CN111120348A - Centrifugal pump fault early warning method based on support vector machine probability density estimation - Google Patents
Centrifugal pump fault early warning method based on support vector machine probability density estimation Download PDFInfo
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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
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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
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Abstract
The invention relates to a centrifugal pump fault early warning method based on support vector machine probability density estimation, which is characterized in that normal and fault vibration data of a centrifugal pump under multiple working conditions are collected, feature extraction is carried out from two aspects of time domain and frequency domain features, information contained in the data is fully mined, dimension reduction processing is carried out on the features, redundant parts of the data are removed, each group of feature information after dimension reduction is not related to each other, and the obtained vibration data effective features can simplify the support vector machine probability density model operation. And setting the minimum value of the probability density of the normal state sample under each working condition as a threshold, and verifying by using the probability value under the fault state. The established threshold values of all working conditions can accurately and effectively divide normal and fault data of the centrifugal pump under all working conditions. The threshold values are set respectively under 6 different working conditions divided by the rotating speed, and the verification result shows that the set threshold values can completely distinguish normal data from fault data, so that the function of fault early warning can be accurately realized.
Description
Technical Field
The application relates to the field of process rotating equipment fault early warning, in particular to fault early warning of a centrifugal pump.
Background
The centrifugal pump is common important equipment in oil and gas pipelines and refining and chemical enterprises, and needs to ensure stable and safe operation of the equipment all the time, so that the safety production of the enterprises is ensured. The centrifugal pump is used as important raw material transportation equipment, so that faults are easy to occur, once faults occur, production is damaged slightly, and serious accidents are caused seriously. Therefore, it is necessary to monitor and diagnose the operation state of the centrifugal pump equipment, and the accident prevention work of the centrifugal pump equipment is also receiving much attention. In the fault early warning process of mechanical equipment, vibration signals are commonly used as a judgment standard, the mechanical vibration signals are formed by mixing periodic signals and random signals, effective vibration threshold values are set by monitoring data such as real-time operation vibration of centrifugal pump equipment, safe and reliable operation of the centrifugal pump equipment is guaranteed, the accident rate can be reduced, regular maintenance can be changed into active maintenance, and the production cost is greatly reduced.
Common fault types in the operation process of the centrifugal pump comprise unbalance, misalignment, shaft bending, foundation looseness, cavitation, bearing fault and collision and abrasion fault, and once the fault occurs, the vibration of the pump body is aggravated, raw material leakage is easily caused, and the potential safety hazard of production is caused. Therefore, a vibration alarm threshold of the centrifugal pump needs to be set to ensure the normal operation of the centrifugal pump, and most commonly, a fixed threshold early warning is set for the centrifugal pump. The early warning of the fixed threshold of the centrifugal pump can achieve the early warning of the faults of the centrifugal pump equipment, avoid the occurrence of some faults and overhaul in time, but because the working condition of the centrifugal pump equipment is changed frequently in the operation process, the early warning system of the fixed threshold can cause the accidents of low-working-condition alarm omission and high-working-condition false alarm due to the change of the working condition. Therefore, it is urgently needed to comprehensively utilize, screen and analyze data to respectively establish corresponding alarm thresholds to replace a single alarm threshold, realize equipment early warning under variable working conditions of equipment, and solve the practical use problem. Compared with the fixed vibration threshold value early warning of a centrifugal pump, the multi-working-condition early warning system is more complex, main vibration characteristic parameters can be changed under stable working conditions under the three conditions of equipment failure, equipment variable working conditions without failure, equipment variable working conditions with failure and the like, the vibration characteristic parameters change along with the working conditions in a nonlinear mode, and the vibration threshold value of the vibration characteristic parameters can be changed accordingly. Therefore, the multi-working-condition early warning firstly needs to research each working condition of the centrifugal pump respectively, reasonably divides the working conditions, and then establishes reasonable vibration characteristic threshold values respectively by combining different operation working conditions of equipment.
In recent years, with the development of big data and artificial intelligence technologies, the application field of the technology is continuously expanded, and many researches on the vibration signal analysis and threshold establishment of equipment based on machine learning appear at home and abroad. The support vector machine is a machine learning method established on the basis of a statistical learning theory and firstly proposed by Vapnik and AT & T Bell laboratory research groups thereof, the method can simultaneously minimize experience risks and confidence ranges, the expected risk minimization is realized by taking training errors as constraint conditions of an optimization problem, and simultaneously, the sample difference is enlarged by introducing two concepts of structural risks and an optimal classification plane and simultaneously adopting a kernel mapping idea. The probability density estimation method of the support vector machine is also commonly used for the research and practice of fault diagnosis and fault early warning of mechanical equipment.
