CN107133632A - A kind of wind power equipment fault diagnosis method and system - Google Patents
A kind of wind power equipment fault diagnosis method and system Download PDFInfo
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- CN107133632A CN107133632A CN201710106483.7A CN201710106483A CN107133632A CN 107133632 A CN107133632 A CN 107133632A CN 201710106483 A CN201710106483 A CN 201710106483A CN 107133632 A CN107133632 A CN 107133632A
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F18/23—Clustering techniques
- G06F18/232—Non-hierarchical techniques
- G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
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- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
- G05B23/0275—Fault isolation and identification, e.g. classify fault; estimate cause or root of failure
- G05B23/0281—Quantitative, e.g. mathematical distance; Clustering; Neural networks; Statistical analysis
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Abstract
The invention discloses a kind of wind power equipment fault diagnosis method and system, its synthetical collection wind power equipment related data, set up data warehouse, guarantee data integrity, data basis is provided for data mining, fault data is extracted from the historical data of data warehouse, fault data is changed, and it is loaded into data warehouse, the fact that to set up Multidimensional Data Model and failure table, initial analysis is carried out to data using clustering, comprehensive Various types of data carries out data relation analysis, it is compared judgement, many intelligent criterions are formed to integrate, wind-powered electricity generation fault diagnosis example explanation is carried out with this intelligent criterion, the present invention has criterion complete, method is advanced, accuracy of judgement, judge to provide new method for electrical equipment fault, overcome the shortcomings and deficiencies of single method, improve the degree of accuracy of Fan Equipment fault diagnosis.
Description
Technical field
The present invention relates to wind power equipment fault diagnosis field, in particular to a kind of wind power equipment method for diagnosing faults and it is
System.
Background technology
Wind turbines are complicated many bodies and multiregion system, blade, wheel hub, gear-box, bearing, the axle of existing rotation
Deng mechanical part, there are the control system and power electronic system of hydraulic system, electrical system and complexity again.If can utilize
The information such as real-time state monitoring data and SCADA can be before catastrophic failure generation, will by failure prediction algorithm and technology
Potential accident sign prediction is identified, can early excise preventative maintenance, it is to avoid accident triggers heavy losses.
And wind power equipment fault diagnosis is to be related to many knowledge, currently for wind power generation unit blade/pitch-controlled system
The more method of research is that the process parameter change of blade and variable pitch controlling mechanism is analyzed, deduced using blower fan electromotive power output
Trend carries out failure predication；Domestic and foreign scholars, using technical fields such as data statistics, fuzzy theorys, achieve one in research
Fixed progress, such as Holst-Jenson are predicted feather using FFT analysis of spectrums to the emulation of pitch-variable system pitch angle error
The fault features of mechanism；And Kusiak research blade unbalanced faults and the prediction algorithm of the insincere failure of pitch angle.
Research is all based on data statistical approach above, and these methods are asymmetric to leaf quality, pitch control structure
Abnormal problem is highly effective, although there is certain advantage in terms of fault diagnosis using these methods, is examined using single
When disconnected pattern carries out fault diagnosis to Fan Equipment, it is weak to have an inferential capability, matching conflict occur, and fault-tolerant ability difference lacks
Point, therefore be difficult identification fatigue damage or the initial failure of mechanical crackle.Therefore, only tied only according to some method is just subjectively lower
Judge by accident or fail to judge by being easily caused, therefore need to be needed research to carry out Accurate Prediction to failure based on data digging method.
The content of the invention
The problem of for wind power equipment fault diagnosis, the present invention seeks to be to provide a kind of based on data clusters and association
The wind power equipment fault diagnosis method and system of rule, it integrates data clusters, the association analysis side that multiple equipment data are carried out
Method, forms many intelligent criterion comprehensive diagnos wind power equipment failures, overcomes the shortcomings and deficiencies of single method, improve Fan Equipment
The degree of accuracy of fault diagnosis.
To achieve the above object, technical scheme is as follows：
A kind of Fault Diagnosis of Fan method, it comprises the following steps:
Clustering is carried out to fault data according to the true table of the Multidimensional Data Model pre-established and failure and rule are associated
Then analyze；
According to cluster analysis result and Association Rule Analysis result, the relation between event of failure is determined；
According to the conditional probability between predetermined event of failure and combination condition probability, determine that mutual shadow occurs for failure
Loud possibility.
