Two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection

Abstract

The application discloses a two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection, and the specific process is as follows: a laser vibration meter and a pressure fluctuation sensor are used to collect main shaft radial vibration displacement signals and impeller outlet pressure pulsations, and two-dimensional joint kurtosis is solved based on the collected two signals; and the running state of the mixed-flow pump is evaluated by using a standard normal distribution and a two-dimensional joint kurtosis reference value. The application solves the problems of low precision and poor reliability of the traditional vibration detection method in identifying complex fault modes.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of waterjet propulsion, and relates to a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection. BACKGROUND

[0002] In a waterjet propulsion, a mixed flow pump is widely used due to its excellent performance. The operation stability of the pump type is a key factor to ensure the performance of the waterjet propulsion system in terms of noise control and overall stability. The causes of the mixed flow pump vibration problem are complex and diverse, including mechanical structure imbalance, fluid dynamics factors and changes in the operating environment. The existing vibration detection methods mainly rely on single-point signal analysis, such as time domain analysis, frequency domain analysis and time-frequency domain analysis. These methods can provide effective diagnostic information in some simple working conditions, but their accuracy and reliability are insufficient when dealing with complex working conditions and nonlinear vibration problems. Especially in the vibration detection of the mixed flow pump start-up, speed change and other transition processes, the fluid characteristics and mechanical characteristics of the pump system are coupled with each other, so that the vibration signal presents a high degree of nonlinearity and non-stationary characteristics. The traditional single-point signal analysis method is difficult to accurately distinguish and diagnose these complex vibration problems. The two-dimensional joint kurtosis analysis method can more comprehensively reflect the characteristics of the vibration signal by combining the time domain signals of two measuring points, and is particularly suitable for processing the vibration signals of the mixed flow pump under complex working conditions. Therefore, developing a mixed flow pump vibration detection technology based on the two-dimensional joint kurtosis analysis method has important practical significance and application value for improving the operation stability and reliability of the pump system. SUMMARY

[0003] The purpose of the application is to provide a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection, which solves the problems of low precision and poor reliability in identifying complex fault modes of the traditional vibration detection method.

[0004] The technical scheme adopted by the application is a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection, and the specific process is as follows: a laser vibration meter and a pressure fluctuation sensor are used to collect the main shaft radial vibration displacement signal and the impeller outlet pressure fluctuation, and the two-dimensional joint kurtosis is solved based on the collected two signals; the standard normal distribution and the two-dimensional joint kurtosis reference value are used to evaluate the operation state of the mixed flow pump.

[0005] The application has the following characteristics:

[0006] Specifically, the following steps are included:

[0007] Step 1: Start the mixed flow pump vibration data acquisition system, and the water flow passes through the inlet flow passage, the impeller, the guide vane and the outlet flow passage in sequence;

[0008] Step 2, collect the spindle vibration displacement signal using a laser vibration meter, and collect the impeller outlet pressure fluctuation signal using a pressure fluctuation sensor, so as to obtain the time series x1 of the spindle vibration displacement signal and the impeller outlet pressure fluctuation signal x2;

[0009] Step 3, calculate the joint probability density function p(x1, x2) of the time series x1 of the vibration displacement signal and the impeller outlet pressure fluctuation signal x2 by using the two-dimensional kernel density function;

[0010] Step 4, integrate p(x1, x2) with respect to x2 in the range (-∞, +∞) to obtain the marginal probability density P(x1) of x1; integrate p(x1, x2) with respect to x1 in the range (-∞, +∞) to obtain the marginal probability density P(x2) of x2;

[0011] Step 5, the individual fourth moment of x1 and x2 and the mixed fourth moment between them;

[0012] Step 6, based on step 4 and step 5, calculate the two-dimensional joint kurtosis of x1 and x2;

[0013] Step 7, calculate the maximum information coefficient of the time series x1 of the vibration displacement signal and the impeller outlet pressure fluctuation signal x2, and determine the reference value K ab of the two-dimensional joint kurtosis through the correlation coefficient;

[0014] Step 8, obtain the two-dimensional joint kurtosis reference value K ab of the signals x1 and x2, and then name the two-dimensional joint kurtosis exceeding the reference value K ab as positive joint kurtosis, and the two-dimensional joint kurtosis lower than the reference value K ab as negative joint kurtosis.