Disclosure of Invention
The invention provides a centrifugal pump fault early warning method based on support vector machine probability density estimation, which aims at the working characteristics of single stable working condition and multiple working conditions of a centrifugal pump and utilizes the practical advantage of a support vector machine in solving the nonlinear problem. The reasonable vibration characteristic alarm threshold is set to solve the problem of early warning of the equipment failure of the centrifugal pump. The method fully utilizes the data mining advantages of the support vector algorithm, respectively establishes the vibration characteristic threshold values of the centrifugal pump equipment under the single stable working condition and the multiple working conditions, and can be used for early warning of the single stable working condition and the multiple working condition faults of the centrifugal pump equipment. The invention adopts the following specific technical scheme:
a centrifugal pump fault early warning method based on support vector machine probability density estimation comprises the following steps: 1. collecting operating vibration data of the centrifugal pump at a plurality of sample points under a single stable working condition, wherein the operating vibration data comprises normal vibration data and fault vibration data; 2. extracting vibration characteristics of the vibration data, including time domain characteristic extraction and frequency domain characteristic extraction, to respectively form a normal vibration data characteristic matrix and a fault vibration data characteristic matrix; 3. performing characteristic dimension reduction processing on the normal vibration data characteristic matrix and the fault vibration data characteristic matrix to respectively obtain a normal vibration data dimension reduction matrix and a fault vibration data dimension reduction matrix; 4. normalizing the dimension reduction matrix to respectively obtain a normal vibration data effective characteristic matrix and a fault vibration data effective characteristic matrix; 5. establishing an empirical distribution function, a training sample set and a kernel function based on the effective characteristic matrix of the normal vibration data, establishing a support vector machine probability estimation model, solving the probability density value of each sample point of the normal vibration data, and taking the minimum probability density value as a single stable working condition probability threshold value; 6. performing the operation of the step 5 based on the effective characteristic matrix of the fault vibration data in the step 4 to solve the probability density value of each sample point of the fault vibration data, so as to check the effectiveness of the single stable working condition probability threshold and adjust the single stable working condition probability threshold if necessary; 7. and (4) changing the working condition of the centrifugal pump, repeating the operation of the steps 1-6, and respectively establishing probability threshold values under different working conditions.
Preferably, the time-domain features in step 2 include kurtosis, root mean square value, maximum value, minimum value, mean value, standard deviation, rectified mean value, kurtosis factor, form factor and impulse factor, and the frequency-domain features include barycentric frequency, root mean square frequency, frequency standard deviation and total energy features.
Preferably, the feature dimension reduction processing in step 3 adopts a PCA feature dimension reduction method.
Preferably, the dimensionality after the dimensionality reduction process in step 3 is determined to be 2 or 3 according to the cumulative contribution rate.
Preferably, the normalization in step 4 is to use the mean value and the standard deviation in the normal vibration data dimension reduction matrix as reference numbers, and divide the mean value subtracted from each data in the normal and fault vibration data dimension reduction matrix by the standard deviation.
Preferably, the solution in step 5 is a solution using a mathematical quadratic programming problem using a method of solving an ill-defined problem.
According to the fault early warning method, normal and fault vibration data of the centrifugal pump under multiple working conditions are collected, feature extraction is carried out on time domain and frequency domain features, information contained in the data is fully mined, dimension reduction processing is carried out on the features, redundant parts of the data are removed, each group of feature information after dimension reduction is not related to each other, and the obtained effective features of the vibration data can simplify the operation of a support vector machine probability density model. And setting the minimum value of the probability density of the normal state sample under each working condition as a threshold, and verifying by using the probability value under the fault state. The established threshold values of all working conditions can accurately and effectively divide normal and fault data of the centrifugal pump under all working conditions. The threshold values are respectively set under 6 different working conditions divided by the rotating speed, and the verification result shows that the set threshold values can completely distinguish normal data from fault data, namely the function of fault early warning can be accurately realized.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a probability density scatter diagram of normal data under the rated speed operation condition of a centrifugal pump;
FIG. 3 is a probability density scatter plot of 20rpm normal operating condition and fault data;
FIG. 4 is a probability density scatter plot of normal and fault data at 60 rpm;
FIG. 5 is a probability density scatter plot of normal and fault data at 90 rpm;
FIG. 6 is a probability density scatter plot of normal and fault data at 120 rpm;
FIG. 7 is a probability density scatter plot of normal and fault data at 180 rpm;
FIG. 8 is a graph of probability density scatter distributions for 300rpm normal and fault data.
