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CN119124337B - Two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection - Google Patents

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

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CN119124337B
CN119124337B CN202411088851.6A CN202411088851A CN119124337B CN 119124337 B CN119124337 B CN 119124337B CN 202411088851 A CN202411088851 A CN 202411088851A CN 119124337 B CN119124337 B CN 119124337B
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kurtosis
joint
signals
pressure pulsation
signal
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CN119124337A (en
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朱国俊
宣奕帆
曹一征
冯建军
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Xian University of Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D15/00—Control, e.g. regulation, of pumps, pumping installations or systems
    • F04D15/0088—Testing machines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L23/00—Devices or apparatus for measuring or indicating or recording rapid changes, such as oscillations, in the pressure of steam, gas, or liquid; Indicators for determining work or energy of steam, internal-combustion, or other fluid-pressure engines from the condition of the working fluid
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
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    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/243—Classification techniques relating to the number of classes
    • G06F18/2433—Single-class perspective, e.g. one-against-all classification; Novelty detection; Outlier detection
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08—Feature extraction
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/12—Classification; Matching

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  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
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  • Data Mining & Analysis (AREA)
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  • Evolutionary Computation (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Mechanical Engineering (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

本发明公开了用于混流泵振动检测的二维联合峭度分析方法，具体过程如下：利用激光测振仪和压力脉动传感器采集主轴径向振动位移信号和叶轮出口压力脉动，并基于采集的两个信号求解二维联合峭度；利用标准正态分布和二维联合峭度基准值，对混流泵的运行状态进行评估。本发明解决了传统振动检测方法在识别复杂故障模式时存在的精度低及可靠性差的问题。

This paper discloses a two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection. 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 these two collected signals. The operating status of the mixed-flow pump is evaluated using a standard normal distribution and a two-dimensional joint kurtosis benchmark value. This method solves the problems of low accuracy and poor reliability of traditional vibration detection methods when identifying complex fault modes.

Description

Two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection
Technical Field
The invention belongs to the technical field of water jet propulsion, and relates to a two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection.
Background
In the water jet propeller, a mixed flow pump is widely used for its excellent performance. The operational stability of this pump type is a key factor in ensuring that the water jet propulsion system behaves in terms of noise control and overall stability. The vibration problem of the mixed flow pump is caused by complex and various factors, including unbalance of a mechanical structure, hydrodynamic factors, change of an operating environment and the like. The existing vibration detection method mainly depends on signal analysis of a single measuring point, such as time domain analysis, frequency domain analysis, time-frequency domain analysis and the like. These methods can provide effective diagnostic information under certain simple conditions, but their accuracy and reliability appear to be inadequate when dealing with complex conditions and nonlinear vibration problems. In particular, in vibration detection during the transient processes of mixed flow pump starting, speed changing and the like, the fluid characteristics and the mechanical characteristics of the pump system are mutually coupled, so that vibration signals show high non-linear and non-stable characteristics, and the traditional single-measuring-point signal analysis method is difficult to accurately distinguish and diagnose the complex vibration problems. The two-dimensional combined kurtosis analysis method can reflect the characteristics of the vibration signal more comprehensively by combining the time domain signals of the two measuring points, and is particularly suitable for processing the vibration signal of the mixed flow pump under the complex working condition. Therefore, the mixed flow pump vibration detection technology based on the two-dimensional combined kurtosis analysis method has important practical significance and application value for improving the running stability and reliability of a pump system.
Disclosure of Invention
The invention aims to provide a two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection, which solves the problems of low precision and poor reliability existing in the traditional vibration detection method when complex fault modes are identified.
The technical scheme includes that the two-dimensional combined kurtosis analysis method for vibration detection of the mixed flow pump comprises the steps of collecting radial vibration displacement signals of a main shaft and pressure pulsation of an impeller outlet by using a laser vibration meter and a pressure pulsation sensor, solving the two-dimensional combined kurtosis based on the collected two signals, and evaluating the running state of the mixed flow pump by using standard normal distribution and two-dimensional combined kurtosis reference values.
