CN110175682A - A kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization - Google Patents
A kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization Download PDFInfo
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Abstract
The invention discloses a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization, this method comprises: obtaining primary data matrix；The primary data matrix includes normal data sample matrix and fault data sample matrix；By Nonlinear Mapping φ by the primary data space reflection into implicit features space, and in implicit features space carry out nonlinear characteristic transformation；Malfunction monitoring model is established using the primary data matrix as training data；Obtain test data；The test data is inputted in the malfunction monitoring model, On-line Fault monitoring is carried out to the test data.Through the invention, it is optimized by kernel functional parameter of the Chaos particle swarm optimization algorithm to core pivot element analysis, to find optimal nonlinear characteristic, and monitor goes out nonlinear fault, to reduce monitoring delay time, improves malfunction monitoring precision.
Description
Technical field
The present invention relates to malfunction monitoring field, in particular to a kind of optimization core pivot element analysis failure based on Chaos-Particle Swarm Optimization
Monitoring method.
Background technique
In recent years, core pivot element analysis method (Kernel Principal Component Analysis, KPCA) conduct
A kind of advanced pca method has been widely used in monitoring the nonlinear characteristic of industrial process.KPCA passes through non-linear
Original input space is mapped to high-dimensional feature space by mapping function, when carrying out nonlinear characteristic transformation, the selection of kernel function
The Monitoring Performance of KPCA can be seriously affected, so selecting suitable kernel function is its key.
The determination of KPCA kernel function mainly has the estimation of k cross validation error, leaving-one method error estimation, but they at present
It is only limitted to existing general kernel function and the predefined parameter optimization based on experience.It is proposed that being solved using gradient descent method
Kernel optimization problem, but the algorithm needs calculating target function to the local derviation of Optimal Parameters, if objective function is to some parameter
When local derviation is not present or can not solve because calculating complexity, kernel optimization cannot be realized using gradient descent method.Somebody
It proposes using Revised genetic algorithum to kernel function optimizing, but genetic algorithm has the complex process of coding and genetic manipulation.
Further, using particle swarm algorithm (Particle Swarm Optimization, PSO) optimizing ability, some researchers will
PSO is applied to the Selection of kernel function of KPCA, but PSO easily falls into local optimum；In view of this, new construction Kernel-Based Methods, i.e. mixed
Synkaryon function is suggested, however, this method can not calculate data characteristics and monitoring model, in failure when selecting kernel function
There are false retrievals and missing inspection in monitoring.
Summary of the invention
The present invention provides a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization, passes through chaotic particle
Colony optimization algorithm optimizes the kernel functional parameter of core pivot element analysis, to find optimal nonlinear characteristic, and accurately supervises
Nonlinear fault is measured, to reduce monitoring delay time, improves malfunction monitoring precision.
According to an aspect of the invention, there is provided a kind of optimization core pivot element analysis malfunction monitoring based on Chaos-Particle Swarm Optimization
Method, comprising the following steps: obtain primary data matrix；The primary data matrix includes normal data sample matrix and failure
Data sample matrix；
By Nonlinear Mapping φ by the primary data space reflection into implicit features space, and implicit features sky
Between middle progress nonlinear characteristic transformation；
Malfunction monitoring model is established using the primary data matrix as training data；
Obtain test data；
The test data is inputted in the malfunction monitoring model, On-line Fault monitoring is carried out to the test data.
Preferably, malfunction monitoring model is established using the primary data matrix as training data, comprising the following steps: logical
Cross formulaIt is normal data by the primary data matrix conversion, and standardizes to the normal data
Processing；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,σm 2) be variable standard deviation
Poor diagonal matrix；
Pass through formulaEstablish mixed kernel function；
Optimize the mixed kernel function parameter by Chaos particle swarm optimization algorithm；
Pass through formula Kij=(φ (Xi) φ(Xj))=k (Xi,Xj) calculate nuclear matrix K；
Pass throughCentralization is carried out to the implicit features space；
(λ is calculated by formula N λ α=K αk,αk), k=1 ..., p, and pass through λi(αi αiThe specification α of)=1k；
Pass through formulaThe normal data is mentioned
Take k-th of characteristic component；
Pass through formulaWithCalculate the normal data
Monitoring and statistics amount T2And SPE；
Pass throughWithCalculate the T of the normal data2And SPE
The control of statistic limits.