Detailed Description
The invention discloses a centrifugal pump multi-working condition fault early warning method based on support vector machine probability density estimation, which is implemented by the flow shown in figure 1 and comprises the following steps: 1. collecting operating vibration data of the centrifugal pump at a plurality of sample points under a single stable working condition, wherein the operating vibration data comprises normal vibration data and fault vibration data; 2. extracting vibration characteristics of the vibration data, including time domain characteristic extraction and frequency domain characteristic extraction, to respectively form a normal vibration data characteristic matrix and a fault vibration data characteristic matrix; 3. performing characteristic dimension reduction processing on the normal vibration data characteristic matrix and the fault vibration data characteristic matrix to respectively obtain a normal vibration data dimension reduction matrix and a fault vibration data dimension reduction matrix; 4. normalizing the dimension reduction matrix to respectively obtain a normal vibration data effective characteristic matrix and a fault vibration data effective characteristic matrix; 5. establishing an empirical distribution function, a training sample set and a kernel function based on the effective characteristic matrix of the normal vibration data, establishing a support vector machine probability estimation model, solving the probability density value of each sample point of the normal vibration data, and taking the minimum probability density value as a single stable working condition probability threshold value; 6. performing the operation of the step 5 based on the effective characteristic matrix of the fault vibration data in the step 4 to solve the probability density value of each sample point of the fault vibration data, so as to check the effectiveness of the single stable working condition probability threshold and adjust the single stable working condition probability threshold if necessary; 7. and (4) changing the working condition of the centrifugal pump, repeating the operation of the steps 1-6, and respectively establishing probability threshold values under different working conditions.
Example 1: single stable working condition of centrifugal pump
The vibration data adopted by the embodiment is the vibration data of the multistage centrifugal pump. The centrifugal pump test bed is composed of a motor, a centrifugal pump, a coupling and a corresponding vibration sensor element. Acceleration vibration sensors are respectively arranged on bearing blocks at two ends of a motor and on bearing blocks at two ends of a centrifugal pump in a horizontal, vertical and axial direction, wherein the sampling frequency Fs of an acceleration vibration signal is 25600Hz, and the number N of sampling points is 16384; the sampling frequency Fs of the velocity signal obtained by integrating the acceleration vibration signal is 2560Hz, and the number N of sampling points is 2560 Hz.
The method comprises the steps of collecting vibration data of the centrifugal pump in a normal state and a typical fault state under the rated rotating speed 2980r/min of the motor, constructing a threshold value according to the normal data, and checking the validity of the threshold value by using several typical fault data. Typical faults include cavitation faults, misalignment faults, unbalance faults, bearing faults, and impeller faults. If misalignment faults are most common in the operation process of various mechanical equipment, the misalignment faults are mainly caused by installation errors and load changes of the equipment, abnormal vibration of a unit is often caused, and the service life of the equipment is shortened; imbalance faults are mainly caused by the fact that the rotor mass is not uniform, and most faults in mechanical equipment are related to imbalance; the pump body is violent when the centrifugal pump generates cavitation, and parts such as an impeller in the pump are seriously damaged.
In order to fully dig vibration data information and avoid information loss caused by different responses of different faults of the centrifugal pump at different measuring points of the centrifugal pump, the information contained in the vibration data is fully utilized to obtain the optimal characteristics representing the running state of the centrifugal pump, the vibration data of the horizontal, vertical and axial measuring points at the two ends of the centrifugal pump are selected for analysis, and the vibration data characteristics are extracted. Not in general, the data used are shown in the following table.
Because a plurality of vibration sources exist in the operation process of the centrifugal pump, in order to more effectively analyze data and achieve the purposes of fault diagnosis and early warning, feature extraction needs to be carried out on the comprehensively screened data. Through feature extraction and feature dimension reduction, data features which objectively reflect normal and fault states can be effectively extracted from redundant vibration signals, the data features are removed from the false and true, the data features are highlighted through various processing and analyzing means, and therefore the accuracy of fault early warning is improved. The traditional frequency spectrum analysis only utilizes the frequency spectrum characteristics of the vibration signal, has certain limitation, and how to extract characteristic parameters from multiple angles such as the vibration signal time domain, the frequency spectrum, the signal entropy and the like fully excavates the characteristic information of the vibration signal, so that the difference between normal data and fault data is maximized, and the method is of great importance for establishing a vibration threshold value. The method mainly extracts the characteristics of the data from two aspects of time domain and frequency domain, wherein the time domain characteristics have the advantages of reflecting the overall characteristics of the equipment and are commonly used for fault detection and trend prediction; the frequency domain characteristics can better reflect the fault type, reason and position. Through the time-frequency domain feature extraction, the data can be more comprehensive, and the information contained in the data can be reflected in multiple angles. According to the collected normal and fault data of the centrifugal pump, respectively extracting time-frequency domain characteristics, and then sequentially forming N multiplied by M characteristic matrixes by each extracted characteristic matrix in each state, wherein N represents the number of data groups, and M represents the characteristic dimension after combination.
Time domain feature extraction
The time domain waveform of a section of signal is processed, namely the time domain waveform of the signal is subjected to statistical analysis, and finally obtained characteristic parameters are the time domain characteristic parameters of the signal. Vibration data x for stable working condition of centrifugal pumpiThe extracted time domain characteristic parameters comprise dimensional parameters and dimensionless parameters, wherein the dimensional parameters mainly extract kurtosis, root mean square value, maximum value, minimum value, mean value, standard deviation and rectified mean value, and the dimensionless parameters extract wave type factors, pulse factors and kurtosis factors, and the total number of the time domain parameters is 10.