The invention is also characterized in that:
The method specifically comprises the following steps:
step 1, starting a vibration data acquisition system of a mixed flow pump, wherein water flow sequentially passes through an inlet flow channel, an impeller, a guide vane and an outlet flow channel;
step 2, acquiring a main shaft vibration displacement signal by using a laser vibration meter, and acquiring an outlet pressure pulsation signal of an impeller by using a pressure pulsation sensor at the same time, so as to obtain a time sequence x 1 of the main shaft vibration displacement signal and an outlet pressure pulsation signal x 2 of the impeller;
Step 3, calculating a joint probability density function p (x 1,x2) of a time sequence x 1 of the vibration displacement signal and an impeller outlet pressure pulsation signal x 2 by adopting a two-dimensional kernel density function;
Step 4, integrating the P (x 1,x2) pair (- ++infinity) range x 2 to obtain the x 1 edge probability density P (x 1), and integrating the P (x 1,x2) pair (- ++infinity) range x 1 to obtain the x 2 edge probability density P (x 2);
Step 5, x 1 and x 2, the individual fourth order moments and the hybrid fourth order moment therebetween;
Step 6, calculating the two-dimensional combined kurtosis of x 1 and x 2 based on the step 4 and the step 5;
Step 7, calculating the maximum information coefficient of the time sequence x 1 of the vibration displacement signal and the impeller outlet pressure pulsation signal x 2, and determining a reference value K ab of the two-dimensional joint kurtosis through the correlation coefficient;
Step 8, after obtaining the two-dimensional joint kurtosis reference value K ab of the signals x 1 and x 2, the two-dimensional joint kurtosis exceeding the reference value K ab is named as positive joint kurtosis, and the two-dimensional joint kurtosis below the reference value K ab is named as negative joint kurtosis.
In step 4, the calculation method of the edge probability densities P (x 1) and P (x 2) using the following formula (1) and formula (2) is:
In the step 5, calculating the independent fourth-order moment of x 1 and x 2 and the mixed fourth-order moment between the independent fourth-order moment and the mixed fourth-order moment through the following formulas (3) - (7);
μ1＝∫∫(x1-E(x1))4p(x1,x2)dx1dx2 (3)
μ2＝∫∫(x2-E(x2))4p(x1,x2)dx1dx2 (4)
μ3＝∫∫(x1-E(x1))4(x2-E(x2))4p(x1,x2)dx1dx2 (5)
Where E (x 1) and E (x 2) represent the mean of x 1 and x 2, respectively, μ 1 and μ 2 represent the individual fourth-order moments of x 1 and x 2, respectively, and μ 3 represents the mixed fourth-order moment between x 1 and x 2.
In the step 6, the two-dimensional joint kurtosis of x 1 and x 2 is calculated according to the following formulas (8) - (10);
wherein, the AndThe variances of x 1 and x 2 are represented, respectively, and K represents the two-dimensional joint kurtosis between the two.
The specific process of the step 7 is as follows:
step 7.1, dividing the time-series signals x 1 and x 2 into interval sets { I 1,I2,……,Ik } and { J 1,J2,……,Jk } respectively, wherein each interval I i and J j represents the division of the signals x 1 and x 2 in a specific numerical range, calculating the probability of each interval, and constructing a joint distribution table by the calculated probabilities, specifically as follows:
Wherein the probability P (I i) represents the likelihood that x 1 falls within interval I i, the probability P (J j) represents the likelihood that x 2 falls within interval J j, and the joint probability P (I i,Jj) represents the likelihood that x 1 falls within interval I i and x 2 falls within interval J j;
Step 7.3, calculating mutual information I (x 1;x2) between two signals by using the joint distribution table constructed in step 7.2, which is specifically as follows:
I(x1;x2)＝H(x1)+H(x2)-H(x1,x2) (17)
Wherein H (x 1) represents the uncertainty of the entropy of the signal x 1 for measuring the probability distribution of x 1 over each interval I i, H (x 2) represents the uncertainty of the entropy of the signal x 2 for measuring the probability distribution of x 2 over each interval J j, H (x 1,x2) represents the joint entropy of the two signals for measuring the uncertainty of the combined distribution of the two signals;
Step 7.4, according to the normal distribution characteristics, the signals x 1 and x 2 are subjected to calculation of different interval division schemes { k 1,k2,…,km }, and for the different interval division schemes { k 1,k2,…,km }, the step 7.3 is performed to calculate different mutual information values Finally, selecting the maximum mutual information value as the maximum information coefficient, and using the maximum information coefficient as the correlation coefficient delta of the time sequence signals x 1 and x 2;
Step 7.5, generating two independent standard normal distribution signals z 1 and z 2, and then converting the two signals into standard normal distribution signals x 3 and x 4 with a specified correlation delta by a linear combination method:
x3＝z1 (19)
And 7.6, replacing x 1 with a standard normal distribution signal x 3 and replacing x 2 with a standard normal distribution signal x 4, and then executing the steps 4 to 6 to obtain a two-dimensional joint kurtosis K ab between the two standard normal distribution signals x 3 and x 4, wherein K ab is used as a two-dimensional joint kurtosis reference value of a time sequence x 1 of a spindle vibration displacement signal and an outlet pressure pulsation signal x 4 of the impeller.
