A pump cavitation state diagnosis method based on characteristic frequency and kurtosis

Abstract

A pump cavitation state diagnosis method based on characteristic frequency and kurtosis, based on a pump operation state monitoring system, obtains the vibration signal when the pump is running; uses a five-point cubic Savitzky-Golay filtering algorithm to perform noise reduction on the original vibration signal; uses short-time Fourier transform to obtain the frequency, amplitude and phase information of the signal, and clarifies the characteristic frequency distribution of cavitation; performs one-third octave analysis on the signal to obtain the law of change of energy in different frequency bands of the signal with the development of cavitation; calculates the kurtosis of the signal and the root mean square value RMS of each frequency band; uses the three parameters of flow state, kurtosis and RMS as input variables of a two-layer BPNN neural network to identify and classify the cavitation state of a centrifugal pump. The present invention can accurately identify and classify the cavitation state of the pump under various flow conditions, realize real-time monitoring of the cavitation state of the pump, improve equipment stability and reliability, and effectively reduce equipment costs and operating and maintenance costs.

Description

Technical Field

[0001] The present invention belongs to the field of pump cavitation state monitoring and diagnosis methods, and specifically relates to a pump cavitation state diagnosis method based on characteristic frequency and kurtosis, which is mainly used to quickly and accurately diagnose the cavitation state of the pump, realize real-time monitoring of the cavitation state of the pump, improve equipment stability and reliability, and effectively reduce equipment costs and its operation and maintenance costs. Background Art

[0002] Cavitation of centrifugal pumps can reduce the performance of the pump, generate vibration and noise, and affect the stable operation of the equipment. Rapid and accurate identification and real-time monitoring of the cavitation state of the centrifugal pump, as well as prevention and control of it, can ensure that the centrifugal pump always maintains the best working state and improve the life and safety of the centrifugal pump. There are several urgent problems to be solved for the identification of the cavitation state of the centrifugal pump: (1) The cavitation of the centrifugal pump is a phenomenon with complex, uncertain and coupled signals, and its manifestation varies depending on the equipment status and working environment. The traditional performance parameter method takes the point where the centrifugal pump head drops by 3% as the cavitation initiation point, which has obvious hysteresis, so a more sensitive characteristic value is needed. (2) Due to changes in the external environment, the data collected by the sensor is subject to unpredictable interference, and the mutation phenomenon of the original data is difficult to avoid. This requires a suitable data denoising method to denoise the signal collected by the sensor. (3) The current traditional identification methods have the disadvantages of low accuracy, slow identification speed, and high experience requirements. Therefore, it is necessary to find a more intelligent centrifugal pump cavitation identification method.

[0003] In response to the above problems, this patent invented a pump cavitation state diagnosis method based on characteristic frequency and kurtosis. This method uses a five-point cubic Savitzky-Golay filtering algorithm to reduce the noise of the original vibration signal, and performs a short-time Fourier transform on the noise-reduced vibration signal to clarify the cavitation characteristic frequency distribution; the signal is analyzed in one-third octave band and the signal kurtosis and the root mean square value of each frequency band are calculated; the flow state, kurtosis and RMS parameters are used as input variables of the double-layer BPNN neural network to identify and classify the centrifugal pump cavitation state, realize the identification and diagnosis of the centrifugal pump cavitation state, improve the reliability of the equipment, and reduce the operation and maintenance costs. Therefore, this method has important academic and engineering application value.

[0004] Existing pump cavitation diagnosis methods have the following disadvantages: 1) The signal is easily interfered with and cannot effectively identify the cavitation state; 2) Traditional identification methods have problems such as low accuracy and slow identification speed. Summary of the invention

[0005] In order to overcome the shortcomings of the existing technology, the present invention provides a pump cavitation state diagnosis method based on characteristic frequency and kurtosis. For the vibration data of the pump under the cavitation state, one-third octave band analysis, kurtosis and RMS calculation and a two-layer BPNN neural network are used to realize accurate identification and diagnosis of the cavitation state.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for diagnosing pump cavitation state based on characteristic frequency and kurtosis comprises the following steps;

[0008] Step 1: Based on the pump operation status monitoring system, a vibration signal of the pump during operation is obtained. The vibration data of the pump during operation is obtained by means of acceleration sensors arranged at different positions of the pump;