1) Dimensional time domain characteristic parameters:
mean value:
maximum value: xmax＝max{xi}
Minimum value: xmin＝min{xi}
Root mean square value:
standard deviation:
kurtosis:
finishing the average value:
2) dimensionless time domain parameters:
form factor:
pulse factor:
kurtosis factor:
the occurrence of a fault can cause the variation of the parameter values of the dimensional time domain characteristics, and simultaneously can cause the bounce due to objective factors, such as the progress of the instrument, the change of working conditions and other factors, which are difficult to distinguish in the actual monitoring is caused by the reason, and the fault has the stability reflecting the fault and lacks the sensitivity reflecting the fault variation. Therefore, it is desirable that the time-domain characteristic parameters only reflect the change of the fault characteristics, but not change due to the change of external instruments, working conditions and other conditions, and thus a certain stability is required. To this end, dimensionless breadth domain parameters are introduced as supplementary features. The dimensionless parameters such as kurtosis factor, form factor and pulse factor can sharply reflect the change of fault characteristics, and meanwhile, the dimensionless parameters do not react to the change of working conditions, so the method is very suitable for monitoring the early state of equipment and judging whether faults exist; but at the same time, because the sensitivity is too high, the continuous development of the fault can continuously cause the parameter change, and the normal and fault characteristic change range cannot be effectively defined, namely the stability is too low. Therefore, in practical process, in order to take the characteristics of two aspects into consideration, the two parameters are often extracted at the same time for comprehensive analysis.
Frequency domain feature extraction
The characteristic parameters obtained by performing frequency domain analysis on the signals are called frequency domain characteristic parameters. Frequency domain analysis is one of the most common signal processing methods in mechanical fault diagnosis. The method mainly comprises the steps of carrying out frequency spectrum analysis, obtaining frequency spectrum by carrying out Fourier transform on a signal time domain waveform signal, and obtaining different frequency domain characteristics by extracting. By combining with time domain analysis, another angle is provided to help analyze the signal characteristics, and various information hidden by the signal is fully mined. For experimental data, firstly, Fourier transform is carried out on the acquired time domain vibration waveform to carry out frequency domain analysis, and the frequency domain analysis of signals comprises amplitude spectrum analysis, phase spectrum analysis and power spectrum analysis. The method mainly adopts amplitude spectrum analysis, obtains the amplitude spectrum through fast Fourier transform, and extracts corresponding parameters as frequency domain characteristics. For the experimental data, the center of gravity frequency, mean square frequency, root mean square frequency and frequency standard deviation are firstly extracted from the frequency domain characteristics.
Center of gravity frequency:
mean square frequency:
root mean square frequency:
standard deviation of frequency:
after the given discrete data is subjected to fast Fourier transform, pairs are obtainedAnd (3) extracting the frequency domain characteristics including the maximum amplitude, the frequency corresponding to the maximum amplitude, the average value and the standard deviation of the amplitudes according to the frequency domain characteristics, and simultaneously extracting the total energy of each frequency band and the energy ratio characteristics of each frequency band. In order to further extract the difference characteristics of the normal data and the fault data, different frequency band intervals are divided for the acceleration signal and the speed signal according to the difference between the acceleration signal and the speed signal Fs, the acceleration signal frequency spectrum is divided into 8 frequency bands at intervals of 1500Hz from 0-12000Hz according to the sampling theorem, the energy ratio of the acceleration signal frequency spectrum is calculated, and the speed signal frequency spectrum is divided into 5 frequency bands at intervals of 200Hz from 0-1000Hz to calculate the energy ratio of the acceleration signal frequency spectrum. Let liFor each frequency band the length of the sequence of amplitude values,
for the ith upper and lower frequency band limits, the calculation formula is as follows:
band energy:
band energy ratio:
in order to fully capture the state information of the centrifugal pump, a plurality of vibration sensors in different directions, such as horizontal, vertical and axial directions, are generally arranged on bearing seats at two supporting ends of the centrifugal pump. Because the vibration transmission paths are different, the responses of different faults at different parts of the centrifugal pump at the measuring points of the vibration sensors are different, and therefore the change of equipment can be captured by monitoring the plurality of vibration sensors at the same time. Based on the method, the characteristics in the vibration signals collected by the vibration measuring points at the two ends of the centrifugal pump are respectively extracted by the characteristic extraction method and are sequentially combined to improve the information content contained in the characteristics. And extracting the time-frequency domain characteristics based on the vibration signal data of each acceleration measuring point and each speed measuring point under the single stable working condition of the centrifugal pump to finally obtain a time-frequency domain characteristic matrix of the normal data and the fault data of the centrifugal pump.
