Research on neural network method for fault diagnosis of hydraulic pump bearings

Abstract: This paper studies the fault diagnosis method of hydraulic pump bearings based on integrated BP network. The frequency domain and inverse frequency domain are used for feature extraction, and the integrated BP network is used for fault diagnosis and identification, which solves the problem of difficulty in proposing fault characteristics of hydraulic pump bearings and difficulty in identifying multiple faults. The test results show that the integrated BP network can effectively diagnose and identify multiple fault modes of hydraulic pump bearings and has strong robustness.
Keywords: hydraulic pump; bearing failure; fault diagnosis; integrated BP network
In the aviation industry, the working performance of the hydraulic system directly affects the safety of the aircraft and the lives of passengers, and the hydraulic pump is the power source of the hydraulic system, so the status monitoring and fault diagnosis of the hydraulic pump are particularly important. Bearing failure is one of the common failure modes of hydraulic pumps. Since the additional vibration caused by bearing failure is weaker than the inherent vibration of the hydraulic pump, it is difficult to separate the fault information from the signal. So far, there is still a lack of very effective methods for fault diagnosis of hydraulic pump bearing failures. This paper proposes feature extraction in the frequency domain and cepstrum domain, aiming to solve the problem of difficult bearing feature extraction and use an integrated BP network to solve multi-fault diagnosis and identification and robustness issues.
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1. Feature extraction of hydraulic pump bearing faults
For mechanical systems, if there is a fault, it will definitely cause additional vibration of the system. Vibration signals are dynamic signals that contain rich information and are very suitable for fault diagnosis. However, if the additional vibration signal is submerged due to the great interference of the inherent signal or external interference to the fault signal, then how to extract useful signals from the vibration signal becomes very critical.
According to the theory of tribology, when a damage occurs on the inner ring, outer ring raceway and roller of the bearing flow surface, the smooth surface of the raceway is destroyed, and every time the roller rolls over the damaged point, a vibration will occur. Assuming that the ceramic bearings are rigid bodies, without considering the influence of contact deformation, and the rollers are pure rollers along the raceway, the damage vibration frequency will be as follows:

When there is damage to the inner raceway, its vibration pulse characteristic frequency is:
fI=frZ(1+dcosα/D)/2
When the outer raceway is damaged, its vibration pulse frequency is:
fo=frZ(1-dcosα/D)/2
When there is a damage on the roller, its vibration pulse characteristic frequency is:
fR=frD(1-d2cosα/D2)/d
Among them: fr – inner ring speed frequency; D – pitch diameter of the bearing; d – diameter of the roller; α – contact angle; Z – number of rollers. ​

In order to overcome the difficulty that the bearing fault signal is weak and easily overwhelmed by the inherent vibration of the hydraulic pump, the following features with strong anti-interference ability are selected as fault diagnosis characteristic parameters. ​

(1) Average energy characteristics of vibration Suppose the vibration acceleration signal measured on the hydraulic pump body is: a(t)={a1(t), a2(t),…, an(t)}

It is the signal after the fault signal is transmitted through the pump body. According to statistical theory, the root mean square of vibration reflects the time domain information of vibration:
The characteristic parameter has the effective value which represents the vibration signal and reflects the average energy of the vibration. ​

(2) Peak characteristics of vibration signals
Pp=max{a(t)}
It is a characteristic quantity that reflects the periodic pulsation in the vibration signal. ​

(3) Cepstrum envelope characteristics Let f(t) be the fault excitation signal, and h(t) be the impulse response of the transmission channel. Their corresponding Fourier transformations have the following relationship:
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In the formula, τ is called the cepstrum frequency; (τ) is the cepstrum spectrum. It can be seen from the above formula that the characteristics of the fault excitation signal and the characteristics of the transmission channel are separated. In general, the fault excitation signal and the transmission channel signal occupy different inversion frequency sections, which can highlight the characteristics of the fault vibration signal. ​

Hilbert transform is used in signal analysis to find the envelope of time domain signals to smooth the power spectrum and highlight fault information. Define signal: for optimal envelope. The essence of the cepstrum envelope model is to perform cepstrum analysis on the signal obtained from the sensor, and then perform envelope extraction on the cepstrum signal, thereby dually highlighting the fault information and providing a basis for extracting fault features with a small signal-to-noise ratio. in accordance with.