[0009] Step 2: Use the quintic cubic Savitzky-Golay filtering algorithm to perform noise reduction on the original vibration signal. The process is as follows:

[0010] SG filtering is a data smoothing method based on local polynomials. By setting a filtering window in the time domain and fitting it using the least squares method, it can effectively remove high-frequency noise while keeping the shape and width of the signal unchanged. Since the pump vibration signal collected by the vibration acceleration sensor is a non-stationary signal containing noise to varying degrees, the Savitzky-Golay convolution smoothing algorithm is used for noise reduction. Suppose a set of signals is x n , n=1,2,3......, one of the window data is x i , i = -m,...,0,...m, the window width is 2m+1, and a k-1 order polynomial is used to fit the data in the window, which is expressed as formula (1):

[0011] y=a 0 +a 1 x+…+a k-1 x k-1 (1)

[0012] In the formula, y is the fitting data, a 0 ~a k-1 The coefficients are obtained; the k-dimensional linear equation system consisting of 2m+1 equations is obtained, and its matrix form is:

[0013] Y (2m+1)×1 =X (2m+1)×k ·A k×1 +B (2m+1)×1 (2)

[0014] When 2m+1>k, the system of equations has a solution, where A=(XT·X) -1 ·X T·Y, therefore, the filtered value Y is:

[0015] Y=X·A=X·(X T ·X) -1 ·X T ·Y (3)

[0016] By moving the filter window from left to right, the smooth sequence of the entire signal after filtering is obtained. After SG filtering, the vibration signal retains its original shape while the pulse interference and noise with a small energy share are removed, and the signal-to-noise ratio is improved;

[0017] Step 3: Use short-time Fourier transform to obtain the frequency, amplitude and phase information of the signal and clarify the cavitation characteristic frequency distribution. The process is as follows:

[0018] Based on step 2, the signal is subjected to short-time Fourier transform; compared with Fourier transform, short-time Fourier transform can reflect the signal's time domain characteristics while reflecting the signal's frequency domain characteristics; short-time Fourier transform is defined as follows:

[0019]

[0020] x(m) is the input signal, ω(m) is the window function; short-time Fourier transform is to cut a signal into multiple segments, perform Fourier transform on each segment, and finally connect them in the time domain; each segment signal taken out is called a frame, and the length of a frame signal is usually 2 n ; To ensure the accuracy of the results, the signals of two adjacent frames must overlap, that is, HopSize, which is 25% to 75% of the frame length;

[0021] Step 4: Perform one-third octave analysis on the signal to obtain the law of change of energy in different frequency bands of the signal with the development of cavitation. The process is as follows:

[0022] Based on step 3, perform one-third octave analysis on the signal; one-third octave spectrum is a common method for testing and analyzing acoustics, human vibration and mechanical vibration; the octave spectrum consists of a series of center frequency points and the RMS value of the signal in the frequency band near the corresponding center frequency; the one-third octave center frequency is:

[0023] f c =1000×10 3n / 30 Hz(n=0,±1,±2,±3,…) (5)

[0024] The current standard stipulates that the center frequency in practical applications should be taken from its approximate value: 1Hz, 25Hz, 1.6Hz, 2Hz, 2.5Hz, 3.15Hz, 4Hz, 5Hz, 6.3Hz, 8Hz, 10Hz, ...; the upper limit frequency f of one-third octave band u, lower limit frequency f l Between the center frequency f c The relationship is:

[0025]

[0026] Perform one-third octave band analysis on the signal to obtain the cavitation noise distribution of the vibration signal and the change law of the energy of each frequency band of the signal with the development of cavitation;

[0027] Step 5, calculating the kurtosis of the signal and the root mean square value RMS of each frequency band: Based on step 4, calculating the kurtosis of the signal and the root mean square value RMS of each frequency band;

[0028] Step 6: Use the flow state, kurtosis and RMS parameters as input variables of the double-layer BPNN neural network to identify and classify the cavitation state of the centrifugal pump.