Further, the process of setting up of the Multidimensional Data Model is：
Extract fan trouble sample data；
The fault sample data to different data sources carry out type conversion and classified to be loaded onto data warehouse；
The true table of the failure pre-established is set up with the dimension table in Multidimensional Data Model by external key and associated.
Further, the step of progress clustering to fault data includes as follows：
The similarity measurement between fault sample data is used as by the use of Euclidean distance；
It is determined that evaluating the criterion function of clustering performance；
Clustering is carried out to each class fault data and final cluster result is obtained using iterative manner, wind-powered electricity generation is completed
The similarity processing of equipment fault.
Further, the expression formula of the similarity measurement is as follows:
Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,
A2,…Ad, to represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,
Xj2,…Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,
...AdSpecific value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent.
Further, the expression formula of the criterion function is as follows:
In formula, p is sampling feature vectors；X ' includes the cluster subset { X ' that number is k1,X’2,...,X’k, each cluster
It is respectively n that the average of subset, which represents point,1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk。
Further, it is described rule analysis is associated to fault data to comprise the following steps：
Set one group of fault message F={ F1,F2,…Fm, fault zone A={ A1,A2,…An, fault correlation rule is
R:X "=>Y implication, wherein X " for rule condition and be F pattern, Y for estimation result and be A pattern, R is
Not only the incidence relation in F but also in A, rule analysis was associated to fault data, determined the item collection support of correlation rule
And confidence level.
Further, the item collection support of above-mentioned determination correlation rule is expressed with following formula：
In formula, the probability that support (λ) descriptions item collection λ occurs, D is all Transaction Sets, count (λ } T) it is transaction set
λ number of transaction is included in D, T merchandises for single, | D | for the All Activity quantity included in transaction set D；
The confidence level of above-mentioned determination correlation rule is expressed with following formula：
In formula,For the ratio between the number of deals comprising λ and Y and number of deals comprising λ.
Further comprise：
Interactional probability occurs for the result combination failure of clustering and Association Rule Analysis to fault data
Carry out comprehensive analysis and find unknown message, auxiliary suggestion is provided to wind power equipment troubleshooting.
The present invention separately provides a kind of Trouble Diagnosis System of Fan, and its system includes as follows：
Cluster Analysis module, is clustered according to the true table of the Multidimensional Data Model and failure that pre-establish to fault data
Analysis calculates the similarity processing for completing wind power equipment failure, and carries out the classification of fault data；The Multidimensional Data Model bag
Include dimension table；
Association Rule Analysis module, for being associated rule analysis to fault data, to determine the item collection of correlation rule
Support and confidence level；
Probabilistic determination module, according to the clustering and Association Rule Analysis result to fault data event, actually to ask
The event of topic is abstract as node, the annexation set up between two or more nodes；Section is calculated from historical data
Conditional probability and combination condition probability between point, and interactional probability occurs for failure judgement.
Further, in the Cluster Analysis module, clustering is carried out to fault data and is calculated as follows：
The similarity measurement between fault data sample is used as by the use of Euclidean distance：
Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,
A2,…Ad, to represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,
Xj2,…Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,
...AdSpecific value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent, apart from smaller,
Sample XiAnd XjMore similar, diversity factor is smaller；Bigger, the sample X of distanceiAnd XjMore dissimilar, diversity factor is bigger；
The criterion function of clustering performance is evaluated in selection：
Where it is assumed that X includes the cluster subset X that number is k1,X2,...,XkThe average of each cluster subset represents point minute
Wei not n1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk；
Preliminary classification is determined, cluster result is obtained with the method for iteration afterwards so that the criterion function for evaluating cluster is obtained
Optimal value.
Synthetical collection wind power equipment related data of the present invention, sets up data warehouse, it is ensured that data integrity, is data mining
Data basis is provided, initial analysis is carried out to data using clustering, comprehensive Various types of data carries out data relation analysis, carried out
Multilevel iudge, forms many intelligent criterions and integrates, carrying out wind-powered electricity generation fault diagnosis example with this intelligent criterion illustrates, the present invention has criterion
Completely, method is advanced, accuracy of judgement, judges to provide new method for electrical equipment fault.
