CN116641941A - Hydraulic system early fault dynamic detection method based on typical variable analysis - Google Patents
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Abstract
The application relates to a dynamic detection method for early faults of a hydraulic system based on typical variable analysis. The method comprises the following steps: collecting working parameters of a hydraulic system of the hydraulic system as a sample data set, carrying out standardized data preprocessing operation on the sample data set to obtain a preprocessed sample data set, constructing two groups of adjacent observation vectors at k time and observation matrixes corresponding to the two groups of observation vectors according to the preprocessed sample data set, analyzing covariance and cross covariance of the observation matrixes, carrying out singular value decomposition of a Hank matrix, and decomposing according to the singular valuesAnalyzing the result and covariance, determining a projection matrix, dividing the projection matrix into two orthogonal subspaces, constructing a state subspace with correlation, and analyzing Hotelling's T at the time point of k by the residual subspace 2 The value and Q statistics and a preset threshold value T UCL 2 And Q UCL And comparing to judge whether the current hydraulic system is in a fault state, thereby improving the accuracy of early fault detection of the dynamic hydraulic system.
Description
Technical Field
The application relates to the technical field of hydraulic system fault detection, in particular to a hydraulic system early fault dynamic detection method based on typical variable analysis.
Background
In modern industry, the influence of hydraulic systems on various engineering equipment is increasingly deepened, and the hydraulic systems have been widely applied to the fields of manufacturing, transportation, construction, energy, agriculture and the like, such as production platforms, vehicle-mounted drilling rigs, mining fully-mechanized mining supports and the like, due to the simple structure, convenient operation and strong output capability. In practical applications, hydraulic systems often operate under a plurality of complex working conditions, so that the possibility of various faults of the hydraulic systems is greatly increased. Therefore, the advanced state monitoring technology plays a vital role in the reliable operation of the hydraulic system, can timely find abnormal deviation caused by component faults, and guides staff to take effective maintenance measures so as to keep the hydraulic system in a high-performance state.
The hydraulic system can be divided into three fault types of burst, intermittent and initial according to the fault evolution characteristics of the hydraulic system. At present, most of the existing research results are focused on monitoring sudden and intermittent faults of a hydraulic system, but the research on an early fault detection method still has a great defect, which brings great hidden trouble to the normal operation of the hydraulic system. Since early failure of a hydraulic system is typically manifested as slow degradation of system performance, if not found in time, the severity of the early failure will increase further, ultimately leading to catastrophic failure of the system.
Through the document search of the prior art, chinese patent publication No. CN202110647378.0, publication date 2021.08.20, patent name: the patent application discloses a real-time early warning method for early faults of a mine hydraulic support system, which comprises the following steps: the application discloses a real-time early warning method for early faults of a mine hydraulic support system, which comprises two stages of offline training and online monitoring, wherein the offline training determines the threshold value of a health index of the hydraulic support system, the online monitoring stage collects working parameters of the hydraulic support system in real time, and the Hotelling's and statistic of the working parameters are compared with the threshold value of the health index to judge whether the hydraulic support system has faults; and taking abnormal change of the correlation between the working parameters of the hydraulic support system as early failure characteristics of the hydraulic support system, projecting sample data of the standardized working parameters of the hydraulic support system into a principal component subspace and a residual subspace by adopting a principal component analysis method, and respectively constructing Hotelling's and statistics on the two subspaces for quantitatively describing the degree of the correlation between the working parameters. The defects are that: the diagnosis method can only detect weak early fault signals, does not consider the time correlation of observed data and the non-Gaussian property of working parameters, and causes insufficient sensitivity and accuracy of early fault detection of the dynamic hydraulic system, so that workers cannot be effectively guided to maintain the hydraulic system according to conditions.
The hydraulic system is in practice a time-varying system, the state of the former moment usually having a great influence on the working state of the latter moment (i.e. the parameters are strongly autocorrelation). In addition, there is uncertainty in load disturbance and system parameters, and the observation result of the system usually shows non-Gaussian characteristics, which makes it difficult to effectively acquire the dynamic characteristics of the hydraulic system only by assuming time independence and Gaussian, so that principal component analysis and partial least squares technology are not suitable for fault detection of a nonlinear dynamic system. The existing principal component analysis and partial least squares improvement technology has been successfully applied to dynamic systems, namely dynamic principal component analysis and dynamic partial least squares, but the extraction of principal components is not necessarily the least dynamic representation, so that when hysteresis variables are involved, anomaly detection is more complex, and the early failure dynamic detection capability is greatly reduced.
Therefore, the accuracy of early fault detection of the current dynamic hydraulic system is low.
