1. Introduction
The shearer is one of most the important pieces of equipment to realize the mechanization and modernization of coal mine production. It is mainly composed of a cutting part, loading part, walking part, and hydraulic elevation system [
1,
2]. In longwall mining faces, the cutting part breaks down the coal from the coal body and loads it into the mining machine of the working conveyor, with a complex system and harsh working environment [
3]. Its stable operation is directly related to the safety and stability of coal mining. Once failure occurs, it causes huge economic losses and hidden dangers of safety production. As the key component of the shearer, the failure rate of the hydraulic heightening system accounts for about 12% of the total failure, and the duration accounts for about 40% of the average time of failure. The causes of failure are diverse and uncertain [
4]. When the traditional identification method is used for fault diagnosis, a large amount of redundant data is obtained, which leads to low efficiency and poor accuracy of fault diagnosis [
5]. Therefore, it is of great significance to establish an efficient and accurate fault diagnosis method for the hydraulic heightening system of the shearer.
Generally speaking, the failure of the hydraulic heightening system mainly occurs in the leakage and mechanical failure of hydraulic pumps, valves, and cylinders [
6]. At present, experts and scholars have various methods for the fault diagnosis of hydraulic systems and internal components. Reference [
7] proposed a deep learning model method based on the combination of a convolutional neural network and long- and short-term memory, which improves the accuracy of the hydraulic system fault diagnosis by improving the ability of data extraction. Article [
8] proposed a new FDI framework for the closed-loop system to diagnose the faults of the hydraulic system, which mainly constructs the performance residual vector for diagnosis and compares the difference between the real and model system stability, accuracy, and speed. In [
9], a fault diagnosis information fusion method of the hydraulic system based on the improved D-S evidence theory and time–space domain was proposed, which uses D-S and decision rules to identify faults. Reference [
10] proposed a fault feature extraction method for hydraulic systems based on a fuzzy ARX model, which has the advantage of extracting nonlinear features for fault classification and diagnoses. Reference [
11] proposed a two-stage radial basis function neural network model for fault classification detection and the fault location of the hydraulic system. In [
12], a scheme combining a regression neural network and metric learning was proposed. Degradation features are extracted from the difference between the actual and estimated outputs to diagnose the faults of the hydraulic system. Reference [
13] optimized the placement and method of sensors in the hydraulic system, improved the efficiency of data acquisition, and realized the efficient fault diagnosis of the hydraulic system. Reference [
14] proposed an adaptive particle swarm optimization algorithm to optimize the BP neural network method. By using a particle purity better than the optimal value and the dynamic fusion strategy to realize the particle swarm search, the hydraulic system diagnosis efficiency was improved. Reference [
15] proposed a new fault diagnosis method which could extract leakage information, directly detect and locate faults in the hydraulic system caused by leakage, and realize intuitive and efficient fault monitoring. In reference [
16], based on the machine learning algorithm and statistical features of vibration monitoring, a C4.5 decision tree algorithm was adopted to extract statistical features from vibration signals to realize the fault diagnosis of the hydraulic system.
Aiming at the fault diagnosis of hydraulic systems, the fault features of the hydraulic pump, valve, and cylinder were extracted for fault diagnosis. Reference [
17] used a cavitation detection framework, including experimental research and numerical signal processing, to detect the strength of cavitation faults in axial piston pumps, so as to improve the accuracy of fault diagnosis. Reference [
18] improved the identification accuracy and optimized the parameters of the hydraulic plunker pump through the improved LeNet-5 and PSO hyperparameter optimization fault diagnoses. In [
19], a three-layer fault diagnosis method based on the Dezert–Smarandache theory was used. A multi-classifier was used to detect the failure of the hydraulic system with the hydraulic valve as the main object. Reference [
20] applied diagnostic methods based on wavelet packet analysis and feature extraction. By optimizing the identification and extraction of the fault features, the hydraulic cylinder leakage of the actuator in the hydraulic system was diagnosed.
