Research on rolling bearing fault feature extraction based on entropy feature

In various fi elds of large or small machinery, rolling bearing in which the status is indispensable, can be said to play an important role in production and life. For such an important rolling bearing, its fault diagnosis must be paid attention to. Need to be specifi c to the rolling element fault, inner ring fault or outer ring fault, so that we can carry out subsequent improvement [1]. If only one standard is used for inspection and maintenance, it will not only have low accuracy, but also consume manpower and material resources. If accurate fault diagnosis can be carried out, prevention fi rst and moderate maintenance can be carried out at the same time to avoid bad effects. It is boundto play a very importantrole in promoting economic and social development.


Introduction
In various fi elds of large or small machinery, rolling bearing in which the status is indispensable, can be said to play an important role in production and life. For such an important rolling bearing, its fault diagnosis must be paid attention to. Need to be specifi c to the rolling element fault, inner ring fault or outer ring fault, so that we can carry out subsequent improvement [1]. If only one standard is used for inspection and maintenance, it will not only have low accuracy, but also consume manpower and material resources. If accurate fault diagnosis can be carried out, prevention fi rst and moderate maintenance can be carried out at the same time to avoid bad effects. It is boundto play a very importantrole in promoting economic and social development.
operation is related to the operation of the whole equipment, so the accurate diagnosis of bearing fault becomes extremely important.
The research of rolling bearing fault diagnosis began around 1960. On the whole, it can be divided into fi ve stages.
The fi rst stage is spectrum analysis in 1950s. The method of spectrum analysis has attracted much attention. However, due to the immature technology at that time, spectrum analysis has not been widely used in the fi eld of bearing fault diagnosis technology because of the disadvantages of interference noise, high price and complex operation.
In the second stage, in the sixties of the 20 th century, the impact pulse meter detection method appeared, which is obviously better than the spectrum analysis, and can directly save the complicated steps. It is still widely used in the fault diagnosis of rolling bearing. In the third stage, in the 1960s1980s, the computer and signal have made great progress under the promotion of the trend of the times, and the more prominent one is the resonance demodulation technology, because the advent of this technologymakes the rolling bearing fault diagnosis technology to a higher level, from birth to maturity step by step [3]. The fourth stage is after the 1980s, the emergence of artifi cial intelligence provides new soil for rolling bearing fault diagnosis, and the emergence of intelligent diagnosis system greatly improves the accuracy of fault diagnosis. Due to the intelligence, the infl uence of human factors is greatly reduced, which has been applied in engineering practice.In order to enable nonsignal analysis specialists to monitor the running state and reduce the engineering cost as much as possible, Janssens proposed a learning model based on convolutional neural network, which learned the function of detecting bearing faults from the vibration signal itself. In view of the nonlinearity and non-stability of the vibration signal of rolling bearing, Ben proposed the mathematical analysis of selecting the most importantintrinsic mode functionby combining the method of extracting energy entropy by empirical mode decomposition. The fi fth stage is after the 21 st century, that is, we now, rolling bearing fault diagnosis technology has taken an epoch-making step, more and more high-tech development, through the virtual instrument fault diagnosis, has become a new beacon, has important practical value [4]. At present, rolling bearing fault diagnosis has been studied all over the world, combining a large number of different research fi elds.
According to the most popular classifi cation method, it can be divided into three kinds, which are modelbased fault diagnosis technology, knowledge-based fault diagnosis technology and data-based fault diagnosis technology.
Because of the national conditions, our country started to study the fault diagnosis much later than other countries. It was not until the late 1970s and the early 1980s that I fi rst came into contact with this fi eld and started formal research. But it is gratifying that with the hard work of Chinese researchers, in the 1990s, the fi eld of fault research has been on the right track, both in theory and practice have made great breakthroughs, and can be applied in production and life. But compared with other countries, China still has a long way to go.

Approximate entropy
Approximate Entropy (ApEn) is a nonlinear dynamic parameter proposed by Pincus in 1991 to measure the complexity and statistical quantifi cation of a sequence. ApEn refl ects the degree of self similarity of sequence in pattern.
The higher the ApEn value is, the lower the possibility that the system can predict it. It gives the situation that the incidence of new pattern increases or decreases with the dimension, so as to refl ect the complexity of data structure. Through the previous, we can know that rolling bearing will produce vibration, and in different failure modes, the vibration signal is also different.
According to the physical meaning of ApEn, different signals mean different complexity, which can be used as features for rolling bearing fault diagnosis [5].
In the normal calculation of approximate entropy, there are too many redundant calculations, which is a waste of time. A fast algorithm of approximate entropy is given in the literature.
Let the original sequencebe u(i),i=0,1,,N,r=0.10.25SD(u) (SD is the standard deviation of sequence u(i)), then the calculation of approximate entropy is more reasonable. If m = 2, then N = 5001000.3.
Calculate the distance matrix d of N×N, and the elements in row I and column j of d are written as d ij Use that elements in d, calculate Take out the fi rst 6000 data and calculate the approximate entropy in a group of 600, as shown in Figure 1.
It is not diffi cult to see that when the rolling bearing is normal, the value of approximate entropy is not large, because under normal conditions, the signal generated is relatively single. When the rolling bearing fails, it will produce a lot of complex information, which will increase the approximate entropy. However, the approximate entropy values of rolling element fault and normal working conditions are very similar, so it is not easy to distinguish them.