Characteristic dimension reduction of centrifugal pump vibration signal
The dimension of the feature matrix extracted from the original vibration data is large, the processing calculation amount is too large, and the information contained in the features is overlapped, so that the dimension reduction processing is required to be carried out on the feature matrix, effective features are obtained, and the features are enhanced. And performing dimensionality reduction on the extracted multi-dimensional time-frequency domain features, projecting the extracted high-dimensional feature matrix to a low-dimensional space, thereby reducing the dimension of the feature matrix, simultaneously eliminating redundant components contained in the features, simplifying the features, realizing secondary extraction of the features and obtaining a final effective feature matrix.
And (3) calculating a dimensionality reduction matrix, namely firstly calculating a covariance matrix of sample characteristics, corresponding eigenvalues and eigenvectors of the covariance matrix, forming a diagonal matrix by the calculated eigenvalues, arranging the eigenvalues from large to small, and arranging the eigenvectors into a matrix according to the magnitude of the eigenvalues. According to the method, the dimension of the feature matrix extracted from the single stable working condition data of the centrifugal pump is reduced to 3 dimensions according to the accumulated contribution rate, namely, the feature vectors of the first 3 rows are selected to form a dimension reduction matrix P.
The PCA characteristic dimension reduction method comprises the following specific steps:
1) and (3) data normalization processing, namely normalizing the data to (0,1) to eliminate the influence of dimensions among different characteristic parameters:
in the formula, X is a characteristic matrix after dimension reduction,
σ is the standard deviation of each dimension of data as the mean of each dimension of data.
2) And (3) solving a covariance matrix:
covariance matrix sigma for calculating standardized feature matrixijThe calculation formula is as follows:
∑ij＝cov(Xi,Xj)
the covariance calculation formula is as follows:
in the formula, X and Y are two-dimensional features of N samples.
3) Performing characteristic decomposition on the covariance matrix to solve an eigenvalue lambda and an eigenvector x corresponding to the eigenvalue:
∑ijthe first m larger eigenvalues λ of the matrixiCorresponding to the variance of the principal component, the eigenvalue lambdaiCorresponding unit feature vector aiThen it corresponds to the principal component FiWith respect to the initial feature matrix X1,X2,……XpWherein the ith principal component FiExpressed as:
Fi＝aiX
the variance contribution α of each principal component is generally availableiDetermining the dimensionality of the feature matrix after dimensionality reduction:
4) determining a reduced feature matrix and a transformation matrix
After determining the dimensionality of the characteristic matrix after dimensionality reduction, solving the characteristic matrix after dimensionality reduction through a transformation matrix and an original characteristic matrix, wherein the transformation matrix is the first m maximum eigenvalue lambadaiCorresponding unit feature vector aiThe formed matrix P ═ (a)1，a2，……am) Namely:
F1,F2,……Fm＝(a1，a2，……am)*(X1,X2,……Xp)
the dimension of the dimensionality reduction matrix can be selected according to the variance contribution rate of each principal component, and is set to αiThe last corresponding m is the dimensionality reduction, and the invention sets αiAnd when the sum is 90%, selecting the number of the characteristic values with the accumulated contribution rate of more than 90% as the dimensionality reduction dimensionality of 3 dimensions.
5) Multiplying the normalized feature matrix by the dimensionality reduction matrix to obtain a dimensionality reduced feature matrix:
X″＝X′*P
6) and (5) carrying out dimension reduction treatment on the fault data according to the steps 1) to 5), wherein the mean value X and the variance sigma in normalization are the mean value and the variance of normal data.
Establishing a training sample set
The effective characteristic matrix NxM extracted from the normal data under the single stable operation condition of the centrifugal pump is provided, wherein N is the number of samples, M is the characteristic dimension, each sample meets the unknown probability yi distribution, and
(x1,y1),(x2,y2),……，(xl,yl)
where l is the number of samples, yi is the probability of each sample, and yi satisfies 0 ≦ yi ≦ 1, and Σ yi ≦ 1, the result of which is unknown.
Can be expressed by constructing an empirical distribution function, i.e.
Where d is the characteristic dimension of the sample, where d equals M, and θ (x) is a piecewise function expressed as
The empirical distribution of each sample can be obtained by solving the empirical distribution function of each sample of the normal data
Complete the sample training set
And (4) constructing.
Constructing probability density model of support vector machine
Constructing probability density based on a support machine thought, performing high-dimensional projection on a sample by utilizing a kernel function, changing a low-dimensional linear indivisible problem into a high-dimensional linear indivisible problem, and performing regression estimation:
where k (x, x)i) Is a kernel function, and satisfies
Is provided with
Therefore, it is
The distribution function is then:
in order to prevent noise interference from causing overfitting, relaxation factor ξ (ξ ≧ 0) and insensitivity loss constant ε are introduced so that the probability distribution of support vector machine fitting is consistent with the empirical probability distribution, namely:
wherein F (x)i) To solve for the sample empirical distribution according to the empirical distribution function,
and estimating the obtained empirical distribution for the probability density of the support vector machine.
