Research on safety detection method of mining coal mining machinery transmission mechanism based on optical sensor

Artificial neural network is the abstraction, simplification and simulation of the human brain, the information processing function of the network is realized by the interaction between neurons, the storage of knowledge and information is manifested in the distributed physical connection between the network components, and the learning and identification of the network is determined by the dynamic evolution of various neuron pieces connected to the coefficient of weight.

An artificial neural network is equivalent to a nonlinear threshold device with multiple inputs and single output. X₀,X₂,⋯,X_m is the information received by the neuron, i.e., the input; W₀,W₁,⋯,W_m is the connection strength, called the weights; b_i is the external input signal; Y_i denotes the output value of this neuron; and θ_i is the threshold, if the weighted sum of the input signals exceeds θ_i, the artificial neural network is activated such that the output of the artificial neuron can be described as: (1) Yi=f(∑ WiXi−θi) \[{{Y}_{i}}=f\left( \sum{{{W}_{i}}}{{X}_{i}}-{{\theta }_{i}} \right)\]

The tansig hyperbolic tangent type S (sigmoid) transfer function is used to map a neuron's input range of (–∞,+∞) to (–1,+1). The Logsig logarithmic type S (sigmoid) transfer function is used to map a neuron's input range of (–∞,+∞) to (0,+1). Both are microscopic and therefore well suited for training neural networks using the BP network algorithm.

Unified neural network training is done using BP algorithm i.e. error back propagation algorithm.The derivation process of BP algorithm is as follows:

Multilayer perceptron network using BP algorithm is one of the most widely used artificial neural networks, which has very important applications in various subject areas. However, because the BP network adopts the gradient descent search and solution algorithm, which inevitably appears in the network learning convergence speed is slow, as well as easy to fall into the local minima and other problems; in addition, in the implementation process, the learning rate and the momentum term of the two parameters can only be selected by experiment and experience to determine, once improperly selected, it will cause the network oscillations, and even lead to the network into the saturation state and does not converge. For this reason, a variety of improvement methods have been proposed, which improve the learning rate to varying degrees, accelerate the convergence of the network, and avoid falling into local minima. Using the parallel computing capability of neural networks, through some self-learning method, useful features can be automatically extracted in the case of unknown statistical characteristics of the input fault signal, and the combination of the two can also improve the sensitivity of the input data to the features, and ultimately achieve the purpose of making the network simplified and the training time shortened. It can also be realized by applying the principal element analysis method to linearly combine the network inputs and reduce the dimensionality of the input vectors.

Maximum feature vector extraction network structure based on Hebbian-learning rule. It corresponds to the input-output relationship as: (9) z=∑ qjxj \[z=\sum{{{q}_{j}}}{{x}_{j}}\] Where: q_j is the network weights; x_j is the input.

The maximum feature vector in the input failure mode sample can be extracted as: (10) Δqj=β(xjz−qjz2)j=1,2,⋯,n \[\Delta {{q}_{j}}=\beta \left( {{x}_{j}}z-{{q}_{j}}{{z}^{2}} \right)j=1,2,\cdots ,n\] Where: x_jz denotes the learning term, which strengthens the connection between the input and the output when the input x_j is correlated with the output z. q_jz² is the damping term, which is used to ensure that the weight ∑ qj2$\sum{q_{j}^{2}}$ constraint is close to 1.

Since similar inputs are likely to belong to the same class, the higher the variance of an input variable, the more likely it is to have good discriminatory power. Principal element analysis utilizes this law to perform a linear combination of the inputs so that the output covariates obtained have a larger variance and a better ability to discriminate between patterns.

Let X_i(i = 1,2,⋯,n) be a m-dimensional sequence of column vectors, where m is the number of parameters in the original input and n is the number of samples in the training data, which should include input signals in normal and various fault states. For the X_i data set, find the unit column vector U such that the linear combination series U^TX_i has the maximum variance. Let the mean of the data set be μ : (11) μ=1n∑i=1nXi \[\mu =\frac{1}{n}\sum\limits_{i=1}^{n}{{{X}_{i}}}\]

Then the mean value of the linear combination series p_i = U^TX_i is: (12) E(p)=1n∑i=1nUTXi=UT1n∑i=1nXi=UTμ \[E\left( p \right)=\frac{1}{n}\sum\limits_{i=1}^{n}{{{U}^{T}}}{{X}_{i}}={{U}^{T}}\frac{1}{n}\sum\limits_{i=1}^{n}{{{X}_{i}}}={{U}^{T}}\mu \]