[0015] In step 4, the calculation method of the marginal probability densities P(x1) and P(x2) is as follows:

[0016]

[0017]

[0018] In step 5, the individual fourth moment of x1 and x2 and the mixed fourth moment between them are calculated by the following formulas (3)-(7):

[0019] μ1=∫∫(x1-E(x1)) 4 p(x1,x2)dx1dx2 (3)

[0020] μ2=∫∫(x2-E(x2)) 4 p(x1,x2)dx1dx2 (4)

[0021] μ3 = ∫∫(x1-E(x1)) 4 (x2-E(x2)) 4 p(x1,x2)dx1dx2 (5)

[0022]

[0023]

[0024] where E(x1) and E(x2) represent the mean of x1 and x2, respectively, μ1 and μ2 represent the individual fourth-order moments of x1 and x2, respectively, and μ3 represents the mixed fourth-order moment between x1 and x2.

[0025] In step 6, the two-dimensional joint kurtosis of x1 and x2 is calculated by the following equations (8) to (10):

[0026]

[0027]

[0028]

[0029] where and represent the variance of x1 and x2, respectively, and K represents the two-dimensional joint kurtosis between them.

[0030] The specific process of step 7 is as follows:

[0031] Step 7.1, divide the time series signals x1 and x2 into interval sets {I1, I2, …, I k} and {J1, J2, …, J k}, respectively, each interval I i and J j represents the division of signal x1 and x2 in a certain value range, calculate the probability of each interval, and construct the joint distribution table by the calculated probability, as follows:

[0032]

[0033]

[0034]

[0035] where the probability P(I i ) represents the likelihood of x1 falling in the interval I i ; the probability P(J j ) represents the likelihood of x2 falling in the interval J j , and the joint probability P(I i , Jj ) represents the likelihood that x1 falls in interval I i and x2 falls in interval J j ;

[0036] Step 7.3, calculate the mutual information I(x1; x2) between the two signals using the joint distribution table constructed in Step 7.2, as follows:

[0037]

[0038]

[0039]

[0040] I(x1; x2) = H(x1) + H(x2) - H(x1, x2) (17)

[0041] where H(x1) represents the entropy of signal x1, which measures the uncertainty of the probability distribution of x1 over the intervals I i ; H(x2) represents the entropy of signal x2, which measures the uncertainty of the probability distribution of x2 over the intervals J j ; H(x1, x2) represents the joint entropy of the two signals, which measures the uncertainty of the combined distribution of the two signals;

[0042] Step 7.4, calculate the different interval division schemes {k1, k2, …, k m} for signals x1 and x2 according to the characteristics of the normal distribution, and for different interval division schemes {k1, k2, …, k m}, execute Step 7.3 to obtain different mutual information values Finally, select the maximum mutual information value as the maximum information coefficient, and take the maximum information coefficient as the correlation coefficient δ of the time series signals x1 and x2;

[0043]

[0044] Step 7.5, generate two independent standard normal distribution signals z1 and z2, and then convert them into standard normal distribution signals x3 and x4 with a specified correlation δ through linear combination:

[0045] x3 = z1 (19)

[0046]

[0047] Step 7.6, replace x1 with standard normal distribution signal x3 and x2 with standard normal distribution signal x4, and then execute Steps 4 to 6 to obtain the two-dimensional joint kurtosis K between the two standard normal distribution signals x3 and x4ab K ab The two-dimensional joint kurtosis reference value of the time series x1 as the main shaft vibration displacement signal and the outlet pressure fluctuation signal x4 of the impeller.

[0048] The beneficial effects of the present application are that the present application improves the accuracy and reliability of the mixed-flow pump vibration detection based on the time-domain signals of two measuring points by using the two-dimensional joint kurtosis analysis method. The maximum information coefficient is used to effectively capture the nonlinear and linear relationship between the signals, making the identification of abnormal vibration characteristics more accurate. The standard normal distribution and the two-dimensional joint kurtosis reference value are used to evaluate the running state of the mixed-flow pump, providing a reliable diagnostic basis, which helps to discover potential problems in time and maintain and optimize. The method is not only suitable for vibration detection of mixed-flow pump system, but also can be applied to vibration analysis of other complex mechanical systems, which has strong universality and practicality, thereby improving the running stability and service life of the equipment and reducing the maintenance cost. Through the joint analysis of the data of the main shaft vibration measuring point and the impeller outlet pressure fluctuation measuring point of the mixed-flow pump, the present application can improve the accuracy and sensitivity of fault detection, identify and prevent potential faults in time, and ensure the normal operation of the equipment and prolong its service life. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 Fig. 1 is a structural schematic diagram of a mixed-flow pump vibration and pressure fluctuation data acquisition test system used in the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0050] Figure 2 Fig. 2 is a position relationship diagram of a laser vibration meter and a pressure fluctuation sensor with measuring point A and measuring point B respectively used in the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0051] Figure 3 Fig. 3 is a flow chart of the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0052] Fig. 4(a) is a vibration displacement signal of measuring point A collected by a laser vibration meter in the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0053] Fig. 4(b) is an impeller outlet pressure fluctuation signal of measuring point B collected by a pressure fluctuation sensor in the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0054] Figure 5 Fig. 5 is a two-dimensional joint kurtosis analysis result in the two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection according to the present application;