There are a variety of state-of-art methods based on deep neural networks. In [
21], a multi-scale edge-labeling graph neural-network-based method was developed under small samples, which take advantage of a graph neural network in the feature extraction of small samples and improved its performance through a multi-scale trick. Reference [
22] proposed a novel entropy-based sparsity measure for the prognosis and development of a sparsogram to select a sensitive filtering band. The measurements were sensitive to pulses and could indicate how sparse the signal was. A sparsogram tool was developed to help choose the right filtering band for envelope analysis. Reference [
23] proposed a fault diagnosis method based on an RBFNN. A series of fault isolation observers based on an RBFNN were designed to completely decouple different faults. The diagnosis results of one component were not affected by other faults, and multiple faults could be diagnosed at the same time. In [
24], a hybrid fault diagnosis method was developed based on relief, a principal component analysis (PCA), and a deep neural network. Relief and PCA were used to select fault features to reduce data dimensions, and deep neural networks were used to improve the accuracy of fault diagnosis. In [
25], based on the laboratory measurement data of the GEROLER motor, the black box model for predicting the operating parameters of the artificial neural network was established. By comparing the static multilayer feedforward network and dynamic NARX neural network, the dynamic NARX neural network provided better results due to its flexibility in processing non-linear dynamic systems. The above fault diagnosis methods are diverse, but there are few fault diagnosis methods for hydraulic systems based on an RS-RBFNN.
Through the analysis of the existing hydraulic system fault diagnosis methods, it can be seen that the diagnosis data is complicated and the diagnosis method is single, resulting in low diagnosis efficiency and accuracy. This paper presents a fault diagnosis method of the shearer hydraulic heightening system based on an RS-RBFNN. First, the RS was used to discretize the dataset and attribute reduction, which removed redundant information and retained the key features of the data [
26]. It laid a data foundation for subsequent feature extraction, shortened the training time of the network, and significantly improved the efficiency. Then, the RBFNN had a strong input and output mapping function, with only the best approximation characteristics. Combined with the better association and memory ability of the RBFNN, the hidden knowledge was mined and the potential rules were objectively described [
27,
28]. Therefore, aiming at the problems of fault data redundancy and the complex mutual relationship of shearer hydraulic heightening systems, compared with the existing single method, the combination method of an RS and RBFNN not only takes advantage of RS data processing, but also combines the best local approximation performance and global optimal characteristics of the RBFNN to achieve a faster and more accurate fault diagnosis.
The organization of this paper is as follows:
Section 2 mainly introduces the RS-RBFNN fault diagnosis model and methods.
Section 3 is the fault simulation analysis of the hydraulic heightening system.
Section 4 presents the process of fault diagnosis with the RS-RBFNN.
Section 5 is the comparison of the three fault diagnosis methods. Finally,
Section 6 draws the conclusion.
2. Models and Methods
Figure 1 shows the whole idea of the RS-RBFNN fault diagnosis method. It mainly included five parts: model building, fault data collection, RS preprocessing (includes cutting the clutter and attribute reduction), RBFNN training diagnosis, and fault output.
2.1. RS Model
Data plays an important role in artificial intelligence. In order to solve complex problems, large amounts of data are often needed and structures are established to process them. An RS is also based on a large amount of data, building models for discretization and attribute reduction [
27,
29].
The data system used was represented by where U is the domain and A is the set of attributes, both of which are non-empty finite sets; where Va is the attribute range; and is the value of an object’s property, , .
Data systems are usually represented by relational tables. As a special information system, decision tables play a key role in decision applications. The row attribute represented our research object, and the column attribute represented the object attribute.
In the data system S, , C represented the set of conditional attributes and D represented the set of decision attributes. If the data system contained a set of C and D, the system was a decision table.
Assume an equivalence relation cluster
L on
U,
,
,
is an equivalence relation in
U, defined as an indistinguishable relation on
P, expressed as:
The indistinguishable relationship divides
U into multiple sets, in which the objects are indistinguishable.
is the knowledge related to all equivalence classes of
in the domain.
is called the basic set of
P in
U, recorded as
U/P. The equivalence class of
is the basic category of knowledge
P. If
T is called the T-elementary knowledge about
U, the equivalence class of
T is called the T-elementary category of
R. There is the knowledge base
, for each subset
and
, the
R lower approximation set and the
R upper approximation set of
X are defined as follows:
The R boundary region of X is defined as ; the R-positive region of X is defined as . The R-negative domain of X is defined as . It can be concluded that .
The set is approximated by the exact sets and . All objects of belong to X. The object of the negative domain must not belong to X, and the object of the boundary domain is not sure whether it belongs to X.
If , then Q is independent and if ind (Q) = ind(P), then Q is a reduction of P. The reduction of the decision table does not affect the original knowledge expression after removing the redundant conditional attributes.
2.2. RBFNN Model
Figure 2 shows the topology structure of the RBFNN used in this study. The RBFNN is a kind of feedforward network, where the number of nodes in the input, hidden, and output layers are
n,
h, and
m, respectively. The input vector of the network is
, the weight matrix is
, and the output vector is
. The activation function of the hidden layer neurons is
Ri in the network, and the
∑ represents the function of the output that is linear in the output layer.
