A recognition method of plunger wear degree of plunger pump using probability neural network

2.1. Sensitivity analysis algorithm

In order to analyze the sensitivity of the characteristic parameters to the fault, we introduce the concept of sensitivity. Sensitivity is the degree of difference between the analyzed parameters and the reference parameters. The sensitivity is calculated as follows:

where $u$ is sensitivity, $X_i$ means the parameters to be analyzed, $X$ represents baseline parameters.

The greater the sensitivity value $u$, the higher the sensitivity. That is to say, the greater the degree of difference in the parameter to be analyzed relative to the reference parameter. The greater the degree of difference in the parameter to be analyzed relative to the reference parameter, the more the fault information is reflected. The purpose of sensitivity analysis is to find out the characteristic parameters with high sensitivity to fault, and use it for fault diagnosis to improve the accuracy of the diagnosis.

2.2. Probabilistic neural network algorithm

Probabilistic neural network (PNN) is a kind of the feedforward networks, which was proposed by Specht D. F. in the 1990s, it used the Parzen window function to calculate the conditional probability density function of the sample to be identified, and then through Bayes classification criteria to complete the classification and identification of the model. Its topology is simple, and its algorithm design is easy, now it has been widely used in pattern recognition, pattern classification and data mining and so on [8].

The network spatial structure of PNN is respectively input layer, pattern layer, summation layer and output layer. Its network topology is shown in Fig. 1.

Fig. 1Probabilistic neural network structure

1) The input layer. The main task of this layer is to accept the input sample data, and then transfer it to the model layer for processing:

where $XI$ is the input vector of the input layer, $YI$ is the output vector. The number of nerve cells which is equal to the dimension of the feature vector of samples.

2) The pattern layer. The task of the pattern layer is to match the passing samples with the non-linear mapping of each pattern category:

The input and output relationships determined by the $j$th neurons of the pattern layer are defined as follows:

where $d$ is the dimension of the input sample; $\sigma$ is the smoothing factor; $i=$1, 2,…, $M$, $j=$1, 2,.., $Gi$; $M$ is the total number of training samples; $G_i$ is the $i$th class of training samples; $X{P}_{ij}$ is the $j$th class of the data of the $i$th class of training sample; $XP$ is the input of the model layer; $Y{P}_{ij}\left(XP\right)$ is the $j$th neuron output of the $i$th class of the pattern layer.

3) The summation layer:

where $X{T}_{ij}$ and $Y{T}_i$ represent the input and output of the $i$th neurons of the summation layer respectively.

4) The output layer.

Based on the Bayes decision rules for minimum misclassification, we can know that:

where $X{E}_i$ is the input of output layer, output $C$ is the category number of the sample.

3.1. Experimental design

In order to study the fault performance and signal characteristics of different plunger wear, we specially designed a set of hydraulic failure simulation experiments.

The experiment used the swash plate type axial plunger pump, the plunger pump have 7 plunger, model 25YCY14-1B, nominal displacement 25 ml/rev, rated speed 1500 r/min. Drive motor type: YE3-132M-4, Rated speed 1500 r/min. Selecting BW14100 vibration acceleration sensor with rigid connection with the pump housing. As shown in Fig. 2.

During the experiment, the main relief valve pressure is set to 8MPa, the vibration signal sampling frequency is 20 KHz. First, collect the normal state of the plunger pump acceleration signal. Then replace the normal parts with faulty parts, and collect the plunger pump acceleration signal of the fault condition. Set the fault: plunger wear 0.2 mm, plunger wear 0.3 mm, plunger wear 0.5 mm. The plunger used is shown in Fig. 3.

Fig. 2Sensor layout

Fig. 3Failure plunger: 1) plunger wear 0.2 mm 2) plunger wear 0.3 mm, 3 plunger wear 0.5 mm

3.2. Spectrum analysis

In the plunger pump failure simulation experiment, we set up a total of eight sensors for data acquisition. In this paper, we used the data of 3# sensor for analysis, Fourier transformed with the collected data, analyzed the spectrum of its low frequency band, found the location of the characteristic frequency, and observed the amplitude at the characteristic frequency. As the actual speed of the plunger pump is 1480 r/min. 1480/60 = 24.67 Hz, we can know the characteristic frequency of plunger wear is 1480/60 = 24.67 Hz through the calculation and analysis. After finding it, we compared all spectrum diagrams, and found that at the characteristic frequency of 24.67 Hz, with the increase of the plunger wear degree, the amplitude of the spectrum increases, as shown as Fig. 4.

Fig. 4The spectrum of plunger wears a different degree

3.3. Characteristic parameter extraction

In order to extract fault information more comprehensive, we extracted 17 time domain characteristic parameters. The 17 characteristic parameters were: Maximum, minimum, peak, peak to-peak, mean, root mean square RMS, standard deviation, energy, skewness, kurtosis, square root amplitude, average amplitude, waveform index, peak index, pulse index, margin index, clearance factor.

3.4. Sensitivity analysis

Each characteristic parameter can reflect a certain fault information. If we are going to analyze the 17 characteristic parameters, it will undoubtedly increase the difficulty of calculation. So, it is wise to choose a part of the characteristic parameters which are the best to reflect the fault information for analysis.

Using the 17 characteristic parameters for sensitivity analysis, the results were shown in Fig. 5.

Fig. 5The feature parameters sensitivity analysis

The above figure shows the sensitivity analysis of the characteristic parameters for each fault. The red curve represents the sensitivity of the plunger wear 0.2 mm fault condition characteristic parameter, the blue curve represents the sensitivity of the plunger wear 0.3 mm fault condition characteristic parameter, the green curve represents the sensitivity of the plunger wear 0.5 mm fault condition characteristic parameter. The black curve represents the mean of the sensitivity of each characteristic parameter of the three states. The cyan dashed line represents the discriminant baseline obtained by calculating the mean of all the characteristic parameters. The mean of the sensitivity of each characteristic parameter (the black curve) exceeds the baseline is considered to be highly sensitive, which will be selected as the characteristic parameter for fault diagnosis. After analysis, there are nine characteristic parameters whose average sensitivity are higher than the baseline. As shown in the Table 2.

After the analysis of the skewness, we discover the skewness is very unstable, and it fluctuates too much. It is not suitable to apply it to PNN for fault diagnosis, so we remove the skewness. Since the physical meanings of the maximum and the minimum are basically the same, we remove the minimum only to keep the maximum. As the pulse index sensitivity is relatively low, we discard the pulse index. At last, we select six feature parameters, such as maximum, peak, peak-to-peak, energy, kurtosis and margin index, as input vectors for fault diagnosis.

3.5. Fault diagnosis

Input the six characteristic parameters selected from the four states into the constructed probabilistic neural network in vector form. Using three sets of data for training, and selecting 60 sets of data for testing. The test results are shown in the Table 3.

While not through the sensitivity analysis only by feeling, we selected six characteristic parameters for fault diagnosis, which can also diagnose the fault. The selected characteristic parameters are: Peak-peak, mean, root mean square RMS, energy, kurtosis, clearance factor. However, compared with characteristic parameters through sensitivity analysis to diagnose fault, the correct rate is lower. The diagnostic results obtained without the sensitivity analysis as shown in Table 4.

As can be seen from the above analysis, it is indeed feasible and effective to identify the degree of plunger wear with PNN. After using the sensitivity analysis of the characteristic parameters, extracting the high sensitivity of the characteristic parameters for state recognition, can better improve the correct rate of recognition.