2. Principle of integrating BP network for fault diagnosis

The organizational structure of the neural network is determined by the domain characteristics of the problem solved. Due to the complexity of fault diagnosis systems, applying neural networks to the design of fault diagnosis systems will be a problem of organizing and learning large-scale neural networks. In order to reduce the complexity of the work and the learning time of the network, this article decomposes the fault diagnosis knowledge set into several logically independent sub-sets, and each sub-set is further decomposed into several rule subsets, and then the network is organized according to the rule subsets. Each rule subset is a mapping of a logically independent subnetwork, and the connection between the rule subsets is represented by the weight matrix of the subnetwork. Each sub-network independently uses the BP learning algorithm for learning and training. Since the decomposed sub-network is much smaller than the original network and the problem is localized, the training time is greatly reduced. The information processing capability of using integrated BP network for hydraulic pump bearing fault diagnosis originates from the nonlinear mechanism characteristics of neurons and BP algorithm, as shown in Figure 1.
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Each sub-network in is a BP network, each sub-network is learned separately by the BP algorithm, and the learning results are integrated by the control network. The learning algorithm of BP network is as follows:
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Map the value of each selected feature parameter (including energy feature, amplitude feature and cepstral envelope feature) x to a single node of the input and output layer of the neural network, and perform regularization processing on it:
xi=0.8(x-xmin)/(xmax-xmin)+0.1　　（8）

The purpose of formula (8) to regularize the characteristic parameters to between (0.1, 0.9) is to avoid the problem of inability to converge in learning caused by the extreme output value of the Sigmoid function. ​

Complete the following operations on the regular value obtained from equation (8) to obtain the weighted value and threshold of each neuron:
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In the formula, j represents the current layer, i represents the previous layer, wij represents the connection weight; cj represents the threshold of the current node; fj represents the output.

3. Research on the robustness of neural networks

The robustness of neural networks refers to the fault tolerance of neural networks to faults. As we all know, the human brain is fault-tolerant. Damage to individual neurons in the brain will not severely degrade its overall performance. This is because each concept in the brain is not stored in just one neuron, but is spread across many neurons. elements and their connections. The brain can learn again so that the knowledge that has been forgotten due to damage to some neurons can be re-expressed in the remaining neurons. Since the neural network is a simulation of the biological neuron network, the biggest feature of the neural network is its “associative memory” function, that is, the neural network can be combined from past knowledge and use it under conditions where part of the information is lost or part of the information is uncertain. The remaining characteristic information makes a correct diagnosis. Table 2 shows the success rate of correct diagnosis and identification when some input features among the six characteristic information of the bearing are incorrect or uncertain.

Neural network robustness statistics table
The diagnosis success rate of input feature uncertain elements is 100% uncertain for one feature parameter, 94% uncertain for two feature parameters, 76% uncertain for three feature parameters, 70% uncertainty for four feature parameters, 20% uncertainty for five feature parameters, and six features. Parameter uncertainty 8%
As can be seen from Table 2, fault diagnosis using integrated neural networks can still make correct judgments even when a large amount of information is lost (nearly half of the characteristic parameters are uncertain), and the success rate is quite high (76% to 100%). Therefore, integrated neural networks can still make correct judgments. Neural networks have strong capabilities5

in conclusion
Because neural networks have various functions such as self-learning, self-organization, and associative memory, the neural network method is very suitable for fault diagnosis research. This paper uses vibration signals in the frequency domain and inverse frequency domain as characteristic parameters, and uses an integrated BP network to realize multi-fault diagnosis and identification of hydraulic pump bearings. Experimental results show that this method has a high success rate and robustness