The method has the beneficial effects that the accuracy and the reliability of the vibration detection of the mixed flow pump are improved by adopting a two-dimensional combined kurtosis analysis method based on the time domain signals of the two measuring points. The nonlinear and linear relation between signals is effectively captured by utilizing the maximum information coefficient, so that the abnormal vibration characteristics are more accurately identified. And the running state of the mixed flow pump is evaluated by using standard normal distribution and two-dimensional combined kurtosis reference values, so that a reliable diagnosis basis is provided, and potential problems can be found in time and maintenance and optimization can be performed. The method is not only suitable for vibration detection of the mixed flow pump system, but also can be popularized and applied to vibration analysis of other complex mechanical systems, and has strong universality and practicability, so that the running stability and the service life of equipment are improved, and the maintenance cost is reduced. By carrying out joint analysis on the data of the vibration measuring point of the main shaft of the mixed flow pump and the pressure pulsation measuring point of the impeller outlet, the invention can improve the accuracy and the sensitivity of fault detection, timely identify and prevent potential faults, ensure the normal operation of equipment and prolong the service life of the equipment.
Drawings
FIG. 1 is a schematic diagram of a system for testing mixed flow pump vibration and pressure pulsation data acquisition employed in a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to the present invention;
FIG. 2 is a diagram showing the positional relationship between a laser vibrometer and a pressure pulsation sensor, respectively, and a measuring point A and a measuring point B, which are adopted in the two-dimensional combined kurtosis analysis method for detecting vibration of a mixed flow pump;
FIG. 3 is a flow chart of a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection of the present invention;
FIG. 4 (a) is a graph showing vibration displacement signals of a measurement point A collected by a laser vibrometer in a two-dimensional combined kurtosis analysis method for vibration detection of a mixed flow pump according to the present invention
FIG. 4 (B) is a two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection of the present invention, wherein the pressure pulsation signal of the impeller outlet of the measuring point B is collected by a pressure pulsation sensor;
FIG. 5 is a two-dimensional joint kurtosis analysis result in the two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection of the present invention;
FIG. 6 is a relationship between a two-dimensional joint kurtosis reference value and a correlation coefficient in a two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to the present invention.
In the figure, an inlet flow channel, an impeller, a guide vane, an outlet flow channel, a pressure pulsation sensor, a driving motor, a laser vibration meter, a main shaft, a data acquisition card and a computer are respectively arranged in the figure, the figure is provided with the inlet flow channel, the impeller, the guide vane, the outlet flow channel, the pressure pulsation sensor, the driving motor, the laser vibration meter, the main shaft and the data acquisition card.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
Example 1
The invention relates to a two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection, which adopts a mixed flow pump vibration and pressure pulsation data acquisition test system as shown in figure 1, and the system sequentially comprises an inlet flow channel 1, an impeller 2, a guide vane 3 and an outlet flow channel 4 according to the water flow direction. As shown in fig. 2, the mixed flow pump test system is provided with two measuring points, namely a measuring point a and a measuring point B, and real-time vibration signals and pressure pulsation signals thereof are respectively acquired for analysis. The mixed flow pump is controlled by a driving motor 6, and for any mixed flow pump device comprising an inlet flow channel 1, an impeller 2, a guide vane 3 and an outlet flow channel 4, two visual windows are formed near the shaft head of the mixed flow pump and used for measuring the vibration of a main shaft 8 by a laser vibration meter 7. The pressure pulsation measuring point is arranged at the impeller outlet of the mixed flow pump, and the pressure pulsation of the mixed flow pump outlet is measured by the pressure pulsation sensor 5. The laser vibration meter 7 and the pressure pulsation sensor 5 are connected with a data acquisition card 9 through a data transmission line, and the data acquisition card 9 is connected with a computer 10.