From the above, it can be known that the establishment of the vibration probability threshold value of the single stable working condition of the centrifugal pump is based on an ill-defined problem in the probability density estimation of the support vector machine, and therefore, a mathematical programming problem needs to be finally established for solving through a minimized risk functional under the constraint condition that the probability distribution accords with experience.
The equation for the mathematical quadratic programming is as follows:
wherein the insensitive loss constant ε can be solved using an empirical formula:
for the present invention, the value is infinitesimal by calculation.
The common kernel functions include linear kernel functions, polynomial kernel functions, gaussian kernel functions, sigmoid functions, and the like, and the kernel functions need to satisfy the following conditions:
the present invention uses a polynomial kernel function as:
then there are:
in the invention, the dimension of the effective characteristic matrix finally extracted from the vibration data of the centrifugal pump under the single stable working condition is 3, so that:
the sum of all sample probabilities is 1, so t should satisfy
Centrifugal pump of the inventionWhen the single stable working condition threshold is established for research, t is made to be 1, so that the calculation is convenient.
By solving the quadratic programming problem, β and k (x, x) can be obtainedi) To obtain a probability density p (x)i). The method comprises the following specific steps:
1) calculating the experience distribution of the samples according to the experience distribution function, and constructing a sample training set
2) Computing k (x, x) from a polynomial kerneli) And K (x, x)i)；
3) Solve the quadratic programming problem to obtain βi；
4) And solving to obtain the probability density value of each sample according to the regression estimation of the support vector machine.
Establishing single stable working condition vibration threshold of centrifugal pump and utilizing fault data to check threshold
According to the support vector machine probability density estimation model, aiming at the single stable working condition of the centrifugal pump, a threshold value is established, and the method comprises the following steps:
step 1: extracting time-frequency domain characteristics of each acceleration and speed vibration measuring point under the single stable normal operation condition of the centrifugal pump according to the time-frequency domain characteristic parameter extraction part to obtain a time-frequency domain characteristic matrix;
step 2: reducing the dimension of the multi-dimensional time-frequency domain feature matrix to three dimensions by utilizing PCA, reducing the features and enhancing the features;
and step 3: solving three-dimensional characteristic empirical distribution of normal data according to an empirical distribution function, and constructing a sample training set;
and 4, step 4: calculating a kernel function symmetric matrix k (x) among all sample points of three-dimensional characteristics of normal data according to a polynomial kernel functioni,xj) And K (x)i,xj) And solving a quadratic programming problem by utilizing a quadprog function in an MATLAB toolbox to obtain a coefficient vector of the three-dimensional characteristics of the normal data (β)1，β2,…，βl)；
Step 5, combining coefficient vectors (β) of three-dimensional features of the normal data1，β2,…，βl)、k(xi,xj) And
and solving the probability density value of each sample point of the normal data under the single stable working condition of the centrifugal pump, wherein the minimum value of the probability density values is a threshold value.
Step 6: repeating the step 1-2, extracting three-dimensional characteristics of misalignment faults, unbalance faults and bearing fault vibration, and solving a kernel function matrix k of the three-dimensional characteristics of the misalignment faults, unbalance faults and bearing fault vibration characteristic data relative to normal data according to a polynomial kernel functionMisalignment fault(xi,xj) And KMisalignment fault(xi,xj)、kUnbalance fault(xi,xj) And KUnbalance fault(xi,xj)、kBearing rolling element failure(xi,xj) And KBearing rolling element failure(xi,xj) Taking the misaligned fault data as an example, the normal sample data set is X0Misalignment of the sample is Xfault。
Step 7, coefficient vector of three-dimensional characteristic of normal data (β)1，β2,…，βl) And are and
and (5) solving the probability density value of each fault data under the single stable working condition of the centrifugal pump.
And 8: and comparing the probability density value of each fault data with the probability density threshold value, wherein the probability density threshold value is larger than the probability density threshold value of each fault data, and then the correct early warning can be achieved.
Fig. 2 shows probability density values obtained by using normal data as samples, which are arranged from small to large. According to the probability density scatter diagram of normal data shown in FIG. 2, the minimum value 0.008693 of the centrifugal pump single stable condition threshold value can be known, and therefore the minimum value 0.008693 of the probability density scatter diagram can be defined as the single condition probability threshold value of the centrifugal pump.