Brief description of the drawings
Fig. 1 is the inventive method schematic flow sheet.
Embodiment
The present invention is further described with specific embodiment below in conjunction with the accompanying drawings.
Referring to Fig. 1, a kind of wind power equipment method for diagnosing faults based on data clusters and correlation rule of the invention, its side
Method is as follows：
(1) data are extracted, from the historical data in data warehouse mainly from blower fan SCADA (data acquisition with
Supervisor control), obtain in the system such as PMS (production management system).
(2) data are changed, data conversion is to change type, size, decimal digits, precision or the field of data
For casement etc..Should be to different data sources, such as in transfer process：TXT, EXCEL, DOC, DB etc. are changed accordingly；
Data type in source data is char types by int Type Changes, and data space-consuming size has 8 bytes to become 4 bytes etc..
(3) data are loaded, the data after conversion are carried out into homogeneous classification is loaded into data warehouse, due to being concerned about
Theme difference the data of data warehouse are set up various Data Marts.For example：When region-of-interest classify related information when
Wait, it is possible to set up the summary information on region；When voltage relevant information is paid close attention to, it is possible to set up on voltage
Summary information.
(4) Multidimensional Data Model and the true table of failure are set up, is that each latitude of the true table surrounding of failure increases by one
Field is interconnected the dimension table by external key and true table, on this basis as the external key of latitude table, it is possible to use
OLAP (Data Environments) technology carries out various complicated inquiries, grasps some essential informations of failure.
(5) to data carry out clustering, clustering be physics or abstract data acquisition system are divided into it is multiple
There is higher similarity, similarity can in every kind of classification after the process of classification, cluster between any two data sample
Calculated, generally represented using the distance between data sample with the specific value of the description attribute according to data sample.It is logical
Cross clustering and handled to complete the similarity of wind power equipment failure, carry out the classification of failure, it is possible to be used as correlation rule
Pretreatment work.Its specific clustering method is as follows：
(A) it is used as the similarity measurement between fault data sample by the use of Euclidean distance.
Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,
A2,…Ad, to represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,
Xj2,…Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,
...AdSpecific value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent, apart from smaller,
Sample Xi, and XjMore similar, diversity factor is smaller；Bigger, the sample X of distanceiAnd XjMore dissimilar, diversity factor is bigger.
(B) criterion function of clustering performance is evaluated in selection.
Where it is assumed that X ' includes the cluster subset X that number is k '1,X’2,...,X’k, the average generation of each cluster subset
Table point is respectively n1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk。
(C) some preliminary classification is selected, cluster result is obtained with the method for iteration afterwards so that the criterion letter of cluster is evaluated
Number obtains optimal value
(6) data are associated with rule analysis, correlation rule is the discovery different pieces of information item from historical data set
Between the relation that influences each other.Give one group of fault message F={ F1,F2,…Fm, fault zone A={ A1,A2,…An, fail close
It is shape such as R to join rule:A=>Y implication, wherein X " for rule condition and be F pattern, Y for estimation result and
It is A pattern.
(a) the item collection support of correlation rule；
The probability that wherein support (X) descriptions item collection X occurs, x is item collection, and count (X≤T) is to include X in transaction set D
Number of transaction, | D | be the All Activity quantity that includes in transaction set D.
(b) confidence level of correlation rule：
In formula,For the ratio between the number of deals comprising λ and Y and number of deals comprising λ.
(2)
(7) diagnostic result is drawn；Comprehensive analysis finally is carried out to cluster and the result of association analysis and finds unknown knowledge, it is right
Wind-powered electricity generation troubleshooting provides auxiliary suggestion.
In addition, also provide a kind of Trouble Diagnosis System of Fan based on data mining in the present embodiment, its specifically include as
Lower module：
Cluster Analysis module, is clustered according to the true table of the Multidimensional Data Model and failure that pre-establish to fault data
Analysis calculates the similarity processing for completing wind power equipment failure, and carries out the classification of fault data；The Multidimensional Data Model bag
Include dimension table；
Association Rule Analysis module, for being associated rule analysis to fault data, to determine the item collection of correlation rule
Support and confidence level；
Probabilistic determination module, according to the clustering and Association Rule Analysis result to fault data event, actually to ask
The event of topic is abstract as node, the annexation set up between two or more nodes；Section is calculated from historical data
Conditional probability and combination condition probability between point, and interactional probability occurs for failure judgement.
