Application of gearbox fault diagnosis by LVQ neural network optimized by wolves

Zhen-jie ZHU, Mei ZHOU

(1Key Laboratory of High-efficiency and Clean Mechanical Manufacture of MOE，National Demonstration Center for Experimental Mechanical Engineering Education，School of Mechanical Engineering, Shandong University， Jinan 250061, China)(2Engineering Training Center,Shandong Jianzhu University， Jinan 250101, China)

Abstract: In order to improve the accuracy of gearbox fault diagnosis, LVQ neural network is used to complete the gearbox fault location and identification, and the wolf pack optimization algorithm is used to optimize the model parameters. In the process of gearbox fault diagnosis, a wolf pack optimization algorithm is introduced. The LVQ neural network weights and thresholds are used as wolves. Individuals with multiple randomly generated weights and thresholds are combined to form wolves. According to the behaviors of wolves swimming, beckoning, and siege, the positions of individual wolves in the wolves are continuously updated to obtain the head wolf with the highest global fitness, in order to achieve the optimal weight and threshold, and determine the optimal gearbox fault diagnosis model. It is proved by experiments that the gearbox fault classification based on wolf pack optimization LVQ neural network has higher classification accuracy.

Key words: Gear shaft failure, Wolf swarm optimization, LVQ neural network, Winning neuron, Fitness

As the main connection of the mechanical power system, the gearbox has become the key link of mechanical power transmission. During the rotation of the gear, the accuracy of gear meshing, the degree of wear resistance of the gearbox, etc. will be affected. Regular maintenance of the gearbox can reduce the negative impact of a faulty gearbox on the mechanical power system. But for maintaining a reliable mechanical power system, it is far from enough to rely on regular maintenance gearbox inspections. It is also necessary to use more advanced methods to troubleshoot various faults of the gearbox, improve the efficiency of gearbox troubleshooting, and further optimize the stability of the mechanical power system operation.

There are many failure factors for gearboxes. Gear missing, broken teeth, cracks, glue peeling, and other reasons will cause gearbox failures in different aspects [1]. According to the position, it can be divided into gear rotation, outer ring, and inner ring failure. According to the cascade relationship of the gearbox, it can be divided into input layer, intermediate layer, and output layer gear failure. In the past 20 years of research on gearbox fault diagnosis, researchers have continuously optimized fault location and troubleshooting methods, and have achieved good results. Reference 2 is a research on the search method of the fault feature index extraction of the gearbox, and emphasizes the important role of the optimal extraction time of the feature index for fault analysis [2]. Reference 3 is a fault location analysis of the shearer used in the industrial and mining industry, and introduces a common fault determination method for the gearbox of the shearer [3]. Reference 4 is to locate and analyze the coupling failure of the gearbox [4]. This paper combines the wolf pack optimization algorithm with the LVQ neural network algorithm to further improve the accuracy of gearbox fault identification.

1 LVQ neural network

Let the initial update step size toη(0)and the total number of iterations toK, where the winning neuralj*satisfies the condition is shown in formula (1).

(1)

The following starts to adjust the weight of the winning neuron. When the network training result is consistent with the actual result, the adjustment method is shown in formula (12) [6].

(2)

When the result of network training is opposite to the actual result, the weight adjustment method is shown in formula (3).

(3)

According to the number of iterations, a dynamic learning rate is established, and the method isη(k)=η(0)(1-k/K). Ifk

2 Gearbox fault model of LVQ neural network based on wolf pack optimization

2.1 LVQ neural network weight and threshold optimization based on wolf pack optimization

A set of weights and thresholds of the LVQ neural network is randomly selected as the data set of a wolf, and multiple groups are selected to construct a wolf pack. Select the reciprocal of the RMSE of the gearbox fault classification as the fitness function, and then calculate the fitness of the wolf. Let’s record the wolf with the lowest RMSE as the head wolf, and the head wolf dataset isM′=[m11m12…m1Mm21…mIM]. Let this set be the coordinate position of the head wolf in the wolf pack. Let the total number of the wolf packs beN, and the coordinate positions of the otherN-1 wolves be described asQl=[ql1ql2…qlkmlJ], where,J=I×M,k=1,2,…,J,l=1,2,…,N.

Part of the data in the data set is used as the direction of the wolves, that is, their role is to explore the direction of the wolves. Then perform simulation training and set the total amount of partial data set toTnum. The method of updating the step size and position ofTnumdata sets is shown in formula (4) [7-8]:

(4)

Sin formula (4) is the step weight,i=1,2,…,Tnum.his the moving direction, andg=1,2,…,h.

Except for the direction wolf, the movement steps and update methods of other wolf sports is shown in formula (5)[9].

(5)

Where,i=1,2,…,N-Tnum-1.dkis the distance between a non-directional wolf and the head wolf, and the value ranges ofdkisdk∈(0,Dk).

(6)

Whereωis the distance weight, which is also an important basis for classification between different datasets.

Based on the updated position data, calculate the fitness of all wolves in the pack. If the fitness is greater than the head wolf, the head wolf data is updated, otherwise the head wolf remains unchanged. The location of the head wolf is the destination, and the prey storage location.

