_{w}} \\ \end{array} \right.$

The cage (which can be equated to the center of the rolling body) has a linear velocity of: (2) vcage=vn+vw2 \[{{v}_{cage}}=\frac{{{v}_{n}}+{{v}_{w}}}{2}\]

Since the rotational speed of the outer ring of the bearing is considered to be 0, then: (3) vcage=vn2=ωnRn2 \[{{v}_{cage}}=\frac{{{v}_{n}}}{2}=\frac{{{\omega }_{n}}{{R}_{n}}}{2}\]

This gives the cage angular velocity: (4) ωcage=vcage(Rn+Rw)/w=(ωn×Rn)/2(Rn+Rw)/2=ωn×RnRn+Rw \[{{\omega }_{cage}}=\frac{{{v}_{cage}}}{{\left( {{R}_{n}}+{{R}_{w}} \right)}/{w}\;}=\frac{{\left( {{\omega }_{n}}\times {{R}_{n}} \right)}/{2}\;}{{\left( {{R}_{n}}+{{R}_{w}} \right)}/{2}\;}=\frac{{{\omega }_{n}}\times {{R}_{n}}}{{{R}_{n}}+{{R}_{w}}}\]

And the inner ring speed is the same as that of the spindle rotor, i.e. ω_n = ω_shaft, then: (5) ωcage=ωshaft×RnRn+Rw \[{{\omega }_{cage}}=\frac{{{\omega }_{shaft}}\times {{R}_{n}}}{{{R}_{n}}+{{R}_{w}}}\]

For the variable flexibility vibration generated by contact load and clearance variations due to the periodic motion of the bearing, the VC frequency can be expressed as: (6) fvc=ωcage×Nb \[{{f}_{vc}}={{\omega }_{cage}}\times {{N}_{b}}\]

The angle at which the j st roller ball turns after time t is φ_j, then: (7) φj=ωcage×t+2πNb(j−1)j=1,2,…,Nb \[{{\varphi }_{j}}={{\omega }_{cage}}\times t+\frac{2\pi }{{{N}_{b}}}\left( j-1 \right)j=1,2,\ldots ,{{N}_{b}}\]

A 5-degree-of-freedom model is developed for the rolling bearing based on the above modeling assumptions for the characteristics of the drive spindle system. The model with four basic degrees of freedom to characterize the bearing inner and outer ring displacement in the x, y direction, based on this add a degree of freedom of the unit mass resonator, used to adjust the stiffness and damping coefficients, Figure 2 for the rolling bearing dynamics model [21].

Figure 2.

Dynamic model of rolling bearing

According to Newton’s second law [22], the kinetic equation characterizing the model can be expressed as: (8) { mnx¨n+cnx˙n+knxn+fx=0mny¨n+cny˙n+knyn+fy=Frmwx¨w+cwx˙w+kwxw−fx=0mwy¨w+(cw+cr)y˙w+(kw+kr)yw−kryb−cry˙b−fy=0mry¨b+cr(y˙b−y˙w)+kr(yb−yp)=0 $\left\{ \begin{array}{*{35}{l}} {{m}_{n}}{{{\ddot{x}}}_{n}}+{{c}_{n}}{{{\dot{x}}}_{n}}+{{k}_{n}}{{x}_{n}}+{{f}_{x}}=0 \\ {{m}_{n}}{{{\ddot{y}}}_{n}}+{{c}_{n}}{{{\dot{y}}}_{n}}+{{k}_{n}}{{y}_{n}}+{{f}_{y}}={{F}_{r}} \\ {{m}_{w}}{{{\ddot{x}}}_{w}}+{{c}_{w}}{{{\dot{x}}}_{w}}+{{k}_{w}}{{x}_{w}}-{{f}_{x}}=0 \\ {{m}_{w}}{{{\ddot{y}}}_{w}}+\left( {{c}_{w}}+{{c}_{r}} \right){{{\dot{y}}}_{w}}+\left( {{k}_{w}}+{{k}_{r}} \right){{y}_{w}}-{{k}_{r}}{{y}_{b}}-{{c}_{r}}{{{\dot{y}}}_{b}}-{{f}_{y}}=0 \\ {{m}_{r}}{{{\ddot{y}}}_{b}}+{{c}_{r}}\left( {{{\dot{y}}}_{b}}-{{{\dot{y}}}_{w}} \right)+{{k}_{r}}\left( {{y}_{b}}-{{y}_{p}} \right)=0 \\ \end{array} \right.$