In the present embodiment, in data are carried out with Cluster Analysis module, clustering is carried out to fault data and is calculated as follows：
The similarity measurement between fault data sample is used as by the use of Euclidean distance：
Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,
A2,…Ad, to represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,
Xj2,…Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,
...AdSpecific value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent, apart from smaller,
Sample Xi, and XjMore similar, diversity factor is smaller；Bigger, the sample X of distanceiAnd XjMore dissimilar, diversity factor is bigger；
The criterion function of clustering performance is evaluated in selection：
Where it is assumed that X includes the cluster subset X that number is k1,X2,...,XkThe average of each cluster subset represents point minute
Wei not n1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk；
Preliminary classification is selected, and cluster result is obtained with alternative manner.
It is described that fault data is associated in rule analysis module, under the item collection support of above-mentioned determination correlation rule is used
Formula is expressed：
In formula, the probability that support (λ) descriptions item collection λ occurs, D is all Transaction Sets, count (λ } T) it is transaction set
λ number of transaction is included in D, T merchandises for single, | D | for the All Activity quantity included in transaction set D；
The confidence level of above-mentioned determination correlation rule is expressed with following formula：
In formula,For the ratio between the number of deals comprising X and Y and number of deals comprising X.
By above-described embodiment, synthetical collection wind power equipment related data of the present invention sets up data warehouse, it is ensured that number
According to integrality, data basis is provided for data mining, initial analysis is carried out to data using clustering, comprehensive Various types of data is entered
Row data relation analysis, is compared judgement, forms many intelligent criterions and integrates, and it is real to carry out wind-powered electricity generation fault diagnosis with this intelligent criterion
Example explanation, the present invention has that criterion is complete, method is advanced, accuracy of judgement, judges to provide new method for electrical equipment fault.
Described above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
It should be understood by those skilled in the art that, embodiments herein can be provided as method, system or computer program
Product.Therefore, the application can be using the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware
Apply the form of example.Moreover, the application can be used in one or more computers for wherein including computer usable program code
The computer program production that usable storage medium is implemented on (including but is not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The application is the flow with reference to method, equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram are described.It should be understood that can be by every first-class in computer program instructions implementation process figure and/or block diagram
Journey and/or the flow in square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided
The processor of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce
A raw machine so that produced by the instruction of computer or the computing device of other programmable data processing devices for real
The device for the function of being specified in present one flow of flow chart or one square frame of multiple flows and/or block diagram or multiple square frames.
These computer program instructions, which may be alternatively stored in, can guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works so that the instruction being stored in the computer-readable memory, which is produced, to be included referring to
Make the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one square frame of block diagram or
The function of being specified in multiple square frames.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that in meter
Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented processing, thus in computer or
The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in individual square frame or multiple square frames.
Claims (10)
1. a kind of Fault Diagnosis of Fan method, it is characterised in that it comprises the following steps:
Clustering and correlation rule point are carried out to fault data according to the true table of the Multidimensional Data Model and failure that pre-establish
Analysis；
According to cluster analysis result and Association Rule Analysis result, the relation between event of failure is determined；
According to the conditional probability between predetermined event of failure and combination condition probability, determine what failure interacted
Possibility.
2. the method as described in claim 1, it is characterised in that the process of setting up of the Multidimensional Data Model is：
Extract fan trouble sample data；
The fault sample data to different data sources carry out type conversion and classified to be loaded onto data warehouse；
The true table of the failure pre-established is set up with the dimension table in Multidimensional Data Model by external key and associated.
3. the method as described in claim 1, it is characterised in that described to include such as the step of carry out clustering to fault data
Under：
The similarity measurement between fault sample data is used as by the use of Euclidean distance；
It is determined that evaluating the criterion function of clustering performance；
Clustering is carried out to each class fault data and final cluster result is obtained using iterative manner, wind power equipment is completed
The similarity processing of failure.