Example 2
As shown in FIG. 3, the two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection is implemented according to the following steps:
Step 1, starting a vibration data acquisition system of the mixed flow pump, wherein water flow sequentially passes through an inlet flow channel 1, an impeller 2, a guide vane 3 and an outlet flow channel 4. The lengths of the inlet runner 1 and the outlet runner 4 are 2 times of the lengths of the impeller 2 and the guide vane 3 so as to ensure that the flow is developed fully and avoid backflow;
And 2, acquiring vibration displacement signals of the main shaft 8 by using a Doppler laser vibrometer 7, and acquiring outlet pressure pulsation signals of the impeller 2 by using a pressure pulsation sensor 5. The collected signals are all collected by the data collection card and transmitted to the computer 10 by the data line. Thereby obtaining a time sequence x 1 of the vibration displacement signal of the main shaft 8 and an outlet pressure pulsation signal x 2 of the impeller 2;
And 3, calculating a joint probability density function p (x 1,x2) of the time sequence x 1 of the vibration displacement signal and the impeller outlet pressure pulsation signal x 2 by adopting a two-dimensional kernel density function. Because the Gaussian kernel function can effectively smooth the data distribution, the Gaussian kernel function is selected for kernel density estimation so as to provide accurate joint probability density estimation;
Step 4, P (x 1,x2) pairs (- ≡, + -infinity) range x 2, an edge probability density P (x 1) of x 1 is obtained. And P (x 1,x2) pairs (- ≡, + -infinity) range x 1, an edge probability density P of x 2 (x 2) is obtained, the calculation method of the edge probability densities P (x 1) and P (x 2) comprises the following steps:
Step 5, calculating independent fourth-order moments of x 1 and x 2 and mixed fourth-order moments between the independent fourth-order moments based on the step 4 through formulas (3) - (7);
μ1＝∫∫(x1-E(x1))4p(x1,x2)dx1dx2 (3)
μ2＝∫∫(x2-E(x2))4p(x1,x2)dx1dx2 (4)
μ3＝∫∫(x1-E(x1))4(x2-E(x2))4p(x1,x2)dx1dx2 (5)
Where E (x 1) and E (x 2) represent the mean of x 1 and x 2, respectively, μ 1 and μ 2 represent the individual fourth-order moments of x 1 and x 2, respectively, and μ 3 represents the mixed fourth-order moment between x 1 and x 2.
Step 6, calculating the two-dimensional combined kurtosis of x 1 and x 2 through the steps (8) - (10) based on the step 4 and the step 5;
wherein, the AndThe variances of x 1 and x 2 are represented, respectively, and K represents the two-dimensional joint kurtosis between the two.
And 7, calculating the maximum information coefficient of the time sequence x 1 of the vibration displacement signal and the impeller outlet pressure pulsation signal x 2, and determining the reference value of the two-dimensional joint kurtosis through the correlation coefficient.