[0029] Furthermore, in step 2, it is specified that a five-point cubic Savitzky-Golay filtering algorithm is used to perform noise reduction processing on the original vibration signal, and the window size and the order of the fitting function in the algorithm are adjusted according to actual conditions; or a singular value decomposition (SVD) algorithm is used to perform noise reduction processing on the original vibration signal.

[0030] Furthermore, in step 3, it is specified that the filtered signal is analyzed by using short-time Fourier transform, and the frame length and HopSize of the signal are adjusted according to actual conditions to obtain the best effect.

[0031] Furthermore, in step 6, it is specified that a double-layer BPNN neural network is used to identify the cavitation state of the pump, or a support vector machine SVM is used to classify and identify the cavitation state.

[0032] The beneficial effects of the present invention are mainly manifested in: 1) the original vibration signal is denoised by a five-point cubic Savitzky-Golay filtering algorithm, thereby improving the signal-to-noise ratio of the vibration signal; 2) the signals of different cavitation states are analyzed by short-time Fourier transform to determine the distribution of cavitation characteristic frequencies; 3) the signal is subjected to one-third octave band analysis to clarify the cavitation harmonic distribution and its changing law with the development of cavitation; 4) the RMS of a part of the frequency band of the signal is selected instead of directly calculating the RMS of the signal, and the kurtosis is used as an input variable at the same time, thereby reducing the interference of irrelevant components in the signal and improving the accuracy of cavitation state identification; 4) the flow state is added to the input variable, so that cavitation diagnosis of multiple flow conditions can be realized, the efficiency of cavitation diagnosis is improved, and a guarantee is provided for the safe and stable operation of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1This is a flow chart of the pump cavitation status diagnosis method based on characteristic frequency and kurtosis.

[0034] Figure 2 It is a schematic diagram of vibration test of pump operation status, where B01 is the motor, B02 is the motor connection frame, B03 is the pump body, B04 is the flexible connector, B05 is the pipeline support frame, B06 is the vibration signal acquisition table, and m1~m5 are acceleration sensors No. 1~5.

[0035] Figure 3 Schematic diagram of the original vibration signal of the pump in the non-cavitation and cavitation states; where (a) represents the non-cavitation state and (b) represents the cavitation state.

[0036] Figure 4 Schematic diagram of the quintic cubic Savitzky-Golay filtering algorithm.

[0037] Figure 5 Schematic diagram of the vibration signal after noise reduction in the non-cavitation and cavitation states of the pump; where (a) represents the non-cavitation state and (b) represents the cavitation state.

[0038] Figure 6 The short-time Fourier transform spectrum diagram of the signal in the non-cavitation state and the cavitation state of the pump; among them, (a) represents the non-cavitation state, and (b) represents the cavitation state.

[0039] Figure 7 This is the graph showing the variation of the kurtosis of the vibration signal at measuring points 1 to 5 with NPSH.

[0040] Figure 8 This is a graph showing the variation of RMS and NPSH in each frequency band of the vibration signal at measuring points 1 to 5.

[0041] Fig. 9 It is a bubble diagram of the kurtosis of the vibration signal at measuring points 1 to 5 and the RMS and NPSH of each frequency band. DETAILED DESCRIPTION

[0042] The present invention will be further described below in conjunction with the accompanying drawings.

[0043] Reference Figures 1 to 9 , a pump cavitation state diagnosis method based on characteristic frequency and kurtosis, comprising the following steps:

[0044] Step 1: Based on the pump operation status monitoring system, obtain the vibration signal of the pump when it is running;

[0045] Step 2: Use the quintic cubic Savitzky-Golay filtering algorithm to perform noise reduction on the original vibration signal;

[0046] Step 3: Use short-time Fourier transform to obtain the frequency, amplitude and phase information of the signal and clarify the characteristic frequency distribution of cavitation;

[0047] Step 4: Perform one-third octave analysis on the signal to obtain the variation law of energy in different frequency bands of the signal with the development of cavitation;

[0048] Step 5: Calculate the kurtosis of the signal and the root mean square value RMS of each frequency band;

[0049] Step 6: Use the flow state, kurtosis and RMS parameters as input variables of the double-layer BPNN neural network to identify and classify the cavitation state of the centrifugal pump.

