# Research on Fault Detection and Automatic Diagnosis Technology of Water Hammer in Centrifugal Pump
## 3 Monitoring Method of Water Hammer Failure  
The traditional state monitoring method of centrifugal pumps collects the vibration signal of a centrifugal pump through a sensor, and after filtering, amplifying and A/D conversion by the sensor, the transceiver transmits the data to the server for fault analysis and diagnosis [18,19]. The water hammer signal is a shock signal, so it has transient and occasional characteristics. When the traditional vibration monitoring system works, a set of dynamic waveform data is often collected and uploaded to the server for analysis and processing, and after the results are displayed, the next set of data collection and analysis is carried out. There is a collection interval between two data collections due to data transmission, storage, network delay and other reasons. The interval between the two sets of data is often too large, even longer than the duration of the water hammer time, and it is prone to the phenomenon of missing judgment because the water hammer signal cannot be collected. On the other hand, although the occurrence of water hammer failure is occasional, it is more destructive to the centrifugal pump [20]. Effectively recording the water hammer time is important for improving the design of pipelines and centrifugal pumps, but so far, there is no effective method for the real-time digital monitoring of water hammer failures in centrifugal pumps.  
In response to the needs of monitoring and diagnosing water hammer faults in centrifugal pumps, this paper designs a new type of digital acquisition and analysis module for centrifugal pumps in order to timely judge the working status of centrifugal pumps. The monitoring and diagnosis process of centrifugal pump water hammer is shown in Figure 3, which is divided into four steps. The specific process is as follows:  
Step 1: The sensor collects the vibration signal of the centrifugal pump. High-pass filtering is performed on the collected raw signal to eliminate interference other than the high-frequency fault frequency of water hammer.  
Step 2: The kurtosis index, pulse index, and margin index of the high-pass filtered data are calculated.  
Step 3: The relevant indices obtained in Step 2 are compared with the normal range to determine if there is a suspected water hammer fault being sent. If there is a suspected occurrence of water hammer failure, vibration signals and fault characteristics are uploaded to the cloud server.  
Step 4: The cloud server receives data and performs further diagnosis.  
The feature extraction of the water hammer fault needs to first filter out the frequency components of the conventional fault in the signal and then restore the filtered signal to the time domain waveform. According to the filtered time domain signal, the kurtosis index \(x_{kur}\), pulse index C and margin index \(L\)[21], which are sensitive to the impact signal, are selected as the characteristic data of the time domain waveform after high-pass filtering to determine whether the centrifugal pump has a water hammer failure. Specifically,  
Figure 3: Flow chart of centrifugal pump water hammer failure monitoring and diagnosis.  
if the kurtosis index, pulse index and margin index simultaneously surpass twice their respective normal levels, it triggers an alarm, indicating that the centrifugal pump might be experiencing a water hammer failure.  
\[x_{kur}=\frac{1}{n}\sum_{t=1}^{n}\left(x(t)-\frac{1}{n}{\sum_{t=1}^{n}x(t)} \right)^{4} \tag{1}\]  
\[C=E_{max}|x(t)|/\frac{1}{n}{\sum_{t=1}^{n}x(t)} \tag{2}\]  
\[L=E_{max}|x(t)|/\left(\frac{1}{n}{\sum_{t=1}^{n}}{|x(t)|}^{1/2}\right)^{2} \tag{3}\]  
where \(x\) is the amplitude of the vibration signal, \(E_{max}\) is the value with the largest difference in vibration amplitude, \(n\) is the number of sampling points and \(t\) is a positive integer.