CN105809203A - Hierarchical clustering-based system steady state detection algorithm - Google Patents
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Abstract
The invention discloses a hierarchical clustering-based system steady state detection algorithm. The algorithm comprises the following steps: for industrial data in a period of continuous time interval, calculating distances between every two types of data to obtain a matrix, finding the minimum distance values in the matrix, combining the minimum distance values into a new type, deleting the new type, carrying out processing to obtain an updated matrix and carrying out iterative computation to obtain an expression matrix of a hierarchical clustering tree; for the expression matrix, carrying out computation from the last iterative numerical value to the first iterative numerical value in sequence so as to obtain clustering result reasonability values of the computations, carrying out solving and computation on the computed clustering result reasonability values to obtain final threshold values, carrying out clustering computation on the industrial data through the final threshold values so as to obtain a final clustering result sequence, and carrying out joint time sequence judgement to obtain system steady state condition. The algorithm disclosed in the invention is strong in applicability and has the effect of avoiding the sharp calculation amount increase phenomenon caused by data dimensionality during the data processing.
Description
Technical field
The present invention relates to a kind of system detecting method, especially relate to a kind of systematic steady state detection algorithm based on hierarchical clustering.
Background technology
In the research to a procedures system, stable state is most important and modal hypothesis.Whether system is in stable state, is directly connected to the follow-up method to the modeling of system, control and optimization.The internal principle of procedures system and structure are complicated, show as physical quantity and there is stronger coupling, and system also exists extremely strong non-linear.When system is in unsteady state, the data characteristic variation of each variable of system acutely, numerically shows as instability or exception, there is relatively large deviation with the input/output relation of real system.Only system is under steady working condition, and parameters and variable just have stronger state consistency.Based on this kind of situation, the evaluation to equipment runnability, the analysis of plant characteristic and controller's effect, it is required for premised on the operation stable state to obtain system.
Development along with process industrial, in actual production process, system and the mode of production all tend to complicating, the procedures system object related to is often multivariate, high dimension and close coupling, and system general performance is non-linear, time variation, uncertainty and imperfection.Although study mechanism and modeling are caused great difficulty by complicated system, but simultaneously because DCS controls the application of system and intelligence instrument so that increasing process data is recorded.Strong and the complicated coupled relation existed between actual each variable in procedures system makes the stability being studied whole system by measurement data become possibility, along with the development of data mining and Statistical Learning Theory and perfect, process industrial field also progressively using related algorithm solving practical problems, creates such as fields such as statistical Process Control.In the problem processing stable state detection, the thought of big data is also different from traditional Study of Control Process method with method, the latter judges whether system is in stablize and carries out decision-making often by several key variables to formulate stable state standard, the former then requires from whole data, system to be analyzed, the result obtained based on total data theoretically will reflect the practical situation of system more comprehensively and truly, therefore can obtain result more accurately and reliably.
Stable state test problems is from last century since the eighties is suggested, domestic and international many scholars are proposed the method for different stable state detections, but due to the complexity of field data, the testing result that much the existing stable state detection means demonstrating effectiveness in l-G simulation test obtains in actual applications is not exactly accurate.And various method is subject to the real needs restriction in itself affect and practical application, the occasion of application is also not quite similar.
Cluster is technology critically important in unsupervised learning field, and for the individuality in data sample is divided into different classifications so that in class, individuality has similarity high as far as possible, individual between class have diversity high as far as possible.Hierarchical clustering thought is proposed in 1967 by JohnsonSC. the earliest, other clusters such as difference and EM and K-means, hierarchical clustering need not give classification number in advance, and does not need iterative optimization procedure, can obtain cluster result by given similarity function and threshold value.Owing to being not related to the problems such as Optimization Solution, therefore can avoid " dimension disaster ", but owing to hierarchical clustering needs to calculate distance between sample between two, complexity can increase by square multiple along with the increase of sample size.