In step 7.1, the time series signals x 1 and x 2 are discretized into a series of finite intervals, and x 1 and x 2 are respectively two time series signals, assuming that x 1 and x 2 have N sample points. The time series x 1 and x 2 are divided into k sections, respectively, resulting in section sets { I 1,I2,……,Ik } and { J 1,J2,……,Jk }, where each section I i represents a dynamically divided portion of the vibration displacement signal x 1 within its range of values, and each section J j represents a dynamically divided portion of the impeller outlet pressure pulsation signal x 2 within its range of values. The partitioning is not a simple halving, but rather is adaptively adjusted according to the data distribution and the need to maximize mutual information to reveal the potential nonlinear relationship between x 1 and x 2;
and 7.2, calculating the distribution frequency of the signal values in each interval, and constructing a joint distribution table. The time-series signals x 1 and x 2 are divided into interval sets { I 1,I2,……,Ik } and { J 1,J2,……,Jk } respectively, and each interval I i and J j represents the division of the signals x 1 and x 2, respectively, within a specific numerical range. the frequency of each interval, i.e. the number of samples in which the signal value falls, is calculated and normalized to the probability. Probability P (I i) represents the likelihood that x 1 falls within interval I i, and probability P (J j) represents the likelihood that x 2 falls within interval J j. The joint probability P (I i,Jj) represents the likelihood that x 1 falls within interval I i and x 2 falls within interval J j. These probabilities are used to construct a joint distribution table showing the probability distribution of the two signals in all possible combinations of intervals to reveal their interrelationships;
And 7.3, calculating mutual information I (x 1;x2) between the two signals by using the constructed joint distribution table. The joint distribution table is a two-dimensional matrix listing all possible combinations of intervals (I i,Jj) and their corresponding joint probabilities P (I i,Jj) for describing the probability distribution of signals x 1 and x 2 falling simultaneously in the respective intervals. Mutual information is a quantization index for measuring the information sharing degree between two signals, and is defined as the difference value between the joint entropy H (x 1,x2) of the two signals and the sum of the respective entropy;
I(x1;x2)＝H(x1)+H(x2)-H(x1,x2) (17)
Where H (x 1) represents the uncertainty of the entropy of the signal x 1 for measuring the probability distribution of x 1 over each interval I i, H (x 2) represents the entropy of the signal x 2 for measuring the uncertainty of the probability distribution of x 2 over each interval J j, H (x 1,x2) represents the joint entropy of the two signals for measuring the uncertainty of the combined distribution of the two signals, and I (x 1;x2) represents the mutual information between the signals x 1 and x 2 reflecting the interdependence and the degree of information sharing between x 1 and x 2.
Step 7.4, the signals x 1 and x 2 are calculated according to the normal distribution characteristics by using different interval division schemes { k 1,k2,…,km }. For different interval division schemes { k 1,k2,…,km }, executing the step 7.3 to calculate different mutual information valuesFinally, selecting the maximum mutual information value as the maximum information coefficient, and using the maximum mutual information value as a correlation coefficient delta of time sequence signals x 1 and x 2;
In step 7.5, two standard normal distribution signals x 3 and x 4 with a correlation δ are constructed. First, two independent standard normal distribution signals z 1 and z 2 are generated, and then the two signals are converted into standard normal distribution signals x 3 and x 4 with specified correlation delta by a linear combination method;
x3＝z1 (19)
Step 7.6, in step 4, step 5 and step 6, x 1 is replaced with a standard normal distribution signal x 3, x 2 is replaced with a standard normal distribution signal x 4, then steps 4 to step 6 are performed to calculate a calculation formula of a two-dimensional joint kurtosis K ab(Kab between the two standard normal distribution signals x 3 and x 4, that is, a process of calculating K by formula (10), and K ab is taken as a two-dimensional joint kurtosis reference value of the outlet pressure pulsation signal x 4 of the impeller 2 and a time series x 1 of the spindle 8 vibration displacement signal.
Step 8, after obtaining the two-dimensional joint kurtosis reference value K ab of the signals x 1 and x 2, the two-dimensional joint kurtosis exceeding the reference value is named as positive joint kurtosis, and the two-dimensional joint kurtosis below the reference value is named as negative joint kurtosis. The larger the positive association kurtosis, the larger the impact and the more the running state deviates from its normal state.