Preferably, the test data is inputted in the malfunction monitoring model, failure is carried out to the test data and is existed
Line monitoring, comprising the following steps: pass through formulaIt is new test data vector by the test data conversion,
And standardization processing is carried out to the new test data vector；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ
=diag (σ1 2,σ2 2,…,σm 2) be variable standard deviation diagonal matrix；
To given test vector xt, utilize [kt]j=[kt(Xt,Xj)] calculate core vector kt∈R1×N, wherein XjIt is normally to grasp
Make data；
Calculate kt,1t=1/N × [1 ..., 1] ∈ R1×N；
Pass throughCalculate the nonlinear principal component of the new test data vector；
Calculate the statistic T of the new test data vector2And SPE；
Monitor the T of the new test data vector2The T of the normal data whether is all larger than with the value of SPE2It unites with SPE
The control of metering limits；
If it is, the test data is abnormal, equipment belonging to the test data breaks down；
If it is not, then the test data is normal, equipment belonging to the test data is without failure.
Preferably, before optimizing the mixed kernel function parameter by Chaos particle swarm optimization algorithm, this method further includes following
Step: the fitness function that definition is suitble to the normal data sample matrix and fault data sample matrix to separate；The adaptation
Spend function is defined as: Fj=ln | Sb/Sw|；WhereinIt is the Scatter Matrix between class；It is the Scatter Matrix in class；L is the number of class；CiIt is the geometric center of each class,It is the geometric center at all kinds of centers；X is data vector.
Preferably, the algorithmic procedure of the Chaos particle swarm optimization algorithm are as follows: 1) parameter is set；Accelerator coefficient c1、c2, group size N, most
Greatly, minimum inertia weight: wminAnd wmax；Adaptive inertia weight coefficient AIWF is defined as:
Wherein iter is the number of iterations；
5) particle i each in population is initialized；Xi, Vi, fi(objective function predicts that error is minimum), pg(in particle
With the particle of optimal function value in group) and pi(particle itself memory)；
6) implement search；Search pg；Search pi；Utilize formulaAnd Xi(t+1)
=Xi(t)+Vi(t+1) X of each particle is updatedi, Vi；Assess the objective function f of all particlesi；
7) retain preceding 20% particle；
5) the chaos local search for implementing particle, updates pgAnd pi；
6) optimum solution that output search is found；
7) search space is reduced；xmin,j=max { xmin,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1xmax,j=min
{xmax,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1；
8) it generates 80% new particle at random in the search space of diminution, and they is assessed.
Preferably, implement the chaos local search of particle, update pgAnd piInclude: that (1) enables k=0, utilizes relational expressionDecision variable xj (k)(j=1,2 ... N) it is mapped to Chaos Variable cxj (k)；(2) it carries out
Next iteration, with cxj k+1=4cxj k(1-cxj k) and xj k+1=xmin,j+cxj k+1(xmax,j-xmin,j) calculate cxj (k+1)；(3)
New solution is assessed with decision variable；(4) if new solution is more preferable than current solution, or reach pre-
The maximum number of iterations of definition then exports new solution with Chaos particle swarm optimization algorithm；Otherwise, k=k+1 is enabled to return to (2) step.
Compared with prior art, beneficial effects of the present invention are as follows:
Through the invention, it is optimized by kernel functional parameter of the Chaos particle swarm optimization algorithm to core pivot element analysis, with
It was found that optimal nonlinear characteristic, and it is accurate and effective monitor out of order generation in time, to reduce monitoring delay time,
Improve malfunction monitoring precision.
Detailed description of the invention
The drawings described herein are used to provide a further understanding of the present invention, constitutes part of this application, this hair
Bright illustrative embodiments and their description are used to explain the present invention, and are not constituted improper limitations of the present invention.In attached drawing:
Fig. 1 is a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization according to an embodiment of the present invention
Flow chart；
Fig. 2 is the flow chart according to an embodiment of the present invention for establishing malfunction monitoring model；
Fig. 3 is the flow chart according to an embodiment of the present invention that On-line Fault monitoring is carried out to test data；
Fig. 4 is the according to embodiments of the present invention one another optimization core pivot element analysis malfunction monitoring based on Chaos-Particle Swarm Optimization
The flow chart of method；
Fig. 5 is the fitness curve of Chaos particle swarm optimization algorithm；
Fig. 6 is the KPCA monitoring result figure using RBF kernel function；
Fig. 7 is the monitoring result figure using CPSO-KPCA optimization nuclear parameter.