From this we get: (13) E(p)2=(UTμ)(μTU)=UT(μ×μT)U \[E{{\left( p \right)}^{2}}=\left( {{U}^{T}}\mu \right)\left( {{\mu }^{T}}U \right)={{U}^{T}}\left( \mu \times {{\mu }^{T}} \right)U\] (14) pi2=(UTXi)(XiU)=UT(Xi×XiT)U \[p_{i}^{2}=\left( {{U}^{T}}{{X}_{i}} \right)\left( {{X}_{i}}U \right)={{U}^{T}}\left( {{X}_{i}}\times X_{i}^{T} \right)U\]

Then the variance of series p_i is calculated: (15) σp2(U)=1n∑i=1npi2−E(p)2=UT[ 1n∑i=1n(xi−μ)(xi−μ)T ]×U \[\sigma _{p}^{2}\left( U \right)=\frac{1}{n}\sum\limits_{i=1}^{n}{p_{i}^{2}}-E{{\left( p \right)}^{2}}={{U}^{T}}\left[ \frac{1}{n}\sum\limits_{i=1}^{n}{\left( {{x}_{i}}-\mu \right)}{{\left( {{x}_{i}}-\mu \right)}^{T}} \right]\times U\]

Let R=1n∑i=1n(xi−μ)(xi−μ)T$R=\frac{1}{n}\sum\limits_{i=1}^{n}{\left( {{x}_{i}}-\mu \right)}{{\left( {{x}_{i}}-\mu \right)}^{T}}$, then R is a m×m symmetric square array.

From the above equations we conclude that finding the maximum value of the variance of the series p_i has been transformed into a problem of finding the maximum value of equation σp2(U)=UTRU${{\sigma }_{p}}^{2}\left( U \right)={{U}^{T}}RU$ subject to the constraints of ∥U∥ = 1. A new equation is constructed using Lagrange multipliers: (16) J(U)=UTRU+λ(1−UTU) \[J\left( U \right)={{U}^{T}}RU+\lambda \left( 1-{{U}^{T}}U \right)\]

The derivation of this equation yields: J′(U) = 2RU–2λU. Let J′(U) = 0, the extreme value of J(U), be obtained from the equation: (17) RU=λU \[RU=\lambda U\]

Substituting the above equation into the formula for finding the variance of series p_i yields: (18) σp2(p)=UTRU=UTλU=λ \[\sigma _{p}^{2}\left( p \right)={{U}^{T}}RU={{U}^{T}}\lambda U=\lambda \]

From this we can see that the input dataset X_i, linearly combined by the eigenvectors U of the square array R, results in a series p_i whose variance is equal to the eigenroot corresponding to U. So the eigenvector U corresponding to the largest eigenroot of the square array is exactly the unit vector we are looking for, i.e., the principal element direction of the input data set.

Since the principal element direction is just a straight line in m-dimensional space, it is only suitable for linearly differentiable pattern recognition. For this type of problem we just need to derive the length of the current state parameter representation in the principal element direction by linear operations, i.e., the network only needs one input to distinguish the class of the current state. For nonlinearly differentiable pattern recognition problems, we must also construct some additional basis vectors in m-dimensional space. Considering that R is a m-dimensional symmetric square matrix whose eigenvectors U₁,U₂,⋯,U_m are perpendicular to each other, a m-dimensional space can be tensored by using U₁,U₂,⋯,U_m as a basis, and the coordinates of x_i in the resulting tensored space are transformed to: (19) Si=∑j=1mUjTXiei \[{{S}_{i}}=\sum\limits_{j=1}^{m}{U_{j}^{T}}{{X}_{i}}{{e}_{i}}\] where e_i is m is the ird unit column vector.

In order to reduce the dimensionality of the network inputs while making the retained covariates highly sensitive to modes, the coordinates in m -dimensional space can be projected into m′ -dimensional space, i.e., making the m′+1th through mth components of S_i zero. This reduces the dimensionality of the inputs while maximizing the variance of the input data in the m′ cardinal directions. The coordinates of the input data X_i in the m′ -dimensional projection space with U₁,U₂,⋯,U_m as the base vector are: (20) S′i=∑j=1m′UjTXie′i \[{{{S}'}_{i}}={{\sum\limits_{j=1}^{{{m}'}}{{{U}_{j}}}}^{T}}{{X}_{i}}{{{e}'}_{i}}\] where ei′${{e}_{i}}\prime $ is the m′ -dimensional ird unit column vector.