[0055] Figure 6It is the relationship between the two-dimensional joint kurtosis reference value and the correlation coefficient in the two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection of the present invention.

[0056] In the figure, 1. inlet flow channel, 2. impeller, 3. guide vane, 4. outlet flow channel, 5. pressure pulsation sensor, 6. drive motor, 7. laser vibrometer, 8. main shaft, 9. data acquisition card, 10. computer. DETAILED DESCRIPTION

[0057] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] Example 1

[0059] The present invention is a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection, and the mixed flow pump vibration and pressure pulsation data acquisition test system used is as follows Figure 1 As shown, the system includes, in accordance with the direction of water flow, an inlet channel 1, an impeller 2, a guide vane 3, and an outlet channel 4. Figure 2 As shown, two measuring points, measuring point A and measuring point B, are set up in the mixed flow pump test system, and their real-time vibration signals and pressure pulsation signals are collected and analyzed. The mixed flow pump is controlled by a drive motor 6. For any mixed flow pump device including an inlet flow channel 1, an impeller 2, guide vanes 3, and an outlet flow channel 4, two visualization windows are opened near the shaft head of the mixed flow pump for a laser vibrometer 7 to measure the vibration of the main shaft 8. A pressure pulsation measurement point is set at the outlet of the mixed flow pump impeller, and the pressure pulsation at the mixed flow pump outlet is measured using a pressure pulsation sensor 5. The laser vibrometer 7 and the pressure pulsation sensor 5 are both connected to a data acquisition card 9 via a data transmission line, and the data acquisition card 9 is connected to a computer 10.

[0060] Example 2

[0061] like Figure 3 As shown, the two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection of the present invention is specifically implemented according to the following steps:

[0062] Step 1: Start the mixed flow pump vibration data acquisition system. The water flows through the inlet channel 1, impeller 2, guide vane 3, and outlet channel 4 in sequence. The length of the inlet channel 1 and outlet channel 4 is set to twice the length of the impeller 2 and guide vane 3 to ensure sufficient flow development and avoid backflow.

[0063] Step 2: Use a Doppler laser vibrometer 7 to collect the vibration displacement signal of the main shaft 8, and use a pressure pulsation sensor 5 to collect the outlet pressure pulsation signal of the impeller 2. Both signals are collected by a data acquisition card and transmitted to a computer 10 via a data line. This yields the time series x1 of the vibration displacement signal of the main shaft 8 and the outlet pressure pulsation signal x2 of the impeller 2.

[0064] Step 3, the joint probability density function p(x1, x2) of the time series x1 of the vibration displacement signal and the impeller outlet pressure fluctuation signal x2 is calculated by using the two-dimensional kernel density function. Since the Gaussian kernel function can effectively smooth the data distribution, the Gaussian kernel function is selected for kernel density estimation to provide accurate joint probability density estimation;

[0065] Step 4, the edge probability density P(x1) of x1 is obtained by integrating p(x1, x2) with respect to x2 in the range of (-∞, +∞), and the edge probability density P(x2) of x2 is obtained by integrating p(x1, x2) with respect to x1 in the range of (-∞, +∞), wherein the calculation method of the edge probability densities P(x1) and P(x2) is as follows:

[0066]

[0067]

[0068] Step 5, the individual fourth-order moments of x1 and x2 and the mixed fourth-order moment between them are calculated based on step 4 by equations (3)-(7);

[0069] μ1=∫∫(x1-E(x1)) 4 p(x1,x2)dx1dx2 (3)

[0070] μ2=∫∫(x2-E(x2)) 4 p(x1,x2)dx1dx2 (4)

[0071] μ3=∫∫(x1-E(x1)) 4 (x2-E(x2)) 4 p(x1,x2)dx1dx2 (5)

[0072]

[0073]

[0074] wherein E(x1) and E(x2) represent the mean values of x1 and x2 respectively, μ1 and μ2 represent the individual fourth-order moments of x1 and x2 respectively, and μ3 represents the mixed fourth-order moment between x1 and x2.