Define the principal curvatures of the ball-raceway contact respectively: (9) ρ11=2Dball,ρ12=2Dball,ρ21=−1fDball,ρ22=2Dball(λ1±λ) \[{{\rho }_{11}}=\frac{2}{{{D}_{ball}}},{{\rho }_{12}}=\frac{2}{{{D}_{ball}}},{{\rho }_{21}}=-\frac{1}{f{{\mathcal{D}}_{ball}}},{{\rho }_{22}}=\frac{2}{{{D}_{ball}}}\left( \frac{\lambda }{1\pm \lambda } \right)\]

Where λ = D_ball cosθ/D_p. D_ball is the diameter of the ball; f is the radius of curvature coefficient of the raceway. θ is the bearing contact angle. D_p is the radius of the bearing pitch circle. For the outer ring, ρ₂₂ should take +. For the inner ring, ρ₂₂ should be taken -.

According to the contact relationship and the geometric relationship of rolling bearings, it can be seen that the two surfaces in the O-point neighborhood range, along the Z-axis distance of the second-order expansion for: (10) Z=12(ρ11+ρ21)X2+12(ρ12+ρ22)Y2 \[Z=\frac{1}{2}\left( {{\rho }_{11}}+{{\rho }_{21}} \right){{X}^{2}}+\frac{1}{2}\left( {{\rho }_{12}}+{{\rho }_{22}} \right){{Y}^{2}}\]

When the elastic object to meet Hooke’s law of contact and produce elastic deformation, will be contact center O of the normal direction of the formation of an elliptical contact area, the contact load is also presented along the region of the elliptic distribution.

Let the total load in the contact area be F, the ratio of elliptical geometric dimensions c = a/b, the integral of formula (10) and solve the transcendental equation about c, and then we can find the size of the elliptical region, the amount of contact deformation: (11) a=(2Σπc2)1/3⋅(3FΣρ(1−v2E))1/3 \[a={{\left( \frac{2\Sigma }{\pi {{c}^{2}}} \right)}^{1/3}}\cdot {{\left( \frac{3F}{\Sigma \rho }\left( \frac{1-{{v}^{2}}}{E} \right) \right)}^{1/3}}\] (12) b=(2k∑π)1/3⋅(3F∑ρ(1−v2E))1/3 \[b={{\left( \frac{2k\Sigma }{\pi } \right)}^{1/3}}\cdot {{\left( \frac{3F}{\Sigma \rho }\left( \frac{1-{{v}^{2}}}{E} \right) \right)}^{1/3}}\] (13) ζ=(πk22∑)1/3⋅2Γπ⋅(3F2∑ρ8(1−v2E)2)1/3 \[\zeta ={{\left( \frac{\pi {{k}^{2}}}{2\Sigma } \right)}^{1/3}}\cdot \frac{2\Gamma }{\pi }\cdot {{\left( \frac{3{{F}^{2}}\Sigma \rho }{8}{{\left( \frac{1-{{v}^{2}}}{E} \right)}^{2}} \right)}^{1/3}}\]

For rolling bearings, the inner raceway and outer raceway contact area of the normal are through the diameter of the center of the ball, so the total contact deformation for the inner and outer raceway deformation of the sum: (14) ζ=ζn+ζw \[\zeta ={{\zeta }_{n}}+{{\zeta }_{w}}\]

where ζ_n = (F/c_n)^2/3, ζ_w = (F/c_w)^2/3.

Thus, the total contact deformation can be expressed as: (15) ζ=(F/csum)2/3 \[\zeta ={{\left( {F}/{{{c}_{sum}}}\; \right)}^{{2}/{3}\;}}\]

where csum=1(cn−2/3+cw−2/3)3/2${{c}_{sum}}=\frac{1}{{{\left( c_{n}^{{-2}/{3}\;}+c_{w}^{{-2}/{3}\;} \right)}^{{3}/{2}\;}}}$.