4. method as claimed in claim 3, it is characterised in that the expression formula of the similarity measurement is as follows:
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Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,A2,…Ad,
To represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,Xj2,…
Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,...AdTool
Body value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent.
5. method as claimed in claim 3, it is characterised in that the expression formula of the criterion function is as follows:
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In formula, p is sampling feature vectors；X ' includes the cluster subset { X ' that number is k1,X’2,...,X’k, each cluster subset
Average represent point be respectively a n1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk。
6. the method as described in claim 1, it is characterised in that the rule analysis that is associated to fault data is including as follows
Step：
Set one group of fault message F={ F1,F2,…Fm, fault zone A={ A1,A2,…An, fault correlation rule is R:X”
=>Y implication, wherein X " for rule condition and be F pattern, Y for estimation result and be A pattern, R is both existed
Incidence relation in A again in F, rule analysis is associated to fault data, determine correlation rule item collection support and can
Reliability.
7. method as claimed in claim 6, it is characterised in that the item collection support following formula table of above-mentioned determination correlation rule
Reach：
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In formula, the probability that support (λ) descriptions item collection λ occurs, D is all Transaction Sets, during count (λ } T) is transaction set D
Number of transaction comprising λ, T merchandises for single, | D | for the All Activity quantity included in transaction set D；
The confidence level of above-mentioned determination correlation rule is expressed with following formula：
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In formula,For the ratio between the number of deals comprising λ and Y and number of deals comprising λ.
8. the method as described in claim 1, it is characterised in that further comprise：
The result combination failure of clustering and Association Rule Analysis to fault data occurs interactional probability and carried out
Comprehensive analysis finds unknown message, and auxiliary suggestion is provided to wind power equipment troubleshooting.
9. a kind of Trouble Diagnosis System of Fan, it is characterised in that its system includes as follows：
Cluster Analysis module, clustering is carried out according to the true table of the Multidimensional Data Model and failure that pre-establish to fault data
The similarity processing for completing wind power equipment failure is calculated, and carries out the classification of fault data；The Multidimensional Data Model includes dimension
Spend table；
Association Rule Analysis module, for being associated rule analysis to fault data, to determine that the item collection of correlation rule is supported
Degree and confidence level；
Probabilistic determination module, according to the clustering and Association Rule Analysis result to fault data event, with practical problem
Event is abstract as node, the annexation set up between two or more nodes；Calculated from historical data node it
Between conditional probability and combination condition probability, and interactional probability occurs for failure judgement.
10. system according to claim 9, it is characterised in that in the Cluster Analysis module, gathered to fault data
Alanysis is calculated as follows：
The similarity measurement between fault data sample is used as by the use of Euclidean distance：
<mrow>
<mi>d</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>d</mi>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mi>i</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein X={ Xm| m=1,2 ..., total } it is data set；The description attribute A that sample in X is d with number1,A2,…Ad,
To represent, and d description attribute is all continuous type attribute；Data sample Xi=(Xi1,Xi2,…Xid), Xj=(Xj1,Xj2,…
Xjd)；Wherein Xi1,Xi2,…XidAnd Xj1,Xj2,…XjdIt is sample X respectivelyiAnd XjD description attribute A of correspondence1,A2,...AdTool
Body value；Sample Xi, and XjBetween similarity the distance between they d (xi,xj) represent, apart from smaller, sample XiWith
XjMore similar, diversity factor is smaller；Bigger, the sample X of distanceiAnd XjMore dissimilar, diversity factor is bigger；
The criterion function of clustering performance is evaluated in selection：
<mrow>
<mi>E</mi>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>k</mi>
</msubsup>
<msub>
<mi>&Sigma;</mi>
<mrow>
<mi>p</mi>
<mo>&Element;</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mo>|</mo>
<mo>|</mo>
<mi>p</mi>
<mo>-</mo>
<msub>
<mi>m</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Where it is assumed that X includes the cluster subset X that number is k1,X2,...,XkThe average of each cluster subset represents point
n1,n2…nk；Sample size in each cluster subset is respectively m1,m2,…,mk；
Preliminary classification is determined, cluster result is obtained with the method for iteration afterwards so that the criterion function for evaluating cluster obtains optimal
Value.
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