Cavitation fault diagnosis of centrifugal pump based on RIME-SDAE

2.1. Data collection

According to the requirements of the standard “GB3216-2016 rotary power pump hydraulic performance acceptance test”, the test bench is built and IS-65-50-160 single-stage centrifugal pump is selected for the test. Some of the design parameters of the pump include: rated flow rate of $Q_d=$50m³/h, rotational speed of $n=$2930 r/min, design head $H=$38m, and the number of vanes $Z=$6. Other equipment on the test stand includes electric motors, torque meters, and data acquisition equipment. The schematic diagram of the test system loop is shown in Fig. 1, and the data acquisition equipment is shown in Fig. 2.

Fig. 1Test system loop

Fig. 2Data acquisition equipment

After the test pump is started and operated normally, the tank is evacuated and cavitated by gradually reducing the pump inlet pressure. Record the relationship between the effective cavitation margin (NPSHa) and the head drop during the pumping process, and collect the vibration signals from the measurement points of the pump body when the centrifugal pump operates under different NPSHa. The position of the vibration sensor and the cavitation characteristic curve of the centrifugal pump are shown in Fig. 3 and Fig. 4.

Fig. 3Position of the vibration sensor

Fig. 4Cavitation characteristic curve of pump

As shown in Fig. 4, with the decrease of NPSHa, the pump head firstly decreases slowly, and after an inflection point, the head decreases sharply, which can be regarded as the cavitation incipient point, corresponding to a 1.5 % decrease in head [8]. At the same time, the engineering generally will be declined by 3 % of the point of head as the point of cavitation occurs. Therefore, the collection of head down 0 %, 1.5 % and 3 % of the point of the vibration signal, used to represent the centrifugal pump is not cavitation, cavitation incipient and severe cavitation state.

Taking the vibration signal in the Z-direction of the sensor as an example, some of its time-domain and frequency-domain plots under different cavitation states are shown in Figs. 5 and 6.

Fig. 5Time domain graph

Fig. 6Frequency domain graph

2.2. Construction of feature vectors

In order to reveal the fault information contained in vibration signals more accurately and comprehensively, multiple data indicators should be extracted from the multi-domain perspective to represent the fault information [9]. It is worth mentioning that energy value and sample entropy are the characteristics of the first eight IMF components obtained by Ensemble Empirical Mode Decomposition, which represent the energy distribution and time complexity of IMF components. Let the signal be $x\left(n\right)$, $n=$ 1,2, …$N$, $N$ is the number of data points of the signal. Table 1 lists 14 commonly used signaling indicators. As shown in Table 1.

Table 1 shows the commonly used signal characteristic indicators, but not all of these signal indicators are related to the centrifugal pump cavitation fault, in order to eliminate redundant indicators, analyze the changes of each indicator in different cavitation states, and find out the indicators that best reflect the changes in the cavitation state of the centrifugal pump for subsequent machine learning identification and classification. Taking the sensor $Z$-direction vibration signal as an example, the changes of its time domain, frequency domain and time frequency indicators with the development of cavitation are shown in Fig. 7, Fig. 8, Fig. 8 and Fig. 10.

Combined with Figs. 5-10, it can be seen that the centrifugal pump cavitation development process, the time domain and frequency domain signal amplitude are increasing, in which the frequency of the frequency domain signal is mainly distributed in the shaft frequency and lobe frequency, with the deepening of the degree of cavitation, the frequency distribution is becoming more and more centralized and more amplitude increase at high frequency, showing the increase in vibration energy. Therefore, the time-domain indicators T2, T3, T4 and T8 reflecting the change of vibration amplitude gradually increase with the development of cavitation, while the time-domain indicators T1, T5, T6 and T7 reflecting the shape of the signal have no significant change; the frequency-domain features F1, F2, F3 and F4 reflecting the spectral distribution gradually increase with the development of cavitation, reflecting the high-frequency component brought by cavitation; the energy value of the IMF component reflecting the vibration energy and complexity is similar to that of the sample entropy feature in the first 2 years. Sample entropy features gradually increase with cavitation development in the first 2-order components, but the difference is not significant in the last 3-order components, indicating that the higher-order components after EEMD decomposition can no longer reflect the characteristics of the original signal. Therefore, the time-domain indicators T2, T3, T4, T8, the frequency-domain indicators F1, F2, F3, F4, and the time-frequency indicators TF11, TF12, TF21, TF22 are selected for the subsequent identification of the cavitation state.

Fig. 7Time domain index

Fig. 8Frequency domain index

Fig. 9Energy value

Fig. 10Sample entropy

3.1. Stacked denoising autoencoder

Self-encoder (AE) is a typical deep learning network including input layer ($x$), hidden layer ($h$) and output layer ($y$), which realizes the reconstruction of the input signal by encoding and decoding, and realizes the feature extraction of the signal by minimizing the reconstruction error, and its structure is shown in Fig. 11. Noise-reducing auto-encoder (DAE) is an improved form of AE, which randomly sets the input layer $x$ to zero according to a certain ratio p through a certain random distribution to obtain a noise-containing data, and then reconstructs the noise-containing data and adjusts the model parameters through AE. By stacking several DAEs, the SDAE can be obtained, and its structure is shown in Fig. 12.

Fig. 11Auto-Encoder network structure

Fig. 12Training of SDAE

3.2. Rime optimization algorithm

The rime optimization algorithm is the latest meta-heuristic algorithm based on natural phenomena, inspired by the growth behavior of rime in nature [10]. The process of RIME is as follows:

1. Soft-rime search strategy, which simulates the movement of soft-rime particles in gray ice and puts forward a soft-rime search strategy.

2. Hard-rime puncture mechanism, which is inspired by the piercing phenomenon during the growth of rime strong wind.

3. Positive greedy selection mechanism, this way of working can effectively filter out the bad solutions in the population, while introducing suboptimal solutions by changing the choice of optimal solutions.