From the above analysis, it can be seen that with the determination of the basic parameters of the rolling bearing and the load, the relevant solution can be obtained based on the Hertz point contact for the subsequent dynamics process.

In the actual operation process, the failure of rolling bearings is generally due to surface spalling, wear, pitting, and gluing.

In this paper, local defects of inner and outer rings are introduced into the above rolling bearing dynamics model to simulate the vibration response signals of rolling bearings under failure conditions.

Based on the kinetic and kinematic analysis of the bearing model in the previous section, the displacements of the raceway center in the transverse and longitudinal directions are set to be x and y, respectively, the initial radial clearance is ζ₀, and the deformation of the rolling element through the damage zone is ζ_e. Therefore, the deformation of the normal contact between the rolling element and the raceway of the jth rolling element is: (16) ζj=xcosφj+ysinφj−ζ0−tjζ0 \[{{\zeta }_{j}}=x\cos {{\varphi }_{j}}+y\sin {{\varphi }_{j}}-{{\zeta }_{0}}-{{t}_{j}}{{\zeta }_{0}}\]

In the formula, τ_j is the judgment quantity, which is used to determine whether the rolling element enters the damage zone and generates damage deformation.

According to the nonlinear Hertz contact theory, the analysis shows that when the jnd rolling body and raceway contact deformation, the contact force can be calculated using (17): (17) Fj=cζjnσj \[{{F}_{j}}=c\zeta _{j}^{n}{{\sigma }_{j}}\]

Where c is the contact stiffness: n is the rolling bearing contact load deflection coefficient, which is generally taken as 1.5 for the bearings studied in this paper: σ_j is the contact switching quantity.

Since the force is generated only when contact occurs between the two elastomers, σ_j is used as the switching quantity for determination: (18) σj={ 0ζj≤01ζj>0 \[{{\sigma }_{j}}=\left\{ \begin{array}{*{35}{l}} 0 & {{\zeta }_{j}}\le 0 \\ 1 & {{\zeta }_{j}}>0 \\ \end{array} \right.\]

According to the above equation, combined with the previous kinematic analysis equation, we can find the rolling bearing in the x, y direction of the partial force is: (19) { Fx=c∑σjζj1.5cosφjFy=c∑σjζj1.5sinφj $\left\{ \begin{array}{*{35}{l}} {{F}_{x}}=c\Sigma {{\sigma }_{j}}\zeta _{j}^{1.5}\cos {{\varphi }_{j}} \\ {{F}_{y}}=c\Sigma {{\sigma }_{j}}\zeta _{j}^{1.5}\sin {{\varphi }_{j}} \\ \end{array} \right.$

In the dynamic model of inner ring failure, the inner ring and shaft segment of a rolling bearing rotate with the shaft. At the same time, the rolling body is also rotating at high speed in synchronization with the constraint of the cage. The contact between the damaged area of the inner ring and the rolling element shows a periodic change. Let the width of the crater damage be L_n, the depth of the damage be H_n, and the radius of the rolling element be r_b.

When the damage vibration condition Ln≤22rbHn−Hn2${{L}_{n}}\le 2\sqrt{2{{r}_{b}}{{H}_{n}}-H_{n}^{2}}$ is satisfied, the rolling body will experience a gap transient and suddenly obtain a certain depth of gap increment. In the simulation process, the damage simulated in this paper meets this condition, due to the rolling body movement to the local defects caused by the amount of change in the bearing clearance ζ_e = h_n, that is: (20) ζc=rb−rb2−(Ln2)2 \[{{\zeta }_{c}}={{r}_{b}}-\sqrt{r_{b}^{2}-{{\left( \frac{{{L}_{n}}}{2} \right)}^{2}}}\]

In the fault model, the relative position of the rolling body and the inner ring is changing in real time, in the damage area arc β, angular position Θ₀, according to the kinematic analysis formula can be known at t moments of the angular position of the jth rolling body, at this time the corresponding position of the inner ring is θ_n = ω_nt+θ₀, so when the angular position of the rolling body θ_j is located in the θ_n < θ_j < θ_n + β, the rolling body enters the damage area, the bearing clearance changes.