Example 3
The method comprises the steps of respectively acquiring a main shaft vibration displacement signal of a measuring point A and an impeller outlet pressure pulsation signal of a measuring point B in the operation process of a mixed flow pump through a laser vibration meter and a pressure pulsation sensor, wherein original signals are shown in fig. 4 (a) and 4 (B), the vibration displacement signal of the measuring point A acquired through the laser vibration meter is shown in fig. 4 (a), the impeller outlet pressure pulsation signal of the measuring point B acquired through the pressure pulsation sensor is shown in fig. 4 (B), the two-dimensional joint kurtosis K is calculated through steps 3, 4, 5 and 6, and the two-dimensional joint kurtosis reference value K ab is calculated through steps 7 and 8, and is shown in fig. 5. As can be seen from FIG. 5, the positive-going combined kurtosis ratio during operation of the mixed-flow pump is 0.08% and reaches a maximum value of 2.98668 at 1.04 s. This means that the mixed-flow pump is most impacted in the whole operation at the time of 1.04s, and the operation state deviates from the normal state. FIG. 6 shows the relationship between the correlation coefficient and the two-dimensional joint kurtosis reference value, and the two-dimensional joint kurtosis reference value can be directly determined by calculating the correlation between signals, so that the on-line monitoring in the running process of the unit is facilitated.
The invention can be used for vibration monitoring of single-stage mixed flow pumps, and vibration analysis of other types of pump systems and complex mechanical systems, such as multistage centrifugal pumps, axial flow pumps, reciprocating pumps and the like. In the applications, the vibration signals and the pressure pulsation signals of a plurality of measuring points are collected, and the running state and the vibration characteristics of the equipment can be more comprehensively reflected by utilizing a two-dimensional combined kurtosis analysis method, so that the accuracy and the reliability of vibration detection are improved, potential faults are timely identified, effective maintenance and optimization are carried out, the running stability and the service life of the equipment are finally improved, and the maintenance cost is reduced.
The invention discloses a two-dimensional combined kurtosis analysis method for mixed flow pump vibration detection, which utilizes a laser vibrometer and a pressure pulsation sensor to collect radial vibration displacement signals of a main shaft and pressure pulsation of an impeller outlet, and solves the two-dimensional combined kurtosis based on the collected two signals. The nonlinear and linear relation between signals is effectively captured by utilizing the maximum information coefficient, so that the abnormal vibration characteristics are more accurately identified. And the running state of the mixed flow pump is evaluated by using standard normal distribution and two-dimensional combined kurtosis reference values, so that a reliable diagnosis basis is provided, and potential problems can be found in time and maintenance and optimization can be performed. The method is not only suitable for vibration detection of the mixed flow pump system, but also can be popularized and applied to vibration analysis of other complex mechanical systems, and has strong universality and practicability, so that the running stability and the service life of equipment are improved, and the maintenance cost is reduced.

Claims (5)