[0075] Step 6, the two-dimensional joint kurtosis of x1 and x2 is calculated based on step 4 and step 5 by equations (8)-(10);

[0076]

[0077]

[0078]

[0079] where, and denote the variances of x1 and x2, respectively, and K denotes the two-dimensional joint kurtosis between them.

[0080] Step 7, Calculate the maximum information coefficient of the time series x1 of the vibration displacement signal and x2 of the impeller outlet pressure fluctuation signal, and determine the reference value of the two-dimensional joint kurtosis through its correlation coefficient.

[0081] Step 7.1, Discretize the time series signals x1 and x2 into a series of finite intervals, respectively, and let x1 and x2 be two time series signals, and assume that x1 and x2 have N sample points. Divide the time series x1 and x2 into k intervals, respectively, to obtain the interval sets {I1, I2, …, I k} and {J1, J2, …, J k}, where each interval I i represents a dynamic division part of the vibration displacement signal x1 in its value range, and each interval J j represents a dynamic division part of the impeller outlet pressure fluctuation signal x2 in its value range. Here, the division is not simply equal division, but is adaptively adjusted according to the data distribution and the need to maximize mutual information, in order to reveal the potential nonlinear relationship between x1 and x2;

[0082] Step 7.2, Calculate the distribution frequency of the signal values in each interval and construct a joint distribution table. Divide the time series signals x1 and x2 into interval sets {I1, I2, …, I k} and {J1, J2, …, J k}, respectively, and each interval I i and J j represents the division of signal x1 and x2 in a particular value range. Calculate the frequency of each interval, i.e. the number of samples whose signal values fall within the interval, and normalize it to a probability. The probability P(I i ) represents the likelihood of x1 falling within interval I i ; the probability P(J j ) represents the likelihood of x2 falling within interval J j . The joint probability P(I i , J j ) represents the likelihood of x1 falling within interval I i and x2 falling within interval J j . These probabilities are used to construct a joint distribution table, which shows the probability distribution of the two signals in all possible interval combinations, in order to reveal their mutual relationship;

[0083]

[0084]

[0085]

[0086] Step 7.3, calculate the mutual information I(x1; x2) between two signals using the constructed joint distribution table. The joint distribution table is a two-dimensional matrix listing all possible interval combinations (I i , J j ) and their corresponding joint probabilities P(I i , J j ), used to describe the probability distribution of signals x1 and x2 falling in the respective intervals simultaneously. Mutual information is a quantitative indicator of the degree of information sharing between two signals, defined as the difference between the joint entropy H(x1, x2) of two signals and the sum of the respective entropies;

[0087]

[0088]

[0089]

[0090] I(x1; x2) = H(x1) + H(x2) - H(x1, x2) (17)

[0091] where H(x1) represents the entropy of signal x1, used to measure the uncertainty of the probability distribution of x1 in each interval I i ; H(x2) represents the entropy of signal x2, used to measure the uncertainty of the probability distribution of x2 in each interval J j ; H(x1, x2) represents the joint entropy of two signals, measuring the uncertainty of the combined distribution of two signals; I(x1; x2) represents the mutual information between signals x1 and x2, reflecting the mutual dependence and information sharing degree between x1 and x2.

[0092] Step 7.4, calculate the different interval division schemes {k1, k2, …, k m} for signals x1 and x2 according to the normal distribution characteristics. For different interval division schemes {k1, k2, …, k m}, execute step 7.3 to obtain different mutual information values Finally, select the maximum mutual information value as the maximum information coefficient, and take it as the correlation coefficient δ of time series signals x1 and x2;

[0093]

[0094] Step 7.5: Construct two standard normally distributed signals x3 and x4 with a correlation of δ. First, generate two independent standard normally distributed signals z1 and z2, and then use a linear combination method to transform these two signals into standard normally distributed signals x3 and x4 with a specified correlation of δ.