Thus, the switching quantity in equation (16) can be expressed as: (21) τj={ 1,| (θn−θj)MOD(2π) |<β0 \[{{\tau }_{j}}=\left\{ \begin{array}{*{35}{l}} 1, & \left| \left( {{\theta }_{n}}-{{\theta }_{j}} \right)MOD\left( 2\pi \right) \right|<\beta \\ 0 & {} \\ \end{array} \right.\]

Where, β = 2 arcsin(L_n/D_n), D_n is the inner ring diameter.

Combined with the above analysis, in the process of inner ring failure dynamics analysis, the gap change quantity under the current failure scale combined with the switching quantity can be calculated by substituting into the analysis process to obtain the vibration response of the inner ring failure.

Outer ring failure dynamics model. The outer ring of the bearing is fixed in the housing, the rotational speed is 0, and the rest of the cases are similar to the inner ring failure. When the rolling body enters the damage area, it will release a certain amount of deformation and produce periodic shock vibration. Let the width of the crater damage be L_w, the depth of the damage be H_w, and the radius of the rolling element be r_b.

Similar to the inner ring failure, when the rolling body enters the damage area after the bearing clearance change amount ζ_c = h_w, that is: (22) ζc=rb−rb2−(Lw2)2 \[{{\zeta }_{c}}={{r}_{b}}-\sqrt{r_{b}^{2}-{{\left( \frac{{{L}_{w}}}{2} \right)}^{2}}}\]

If the radian size of the damage region is β, its angular position is θ_w.

Thus, the switching quantity in Eq. (16) can be expressed as: (23) τj={ 1,| (θw−θj)MOD(2π) |<β0 \[{{\tau }_{j}}=\left\{ \begin{array}{*{35}{l}} 1,\left| \left( {{\theta }_{w}}-{{\theta }_{j}} \right)MOD\left( 2\pi \right) \right|<\beta \\ 0 \\ \end{array} \right.\]

where β = 2 arcsin(L_n/D_w), D_w are the outer ring diameters.

Having determined the variation of the clearance between the rolling element and the raceway, the dynamics of the failure model can be solved in conjunction with the dynamics model.

Wavelet transform has a better signal processing effect [23]. This can not only process the non-smooth raw data, but also make full use of the advantages of two-dimensional convolutional neural networks in image feature extraction. After wavelet transform, the signal W_φ(a,b) is generally represented as: (24) Wφ(a,b)=1a∫x(t)φ*(t−ba)dt,a<0 \[{{W}_{\varphi }}\left( a,b \right)=\frac{1}{\sqrt{a}}\int{x\left( t \right)}{{\varphi }^{*}}\left( \frac{t-b}{a} \right)dt,a<0\]

Where, x(t) is the search distance, φ is the mother wavelet, φ^* is the complex covariant mother wavelet, a is the scale factor and b is the time shift factor. The key of wavelet transform is to choose the wavelet basis function, other parts of the signal with different status quo characteristics will be suppressed. Morlet wavelet is characterized by symmetry and smoothness. In this study Morlet wavelet is chosen as the basis function of wavelet transform.

Convolutional neural network (CNN), as a classical model for deep learning, is a deep feed-forward neural network characterized by weight sharing and local connectivity. It consists of several parts: input layer, convolutional layer, pooling layer, fully connected layer and output layer.

In the convolutional layer, different weights through each convolutional kernel correspond to a kind of feature extraction. If one wants to obtain the same receptive field of a one-dimensional vibration signal of a motor, this can be done by stacking small convolutional kernels, but it brings certain problems and makes the training parameters increase. Therefore, the deep convolutional network structure on the visual field is not suitable for motor bearing fault diagnosis, so the expression of wide convolutional kernel is used: (25) yl+1,m(n)=wl,m*xl(n)+bl,m \[{{y}_{l+1,m}}\left( n \right)={{w}_{l,m}}*{{x}_{l}}\left( n \right)+{{b}_{l,m}}\]

where w_l,m is the weight matrix of the m nd filter; b_l,m represents the bias term; and x_l(n) denotes the n th input, and the wide convolution kernel is computed by the above equation.