When the wolves arrive at their destination, follow the command of the leader, and carry out siege. The calculation method of movement step and position update is shown in formula (7) [10].

(7)

Wherez=1,2,…,N-1,λis a random number, and the value range isλ∈[-1,1].

Calculate the fitness of other wolves during the siege. If it is larger than the head wolf, update the head wolf data, otherwise the head wolf remains unchanged. Finally, according to the fitness ranking, remove the small fitness wolf and update the wolf group. According to the data of the head wolf, if its fitness reaches the accuracy of the LVQ neural network’s gearbox fault classification or the maximum number of iterations, the algorithm stops.

2.2 LVQ neural network gearbox fault diagnosis model based on wolf pack algorithm

The process of optimizing the head wolf position obtained by wolf pack optimization is actually the process of solving the LVQ neural network weight and threshold optimal solution. With the optimal solution of weights and thresholds, the gearbox fault diagnosis model of LVQ neural network can be determined. During the wolf pack optimization algorithm, the position of the entire wolf pack needs to be continuously updated. And according to the fitness comparison, timely update the position of the head wolf. The parameter adjustment method of this neural network model is highly efficient, and each iteration increases the fitness value.

The main process of LVQ neural network gearbox fault diagnosis using wolf pack optimization is shown Fig.1.

Fig.1 Flow chart of LVQ neural network gearbox fault diagnosis optimized by wolves

3 Example simulation

In order to verify the performance of the wolf pack optimized LVQ neural network for gearbox fault diagnosis, an example simulation was performed. The gearbox failure data of a machinery company for 5 years is selected as the simulation object. According to the year, it is set as data set 1, data set 2, data set 3, data set 4 and data set 5, respectively. The LVQ neural network algorithm optimized by the wolf pack was used to classify the faults of the rolling bearing of the gearbox, and the performance of the wolf pack optimized was simulated.

3.1 Gearbox bearing fault simulation

First, according to the operation of the gearbox, the characteristics and evaluation indicators of the three common faults of the gearbox are extracted [11-12], as shown in Table 1.

Table 1 Main characteristics and evaluation indexes

Among them,xiis the signal point collected in the time domain of the gearbox operation,i=1,2,…,N,N=1 024. Select data training samples according to the indicators in Table 1. The sample indicator isX=(f1,f2,f3,f4,p4). Then perform LVQ neural network training. The number of output neurons is 4, and the values of the output neurons and the corresponding gearbox failure conditions are shown in Table 2.

After several calculations, the model is used to simulate the operation data of the gearbox. Some results are shown in Table 3.

Table 2 Operation of gearbox

Table 3 Simulation results of LVQ neural network optimized by wolves

It can be seen from Table 3 that according to the actually obtained nerve playing two outputs, compared with the standard output, the fault is completely identified, and the recognition effect is better in most cases. But at the 6th time, the output of the neural network is (0.077 1, 0.532 9, 0.667 2, 0.127 9), and the standard output is (0, 0, 1, 0), and the recognition effect is poor. Because the output missing tooth failure rate reached 0.532 9, and the broken tooth failure reached 0.667 2. Although the final system judges the fault as a broken tooth fault, the recognition effect of the two faults is not ideal and needs to be further improved in subsequent studies.

3.2 Wolf pack optimization performance comparison

In order to analyze the influence of the introduction of the wolf pack optimization on the fault location of LVQ neural network gearboxes, 1,000 samples were taken from each of five data sets for LVQ neural network gearbox fault classification and wolf pack optimized LVQ neural network gearbox fault classification. According to the classification results, statistically correct the average value of the classification. The simulation results are shown in Fig.2 and Fig.3.

Fig.2 Average accuracy comparison results

Fig.3 Standard deviation comparison results

As can be seen from Fig.2 and Fig.3, compared with the LVQ neural network algorithm, the gearbox fault analysis of the LVQ neural network optimized by Wolf Pack has higher accuracy and better stability. Especially for data set 5, the average accuracy and standard deviation are 99.07% and 0.31%, respectively, and the performance of fault classification is the best in all data sets.

3.3 Accuracy of fault identification with different sample sizes

In order to further verify the fault analysis performance of the Wolf Pack optimized LVQ neural network, the number of training samples and test samples were changed, and the accuracy of fault classification was calculated. The simulation results are shown in Table 4.Table 1 Comparison of output results of different algorithms.

It can be seen from Table 4 that when the number of samples is changed, the change of the fault recognition accuracy rate is small, and all remain above 86%, indicating that the gearbox fault classification stability of the LVQ neural network optimized by the Wolf Pack is high.

Table 4 Fault identification accuracy of different sample sizes

4 Conclusion

In this paper, the wolf pack optimization LVQ neural network is used to complete the gearbox failure analysis. The experimental results show that the proposed method has the characteristics of high accuracy and strong stability. However, optimizing the weight and threshold of the LVQ neural network through the wolf pack will increase the computing time. Therefore, follow-up research needs to be further optimized in terms of algorithm efficiency to improve the adaptability of the algorithm to gearbox failure analysis. The specific operation process should reasonably set the size of the neural network, and by fine-tuning the main parameters of the wolf pack optimization algorithm, a better gearbox fault classification result can be obtained.