Sample entropy
In Count the number of d ij less than the similarity tolerance r and the ratio of the number to the total number of d ij N-m-1, and record it as Take the fi rst 6000 data, take 600 as a group, and calculate the sample entropy, as shown in Figure 2.
It is not diffi cult to see that the inner ring fault, rolling element fault and normal working conditions are very diffi cult to distinguish, but the outer ring fault can be distinguished.

Information entropy
Claude E. Shannon, one of the originators of information theory, defi ned information (entropy) as the probability of occurrence of discrete random events.
X represents a random variable, the value of which is Generally speaking, when a kind of information has a higher probability of occurrence, it means that it has been spread more widely, or that it has been cited to a higher degree. We can think that from the perspective of information dissemination, information entropy can express the value of information. In this way, we have a standard to measure the value of information, and we can make more inferences about knowledge fl ow.
Take the fi rst 6000 data and calculate the information entropy in a group of 600, as shown in Figure 3.  • The approximate entropy, sample entropy and information entropy of ten groups of data are calculated.
• Compared with the extracted entropy feature.
• According to the absolute value of the difference with the entropy characteristic scale, which bearing working state is closest to the test data can be judged. Three kinds of entropy in the case of independent judgment have no small disadvantages, it is easy to misjudge the situation, need to be further processed. So I started to study the extraction of rolling bearing fault features through the joint analysis of approximate entropy, sample entropy and information entropy. The data is taken from the Western Reserve University. Under the working condition of 2 HP load, 0.1778 mm fault diameter and 1750 R / min rotating speed, the vibration acceleration signals under four different modes are obtained. There are four groups corresponding to different modes, with 60000 data in each group. Each group is divided into 10 sections, with 6000 data in each section. Each section is divided into 10 sections, with 600 data in each section Each section calculates an approximate entropy, sample entropy and information entropy, and each group has ten entropy values to do mean processing, which can get ten approximate entropy mean values, sample entropy mean values, and information entropy mean values of each section. shown in Figures 8-10.

Simulation experiment
As can be seen from Fig, for each Table 1, each column corresponds to the entropy feature vector under the working condition.
Then, the same entropy characteristic column vectors obtained from the same four test data are used to form the test data entropy characteristic matrix.
Taking the average entropy feature vector as the benchmark, we compareit with the test data entropyfeature vector, that is, take the absolute value after the difference, and get four new vectors. The four new vectors are combined into an entropy characteristic matrix, and the minimum value of each row in the matrix is taken out. The maximum number of columns corresponding to the minimum value is the closest test data to the fault mode. However, in rare cases, three kinds of entropy features will judge three kinds of fault modes. At this time, the fault mode corresponding to the maximum discrimination approximate entropy mean value will be taken as the fi nal fault mode of test data.
After the early stage of rolling bearing fault feature extraction, we have extracted the approximate entropy mean value, sample entropy mean value and information entropy mean value of four rolling bearing fault modes. By comparing the feature vectors, we can effectively distinguish the four fault modes. A 6000 data matrix is randomly generated by using the data, and the fault feature of the matrix is extracted, and the fault condition is determined. Then the results are compared with the previously established standard, and each group is tested 500 times, at least 10 groups are done to test its accuracy. Based on the above description, the simulation experiment is started. It is also taken from the Western      Figure 11.
If the difference between the mean approximate entropy and the mean information entropy of the inner ring fault is the smallest, it is judged that the test data is the inner ring fault mode. The same is true for other failure modes. The test vector in the test data is extracted, which is different from the entropyeigenvector,and the minorityis subordinate to the majority. This paper focuses on the special case. The difference between the feature vector and the test vector is selected in the case of rolling element failure in Figure 12, Table 2.
It can be seen that the approximate entropy feature gets the minimum value in rolling element fault, the sample entropy feature gets the minimum value in inner ring fault, and the information entropy feature gets the minimum value in normal condition. At this time, we select the condition corresponding to the approximate entropy feature as the fi nal result.

Conclusion
Based on approximate entropy, sample entropy and information entropy, a joint diagnosis method for rolling bearing fault is proposed.
According to the characteristics of entropy signal, fault diagnosis is carried out. The experimental results show that the accuracy of the three entropy joint fault diagnosis methods is more than ninety-seven percent. And it can correctly identify each bearing state, which verifi es the effectiveness of the fault diagnosis method 2.