The activation layer allows the nonlinearity of the network after convolution of the output to be enhanced, which increases the feature representation of the model. Common activation functions in the field of fault diagnosis are the Sigmoid function and the ReLU function, the network uses the latter, for the training process to produce some of the risks, such as gradient disappearance and gradient explosion, can play a significant role in reducing the role of; part of the neuron output results can be accelerated in the convergence of the CNN at the same time to make part of the neuron output value to 0, to avoid overfitting, accelerate the training of the network, its expression is as follows: (26) al+1,m(n)=max{ 0,yl+1,m(n) } \[{{a}_{l+1,m}}\left( n \right)=\max \left\{ 0,{{y}_{l+1,m}}\left( n \right) \right\}\]

where a_l+1,m(n) is the output value after y_l+1,m(n) activation and max(·) denotes the ReLU activation function.

When the convolutional layer directly extracts features and classifies them, it generates a relatively large amount of computation and, in this case, promotes the phenomenon of overfitting, which is usually achieved by adding a pooling layer after the convolutional layer. The role of pooling is to reduce the feature mapping dimensions and maintain the invariance of the features. If maximum pooling is used, there are two main advantages, on the one hand, the parameters can be reduced and on the other hand, the fault features of periodic time-frequency signals are maximally preserved. The expression is as follows: (27) pl+1(n)=max(n−1)H+1≤i≤nH{ ql,m(i) } \[{{p}_{l+1}}\left( n \right)=\underset{\left( n-1 \right)H+1\le i\le nH}{\mathop{\max }}\,\left\{ {{q}_{l,m}}\left( i \right) \right\}\]

where q_l,m(i) denotes the value of the i th neuron in the m rd filter in layer l, in i ϵ[(n–1)H+1,nH], H is the width of the pooling zone, and p_l+1(n) denotes the output value after the pooling operation.

Long Short-Term Memory Network (LSTM) is a variant of Recurrent Neural Network (RNN) that processes sequential data.It is capable of holding short-term memory for long periods of time and is able to solve gradient explosions and gradients in recurrent neural networks.

The gate structure of LSTM contains forgetting gates, input gates and output gates. In order to enhance the learning ability of LSTM and improve the extraction of temporal features. In this paper, a bidirectional long and short-term memory network (BiLSTM) is used, which calculates the effect of the current input on the forward hidden state (forward propagation), and also considers the effect of the subsequent information on the current state (back propagation). The computational equation is shown in (28): (28) ht→=f(w1xt+w2h→t−1)ht←=f(w3xt+w4ht+1←)Yt=g(w5h→t+w6ht←)} \[\left. \begin{align} & \overrightarrow{{{h}_{t}}}=f\left( {{w}_{1}}{{x}_{t}}+{{w}_{2}}{{\overrightarrow{h}}_{t-1}} \right) \\ & \overleftarrow{{{h}_{t}}}=f\left( {{w}_{3}}{{x}_{t}}+{{w}_{4}}\overleftarrow{{{h}_{t+1}}} \right) \\ & {{Y}_{t}}=g\left( {{w}_{5}}{{\overrightarrow{h}}_{t}}+{{w}_{6}}\overleftarrow{{{h}_{t}}} \right) \\ \end{align} \right\}\]

where ht→$\overrightarrow{{{h}_{t}}}$, h←t${{\overleftarrow{h}}_{t}}$ and Y_t are the outputs of the forward hidden layer state, the inverse hidden layer state and the hidden layer state at moment t, respectively, x_t is the vector of inputs at moment t, f is the LSTM unitary function, and w is the weight vector.