The maximum probability value of the misalignment fault data is 5.04 multiplied by 10-22Its minimum probability value approaches 0; the maximum probability value of the unbalanced fault data is 2.58 multiplied by 10-60The minimum probability value approaches zero indefinitely; the maximum probability value of the bearing outer ring fault is 2.82 multiplied by 10-120The minimum probability value approaches zero indefinitely; the maximum probability value of the data under the unbalanced fault and the cavitation fault is 4.88 multiplied by 10-98The minimum probability value approaches zero indefinitely; the maximum probability value of bearing outer ring fault and cavitation fault is 8.07 multiplied by 10-56The minimum probability value approaches zero indefinitely. It can be seen that the probability values of different fault states are far lower than the probability threshold established by normal data, so that the probability threshold 0.008693 established according to the normal vibration data is reasonable, the misalignment fault, the imbalance fault, the bearing outer ring fault, the imbalance fault and cavitation fault combined fault, the bearing outer ring fault and cavitation fault combined fault can be accurately pre-warned, and the validity of the method for establishing the vibration threshold based on the probability density estimation of the support vector machine is verified.
Example 2: multiple operating modes
And simulating the multi-working-condition operation data of the centrifugal pump by using the simple bearing test bed data. Constructing a vibration threshold value based on normal data, and simulating three typical faults of a bearing: bearing inner race faults, bearing outer race faults and bearing rolling body faults, and the effectiveness of the established vibration threshold is checked by utilizing fault data. The operation speed is divided into 6 working conditions according to different operation speeds in the experiment, and the working conditions are respectively the rotation speeds of 20rpm, 60rpm, 90rpm, 120rpm, 180rpm and 300 rpm. The acquired vibration signal is an acceleration signal, the sampling frequency is 262144Hz, and for the convenience of analysis, the data acquired in 0.64s is taken as a data sample point. The data used are shown in the table below.
The problem of missed alarm and false alarm existing in the traditional fixed alarm threshold is solved, namely, under different operation conditions, the vibration level of the unit is different, and the vibration condition of the unit under different vibration levels cannot be judged only through a certain fixed threshold, so that the vibration threshold needs to be set up respectively for different operation conditions to meet the early warning requirements of the unit under multiple operation conditions.
Multi-working-condition vibration threshold establishing step
The method for establishing the vibration threshold value of the centrifugal pump based on the probability density estimation of the support vector machine under the single stable working condition of the centrifugal pump respectively establishes the vibration probability threshold value under each working condition for each stable operation working condition so as to solve the problems of easy generation of false alarm and missing alarm of the fixed alarm threshold value, and comprises the following establishing steps:
step 1: the equipment operation conditions are divided according to the load or the rotating speed, and the equipment operation conditions are divided according to the rotating speed, namely the operation conditions with the rotating speeds of 20rpm, 60rpm, 90rpm, 120rpm, 180rpm and 300 rpm.
Step 2: extracting vibration data characteristic parameters under each stable operation condition based on the time-frequency domain characteristic parameters extracted under the stable work card;
and step 3: and reducing the dimension of the characteristic parameters under each working condition by using a PCA algorithm, and reducing the dimension of the normal and fault data characteristics under each working condition to 2 dimensions according to the accumulated contribution rate of more than 90%.
And 4, step 4: and solving the empirical distribution of the normal data under each working condition according to the empirical distribution function, and constructing a training sample set under each working condition.
And 5: according to the polynomial kernel function selected by the invention, the kernel function matrix of the vibration data and the fault data under each working condition is solved.
Step 6: solving a characteristic coefficient matrix of normal data under each working condition according to a quadratic programming problem, solving the probability density of the normal data and fault data under each working condition based on the probability density regression estimation of the support vector machine, selecting the minimum probability value of the normal data under each working condition as a threshold, and checking the effectiveness of the threshold by using the fault data.
And (4) solving according to the steps 1-6 to obtain the vibration probability threshold values of all the working conditions as shown in the following table.
Referring to fig. 3, under the condition of 20rpm, the difference of the characteristic distribution between the fault data and the normal data is obvious, and the fault probability value approaches to 0 infinitely when the threshold value defined by the minimum value of the normal data probability is 0.02516. Therefore, it can be obtained that: under the working condition of 20rpm, the vibration probability threshold value of the working condition is defined as the minimum value 0.02516 of the normal data probability value, and fault early warning can be accurately realized.
Referring to fig. 4, under the 60rpm condition, the probability value of the fault data is infinitely close to 0 and is lower than the threshold value set by the normal data, so that the set threshold value can be considered to be satisfactory. Therefore, it can be obtained that: under the working condition of 60rpm, the vibration probability threshold value of the working condition is defined as the minimum value 0.002207 of the normal data probability value, and fault early warning can be realized.
Referring to fig. 5, it can be seen that: under the operating condition of 90rpm, the vibration probability threshold value of the operating condition is defined as the minimum value 0.02351 of the normal data probability value, and fault early warning can be realized.
Referring to fig. 6, it can be seen that: under the 120rpm operating condition, the vibration probability threshold value of the operating condition is defined as the minimum value 0.04086 of the normal data probability value, so that fault early warning can be realized.
Referring to fig. 7, it can be seen that: under the operation condition of 180rpm, the vibration probability threshold value of the condition is defined as the minimum value 0.03872 of the normal data probability value, and fault early warning can be realized.