[0095] x3=z1 (19)

[0096]

[0097] Step 7.6: In steps 4, 5, and 6, replace x1 with the standard normal distribution signal x3 and x2 with the standard normal distribution signal x4. Then, perform steps 4 to 6 to calculate the two-dimensional joint kurtosis K between the two standard normal distribution signals x3 and x4. ab (K ab The calculation formula is the process of calculating K in formula (10), K ab It is the two-dimensional joint kurtosis reference value of the time series x1 of the vibration displacement signal of the main shaft 8 and the outlet pressure pulsation signal x4 of the impeller 2.

[0098] Step 8: Obtain the two-dimensional joint kurtosis benchmark value K of signals x1 and x2 ab After that, the two-dimensional joint kurtosis that exceeds the benchmark value is named positive joint kurtosis, and the one that is lower than the benchmark value is negative joint kurtosis. The larger the positive joint kurtosis, the greater the shock and the more the operating state deviates from its normal state.

[0099] Example 3

[0100] The present invention collects the main shaft vibration displacement signal of measuring point A and the impeller outlet pressure pulsation signal of measuring point B during the operation of the mixed flow pump by using a laser vibrometer and a pressure pulsation sensor, respectively. The original signals are shown in Figures 4(a) and 4(b). Figure 4(a) is the vibration displacement signal of measuring point A collected by the laser vibrometer; Figure 4(b) is the impeller outlet pressure pulsation signal of measuring point B collected by the pressure pulsation sensor; the two-dimensional joint kurtosis K is calculated through steps 3, 4, 5 and 6, and the two-dimensional joint kurtosis reference value K is calculated through steps 7 and 8. ab ,like Figure 5 As shown. Figure 5 As can be seen from the figure, the positive joint kurtosis accounts for 0.08% during the operation of the mixed flow pump, and the positive joint kurtosis reaches a maximum value of 2.98668 at 1.04s. This indicates that at this moment of 1.04s, the mixed flow pump experienced the greatest impact in the entire operation, and the operating state deviated from its normal state. Figure 6 The relationship between the correlation coefficient and the two-dimensional joint kurtosis benchmark value is demonstrated. By calculating the correlation between the signals, the benchmark value of the two-dimensional joint kurtosis can be directly determined to facilitate online monitoring during unit operation.

[0101] The application can be used for vibration monitoring of single-stage mixed-flow pumps, but not limited to, and can also be used for vibration analysis of other types of pump systems and complex mechanical systems, such as multi-stage centrifugal pumps, axial flow pumps, reciprocating pumps, etc. In these applications, by collecting vibration signals and pressure fluctuation signals of multiple measuring points, and using the two-dimensional joint kurtosis analysis method, the running state and vibration characteristics of the equipment can be more comprehensively reflected, thereby improving the accuracy and reliability of vibration detection, identifying potential faults in time, performing effective maintenance and optimization, and ultimately improving the running stability and service life of the equipment, and reducing maintenance costs.

[0102] The two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection uses a laser vibration meter and a pressure fluctuation sensor to collect the radial vibration displacement signal of the main shaft and the pressure fluctuation at the outlet of the impeller, and solves the two-dimensional joint kurtosis based on the two collected signals. The maximum information coefficient effectively captures the nonlinear and linear relationship between the signals, making the identification of abnormal vibration characteristics more accurate. The standard normal distribution and two-dimensional joint kurtosis reference value are used to evaluate the running state of the mixed-flow pump, providing a reliable basis for diagnosis, which helps to discover potential problems in time and perform maintenance and optimization. This method is not only suitable for vibration detection of mixed-flow pump systems, but also can be applied to vibration analysis of other complex mechanical systems, and has strong universality and practicality, thereby improving the running stability and service life of the equipment, and reducing maintenance costs.