[0050] The pump cavitation state diagnosis method based on characteristic frequency and kurtosis of this embodiment is specifically implemented as follows:

[0051] Step 1: Based on the pump operation status monitoring system, obtain the vibration signal of the pump when it is running;

[0052] The vibration data of the pump during operation is obtained with the help of acceleration sensors arranged at different positions of the pump. Figure 2 It is a pump vibration test system, which includes B01 motor, B02 motor connection frame, B03 pump body, B04 flexible connector, B05 pipeline support frame, B06 vibration signal acquisition table, and m1~m5 are acceleration sensors No. 1~5. When the pump is running, the original vibration data of the pump under different working conditions is obtained through vibration acceleration sensors No. 1~5 distributed in different positions, and sent to the host computer through the vibration signal acquisition table; Figure 3 It is the original vibration signal of the pump in non-cavitation and cavitation states;

[0053] Step 2: Use the quintic cubic Savitzky-Golay filtering algorithm to perform noise reduction on the original vibration signal;

[0054] SG filtering is a data smoothing method based on local polynomials. By setting a filtering window in the time domain and fitting it using the least squares method, it can effectively remove high-frequency noise while keeping the shape and width of the signal unchanged. Since the pump vibration signal collected by the vibration acceleration sensor is a non-stationary signal containing varying degrees of noise, the Savitzky-Golay convolution smoothing algorithm is used for noise reduction; its principle is as follows Figure 4 As shown; suppose a set of signals is x n (n=1,2,3......), one of the window data is x i (i=-m,...,0,...m), the window width is 2m+1, and the k-1 order polynomial is used to fit the data in the window, which is expressed as formula (1):

[0055] y=a 0 +a 1 x+…+a k-1 xk-1 (1)

[0056] In the formula, y is the fitting data, a 0 ~a k-1 are coefficients; we can get a k-dimensional linear equation system consisting of 2m+1 equations, and its matrix form is:

[0057] Y (2m+1)×1 =X (2m+1)×k ·A k×1 +B (2m+1)×1 (2)

[0058] When 2m+1>k, the system of equations has a solution, where A=(XT·X) -1 ·X T ·Y, therefore, the filtered value Y is:

[0059]

[0060] By moving the filter window from left to right, the smooth sequence of the entire signal after filtering can be obtained. After SG filtering, the vibration signal retains its original shape while removing pulse interference and noise with a small energy ratio, improving the signal-to-noise ratio. The vibration signals of the pump in the non-cavitation and cavitation states after noise reduction are as follows: Figure 5 As shown;

[0061] Step 3: Use short-time Fourier transform to obtain the frequency, amplitude and phase information of the signal and clarify the characteristic frequency distribution of cavitation;

[0062] Based on step 2, the signal is subjected to short-time Fourier transform; compared with Fourier transform, short-time Fourier transform can reflect the signal's time-domain characteristics while reflecting the signal's frequency-domain characteristics; short-time Fourier transform is defined as follows:

[0063]

[0064] x(m) is the input signal, ω(m) is the window function; short-time Fourier transform is to cut a signal into multiple segments, perform Fourier transform on each segment, and finally connect them in the time domain; each segment signal taken out is called a frame, and the length of a frame signal is usually 2 n ; To ensure the accuracy of the results, the signals of two adjacent frames must overlap, that is, HopSize, which can be 25% to 75% of the frame length;

[0065] Take the frame length as 1024, HopSize as 512, and perform short-time Fourier transform on the signal; the short-time Fourier transform spectrum of the signal in the non-cavitation state and the cavitation state is as follows: Figure 6 As shown;

[0066] Step 4: Perform one-third octave analysis on the signal to obtain the variation law of energy in different frequency bands of the signal with the development of cavitation;

[0067] Based on step 3, perform one-third octave analysis on the signal; one-third octave spectrum is a common method for testing and analyzing acoustics, human vibration and mechanical vibration; the octave spectrum consists of a series of center frequency points and the effective value (RMS) of the signal in the frequency band near the corresponding center frequency; the one-third octave center frequency is:

[0068] f c =1000×10 3n / 30 Hz(n=0,±1,±2,±3,…) (5)