Referring to fig. 8, it can be seen that: under the operation condition of 300rpm, the vibration probability threshold value of the condition is defined as the minimum value 0.02565 of the normal data probability value, so that fault early warning can be realized.
In conclusion, the simple bearing test bed data is used for simulating the multi-working-condition operation data of the centrifugal pump, the fault data under each working condition is used for detecting the threshold set by the normal data under each working condition, the fault can be effectively pre-warned, and the effectiveness of the method for establishing the vibration threshold based on the probability density estimation of the support vector machine is verified.
The attached drawings are as follows:
Claims (7)
1. a centrifugal pump fault early warning method based on support vector machine probability density estimation is characterized by comprising the following steps:
1) acquiring running vibration data of the centrifugal pump with a plurality of sample points under a single stable working condition, wherein the running vibration data comprises normal vibration data and fault vibration data;
2) extracting vibration characteristics of the vibration data, including time domain characteristic extraction and frequency domain characteristic extraction, and respectively forming a normal vibration data characteristic matrix and a fault vibration data characteristic matrix;
3) performing characteristic dimension reduction processing on the normal vibration data characteristic matrix and the fault vibration data characteristic matrix to respectively obtain a normal vibration data dimension reduction matrix and a fault vibration data dimension reduction matrix;
4) normalizing the dimension reduction matrix to respectively obtain a normal vibration data effective characteristic matrix and a fault vibration data effective characteristic matrix;
5) establishing an empirical distribution function, a training sample set and a kernel function based on the effective characteristic matrix of the normal vibration data, establishing a support vector machine probability estimation model, solving the probability density value of each sample point of the normal vibration data, and taking the minimum probability density value as a single stable working condition probability threshold value;
6) performing the operation of the step 5) based on the effective characteristic matrix of the fault vibration data in the step 4, solving the probability density value of each sample point of the fault vibration data to solve the probability density value of each sample point of the fault vibration data for checking the effectiveness of the single stable working condition probability threshold, specifically, solving to obtain the probability density value of normal data by establishing a support vector machine probability density model, taking the minimum probability density value as the vibration probability threshold, setting the effectiveness of the probability density threshold for checking, and obtaining a coefficient vector (β) based on the characteristics of the normal data1，β2,…，βl) And support vector probabilistic regression estimation
Obtaining the probability density value of the fault sample point, comparing the vibration probability threshold value with the probability density value corresponding to the fault sample point, and when the fault sample point is in faultWhen the probability density value is smaller than the vibration probability threshold value, the probability distribution of the fault sample is not the probability distribution of the normal sample, and the fault sample can be regarded as abnormal, so that fault alarm is realized. When the probability density values of the fault samples are smaller than the vibration probability threshold, the vibration probability threshold can give an early warning to all the fault samples, and the vibration probability threshold is effective.
2. The method of claim 1, wherein the method for early warning of the failure of the centrifugal pump based on the probability density estimation of the support vector machine further comprises the following steps:
7) and changing the working condition of the centrifugal pump, repeating the operation of the steps 1-6, and respectively establishing probability threshold values under different working conditions.
3. A centrifugal pump failure early warning method according to claim 1 or 2, characterized in that: the time domain characteristics in the step 2 comprise kurtosis, root mean square value, maximum value, minimum value, mean value, standard deviation, rectified mean value, kurtosis factor, waveform factor and impulse factor, and the frequency domain characteristics comprise barycentric frequency, root mean square frequency, frequency standard deviation, total energy characteristics and energy ratio characteristics of each frequency band.
4. A centrifugal pump failure early warning method according to claim 1 or 2, characterized in that: and 3, performing feature dimension reduction processing in the step 3 by adopting a PCA feature dimension reduction method.
5. A centrifugal pump failure early warning method according to claim 1 or 2, characterized in that: and 3, determining the dimensionality after the dimensionality reduction treatment in the step 3 to be 3 or 2 according to the accumulated contribution rate. After the characteristic matrix is subjected to standardization processing, the covariance matrix is solved, then the characteristic of the covariance matrix is decomposed to obtain characteristic values, the characteristic values are sorted from large to small, the percentage of the sum of the first characteristic values in the sum of the total characteristic values is the contribution rate, the contribution rate of the first 3 characteristic values is more than 90% under the single stable working condition of the centrifugal pump, and the contribution rate of the first 2 characteristic values is more than 90% under the multiple working conditions.
6. A centrifugal pump failure early warning method according to claim 1 or 2, characterized in that: the normalization processing in the step 4 is to use the mean value and the variance in the normal vibration data dimension reduction matrix as reference numbers, and to subtract the mean value from each data in the normal and fault vibration data dimension reduction matrix and divide the difference by the square.
7. A centrifugal pump failure early warning method according to claim 1 or 2, characterized in that: the solving of the probability density value of each sample point of the normal vibration data in the step 5 is to solve by using a mathematical quadratic programming problem by using a method for solving an indeterminate problem.
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