Specific embodiment
Below in conjunction with attached drawing of the present invention, technical solution of the present invention is described, but described embodiment is only
A part of the embodiment of the present invention, based on the embodiments of the present invention, those of ordinary skill in the art are not making creative labor
Every other embodiment obtained under the premise of dynamic, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization, Fig. 1
It is a kind of flow chart of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization according to an embodiment of the present invention, such as
Shown in Fig. 1, comprising the following steps:
Step S101: primary data matrix is obtained；Primary data matrix includes normal data sample matrix and fault data
Sample matrix；
Step S102: by Nonlinear Mapping φ by primary data space reflection into implicit features space, and implicit
Nonlinear characteristic transformation is carried out in feature space；
Step S103: malfunction monitoring model is established using primary data matrix as training data；
Step S104: test data is obtained；
Step S105: by test data input fault monitoring model, On-line Fault monitoring is carried out to test data.
In implementation process, in step s 103, malfunction monitoring model is established using primary data matrix as training data
Specific embodiment are as follows: pass through formulaIt is normal data by primary data matrix conversion, and to normal data
Carry out standardization processing；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,σm 2) it is to become
The standard deviation diagonal matrix of amount；Pass through formulaEstablish mixed nucleus letter
Number；Optimize mixed kernel function parameter by Chaos particle swarm optimization algorithm；Pass through formula Kij=(φ (Xi) φ(Xj))=k (Xi,Xj)
Calculate nuclear matrix K；Pass throughCentralization is carried out to implicit features space；Pass through formula N λ α=K α
Calculate (λk,αk), k=1 ..., p, and pass through λi(αi αiThe specification α of)=1k；Pass through formulaK-th of characteristic component is extracted to normal data；Pass through
FormulaWithCalculate the monitoring and statistics amount T of normal data2With
SPE；Pass throughWithCalculate the T of normal data2With SPE statistic
Control limit.
The flow chart for establishing malfunction monitoring model using primary data matrix as training data is as shown in Figure 2.
In step s105, by test data input fault monitoring model, On-line Fault monitoring is carried out to test data
Specific embodiment are as follows: pass through formulaIt is new test data vector by test data conversion, and to new
Test data vector carries out standardization processing；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,
σ2 2,…,σm 2) be variable standard deviation diagonal matrix；To given test vector xt, utilize [kt]j=[kt(Xt,Xj)] calculate
Core vector kt∈R1×N, wherein XjIt is normal operational data；Calculate kt,1t=1/N ×
[1,…,1]∈R1×N；Pass throughCalculate the non-linear master of new test data vector
Member；Calculate the statistic T of new test data vector2And SPE；Monitor the T of new test data vector2It is whether equal with the value of SPE
Greater than the T of normal data2Control with SPE statistic limits；If it is, test data is abnormal, equipment belonging to test data
It breaks down；If it is not, then test data is normal, equipment belonging to test data is without failure.
In step s 103, further, before by Chaos particle swarm optimization algorithm optimization mixed kernel function parameter, it is also necessary to fixed
The fitness function of justice suitable normal data sample matrix and the separation of fault data sample matrix；Fitness function is defined as: Fj=ln |
Sb/Sw|；WhereinIt is the Scatter Matrix between class；
It is the Scatter Matrix in class；L is the number of class；CiIt is the geometric center of each class,It is all kinds of centers
Geometric center；X is data vector.
The flow chart for carrying out On-line Fault monitoring to test data is as shown in Figure 3.
Further, the algorithmic procedure of Chaos particle swarm optimization algorithm are as follows: 1) parameter is set；Accelerator coefficient c1、c2, group size N, most
Greatly, minimum inertia weight: wminAnd wmax；Adaptive inertia weight coefficient AIWF is defined as:
Wherein iter is the number of iterations；2) particle i each in population is initialized；Xi, Vi, fi(objective function predicts error most
It is small), pg(with the particle of optimal function value in population) and pi(particle itself memory)；3) implement search；Search pg；It looks into
Look for pi；Utilize formulaAnd Xi(t+1)=Xi(t)+Vi(t+1) each particle is updated
Xi, Vi；Assess the objective function f of all particlesi；4) retain preceding 20% particle；5) the chaos local search for implementing particle, updates
pgAnd pi；6) optimum solution that output search is found；7) search space is reduced；xmin,j=max { xmin,j, xg,j-r(xmax,j-
xmin,j), 0 < r < 1xmax,j=min { xmax,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1；8) in the search space of diminution
80% new particle is generated at random, and they are assessed.