In this paper, by using soft attention mechanism [24], a fully distinguishable deterministic mechanism, the gradient is propagated through the attention mechanism and the rest of the network. Its core idea is to assign reasonable weights to different feature vectors, focusing attention to highlight key features ignoring some useless information, so as to improve the prediction accuracy of the model. The specific formula is as follows:

1) The fault features are processed through the attention mechanism layer, multiplied with the weights plus bias, mapped by hyperbolic tangent to the range of [-1, 1], and the feature weight coefficients are calculated as shown in Eq. (29): (29) ui=tanh(wyi+b) \[{{u}_{i}}=\tanh \left( w{{y}_{i}}+b \right)\]

where tanh(·) is the hyperbolic tangent function, w is the weight of the neuron, and b is the deviation of the neuron.

From the above analysis, it can be seen that in this mechanism, by adjusting the weights, the soft-attention mechanism can dynamically allocate the attention according to the different parts of the input data in order to better capture the key information in the data.

Dropout is a commonly used regularization technique to prevent neural networks from overfitting. Since some neurons are randomly dropped during each training, it is equivalent to training several different sub-networks and improves the generalization ability of the model. Overfitting of the network training is prevented by setting a portion of the output to zero. The calculation formula is as follows: (32) r=ma(Wv) \[r=ma\left( Wv \right)\]

where m is the probability that the remaining 1-P is not set to 0, a is the activation function, W is the weight, w is the weight vector, v and r are the outputs, and m and a(Wv) mean the multiplication of the individual elements.

In this paper, we propose a network model of CNN-Attention-BiLSTM, and the main components contain the following parts: four convolutional layers and pooling|layers, one fully connected layer and a hidden layer, where the hidden layer is a 128 BiLSTM network layer of the attention mechanism as well as a Softmax layer composition. The activation function is ReLU and the pooling function is maximum pooling.

In bearing fault diagnosis, the bearing signal data is collected through sensors and divided into training, testing, and validation samples.In the process of fault diagnosis, batch normalization is introduced to stabilize the feature distribution. BiLSTM and attention mechanisms are used to extract key features, and Dropout enhances the generalization ability of the model. Finally, the training set is loaded for feature fusion and Softmax classification to determine the fault type and continuously optimize the model performance.

Due to the different operating environments in which the bearings are located, resulting in unusually complex operation and unpredictable fault conditions, it is more difficult to interpret and analyze the signals.It is easy to cause the traditional deep learning model is prone to overfitting and underfitting problems.This model has high recognition accuracy under variable operating conditions and noisy environments, which effectively improves the accuracy and stability of bearing fault diagnosis. The fault diagnosis process is shown in Figure 3:

Figure 3.

Flow chart of fault diagnosis

In this paper, based on the railroad track failure dynamics modeling of the speed of 300-1800rpm under different working conditions, respectively, no failure, outer ring failure, inner ring failure, and rolling element failure state of the rolling bearing work of the vibration characteristics of the response of the simulation analysis, the calculation results are more accurate, of which the speed of 900rpm when the above failure of rolling bearing failure characteristics of the frequency of the simulation results and the theory of the frequency of the rolling bearing. Calculation results are shown in Table 1. Combined with the analysis of the time domain and frequency domain, the outer ring failure, inner ring failure and rolling element failure rolling bearing vibration acceleration signal in the speed conditions and no fault rolling bearing signals there are obvious differences, the fault bearing vibration signal there is a significant impact phenomenon, due to the existence of faults in the structure of the rolling bearing vibration impact, the impact frequency is the characteristic frequency of the fault. The fault characteristic frequency obtained is very close to the theoretical calculation results, the simulation results and the theoretical value of the error is small, the maximum error of the outer ring faulty bearings is 0.363%, the maximum error of the inner ring faulty bearings is 0.813%, the maximum error of the rolling element faulty bearings is 0.968%, which are all within the reasonable range. According to the above analysis results, it shows that the simulation analysis of the vibration characteristic response of rolling bearings based on the dynamic modeling of railroad track failure is accurate.