[0069] The current standards in my country stipulate that the center frequency in practical applications should be taken from its approximate values: 1Hz, 25Hz, 1.6Hz, 2Hz, 2.5Hz, 3.15Hz, 4Hz, 5Hz, 6.3Hz, 8Hz, 10Hz, ...; the upper limit frequency f of one-third octave band u , lower limit frequency f l Between the center frequency f c The relationship is:

[0070]

[0071] Perform one-third octave band analysis on the signal to obtain the cavitation noise distribution of the vibration signal and the change law of the energy of each frequency band of the signal with the development of cavitation;

[0072] Step 5: Calculate the kurtosis of the signal and the root mean square value RMS of each frequency band;

[0073] Based on step 4, calculate the signal kurtosis and the RMS value of each frequency band. The change of signal kurtosis with NPSH is shown in the figure Figure 7 As shown; the frequency bands with center frequencies of 50Hz, 315Hz, 630Hz and 3150Hz were selected to calculate RMS. The change of RMS with NPSH is shown as follows Figure 8 As shown; the bubble charts of NPSH, kurtosis and RMS are shown in Fig. 9 As shown;

[0074] Step 6: Use the flow state, kurtosis and RMS parameters as input variables of the double-layer BPNN neural network to identify and classify the cavitation state of the centrifugal pump.

[0075] Based on steps 1-5, a pump cavitation state diagnosis method based on characteristic frequency and kurtosis was established to achieve accurate identification and diagnosis of pump cavitation state. The flow rate of the vibration signal, the kurtosis K of each measuring point under the flow rate, and the RMS (RMS1~RMS6) of the signal in the frequency band with center frequencies of 1250Hz, 1600Hz, 2000Hz, 2500Hz, 3150Hz and 4000Hz were used as input features, and the cavitation state of the centrifugal pump was used as the output feature. BPNN was used for training. The number of fully connected layers of BPNN is 2, each layer has 10 neurons, and the linear rectification function is used as the activation function. The number of iterations is 1000. In order to enable the model to diagnose the cavitation state of any flow condition, the small flow condition is defined as feature-1, the rated flow condition is defined as feature 0, and the large flow condition is defined as feature 1; the non-cavitation state is defined as 0, and the cavitation state is defined as 1. The input features and output features are shown in Table 1:

[0076]

[0077] Table 1

[0078] The total number of samples is 880. To avoid the accidental error, 70% of the data, i.e. 616 data, are randomly selected for model training each time, and the remaining 264 data are used to verify the model effect. The training and verification are repeated four times. 0 represents no cavitation, and 1 represents cavitation. The results of the four trainings are shown in Table 2. The quality of the model effect can be expressed by the accuracy rate, which refers to the proportion of the number of correctly predicted samples to the total number of samples. It can be seen that the results of the four tests are all above 97%, with a high accuracy rate. Table 2 shows the accuracy of model training and testing.

[0079]

[0080] Table 2

[0081] In addition, the performance of the model can also be evaluated using two indicators: the true positive rate (TPR) and the positive predicted value (PPV). TPR represents the proportion of correctly classified observations in the true category, and PPV represents the proportion of positive categories when the model predicts that they are positive. The calculation formulas for TPR and PPV are as follows:

[0082]

[0083]

[0084] TP: The number of samples correctly predicted by the model as positive categories;

[0085] FN: The number of positive samples predicted by the model as negative samples;

[0086] FP: The number of negative class samples predicted by the model as positive class;

[0087] Table 3 shows the TPR and PPV of the four model trainings. It can be seen that the diagnostic effect of the four training models is good, and the TPR and PPV are mostly above 90%, which proves the feasibility of the model for cavitation diagnosis.

[0088]

[0089] Table 3

[0090] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also includes equivalent technical means that can be thought of by those skilled in the art based on the inventive concept.