Further, the chaos local search of above-mentioned implementation particle updates pgAnd piInclude: that (1) enables k=0, utilizes relationship
FormulaDecision variable xj (k)(j=1,2 ... N) it is mapped to Chaos Variable cxj (k)；(2) into
Row next iteration, with cxj k+1=4cxj k(1-cxj k) and xj k+1=xmin,j+cxj k+1(xmax,j-xmin,j) calculate cxj (k+1)；
(3) new solution is assessed with decision variable；(4) if new solution is more preferable than current solution, Huo Zheda
To predefined maximum number of iterations, then new solution is exported with Chaos particle swarm optimization algorithm；Otherwise, k=k+1 is enabled to return to the
(2) step.
Through the above steps, it is optimized by kernel functional parameter of the Chaos particle swarm optimization algorithm to core pivot element analysis,
To find optimal nonlinear characteristic, and monitor goes out nonlinear fault, to reduce monitoring delay time, improves failure
Monitoring accuracy.
In order to keep technical solution of the present invention and implementation method clearer, below in conjunction with preferred embodiment in fact
Existing process is described in detail.
Embodiment one
The present embodiment provides a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization, as shown in figure 4,
Fig. 4 is the stream of the according to embodiments of the present invention one another optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization
Cheng Tu, comprising the following steps:
Step S401: primary data matrix is obtained；Primary data matrix includes normal data sample matrix and fault data
Sample matrix；
Step S402: by Nonlinear Mapping φ by primary data space reflection into implicit features space, and implicit
Nonlinear characteristic transformation is carried out in feature space；
In the embodiment of the present invention, the concrete principle of core pivot element analysis method are as follows:
A given primary data matrix X, with M sampling, to N number of variable sampling M times, then covariance C can be with non-linear defeated
Enter the Nonlinear Mapping φ in space to indicate, to obtain linear character space F, it may be assumed that
The eigenvalue problem in feature space is solved it is necessary to calculate feature vector V, i.e. λ > 0, V ≠ 0, by (2) formula:
Then the dot product in F is calculated to avoid " dimension disaster ", by formula (2) left side multiplied by φ (X with kernel functionk), it obtains: λ
(φ(Xk) V)=(φ (Xk) CV), k=1,2 ..., N (3)
Feature vector V may be expressed as:Wherein α=(α1,α2,…,αN)TBe coefficient arrange to
Amount；
Define N row and N column matrix K；Kij=(φ (Xi) φ(Xj))=k (Xi,Xj) (5)
K meetsWherein IN=1/N；
Factor alphajCharacteristic value calculate depend on kernel function, it may be assumed that N λ α=K α (7)
Solve (λk,αk), k=1 ..., p need to be standardized using formula (8)；Wherein αkWith the positive feature vector of maximum of pJust
It hands over, i.e. λ1≥λ2≥…≥λpWhen, have: λi(αiαi)=1 (8)
The feature pivot t of k-th of KPCAkIt can be by the way that φ (x) be projected VkUpper acquisition, it may be assumed that
The core pivot element analysis KPCA transform characteristics vector that formula (9) calculate new samples vector can also be used；
Step S403: pass through formulaIt is normal data by primary data matrix conversion, and to normal data
Carry out standardization processing；
In the embodiment of the present invention, μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,σm 2)
It is the standard deviation diagonal matrix of variable；
Step S404: pass through formulaEstablish mixed kernel function；
In the embodiment of the present invention, above-mentioned mixed kernel function is combined based on Radial basis kernel function and Polynomial kernel function
What hybrid modeling new method was established, kernel function can be made in this way while there is good study and generalization ability；
Further, above-mentioned Radial basis kernel function:It is a local kernel function, tool
There is good learning ability, wherein nuclear parameter δ is the width of RBF；
Above-mentioned polynomial function: Kpoly(xi,xj)=(xi xj+1)d, it is a global kernel function, has extensive well
Ability, wherein nuclear parameter d is polynomial number；
Before carrying out KPCA, parameter lambda, D and σ need to be optimized；
Step S405: mixed kernel function parameter is optimized by Chaos particle swarm optimization algorithm；
As an alternative embodiment, Chaos particle swarm optimization algorithm is the adaptive inertia weight system to particle swarm algorithm