Disclosure of Invention
Based on the above, it is necessary to provide a hydraulic system early failure dynamic detection method based on typical variable analysis, which can improve the accuracy of early failure detection of a dynamic hydraulic system.
A hydraulic system early failure dynamic detection method based on typical variable analysis, the method comprising:
acquiring hydraulic system working parameters of a hydraulic system in a preset time period in real time as a sample data set, wherein the hydraulic system working parameters comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature;
carrying out standardized data preprocessing operation on the sample data in the sample data set to obtain a preprocessed sample data set;
constructing observation vectors y adjacent to k time according to the preprocessed sample data set p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y f,k Corresponding observation matrix Y f ；
According to the observation matrix Y p And an observation matrix Y f Analyzing the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp ；
Based on the covariance sigma pp The covariance sigma ff The cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out, and a singular value decomposition result is obtained;
based on the singular value decomposition result and the observation matrix Y p Covariance sigma of (2) pp Analysis is performed to determine a projection matrix J x and F；
according to the projection matrix J x And F, to observe vector y p,k Dividing into two orthogonal subspaces, constructing a state subspace z with correlation k The rest is residual sub-spaceInterval e k ；
According to state subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 Values of (2)Sum Q statistics Q k ；
The Hotelling's T 2 Values of (2)Sum Q statistics Q k And a preset threshold value T UCL 2 and QUCL Comparing when->Or Q k ＞Q UCL And when the current hydraulic system is judged to be in a fault state, otherwise, the current hydraulic system is judged to be in a normal state.
In one embodiment, the data normalization preprocessing operation expression is:
wherein μ is the mean vector of the random variables, μ= [ μ ] 1 ,…,μ i …,μ n ]，∈ i I epsilon 1,2, …, n and n are the number of sample data in the sample data; d (D) σ As a matrix of variances of the random variables, the variance of the ith random variable, X is the sample data, and X is the sample data after preprocessing.
In one embodiment, the method constructs the observation vectors y adjacent to each other at the k moment according to the preprocessed sample data set p,k And viewingMeasuring vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y p,k Corresponding observation matrix Y f Comprising:
according to the preprocessed sample data set, two groups of observation vectors y adjacent at the time k p,k and yf,k The analytical formulas of (a) are respectively as follows:
wherein p and f are two sets of observation vectors y, respectively p,k and yf,k Length, y of k For sample data at time k, q is the amount of hysteresis in the time window,is a real number, m is the length of the time window;
two groups of observation vectors y p,k and yf,k Respectively defined as a column matrix form to obtain two groups of observation matrixes Y p and Yf Observation matrix Y p and Yf The expressions of (2) are respectively:
wherein M is the number of observation vectors in the observation matrix, m=n-2q+1, n is the number of sample data in the sample data set.
In one embodiment, the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp The expressions of (2) are respectively:
wherein the superscript T denotes a transpose.
In one embodiment, the step of generating the second signal is based on the covariance Σ pp Covariance sigma ff Sum of cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the expression is:
wherein U is the left singular column vector of H, V is the right singular column vector of H, and D is the diagonal matrix of ordered singular values.
In one embodiment, the projection matrix J x And F has the expression:
wherein I is an identity matrix, V x Is a reduction matrix consisting of the first x columns of V.
In one embodiment, the state machineSpace z k And residual subspace e k The expressions of (2) are respectively:
wherein ,Vx About Jian Juzhen, which is composed of the first x columns of V, I is the identity matrix.
In one embodiment, the state-dependent subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 And the expression of the Q statistic is:
wherein ,hotelling's T at time k 2 Value, Q k Is the Q statistic at the k time point.