Railroad track fault diagnosis network model parameters mainly include CNN parameters (convolution kernel size k and number of convolution kernels N). The specific parameter settings are as follows.The size and number of convolution kernels of CNN parameters have an important impact on model training. In order to obtain the optimal convolution kernel size and number for the railroad track fault diagnosis network model, take the bearing data under 735W load as an example, according to the grid search method, set the convolution step size, pooling step size and window size to 4, the number of augmentation nodes to 130, the nonlinear activation function to tanh function, and the regularization coefficient λ = 2 × 10-30, and analyze the convolution kernel size and number on the accuracy of fault classification. Impact. The diagnostic results for different convolutional kernel sizes and numbers are shown in Fig. 4. It can be found that: the diagnosis accuracy of large convolution kernel is higher than that of small convolution kernel, and the accuracy gradually increases with the increase of the number of convolution kernel N. However, when N is larger than 18, the range of variation is small and overfitting phenomenon is easy to occur. Therefore, the parameters of this study were set to k=27 and N=18.

Figure 4.

The diagnosis of the nuclear size and number of different convolution

In order to verify the classification performance of the railroad track fault diagnosis network model for different faults and the reliability of the results, the bearing data under the three loads of 735, 1470 and 2205W are selected for the experiments, F1 is the model proposed in this paper, F2 is the model without adding the attention mechanism, F3 is the model of Dropout in CNN, and F4 is the traditional CNN model. The average value is taken as the final experimental result.The average accuracy of the four models under different loads is shown in Table 2. As can be seen from Table 2: comparing F1 and F2 models, the average accuracy of F1 is 99.50%, which is 3.83% higher than the average accuracy of F2. It shows that adding the attention mechanism can improve the classification ability of the model. Comparing F3 and F1, the average accuracy of F3 is 2.64% lower than that of F1. The accuracy of F4 is significantly inferior to that of the other three models.It can be seen that the railroad track fault diagnostic network model with the addition of the attention mechanism and Dropout in BiLSTM has better performance in bearing fault diagnosis.

In order to study the training and testing efficiency of the above methods, the training time and testing time of the four models are analyzed, and the analysis results are shown in Fig. 5. It can be seen that: although F2 is faster than the training speed of F1, the latter has a high accuracy rate, and the difference in training time is only 0.02 s. The training time of F3 and F4 is 0.15 s and 0.25 s more than that of F1 respectively, and the model of F1 has a higher accuracy rate, which indicates that the railroad track fault diagnosis network model in this paper consumes a smaller training time to improve a higher accuracy rate.

Figure 5.

Model training time and test time

In order to further visualize and understand the classification ability of the railroad track fault diagnosis network model of this paper for different railroad track faults, the model extracted features are reduced to a two-dimensional plane by t-distributed neighborhood embedding visualization technique. The raw data features are visualized as shown in Fig. 6, where different colors represent different bearing state categories. From Fig. 6, it can be seen that the distribution of the original data is chaotic, and it is difficult to distinguish each fault category. Fig. 7 and Fig. 8 show the results of the data fault feature visualization with the addition of the BiLSTM network and with the addition of the BiLSTM network and the attention mechanism, respectively. From Fig. 7, it can be seen that after adding the BiLSTM network it is possible to obtain a clear separation of the 10 kinds of fault features, and from Fig. 8 it can be seen that after the addition of the BiLSTM network and attention mechanism it is possible to obtain the 10 kinds of fault features. As can be seen in Figure 8, the distribution of the 10 kinds of railroad track fault features is more tightly aggregated after the addition of a BiLSTM network and attention mechanism together. The results show that the model of this paper with the addition of BiLSTM network and attention mechanism has strong feature extraction capability and classification performance, which can distinguish several different kinds of railroad track faults, and the diagnosis ability of different faults is stronger.

Figure 6.

Raw data

Figure 7.

After the attention mechanism is added

Figure 8.

Add the attention mechanism and the BiLSTM

In order to verify the effectiveness of the model, a comparison experiment between the model of this paper and the fault diagnosis model based on BP network is established, and the comparison results are shown in Fig. 9. When performing parameter optimization, the initial adaptation value and convergence value of this paper’s model are smaller than that of the BP network-based fault diagnosis model. Moreover, the model in this paper reaches convergence around 11 iterations, and the fault diagnosis model based on BP network reaches convergence around 23 iterations, indicating that the model in this paper converges faster than the fault diagnosis model based on BP network.

Figure 9.

Calibration curve contrast