Number (Adaptive Inertia Weight Factor, AIWF) carries out the particle group optimizing of global search and chaos local search
Algorithm, algorithmic procedure are as follows:
1. parameter: accelerator coefficient c is arranged1、c2, group size N, maximum, minimum inertia weight: wminAnd wmax.Adaptive inertia
Weight coefficient AIWF is defined as:Wherein iter is the number of iterations；
2. each particle i initialization in pair population: Xi, Vi, fi(objective function predicts that error is minimum), pg(in particle
With the particle of optimal function value in group) and pi(particle itself memory)；
3. implementing search: (1) searching pg；(2) p is searchedi；(3) formula is utilized
And Xi(t+1)=Xi(t)+Vi(t+1) X of each particle is updatedi, Vi；(4) the objective function f of all particles is assessedi；
4. retaining preceding 20% particle；
5. implementing the chaos local search of particle, p is updatedgAnd pi；
(1) k=0 is enabled, relational expression is utilizedDecision variable xj (k)(j=1,2 ...
N) it is mapped to Chaos Variable cxj (k)；(2) next iteration is carried out, calculates cx with following formulaj (k+1): cxj k+1=4cxj k(1-
cxj k), xj k+1=xmin,j+cxj k+1(xmax,j-xmin,j)；(3) new solution is assessed with decision variable；(4) if new solution
Certainly scheme is more preferable than current solution, or reaches predefined maximum number of iterations, then is calculated with chaotic particle swarm optimization
Method exports new solution, otherwise, k=k+1 is enabled to return to the 5.th (2) step；
6. if satisfied, then stopping criterion, exports the optimum solution up to the present found；
7. reducing search space: xmin,j=max { xmin,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1xmax,j=min
{xmax,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1；
8. generating 80% new particle at random in the search space of diminution, and they are assessed；Finally, enabling k=k
+ 1 returns to step 3；
Join as an alternative embodiment, above-mentioned steps S405 optimizes mixed kernel function by Chaos particle swarm optimization algorithm
Before number, needs first to define and be suitable for the fitness function that normal data set is separated with fault data collection；In the embodiment of the present invention,
Above-mentioned fitness function is defined as: Fj=ln | Sb/Sw|, whereinIt is the divergence between class
Matrix,It is the Scatter Matrix in class, L is the number of class, CiIt is the geometry of each class
Center,It is the geometric center at all kinds of centers, X is data vector, FjIt is bigger, then the separation degree of class
Higher, i.e. malfunction monitoring ability is stronger；And test assessment is carried out to select best configuration and most subtotal by using data set
Calculation amount；FjIncrease to always its value variation it is not fairly obvious until, as shown in the fitness curve of Fig. 5 Chaos particle swarm optimization algorithm；
Step S406: pass through formula Kij=(φ (Xi) φ(Xj))=k (Xi,Xj) calculate nuclear matrix K；
Step S407: pass throughCentralization is carried out to implicit features space；
Step S408: (λ is calculated by formula N λ α=K αk,αk), k=1 ..., p, and pass through λi(αi αiThe specification α of)=1k；
Step S409: pass through formulaTo normal number
According to extracting k-th of characteristic component；
Step S410: pass through formulaWith
Calculate the monitoring and statistics amount T of normal data2And SPE；
Step S411: pass throughWithCalculate the T of normal data2
Control with SPE statistic limits；
Step S412: test data is obtained；
Step S413: pass through formulaIt is new test data vector by test data conversion, and to new
Test data vector carries out standardization processing；
In the embodiment of the present invention, μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,σm 2)
It is the standard deviation diagonal matrix of variable；
Step S414: to given test vector xt, utilize [kt]j=[kt(Xt,Xj)] calculate core vector kt∈R1×N；
In the embodiment of the present invention, above-mentioned XjIt is normal operational data；
Step S415: k is calculatedt,1t=1/N × [1 ..., 1] ∈ R1×N；
Step S416: pass throughCalculate the non-linear of new test data vector
Pivot；
Step S417: the statistic T of new test data vector is calculated2And SPE；
Step S418: the T of new test data vector is monitored2The T of normal data whether is all larger than with the value of SPE2And SPE
The control of statistic limits；If so, thening follow the steps S419；If not, thening follow the steps S420；
Step S419: test data is abnormal, and equipment belonging to test data breaks down；
Step S420: test data is normal, and equipment belonging to test data is without failure.