In one embodiment, the preset threshold value T UCL 2 and QUCL The training method is obtained by offline training, and the training mode is as follows:
collecting hydraulic system working parameters of a hydraulic system as a training sample data set, wherein the hydraulic system working parameters comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature;
carrying out standardized data preprocessing operation on the training sample data in the training sample data set to obtain a preprocessed training sample data set;
defining a plurality of time nodes t according to the preprocessed training sample data set, and constructing observation vectors y adjacent to each other at the time t for the time nodes t p,t And observation vector y f,t And an observation vector y p,t Corresponding observation matrixAnd observation vector y f,t Corresponding observation matrix->
According to the observation matrixAnd the observation matrix->Analysis of the observation matrix>Covariance +.>Observation matrix->Covariance +.>Observation matrix->And observation matrix->Cross covariance +.>
According to the covarianceCovariance->And cross covariance->Singular value decomposition of the Hank matrix H is carried out, and a singular value decomposition result is obtained;
based on the singular value decomposition result and the observation matrixCovariance +.>Analysis is carried out to determine the projection matrix-> and />
According to the projection matrix and />To observe vector y p,t Dividing into two orthogonal subspaces, constructing a state subspace with correlation +.>The rest is residual subspace->
According to state subspaceAnd residual subspace->Analysis Hotelling's T at time t 2 And Q statistics, obtaining Hotelling's T for a plurality of time nodes t 2 And Q statistics;
hotelling's T according to a plurality of time nodes t 2 And Q statistics, analyzing by adopting an adaptive kernel density estimation algorithm to obtain a preset threshold value T UCL 2 and QUCL 。
According to the hydraulic system early fault dynamic detection method based on typical variable analysis, the hydraulic system working parameters of the hydraulic system are acquired in a preset time period to serve as sample data sets, sample data in the sample data sets are subjected to standardized data preprocessing operation, a preprocessed sample data set is obtained, and observation vectors y adjacent to k time are constructed according to the preprocessed sample data set p,k And observation vector y f,k And respectively corresponding observation matrix Y p And an observation matrix Y f According to the observation matrix Y p And an observation matrix Y f Analyzing the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp Based on the covariance Σ pp The covariance sigma ff The cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the singular value decomposition result and the observation matrix Y are used for obtaining a singular value decomposition result p Covariance sigma of (2) pp Analysis is performed to determine a projection matrix J x And F, according to the projection matrix J x And F, to observe vector y p,k Dividing into two orthogonal subspaces, constructing a state subspace z with correlation k The rest is residual subspace e k Hotelling's T at the k time point was analyzed 2 Values of (2)Sum Q statistics Q k The Hotelling's T 2 Value of->Sum Q statistics Q k And a preset threshold value T UCL 2 and QUCL Comparing, when T 2 ＞T UCL 2 Or Q > Q UCL And when the current hydraulic system is judged to be in a fault state, otherwise, the current hydraulic system is judged to be in a normal state, so that the accuracy of early fault detection of the dynamic hydraulic system is improved.
Drawings
FIG. 1 is a flow diagram of a hydraulic system early failure dynamic detection method based on a typical variable analysis in one embodiment;
FIG. 2 is a graph of the effect of a conventional univariate thresholding method (Pauta criterion) on detection of oil pressure after pump on a hydraulic system;
FIG. 3 is a graph of the effect of a prior univariate thresholding method (Pauta criterion) on hydraulic system detection based on pre-filter oil pressure;
FIG. 4 is a graph of the effect of a conventional univariate thresholding method (Pauta criterion) on detection of oil pressure after a filter on a hydraulic system;
FIG. 5 is a graph of the effect of a conventional univariate thresholding method (Pauta criterion) on detection of oil temperature after a filter on a hydraulic system;
FIG. 6 shows the prior art multivariate statistical method (principal component analysis) on hydraulic system for T 2 An implementation effect diagram of the threshold value;
FIG. 7 is a graph showing the effect of a prior art multivariate statistical method (principal component analysis) on the Q threshold value of a hydraulic system;
FIG. 8 shows the method for dynamically detecting early faults of a hydraulic system based on typical variable analysis according to the present application with respect to T on the hydraulic system 2 An implementation effect diagram of the threshold value;
fig. 9 is a diagram showing the implementation effect of the dynamic detection method for early failure of the hydraulic system based on the typical variable analysis on the Q threshold value of the hydraulic system.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In one embodiment, as shown in fig. 1, a method for dynamically detecting early faults of a hydraulic system based on typical variable analysis is provided, and the method is applied to a terminal for carrying out online monitoring on the hydraulic system for example, and comprises the following steps:
step 1-1, acquiring working parameters of a hydraulic system of the hydraulic system in a preset time period in real time as a sample data set, wherein the working parameters of the hydraulic system comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature.
The preset time period may be set according to practical situations, such as the first 10 minutes, the first 20 minutes, the first 30 minutes, and so on.
In one example, the preset time period is set to the first 10 minutes, namely: and acquiring the working parameters of the hydraulic system within the first 10 minutes as a sample data set.
Common faults of the hydraulic system include pump faults, pipeline leakage and filter blockage in 3 modes; the monitored hydraulic system operating parameters included pump-after oil pressure, filter-before oil pressure, filter-after oil temperature 4 types.
And step 1-2, carrying out standardized data preprocessing operation on the sample data in the sample data set to obtain a preprocessed sample data set.
It will be appreciated that the analysis of typical variables may be facilitated by the standardized preprocessing operations performed on the collected data sample sets due to the different dimensions of the system operating parameters.