Claims

1. A two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection, characterized by: The specific process is as follows: a laser vibrometer and a pressure pulsation sensor are used to collect the main shaft radial vibration displacement signal and the impeller outlet pressure pulsation. The two-dimensional joint kurtosis is calculated based on the two collected signals. The operating status of the mixed flow pump is evaluated using the standard normal distribution and the two-dimensional joint kurtosis benchmark value. The specific steps include: Step 1: Start the mixed flow pump vibration data acquisition system, and the water flows through the inlet flow channel (1), the impeller (2), the guide vane (3) and the outlet flow channel (4) in sequence; Step 2: Use the laser vibrometer (7) to collect the vibration displacement signal of the main shaft (8), and use the pressure pulsation sensor (5) to collect the outlet pressure pulsation signal of the impeller (2), so as to obtain the time series of the vibration displacement signal of the main shaft (8) x 1 and the outlet pressure pulsation signal of impeller (2) x 2; Step 3: Use the two-dimensional kernel density function to calculate the time series of the vibration displacement signal x 1 and impeller outlet pressure pulsation signal x 2 joint probability density function p ( x 1, x 2); Step 4: p ( x 1, x 2) For the range of (-∞, +∞) x 2 Integrate and get x The marginal probability density of 1 P ( x 1); p ( x 1, x 2) For the range of (-∞, +∞) x 1 is integrated to obtain x The marginal probability density of 2 P ( x 2); Step 5, calculate x 1 and x 2 and the mixed fourth-order moment between them; Step 6: Based on steps 4 and 5, calculate x 1 and x 2D joint kurtosis; Step 7: Calculate the time series of the vibration displacement signal x 1 and impeller outlet pressure pulsation signal x 2, and determine the benchmark value of the two-dimensional joint kurtosis by the correlation coefficient K ab ; Step 8, obtain x 1 and x 2D joint kurtosis benchmark value K ab After that, it will exceed the benchmark value K ab The two-dimensional joint kurtosis is named positive joint kurtosis, which is lower than the reference value K ab The joint kurtosis is negative.

2. The two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to claim 1, characterized in that: In step 4, the marginal probability density is calculated using the following formulas (1) and (2): P ( x 1) and P ( x 2) is calculated as follows: in, x 1 is the time series of the vibration displacement signal of the main shaft (8), x 2 is the outlet pressure pulsation signal of impeller (2).

3. The two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to claim 2, characterized in that: In step 5, the following formulas (3) to (7) are used to calculate x 1 and x 2 and the mixed fourth-order moment between them; in, E ( x 1) and E ( x 2) Respectively x 1 and x The mean of 2, μ 1 and μ 2 respectively represent x 1 and x The individual fourth moment of 2, μ 3 means x 1 and x 2 between the mixed fourth-order moments.

4. The two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to claim 3, characterized in that: In step 6, the following formulas (8) to (10) are used to calculate x 1 and x 2D joint kurtosis; in, and Respectively x 1 and x The variance of 2, K represents the two-dimensional joint kurtosis between the two.

5. The two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to claim 4, characterized in that: The specific process of step 7 is as follows: Step 7.1: Convert the time series signal x 1 and x 2 are divided into interval sets { I 1, I 2,……, I k }and{ J 1, J 2,……, J k }, each interval I i and J j Represents signals x 1 and x 2. Divide within a specific numerical range, calculate the probability of each interval, and construct a joint distribution table based on the calculated probabilities, as follows: Among them, the probability P ( I i )express x 1 falls within the interval I i possibility; probability P ( J j )express x 2 falls in the interval J j The possibility, joint probability P ( I i , J j )express x 1 falls within the interval I i and x 2 falls in the interval J j possibility; Step 7.3, calculate the mutual information between the two signals using the joint distribution table constructed in step 7.2 I ( x 1; x 2), as follows: in, H ( x 1) Indicates a signal x The entropy of 1 is used to measure x 1In each interval I i uncertainty in the probability distribution over ; H ( x 2) Indicates signal x The entropy of 2 is used to measure x 2In each interval J j uncertainty in the probability distribution over ; H ( x 1, x 2) represents the joint entropy of two signals, which measures the uncertainty of the combined distribution of the two signals; Step 7.4, according to the normal distribution characteristics, the signal x 1 and x 2. Different interval partitioning schemes { k 1, k 2,…, k m } calculation, for different interval partitioning schemes { k 1, k 2,…, k m }, execute step 7.3 to calculate different mutual information values ; Finally, the maximum mutual information value is selected as the maximum information coefficient, and the maximum information coefficient is used as the time series signal x 1 and x The correlation coefficient of 2ẟ; Step 7.5, generate two independent standard normal distribution signals z 1 and z 2. Then, these two signals are transformed into standard normal distribution signals with specified correlation ẟ by linear combination method. x 3 and x 4: Step 7.6, use the standard normal distribution signal x 3 instead x 1. Standard Normal Distribution Signal x 4 instead x 2. Then perform steps 4 to 6 to obtain two standard normal distribution signals x 3 and x 2D joint kurtosis between 4 K ab ,Will K ab As the time series of the vibration displacement signal of the main shaft (8) x 1 and the outlet pressure pulsation signal of impeller (2) x 2 is the two-dimensional joint kurtosis benchmark value.

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