For example, in rolling process, when the parameter value of looping car is too many lower than tension lower limit, it sometimes appear that steel
Failure with fracture.For the safe operation for guaranteeing production line, product quality is improved, relevant technique ginseng need to be carried out to loop trolley
Number monitoring, finds failure as early as possible.Here application CPSO-KPCA process monitoring method monitoring loop trolley above is intercoupled
With nonlinear process parameter.
Technological parameter relevant to looping car has 38 in rolling process.Just using one respectively comprising 1000 observations
Regular data collection and a fault data collection are modeled as training dataset.Using making normal data and number of faults in CPSO
According to class between the maximum fitness function of geometric distance, and obtained the optimized parameter of mixed kernel function using CPSO algorithm: λ=
0.95, σ=3.0, D=5.
Initial parameter using CPSO algorithm is as shown in table 1, and it is best to select to carry out test assessment by using data set
Configuration and minimum of computation amount.
Fig. 5 gives the fitness curve of CPSO algorithm.
Then pass throughWithCalculate T2With the statistics of SPE
Control limit.Then, KPCA is set as 7.5 RBF kernel function and based on the KPCA of CPSO to identical test data using parameter
It is monitored on-line, T2With SPE monitoring figure (the present embodiment to be out of order occur when 200 test data results) show respectively
In Fig. 6 and Fig. 7.
As seen from Figure 6, figure, T are monitored using the KPCA of RBF kernel function2With SPE statistical monitoring value until test data
155, test data 147 just monitors failure.And as can be seen from Figure 7, optimize the monitoring result of nuclear parameter with CPSO-KPCA, with
It is compared using the KPCA monitoring result of RBF kernel function, T2It is just supervised respectively since data 126 and 122 with SPE statistical monitoring figure
Failure generation is measured.
Table 2 calculates the monitoring rate that is out of order side by side, as can be seen from Table 2, on the one hand, the monitoring rate of PSO-KPCA monitoring method
It is higher than the KPCA monitoring method using RBF kernel function；On the other hand, it is obvious that the T of CPSO-KPCA2It is supervised with the failure of SPE
Survey rate is above KPCA the and PSO-KPCA monitoring method using RBF kernel function, and almost may be used using the method for CPSO-KPCA
100% monitoring is out of order, in addition, comparing from Fig. 6 using RBF kernel function KPCA monitoring result and Fig. 7 CPSO-KPCA monitoring result
It can be seen that CPSO-KPCA monitoring result also postpones without any monitoring.
Using the result shows that, CPSO-KPCA can efficiently extract the nonlinear characteristic of process variable, and can be by fault data
It is more effectively separated with normal data.CPSO-KPCA is to T2It is more sensitive with the monitoring of SPE statistic, and postpone smaller.CPSO-
KPCA ratio RBF kernel function KPCA method can earlier, more accurately monitor the generation of failure, have more superior Monitoring Performance.
Table 1
Table 2
In summary, through the foregoing embodiment, joined by kernel function of the Chaos particle swarm optimization algorithm to core pivot element analysis
Number optimize, to find optimal nonlinear characteristic, and it is accurate and effective monitor out of order generation in time, to reduce
Delay time is monitored, malfunction monitoring precision is improved.
Claims (6)
1. a kind of optimization core pivot element analysis fault monitoring method based on Chaos-Particle Swarm Optimization, which comprises the following steps:
Obtain primary data matrix；The primary data matrix includes normal data sample matrix and fault data sample matrix；
By Nonlinear Mapping φ by the primary data space reflection into implicit features space, and in implicit features space
Carry out nonlinear characteristic transformation；
Malfunction monitoring model is established using the primary data matrix as training data；
Obtain test data；
The test data is inputted in the malfunction monitoring model, On-line Fault monitoring is carried out to the test data.