In one embodiment, the data normalization preprocessing operation expression is:
wherein μ is the mean vector of the random variables, μ= [ μ ] 1 ,…,μ i …,μ n ]，μ i I epsilon 1,2, …, n and n are the number of sample data in the sample data set; d (D) σ As a matrix of variances of the random variables, the variance of the ith random variable, X is the sample data, and X is the sample data after preprocessing.
Step 1-3, constructing the adjacent observation vectors y at the k moment according to the preprocessed sample data set p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y f,k Corresponding observation matrix Y f 。
In one embodiment, the method constructs the observation vector y adjacent at the k moment according to the preprocessed sample data set p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y p,k Corresponding observation matrix Y f Comprising:
according to the preprocessed sample data set, two groups of observation vectors y adjacent at the time k p,k and yf, The analytical formula of k is:
wherein,p and f are two sets of observation vectors y, respectively p,k and yf,k Length, y of k For sample data at time k, q is the amount of hysteresis in the time window,is a real number, m is the length of the time window;
two groups of observation vectors y p,k and yf,k Respectively defined as a column matrix form to obtain two groups of observation matrixes Y p and Yf Observation matrix Y p and Yf The expressions of (2) are respectively:
wherein M is the number of observation vectors in the observation matrix, m=n-2q+1, n is the number of sample data in the sample data set.
It will be appreciated that for a sample data set having n sample data, a total of m=n-2q+1 observation vectors can be obtained by a movement of one time window. Observation matrix Y p and Yf Respectively, are derived from the movement of a time window.
Step 1-4, according to the observation matrix Y p And an observation matrix Y f Analyzing the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp 。
In one embodiment, the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp The expressions of (2) are respectively:
wherein the superscript T denotes a transpose.
It should be appreciated that since the typical variable analysis is to build the state space of the system by finding the difference with the greatest correlation, the linear combination of the two sets of variables that are adjacent at time k. Can be obtained by setting a T (y f,k) and bT (y p,k ) The correlation of these two sets of variables, being a linearly combined coefficient vector, can be expressed as:
wherein ,∑pp 、∑ ff and ∑fp Respectively represent two groups of variables (Y p and Yf ) Is used to estimate the trend of the two sets of variables.
Thereby obtaining the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp The expressions of (2) may be:
wherein the superscript T denotes a transpose.
Step 1-5, according to the covariance Σ pp The covariance sigma ff The cross covariance Σ fp And performing singular value decomposition of the Hank matrix H to obtain a singular value decomposition result.
In one embodiment, the step of generating the second signal is based on the covariance Σ pp Covariance sigma ff Sum of cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the expression is:
wherein U is the left singular column vector of H, V is the right singular column vector of H, and D is the diagonal matrix of ordered singular values.
wherein ：
wherein r is the rank of the Hanker matrix H, and the ith singular vector u i and vi Corresponding to the coefficients of the linear combination of the system variables, σ i Is the correlation of the ith combined variable, i.e., the typical variable, i.e., 1,2 … r.
Step 1-6, according to the singular value decomposition result and theThe observation matrix Y p Covariance sigma of (2) pp Analysis is performed to determine a projection matrix J x and F.
In one embodiment, the projection matrix J x And F has the expression:
wherein I is an identity matrix, V x Is a reduction matrix consisting of the first x columns of V.
Step 1-7, according to the projection matrix J x And F, to observe vector y p,k Dividing into two orthogonal subspaces, constructing a state subspace z with correlation k The rest is residual subspace e k 。
In one embodiment, the state subspace z k And residual subspace e k The expressions of (2) are respectively:
wherein ,Vx About Jian Juzhen, which is composed of the first x columns of V, I is the identity matrix.
Wherein the state subspace is represented by the first x typical variables and represents the main characteristics of system measurement; the residual subspace is represented by the remaining representative variables, representing the remaining information of the system measurements.
Step 1-8, according to state subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 Values of (2)Sum Q statistics Q k 。
In one embodiment, the state-dependent subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 Values of (2)Sum Q statistics Q k The expression of (2) is:
wherein ,hotelling's T at time k 2 Value, Q k Is the Q statistic at the k time point.
Step 1-9, hotelling's T 2 Values of (2)Sum Q statistics Q k And a preset threshold value T UCL 2 and QUCL Comparing when->Or Q k ＞Q UCL And when the current hydraulic system is judged to be in a fault state, otherwise, the current hydraulic system is judged to be in a normal state.
Wherein, according to the fault determination rule of the hydraulic system,i.e. when the multivariate statistic->Or Q k And an abnormal alarm is issued when the data fluctuation of (1) exceeds the upper control limit.