In order to efficiently complete the experimental part of this test, I complete all the diagnostic model building process in the laboratory specification model S822LC IBM high-performance computing platform, equipped with NVIDIA Tesla K80GPU and model V5000 disk storage array. GPU is used to accelerate the computing speed of the model, and disk storage array is used for the storage of data.

The master meta-analysis-neural network model constructed in this paper is done under the TensorFlow framework. TensorFlow 1.0 is installed and the compilation environment of Jupyter Notebook is configured for remote access. By accessing the command side to enter the Python environment, TensorFlow was successfully launched, indicating the completion of the software platform construction.

The four vibration measurement points in the region for vibration signal acquisition experiments, through the collection of raw signal sample data in accordance with the four measurement point locations, six fault states for grouping, labeling, collection of sample information contains a total of 5,400 groups of samples, each fault state contains the number of samples of 900 groups, each sample contains 100 samples, the formation of 5,400 100-dimensional sample space, each set of data Each set of data contains the state labeling information of the high-speed zone spur gear system, and constitutes the corresponding data set. It is divided into 3:1 according to the ratio, the former part is used as labeled training dataset to complete the modeling of coal mining machinery drive mechanism fault identification, and the latter part is used as unlabeled information to verify the feasibility and accuracy of the coal mining machinery drive mechanism fault diagnosis model. The fault sample information of its high-speed spur gear train is shown in Table 1.

Similarly, the use of optical sensor acquisition of the four vibration measurement points in the low-speed region of the vibration signal acquisition experiments, the establishment of the fault characteristics of the sample set, the low-speed region of the planetary wheel system of the fault sample information as shown in Table 2.

The sample set B of the high-speed planetary gear train measurement point region is normalized by input vectors, where the normalized feature vectors of data set B are shown in Table 3.

The feature vectors of the obtained test sample set are input into the traditional support vector machine, BPDBN diagnostic model and master element analysis-neural network diagnostic model for diagnostic experiments, respectively. The test results of the high-speed zone transmission mechanism fault diagnosis model are shown in Fig. 5, where (a) ~ (c) are support vector machine, BPDBN, and principal element analysis-neural network, respectively.

Figure 5.

Test results of fault diagnosis model for high-speed transmission system

To summarize the diagnostic effect of the above models, this section uses the confusion matrix to comprehensively reflect the diagnostic rate of the current model, the traditional support vector machine diagnostic results shown in Table 4, the supervised BPDBN network model diagnostic results shown in Table 5, and the principal meta-analysis-neural network diagnostic results shown in Table 6, where each row is the actual type of the sample, and each column is the type of diagnostic results of the model. Testing the same data for the three methods, the recognition accuracy of BPDBN is higher than SVM, but the recognition accuracy of bearing outer ring faults is still lower than 90%, while the recognition accuracy of principal element analysis-neural network reaches 97.28% in the whole high-speed spur gear train, which is higher than that of SVM and supervised BPDBN model. In the experiment of high-speed spur gear system, the recognition rate of all kinds of failure modes of the coal mining machine transmission mechanism fault diagnosis model based on principal element analysis-neural network proposed in this paper reaches more than 95%, which proves that the model can effectively identify all kinds of failure modes of the transmission system, especially in the broken tooth fault of the transmission system, the recognition rate reaches the highest.

In order to facilitate the diagnosis of each model and reduce computational errors, the same sample set B of the low-speed planetary gear train measurement point area is normalized by input vectors, and due to the limited space, the detailed data table will not be given. The feature vectors of the test sample set are input into the traditional support vector machine, BPDBN diagnostic model, and the main element analysis-neural network diagnostic model for diagnostic experiments. The results of the low-speed zone fault test experiments are shown in Fig. 6.

Figure 6.

Low speed zone fault test results

The diagnostic results of the above three models are summarized, and similarly, the confusion matrix is used to comprehensively reflect the recognition rate of the current model in the low-speed planetary wheel system, the traditional support vector machine diagnostic results are shown in Table 7, the supervised BPDBN network model diagnostic results are shown in Table 8, and the principal element analysis-neural network diagnostic results are shown in Table 9, with the actual type of samples for each row, and the diagnostic results of the model for each column Type. The experimental results show that relative to the high-speed zone spur gear train, the diagnostic accuracy of the principal element analysis-neural network-based fault diagnosis model of coal mining machinery transmission mechanism is reduced in the low-speed zone planetary gear train, but it is still higher than that of the traditional support vector machine and supervised BPDBN model. The reason for the lower diagnostic efficiency compared with the high-speed spur gear zone may be due to the fact that the working environment of the planetary gearbox is more complex than that of the high-speed spur gear train, and the nonlinear characteristics of the signal features are more obvious.