2. the method according to claim 1, wherein establishing event for the primary data matrix as training data
Hinder monitoring model, comprising the following steps:
Pass through formulaIt is normal data by the primary data matrix conversion, and the normal data is advised
Generalized processing；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,σm 2) be variable mark
Quasi- deviation diagonal matrix；
Pass through formulaEstablish mixed kernel function；
Optimize the mixed kernel function parameter by Chaos particle swarm optimization algorithm；
Pass through formula Kij=(φ (Xi)φ(Xj))=k (Xi,Xj) calculate nuclear matrix K；
Pass throughCentralization is carried out to the implicit features space；
(λ is calculated by formula N λ α=K αk,αk), k=1 ..., p, and pass through λi(αiαiThe specification α of)=1k；
Pass through formulaKth is extracted to the normal data
A characteristic component；
Pass through formulaWithCalculate the prison of the normal data
Survey statistic T2And SPE；
Pass throughWithCalculate the T of the normal data2It is counted with SPE
The control of amount limits.
3. according to the method described in claim 2, it is characterized in that, the test data is inputted the malfunction monitoring model
In, On-line Fault monitoring is carried out to the test data, comprising the following steps:
Pass through formulaIt is new test data vector by the test data conversion, and to the new test number
Standardization processing is carried out according to vector；Wherein μ=[μ1,μ2,…,μm] be variable mean vector, Dσ=diag (σ1 2,σ2 2,…,
σm 2) be variable standard deviation diagonal matrix；
To given test vector xt, utilize [kt]j=[kt(Xt,Xj)] calculate core vector kt∈R1×N, wherein XjIt is normal operating number
According to；
Calculate kt,1t=1/N × [1 ..., 1] ∈ R1×N；
Pass throughCalculate the nonlinear principal component of the new test data vector；
Calculate the statistic T of the new test data vector2And SPE；
Monitor the T of the new test data vector2The T of the normal data whether is all larger than with the value of SPE2With SPE statistic
Control limit；
If it is, the test data is abnormal, equipment belonging to the test data breaks down；
If it is not, then the test data is normal, equipment belonging to the test data is without failure.
4. according to the method described in claim 2, it is characterized in that, optimizing the mixed kernel function by Chaos particle swarm optimization algorithm
It is further comprising the steps of before parameter:
The fitness function that definition is suitble to the normal data sample matrix and fault data sample matrix to separate；The fitness
Function is defined as:WhereinIt is the Scatter Matrix between class；It is the Scatter Matrix in class；L is the number of class；CiIt is the geometric center of each class,It is the geometric center at all kinds of centers；X is data vector.
5. according to the method described in claim 2, it is characterized in that, the algorithmic procedure of the Chaos particle swarm optimization algorithm are as follows: 1) set
Set parameter；Accelerator coefficient c1、c2, group size N, maximum, minimum inertia weight: wminAnd wmax；Adaptive inertia weight coefficient AIWF
Is defined as:Wherein iter is the number of iterations；
2) particle i each in population is initialized；Xi, Vi, fi(objective function predicts that error is minimum), pg(in population
Particle with optimal function value) and pi(particle itself memory)；
3) implement search；Search pg；Search pi；Utilize formulaAnd Xi(t+1)=Xi
(t)+Vi(t+1) X of each particle is updatedi, Vi；Assess the objective function f of all particlesi；
4) retain preceding 20% particle；
5) the chaos local search for implementing particle, updates pgAnd pi；
6) optimum solution that output search is found.
7) search space is reduced；xmin,j=max { xmin,j, xg,j-r(xmax,j-xmin,j), 0 < r < 1xmax,j=min { xmax,j,
xg,j-r(xmax,j-xmin,j), 0 < r < 1；
8) it generates 80% new particle at random in the search space of diminution, and they is assessed.
6. according to the method described in claim 5, it is characterized in that, the chaos local search of implementation particle, updates pgAnd piPacket
It includes: (1) enabling k=0, utilize relational expressionDecision variable xj (k)(j=1,2 ... N) mapping
To Chaos Variable cxj (k)；(2) next iteration is carried out, with cxj k+1=4cxj k(1-cxj k) and xj k+1=xmin,j+cxj k+1
(xmax,j-xmin,j) calculate cxj (k+1)；(3) new solution is assessed with decision variable；(4) if new solution ratio is worked as
Preceding solution is more preferable, or reaches predefined maximum number of iterations, then is exported newly with Chaos particle swarm optimization algorithm
Solution；Otherwise, k=k+1 is enabled to return to (2) step.
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