1.用于混流泵振动检测的二维联合峭度分析方法，其特征在于：具体过程如下：利用激光测振仪和压力脉动传感器采集主轴径向振动位移信号和叶轮出口压力脉动，并基于采集的两个信号求解二维联合峭度；利用标准正态分布和二维联合峭度基准值，对混流泵的运行状态进行评估；1. A two-dimensional joint kurtosis analysis method for mixed-flow pump vibration detection is characterized by the following process: using a laser vibrometer and a pressure pulsation sensor to collect the main shaft radial vibration displacement signal and the impeller outlet pressure pulsation, and calculating the two-dimensional joint kurtosis based on the two collected signals; using the standard normal distribution and the two-dimensional joint kurtosis benchmark value to evaluate the operating status of the mixed-flow pump; 具体包括如下步骤：The specific steps include: 步骤1，启动混流泵振动数据采集系统，水流依次经过进口流道（1）、叶轮（2）、导叶（3）及出口流道（4）；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; 步骤2，使用激光测振仪（7）采集主轴（8）振动位移信号，同时使用压力脉动传感器（5）采集叶轮（2）的出口压力脉动信号，从而获得主轴（8）振动位移信号的时间序列x 1和叶轮（2）的出口压力脉动信号x 2；Step 2: Using a laser vibrometer (7) to collect the vibration displacement signal of the main shaft (8), and using a pressure pulsation sensor (5) to collect the outlet pressure pulsation signal of the impeller (2), thereby obtaining a time series x1 of the vibration displacement signal of the main shaft (8) and a pressure pulsation signal x2 of the outlet pressure pulsation signal of the impeller ( 2 ); 步骤3，采用二维核密度函数计算振动位移信号的时间序列x 1和叶轮出口压力脉动信号x 2的联合概率密度函数p(x 1，x 2)；Step 3: Use a two-dimensional kernel density function to calculate the joint probability density function p ( x 1 , x 2 ) of the time series of the vibration displacement signal x 1 and the impeller outlet pressure pulsation signal x 2 ; 步骤4，将p(x 1，x 2)对(-∞，+∞)范围内的x 2进行积分，得到x 1的边缘概率密度P(x 1)；将p(x 1, x 2)对(-∞，+∞)范围内的x 1进行积分，得到x 2的边缘概率密度P(x 2)；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 ; 步骤5，计算x 1和x 2的单独四阶矩以及二者之间的混合四阶矩；Step 5, calculate the individual fourth-order moments of x1 and x2 and the mixed fourth-order moment between them ; 步骤6，基于步骤4和步骤5，计算x 1和x 2二维联合峭度；Step 6: Based on steps 4 and 5 , calculate the two-dimensional joint kurtosis of x1 and x2 ; 步骤7，计算振动位移信号的时间序列x 1和叶轮出口压力脉动信号x 2的最大信息系数，并通过相关性系数确定二维联合峭度的基准值K ab；Step 7: Calculate the maximum information coefficient of the time series of the vibration displacement signal x1 and the impeller outlet pressure pulsation signal x2 , and determine the reference value Kab of the two-dimensional joint kurtosis through the correlation coefficient; 步骤8，获得x 1和x 2的二维联合峭度基准值K ab后，将超过基准值K ab的二维联合峭度命名为正联合峭度，将低于基准值K ab的为负联合峭度。Step 8: After obtaining the two-dimensional joint kurtosis benchmark value Kab of x1 and x2 , the two-dimensional joint kurtosis that exceeds the benchmark value Kab is named positive joint kurtosis, and the two-dimensional joint kurtosis that is lower than the benchmark value Kab is named negative joint kurtosis. 2.根据权利要求1所述的用于混流泵振动检测的二维联合峭度分析方法，其特征在于：所述步骤4中，采用如下公式（1）和公式（2）边缘概率密度P(x 1)和P(x 2)的计算方法为：2. The two-dimensional joint kurtosis analysis method for mixed flow pump vibration detection according to claim 1 is characterized in that: in step 4, the marginal probability densities P ( x 1 ) and P ( x 2 ) are calculated using the following formulas (1) and (2): 其中，x 1为主轴（8）振动位移信号的时间序列，x 2为叶轮（2）的出口压力脉动信号。Among them, x1 is the time series of the vibration displacement signal of the main shaft (8), and x2 is the outlet pressure pulsation signal of the impeller (2). 3.根据权利要求2所述的用于混流泵振动检测的二维联合峭度分析方法，其特征在于：所述步骤5中，通过如下公式（3）~（7）计算x 1和x 2的单独四阶矩以及二者之间的混合四阶矩；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 individual fourth-order moments of x1 and x2 and the mixed fourth-order moment between the two are calculated by the following formulas (3) to (7); 其中，E(x 1)和E(x 2)分别表示x 1和x 2的均值，μ 1和μ 2分别表示x 1和x 2的单独四阶矩，μ 3表示x 1和x 2之间的混合四阶矩。Where E ( x1 ) and E ( x2 ) represent the means 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 . 