Claims

1. A pump cavitation state diagnosis method based on characteristic frequency and kurtosis, characterized in that: The method comprises the following steps: Step 1: Based on the pump operation status monitoring system, a vibration signal of the pump during operation is obtained. The vibration data of the pump during operation is obtained by means of acceleration sensors arranged at different positions of the pump; Step 2: Use the quintic cubic Savitzky-Golay filtering algorithm to perform noise reduction on the original vibration signal. The process is as follows: SG filtering is a data smoothing method based on local polynomials. By setting a filtering window in the time domain and fitting it using the least squares method, it can effectively remove high-frequency noise while keeping the shape and width of the signal unchanged. Since the pump vibration signal collected by the vibration acceleration sensor is a non-stationary signal containing noise to varying degrees, the Savitzky-Golay convolution smoothing algorithm is used for noise reduction. Suppose a set of signals is x n , n=1,2,3......, one of the window data is x i , i = -m,...,0,...m, the window width is 2m+1, and a k-1 order polynomial is used to fit the data in the window, which is expressed as formula (1): y=a0+a1x+...+a k-1 x k-1 (1) In the formula, y is the fitting data, a0~a k-1 As coefficients, we get a k-dimensional linear equation system consisting of 2m+1 equations, whose matrix form is: Y (2m+1)×1 =X (2m+1)×k ·A k×1 +B (2m+1)×1 (2) When 2m+1>k, the system of equations has a solution, where A=(XT·X) -1 ·X T ·Y, therefore, the filtered value Y is: Y=X·A=X·(X T ·X) -1 ·X T ·Y (3) By moving the filter window from left to right, the smooth sequence of the entire signal after filtering is obtained. After SG filtering, the vibration signal retains its original shape while the pulse interference and noise with a small energy share are removed, and the signal-to-noise ratio is improved; Step 3: Use short-time Fourier transform to obtain the frequency, amplitude and phase information of the signal and clarify the cavitation characteristic frequency distribution. The process is as follows: Based on step 2, the signal is subjected to short-time Fourier transform; compared with Fourier transform, short-time Fourier transform can reflect the signal's time-domain characteristics while reflecting the signal's frequency-domain characteristics; short-time Fourier transform is defined as follows: x(m) is the input signal, ω(m) is the window function; short-time Fourier transform is to cut a signal into multiple segments, perform Fourier transform on each segment, and finally connect them in the time domain; each segment signal taken out is called a frame, and the length of a frame signal is 2 n ; To ensure the accuracy of the results, the signals of two adjacent frames must overlap, that is, HopSize, which is 25% to 75% of the frame length; Step 4: Perform one-third octave analysis on the signal to obtain the law of change of energy in different frequency bands of the signal with the development of cavitation. The process is as follows: Based on step 3, perform one-third octave analysis on the signal; one-third octave spectrum is a common method for testing and analyzing acoustics, human vibration and mechanical vibration; the octave spectrum consists of a series of center frequency points and the RMS value of the signal in the frequency band near the corresponding center frequency; the one-third octave center frequency is: f c =1000×10 3n / 30 Hz(n=0,±1,±2,±3,…)(5) The upper frequency f of the one-third octave band u , lower limit frequency f l Between the center frequency f c The relationship is: Perform one-third octave band analysis on the signal to obtain the cavitation noise distribution of the vibration signal and the change law of the energy of each frequency band of the signal with the development of cavitation; Step 5, calculating the kurtosis of the signal and the root mean square value RMS of each frequency band: Based on step 4, calculating the kurtosis of the signal and the root mean square value RMS of each frequency band; Step 6: Use the flow state, kurtosis and RMS parameters as input variables of the double-layer BPNN neural network to identify and classify the cavitation state of the centrifugal pump.

2. A method for diagnosing pump cavitation status based on characteristic frequency and kurtosis as claimed in claim 1, characterized in that: In the step 2, it is specified that the original vibration signal is subjected to noise reduction processing by using a five-point cubic Savitzky-Golay filtering algorithm, in which the window size and the order of the fitting function are adjusted according to the actual situation; or the original vibration signal is subjected to noise reduction processing by using a singular value decomposition denoising SVD algorithm.

3. A method for diagnosing pump cavitation status based on characteristic frequency and kurtosis as claimed in claim 1 or 2, characterized in that: In the step 3, it is specified that the filtered signal is analyzed by using short-time Fourier transform, and the frame length and HopSize of the signal are adjusted according to the actual situation to obtain the best effect.

4. A method for diagnosing pump cavitation status based on characteristic frequency and kurtosis as claimed in claim 1 or 2, characterized in that: In the step 6, it is specified that a double-layer BPNN neural network is used to identify the cavitation state of the pump, or a support vector machine SVM is used to classify and identify the cavitation state.

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