According to the hydraulic system early fault dynamic detection method based on typical variable analysis, the hydraulic system working parameters of the hydraulic system are acquired in a preset time period and are used as sample data sets, sample data in the sample data sets are subjected to standardized data preprocessing operation, the preprocessed sample data sets are obtained, and observation vectors y adjacent at k moments are constructed according to the preprocessed sample data sets p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y f,k Corresponding observation matrix Y f According to the observation matrix Y p And an observation matrix Y f Analyzing the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp Based on the covariance Σ pp The covariance sigma ff The cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the singular value decomposition result and the observation matrix Y are used for obtaining a singular value decomposition result p Covariance sigma of (2) pp Analysis is performed to determine a projection matrix J x And F, according to the projection matrix J x And F, to observe vector y p,k Dividing into two orthogonal subspaces, constructing a state subspace z with correlation k The rest is residual subspace e k Hotelling's T at the k time point was analyzed 2 And Q statistics, the Hotelling's T 2 And Q statistics and a preset threshold value T UCL 2 and QUCL Comparing, when T 2 ＞T UCL 2 Or Q > Q UCL And when the current hydraulic system is judged to be in a fault state, otherwise, the current hydraulic system is judged to be in a normal state, so that the accuracy of early fault detection of the dynamic hydraulic system is improved.
In one embodiment, a deviceThe preset threshold value T UCL 2 and QUCL The training method is obtained by offline training, and the training mode is as follows:
step 2-1, collecting hydraulic system working parameters of a hydraulic system as a training sample data set, wherein the hydraulic system working parameters comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature.
And 2-2, carrying out standardized data preprocessing operation on the training sample data in the training sample data set to obtain a preprocessed training sample data set.
The data standardization preprocessing operation expression is as follows:
wherein μ is the mean vector of the random variables, μ= [ μ ] 1 ,…,μ i ,…,μ N ]，μ i I epsilon 1,2, …, N and N are the number of sample data in the training sample data set; d (D) σ As a matrix of variances of the random variables, variance of the ith random variable, +.>For training sample data, ++>Is the training sample data after pretreatment.
Step 2-3, defining a plurality of time nodes t according to the preprocessed training sample data set, and constructing observation vectors y adjacent to each other at the time t for the time nodes t p,t And observation vector y f,t And an observation vector y p,t Corresponding observation matrixAnd observation vector y f,t Corresponding observation matrix->
In one embodiment, the construction is performed to construct the observation vector y adjacent to the time t p,t And observation vector y f,t And an observation vector y p,t Corresponding observation matrixAnd observation vector y f,t Corresponding observation matrix->Comprising the following steps:
according to the preprocessed training sample data set, two groups of adjacent observation vectors y at the time t p,t and yf,t The analytical formulas of (a) are respectively as follows:
wherein p and f are two sets of observation vectors y, respectively p,t and yf,t Length, y of t For training sample data at time t, q is the amount of hysteresis in the time window,is a real number, m is the length of the time window;
two groups of observation vectors y p,t and yf,t Respectively defined as a column matrix form to obtain two groups of observation matrixes and />Observation matrix-> and />The expressions of (2) are respectively:
wherein M is the number of observation vectors in the observation matrix, m=n-2q+1, N is the number of training sample data in the training sample data set.
It will be appreciated that for a training sample data set having N training sample data, a total of m=n-2q+1 observation vectors can be obtained by a movement of one time window. Observation matrix and />Respectively, are derived from the movement of a time window.
Step 2-4, according to the observation matrixAnd the observation matrix->Analysis of the observation matrix>Covariance of (2)Observation matrix->Covariance +.>Observation matrix->And observation matrix->Cross covariance +.>
In one embodiment, the observation matrixCovariance +.>The observation matrix->Covariance +.>Said observation matrix->And the observation matrix->Cross covariance +.>The expressions of (2) are respectively:
/>
wherein the superscript T denotes a transpose.
Step 2-5, according to the covarianceCovariance->And cross covariance->And performing singular value decomposition of the Hank matrix H to obtain a singular value decomposition result.
In one embodiment, the said method is based on the covarianceCovariance->And cross covariance->Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the expression is:
wherein U is the left singular column vector of H, V is the right singular column vector of H, and D is the diagonal matrix of ordered singular values.
Step 2-6, according to the singular value decomposition result and the observation matrixCovariance +.>Analysis is carried out to determine the projection matrix-> and />
In one embodiment, the projection matrix and />The expression of (2) is:
wherein I is an identity matrix, V x Is a reduction matrix consisting of the first x columns of V.