4.根据权利要求3所述的用于混流泵振动检测的二维联合峭度分析方法，其特征在于：所述步骤6中，通过如下公式（8）~（10）计算x 1和x 2二维联合峭度；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 two-dimensional joint kurtosis of x1 and x2 is calculated by the following formulas ( 8 ) to (10); 其中，和分别表示x 1和x 2的方差，Ｋ表示二者之间的二维联合峭度。in, and represent the variance of x1 and x2 respectively, and K represents the two-dimensional joint kurtosis between them. 5.根据权利要求4所述的用于混流泵振动检测的二维联合峭度分析方法，其特征在于：所述步骤7的具体过程为：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: 步骤7.1，将时间序列信号x 1和x 2分别划分为区间集合{I 1，I 2，……，I k}和{J 1，J 2，……，J k}，每个区间I i和J j分别代表信号x 1和x 2在特定数值范围内的划分，计算每个区间的概率，并通过计算得到的概率构建联合分布表，具体如下：Step 7.1: Divide the time series signals x1 and x2 into the interval sets { I1 , I2 , ..., Ik } and { J1 , J2 , ..., Jk } , respectively . Each interval Ii and Jj represents the division of signals x1 and x2 within a specific numerical range . Calculate the probability of each interval and construct a joint distribution table based on the calculated probabilities, as follows: 其中，概率P(I i)表示x 1落在区间I i的可能性；概率P(J j)表示x 2落在区间J j的可能性，联合概率P(I i，J j)表示x 1落在区间I i且x 2落在区间J j的可能性；Among them, the probability P ( I i ) represents the possibility that x 1 falls in interval I i ; the probability P ( J j ) represents the possibility that x 2 falls in interval J j ; the joint probability P ( I i , J j ) represents the possibility that x 1 falls in interval I i and x 2 falls in interval J j ; 步骤7.3，利用步骤7.2构建的联合分布表计算两个信号之间的互信息I(x 1；x 2)，具体如下：Step 7.3: Calculate the mutual information I ( x 1 ; x 2 ) between the two signals using the joint distribution table constructed in step 7.2, as follows: 其中，H(x 1)表示信号x 1的熵用于度量x 1在各个区间I i上的概率分布的不确定性；H(x 2)表示信号x 2的熵用于度量x 2在各个区间J j上的概率分布的不确定性；H(x 1,x 2)表示两个信号的联合熵，度量了两个信号组合分布的不确定性；Where H ( x 1 ) represents the entropy of signal x 1 , which is used to measure the uncertainty of the probability distribution of x 1 on each interval I i ; H ( x 2 ) represents the entropy of signal x 2 , which is used to measure the uncertainty of the probability distribution of x 2 on each interval J j ; H ( x 1 , x 2 ) represents the joint entropy of the two signals, which measures the uncertainty of the combined distribution of the two signals; 步骤7.4，根据正态分布特性将信号x 1和x 2进行不同的区间划分方案{k 1，k 2，…，k m}的计算，针对不同的区间划分方案{k 1，k 2，…，k m}，执行步骤7.3计算得到不同的互信息值；最终，选取最大互信息值作为最大信息系数，并将最大信息系数作为时间序列信号x 1和x 2的相关性系数ẟ；Step 7.4: According to the normal distribution characteristics , the signals x1 and x2 are divided into different intervals { k1 , k2 , ... , km } . For different interval division schemes { k1 , k2 , ..., km }, 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 correlation coefficient ẟ of the time series signals x 1 and x 2 ; 步骤7.5，生成两个独立的标准正态分布信号z 1和z 2，然后通过线性组合的方法将这两个信号转换为具有指定相关性ẟ的标准正态分布信号x 3和x 4：In step 7.5, generate two independent standard normal distribution signals z 1 and z 2 , and then transform these two signals into standard normal distribution signals x 3 and x 4 with the specified correlation ẟ by linear combination: 步骤7.6，用标准正态分布信号x 3代替x 1、标准正态分布信号x 4代替x 2，然后执行步骤4至步骤6，得到两个标准正态分布信号x 3和x 4之间的二维联合峭度K ab，将K ab作为主轴（8）振动位移信号的时间序列x 1和叶轮（2）的出口压力脉动信号x 2的二维联合峭度基准值。In step 7.6, replace x 1 with the standard normal distribution signal x 3 and x 2 with the standard normal distribution signal x 4, and then execute steps 4 to 6 to obtain the two-dimensional joint kurtosis Kab between the two standard normal distribution signals x 3 and x 4. Kab is used as the two-dimensional joint kurtosis reference value of the time series x 1 of the vibration displacement signal of the main shaft ( 8) and the outlet pressure pulsation signal x 2 of the impeller (2).
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