In the network structure, the basis functions of the hidden layer are radial basis functions as activation functions, which are radially symmetric [
30]. The most commonly used Gauss function can be expressed as follows:
where
is the center of the
ith basis function;
is the variance of the
ith basis function; and
is the hidden layer activation function corresponding to the input
xi.
The input and hidden layers of the network have a nonlinear relationship, and the hidden and output layers have a linear relationship [
31]. The output of the network is as follows:
where
is the adjustment weight between the output and hidden layers and
q is the number of output layer nodes.
2.3. RS-RBFNN Fault Diagnosis Model
Figure 3 shows the flow chart of fault diagnosis model based on the RS-RBFNN. The specific flow is as follows.
The model of the hydraulic heightening system was established, and the typical faults in the system were taken as the research object. Pressure, flow, displacement, and speed sensors were used to collect the fault data.
RS theory was used to construct the original fault decision table. The fault symptoms that occurred many times in the system were taken as the condition attributes, and the fault type was taken as the decision attribute to generate the original fault decision table. The data of the original fault decision table was discretized at an equal distance. Then, using the attribute reduction based on genetic algorithm, the redundant conditional attributes were deleted under the condition of retaining the key input information, and the minimum set of conditional attributes was obtained.
The minimum attribute reduction set was used as the input of the RBFNN. The mapping relationship between the fault symptoms and categories of the RBF neural network was used for learning and training. Finally, the fault diagnosis classification results of the shearer hydraulic heightening system were obtained.
5. Simulation Comparison
To further verify the effectiveness of the proposed method, a variety of simulation methods were compared. Two other mainstream fault diagnosis schemes are introduced: BPNN and RBFNN.
The BPNN diagnosis method is the most traditional neural network diagnosis method, which belongs to a nonlinear forward network. The main idea of diagnosis is to input data samples and use a back-propagation algorithm to adjust the weights and deviations of the network so that the output vector is as close as possible to the expected vector. When the error square sum of the network output layer is less than the specified error, the diagnosis method training is completed [
32,
33]. However, the network connection mode is “weight connection”, and the convergence speed is slow. A BPNN is trained and tested by using the original fault decision table.
RBFNN diagnostic methods, similar to those of a BPNN as described above, are a class of commonly used three-layer feedforward networks that can be used for both function approximation and pattern classification. They have the best approximation performance and global optimal characteristics, and the training speed is fast. An RBFNN uses the original fault decision table to train and test the network.
The RS-RBFNN diagnosis method is based on RBFNN diagnosis. Using an RS to reduce the original fault decision table, the minimum condition attribute set is obtained for training. The number of hidden nodes of the network is the optimal number of nodes according to multiple simulations.
Table 6 shows the comparison parameter of the three neural network simulations.
The diagnostic results of the three typical fault diagnosis methods were obtained with a simulation comparison, as shown in
Figure 11. The RS-RBFNN diagnosis method had the best fault diagnosis performance, and its average diagnostic accuracy can reach 98.68%. The diagnostic effect of an RBFNN was lower than that of an RS-RBFNN, and the average diagnostic accuracy was 92.59%. A BPNN had the worst diagnostic effect, and its average diagnostic accuracy was only 83.09%.
6. Conclusions
Aiming at the requirements of high efficiency and high precision for the fault diagnosis of hydraulic heightening systems, this paper proposes a fault diagnosis method based on an RS-RBFNN. The original fault data was extracted by establishing the shearer hydraulic heightening system model. The ability of RS theory was utilized to process redundant data, including discretizing processing and attribute reduction, which provided better data input for fault diagnosis. The mapping relationship between the fault symptoms and fault categories of the RBF neural network was used for learning and training. The average accuracy of the final diagnosis result was 98.68%.
To verify the accuracy of the proposed method, two other mainstream fault diagnosis schemes were introduced for comparison: the BPNN and RBFNN methods. The results showed that the RS-RBFNN diagnosis method had the best fault diagnosis performance, and its average diagnostic accuracy could reach 98.68%, which was higher than that of the RBFNN by about 6.09%, and higher than that of the BPNN by 15.59%.
For the shearer hydraulic heightening system, the method was proved to be effective. In the future, this method can be extended to the fault diagnosis of hydraulic systems of various machines, including excavators, cranes, forklifts, and heavy trucks.