Step 2-7, according to the projection matrix and />To observe vector y p,t Dividing into two orthogonal subspaces, constructing a state subspace with correlation +.>The rest is residual subspace->
In one embodiment, the state subspaceAnd residual subspace->The expressions of (2) are respectively:
wherein ,Vx About Jian Juzhen, which is composed of the first x columns of V, I is the identity matrix.
Step 2-8, according to the state subspaceAnd residual subspace->Analysis Hotelling's T at time t 2 And Q statistics, obtaining Hotelling's T for a plurality of time nodes t 2 And Q statistics.
In one embodiment, the state-dependent subspaceAnd residual subspace->Analysis Hotelling's T at time t 2 The value T of (2) t 2 Sum Q statistics Q t The expression of (2) is:
wherein ,Tt 2 Hotelling's T at time t 2 Value, Q t Is the Q statistic at time t.
Step 2-9 Hotelling's T according to a plurality of time nodes t 2 And Q statistics, analyzing by adopting an adaptive kernel density estimation algorithm to obtain a preset threshold value T UCL 2 and QUCL 。
It should be understood that the number of sample data in the training sample data set is N, each time node adopts one sample data, and each time node is regarded as a primary time node t correspondingly, and corresponding Hotelling's T is calculated 2 And Q statistics, N Hotelling's T can be obtained 2 And N Q statistics.
The analysis principle of the self-adaptive kernel density estimation algorithm is as follows:
setting an initial bandwidth h 0 For a set of random variables { u } 1 ,u 2 ,...,u i ...,u N I e 1,2, …, N, local bandwidth factor τ is obtained by calculating each random variable u i The formula is as follows:
wherein ,for the initial adaptive probability density estimation result, u is the current random variable and h is the bandwidth determined during the kernel density estimation. K (·) represents a kernel function for fitting the probability distribution of training sample data, the application selects a Gaussian kernel function with the formula:
where e is a natural constant and c is a variable in a gaussian kernel function.
Step 2-9-2: by local bandwidth factor tau i Modifying the initial bandwidth h 0 Obtaining a final adaptive probability density estimation result
Calculating each random variable u to obtain local bandwidth factor tau i The formula is as follows:
where α is a sensitivity factor.
By local bandwidth factor tau i Modifying the initial bandwidth h 0 Obtaining a final adaptive probability density estimation resultFinal adaptive probability density estimation>The expression of (2) is:
wherein at a preset confidence levelUnder, estimating the result according to the final adaptive probability density +.>Derivation of Hotelling's T 2 And threshold value of Q statistic:
at a preset confidence levelNext, the final adaptive probability density estimation result is used +.>Each Hotelling's T was analyzed 2 Probability density estimation results corresponding to the value of each Q statistic and using Hotelling T according to the probability density estimation results 2 And a threshold value of Q statistics, from each Hotelling's T 2 Corresponding threshold values are determined from the values of (1) and (b) of each Q statistic, hotelling T 2 And the analytical formula for the threshold value of the Q statistic is:
it should be appreciated that for probability density functionsCorresponding Hotelling T 2 And Q statistics threshold value analysis, setting the variable u in the adaptive probability density estimation as Hotelling T at the time T 2 And Q statistics at N Hotelling's T 2 From the value of (a) and the value of the N Q statistics, hotelling's T is determined by the analytical formula of the threshold value 2 And a threshold value for Q statistics. />
It should be appreciated that the above is based on a typical variable componentThe analyzed hydraulic system early fault dynamic detection method adopts a mode of combining typical variable analysis and a self-adaptive kernel density function algorithm to carry out early fault dynamic detection, so that the dynamic detection capability of the hydraulic system early fault can be improved; construction of state subspace z with strong correlation based on observation vector by classical variable analysis k And residual subspace e k The problem of time correlation of the observed variable is solved, and a basis is provided for dynamic detection and index construction of the hydraulic system; according to the difference of sample point density distribution and non-Gaussian property of working parameters, the bandwidth h of a probability density function is adaptively adjusted by adopting an adaptive kernel density estimation algorithm, so that the probability density estimation value is ensured to be closer to a true value, and the threshold value T entering early failure can be accurately determined UCL 2 and QUCL The accuracy of early failure dynamic detection of the hydraulic system can be effectively improved.
In one embodiment, the present application takes as an example a hydraulic lubrication system of a large marine power plant, considering that the working state of the lubrication system is critical to the large marine power plant, and the lubrication oil pressure and temperature are the key parameters for the control of the lubrication system. Considering the frequency and severity of faults occurring, three types of progressive faults are common in marine power plant hydraulic lubrication systems, namely "pump failure", "pipe leakage" and "filter plugging". The performance of the hydraulic lubrication system is described by four key operating parameters, namely "pump-after-oil pressure", "filter-before-oil pressure", "filter-after-oil pressure" and "filter-after-oil temperature", respectively. The working parameters are collected by a PCI-6225 data collection system, and the collected data is preprocessed by median filtering so as to reduce measurement noise. The ship power device works under three typical working conditions of 1800r/min full load of 25%, 50% and 75%, and a training data set and a testing data set are constructed by utilizing collected system working parameters. The training data set consists of normal data for determining control limits for system parameters, and the test data set consists of normal data and fault data for evaluating the performance of the fault detection method.
The application builds a hydraulic system experiment test platform, and tests four types of pump failure, pipeline leakage, filter blockage and normal under three working conditions of 25%, 50% and 75% respectively. For ease of description and analysis, taking "pump failure" at 50% condition as an example, a univariate thresholding method (Pauta criterion), a multivariate statistical method (principal component analysis) and a multivariate statistical method (typical variable analysis) are used for description, respectively.
The existing univariate thresholding method (Pauta criterion) implements effect maps on hydraulic systems as shown in FIGS. 2-5. The first 100 blue points are normal data, the last 400 red points are fault data, and the upper and lower red dotted lines respectively correspond to the upper limit and the lower limit of the detection threshold. As can be seen in fig. 2-5, a small fraction of the faults can be detected in the "post-filter oil pressure" and "post-filter oil temperature" operating parameters, but the remaining two conditions are almost undetectable. The total detection rate is 36%, and the detection effect is not ideal.
The prior art multivariate statistical methods (principal component analysis) as shown in fig. 6-7 implement effect graphs on hydraulic systems. In the principal component analysis and detection method based on Hotelling's statistics, a black solid line is a variation waveform of the statistics, and a red dotted line is a threshold value of the statistics obtained by training. It can be seen from fig. 6-7 that most faults can be effectively detected by using the 4 operating parameters of the method, but a large number of fault data points are lower than the threshold value, so that effective detection cannot be obtained. The total detection rate is 74.75%, and the detection result is relatively common.
The effect of the multivariate statistical method of the present application (typical variable analysis) on hydraulic systems is illustrated in figures 8-9. It can be seen in the typical variate analysis detection method based on Hotelling's statistics that of the 4 operating parameters, no matter for Hotelling's T 2 And Q statistics, wherein almost all fault data points are above a threshold value, only a few fault data points are below the threshold value, and the detection rate is 86.75%. The normal data points are all lower than the threshold value, and the misdiagnosis rate is 0. Compared with the Pauta criterion and the principal component analysis method, the detection rate of the typical variable analysis method is obviously improved, the comprehensive detection effect is ideal, and the expected target is met.
In summary, aiming at the defects of the existing method in terms of time independence of assumed observation data and Gaussian performance of working parameters, the method for dynamically detecting the early faults of the hydraulic system based on typical variable analysis is provided. Taking a hydraulic lubrication system of a ship power plant as an example, the feasibility of the application is illustrated. Assuming three typical workloads and speeds and three common hydraulic system faults, the Pauta criterion and principal component analysis method based on multivariate statistical process monitoring are compared to a method that combines typical variable analysis with adaptive kernel density estimation. The result shows that the early failure which is difficult to detect by the traditional Pauta criterion can be effectively detected by adopting the multivariate statistical process monitoring method, and the detection rate of the hydraulic system can be further improved by utilizing the multivariate statistical process monitoring technology combining the self-adaptive kernel density estimation and the typical variable analysis, so that the advancement of the application is illustrated. The application can obviously improve the detection rate of early faults of the hydraulic system and provides an effective technology for monitoring the state of the hydraulic system.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (9)
1. A hydraulic system early failure dynamic detection method based on typical variable analysis, the method comprising:
acquiring hydraulic system working parameters of a hydraulic system in a preset time period in real time as a sample data set, wherein the hydraulic system working parameters comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature;
carrying out standardized data preprocessing operation on the sample data in the sample data set to obtain a preprocessed sample data set;
constructing observation vectors y adjacent to k time according to the preprocessed sample data set p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y f,k Corresponding observation matrix Y f ；
According to the observation matrix Y p And an observation matrix Y f Analyzing the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp ；
Based on the covariance sigma pp Said covariance v ff The cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out, and a singular value decomposition result is obtained;
based on the singular value decomposition result and the observation matrix Y p Covariance sigma of (2) pp Analysis is performed to determine a projection matrix J x and F；
according to the projection matrix J x And F, to observe vector y p,k Dividing into two orthogonal subspaces, constructing a state subspace z with correlation k The rest is residual subspace e k ；
According to state subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 Values of (2)Sum Q statistics Q k ；
The Hotelling's T 2 Values of (2)Sum Q statistics Q k And a preset threshold value T UCL 2 and QUCL Comparing whenOr Q k ＞Q UCL And when the current hydraulic system is judged to be in a fault state, otherwise, the current hydraulic system is judged to be in a normal state.
2. The method of claim 1, wherein the data normalization preprocessing operation expression is:
wherein μ is the mean vector of the random variables, μ= [ μ ] 1 ,…,μ i ,…,μ n ]，μ i I epsilon 1,2, …, n and n are the number of sample data in the sample data set; d (D) σ As a matrix of variances of the random variables, the variance of the ith random variable, X is the sample data, and X is the sample data after preprocessing.
3. The method according to claim 2, wherein said constructing observation vectors y adjacent at time k from said preprocessed sample data set p,k And observation vector y f,k And an observation vector y p,k Corresponding observation matrix Y p And observation vector y p,k Corresponding observation matrix Y f Comprising:
according to the preprocessed sample data set, two groups of observation vectors adjacent at the k momenty p,k and yf,k The analytical formulas of (a) are respectively as follows:
wherein p and f are two sets of observation vectors y, respectively p,k and yf,k Length, y of k For sample data at time k, q is the amount of hysteresis in the time window,is a real number, m is the length of the time window;
two groups of observation vectors y p,k and yf,k Respectively defined as a column matrix form to obtain two groups of observation matrixes Y p and Yf Observation matrix Y p and Yf The expressions of (2) are respectively:
wherein M is the number of columns of the observation matrix, m=n-2q+1, n is the number of sample data in the sample data set.
4. A method according to claim 3, characterized in that the observation matrix Y p Covariance sigma of (2) pp The observation matrix Y f Covariance sigma of (2) ff The observation matrix Y p And the observation matrix Y f Cross covariance sigma of (2) fp The expressions of (2) are respectively:
wherein the superscript T denotes a transpose.
5. The method according to claim 4, wherein said determining said covariance Σ pp Covariance sigma ff Sum of cross covariance Σ fp Singular value decomposition of the Hank matrix H is carried out to obtain a singular value decomposition result, and the expression is:
wherein U is the left singular column vector of H, V is the right singular column vector of H, and D is the diagonal matrix of ordered singular values.
6. The method of claim 5, wherein the projection matrix J x And F has the expression:
wherein I is an identity matrix, V x Is composed of the front x columns of VIs a reduced matrix of (a).
7. The method of claim 6, wherein the state subspace z k And residual subspace e k The expressions of (2) are respectively:
wherein ,Vx About Jian Juzhen, which is composed of the first x columns of V, I is the identity matrix.
8. The method of claim 7, wherein the state-dependent subspace z k And residual subspace e k Hotelling's T at the k time point was analyzed 2 The value T of (2) k 2 Sum Q statistics Q k The expression of (2) is:
wherein ,hotelling's T at time k 2 Value, Q k Is the Q statistic at the k time point.
9. The method according to claim 8, wherein the preset threshold value T UCL 2 and QUCL Obtaining by offline trainingThe training mode is as follows:
collecting hydraulic system working parameters of a hydraulic system as a training sample data set, wherein the hydraulic system working parameters comprise: pump-after oil pressure, filter-before oil pressure, filter-after oil pressure, and filter-after oil temperature;
carrying out standardized data preprocessing operation on the training sample data in the training sample data set to obtain a preprocessed training sample data set;
defining a plurality of time nodes t according to the preprocessed training sample data set, and constructing observation vectors y adjacent to each other at the time t for the time nodes t p,t And observation vector y f,t And an observation vector y p,t Corresponding observation matrixAnd observation vector y f,t Corresponding observation matrix->
According to the observation matrixAnd the observation matrix->Analysis of the observation matrix>Covariance +.>Observation matrixCovariance +.>Observation matrix->And observation matrix->Cross covariance +.>
According to the covarianceCovariance->And cross covariance->Singular value decomposition of the Hank matrix H is carried out, and a singular value decomposition result is obtained;
based on the singular value decomposition result and the observation matrixCovariance +.>Analysis is carried out to determine the projection matrix-> and />
According to the projection matrix and />To observe vector y p,t Dividing into two orthogonal subspaces, constructing a state subspace with correlation +.>The rest is residual subspace->
According to state subspaceAnd residual subspace->Analysis Hotelling's T at time t 2 And Q statistics, obtaining Hotelling's T for a plurality of time nodes t 2 And Q statistics;
hotelling's T according to a plurality of time nodes t 2 And Q statistics, analyzing by adopting an adaptive kernel density estimation algorithm to obtain a preset threshold value T UCL 2 and QUCL 。
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