The flow chart of Traditional calculating methods structure such as Fig. 1, it is assumed that having N number of individual of sample in sample data sets to be clustered, the algorithm of hierarchical clustering specifically has the steps:
1) definition similarity function and algorithm end condition threshold value (being generally maximum inter-object distance or infima species spacing)；
2) being gathered by each individuality in data set is a class, altogether N class；
3) current data set is allocated as k class, calculates the similarity between every class, d (i, j) represents the similarity between i and j class, if d (i j) is minima in current similarity set between any two, then merges i-th and jth class.Now cluster number is become k-1 by k；
4) calculating end condition value now, if meeting threshold value, terminating algorithm；
5) 3 are returned to), as k=1, all of sampled point is all gathered for same class, and clustering algorithm cannot continue, then algorithm stops.
Thus, traditional method major downside is that the dependency to process object is strong, and universality is poor, and carries out stable state detection mainly for single argument, and therefore the suitability is not strong, and cannot avoid the problem processing the amount of calculation sharp increase produced in data because of data dimension.
Summary of the invention
In order to solve Problems existing in background technology, the present invention proposes a kind of stable state detection algorithm based on hierarchical clustering.
The technical solution used in the present invention is:
STEP1 generates clustering tree:
1.1) comprised to the industrial data { d of N number of sampled point one period of continuous time in intervali, i=1,2,3 ..., N, in set, sampled point is as class, diRepresent the industrial data of class；
1.2) calculating all distances between class between two, obtain the matrix A of N × N, in matrix A, the element of i row j row is designated as aij, aii=0, aijRepresent class diWith class djBetween distance, the matrix A obtained is as follows:
1.3) the lowest distance value a in matrix A is foundmn, amnFor its class spacing.amnRepresent that m class and the n-th class are closest class, m class and the n-th class are merged into a new class, m row in puncture table A, n row, m row and n row, adopt step 1.2 by class remaining in matrix A again with merging the new class obtained) identical mode carries out the matrix A after processing acquisition renewal；
1.4) step 1.2 is repeated)～1.3) be iterated, until matrix A becomes the matrix of 1 × 1, record m, n and a in each iterative processmn, constitute the expression matrix Z of N × 3 of hierarchical clustering tree；
STEP2 threshold value is chosen:
2.1) for expression matrix Z, last iterative numerical calculate successively to the order of first time iterative numerical and be calculated in the following ways:
With current lowest distance value amnFor threshold value to industrial data { diCarrying out cluster calculation, the cluster result sequence obtained is Tk, k represents iteration ordinal number, cluster result sequence TkIt is the integer sequence of 1 × N, wherein, TkI () represents cluster result sequence TkI-th cluster result, Tk(i)=p；Cluster result sequence T is asked in calculatingkDifference sequence D, be namely that each adjacent element in sequence is subtracted each other acquisition difference, calculate in difference sequence D the number of zero as cluster result reasonability value D_zero (k).
2.2) cluster result reasonability value sequence D_zero it is made up of each calculated cluster result reasonability value D_zero (k), calculate the difference sequence asking for cluster result reasonability value sequence D_zero, namely it is that each adjacent element in sequence is subtracted each other acquisition difference, therefrom find the sequence number k at difference value maximum in difference sequence and place thereof, and with Z3kAs final threshold value.
Described step STEP2 is calculated, to the order of first time iterative numerical, the centre time iterative numerical referring to first time iterative numerical or the k=N/2 calculating k=1 by last iterative numerical successively.
When k is too little, the result of cluster is nonsensical to final stable state identification, is typically chosen the k=N/2 stop condition as algorithm to reduce amount of calculation.
STEP3 combines sequential and judges stable state:
Element T in final cluster result sequence TiIf meeting the following conditions, then it is assumed that the system between m-th sampled point to the m+k-1 sampled point is in stable state:
Ti=c, i=m, m+1, m+2 ..., m+k-1
Wherein, TiFor the cluster result that the i-th sampled point in final cluster result sequence T is corresponding, c represents result constant, k=τ/Ts, τ is above-mentioned time span threshold value, TsSampling time interval for data.
The size of τ is determined according to the time response of institute's object of study, generally takes τ=3t*, t*Unit-step response regulating time for system.
Described step 1.3) the middle end merged in the matrix A after the new class obtained is placed in renewal, end adds the row/column of new can be denoted as [a1(N+1)a2(N+1)…]T。
In described matrix A, the ranks digital number of remaining class remains unchanged, the ranks rank-numeral merging the new class obtained adopts new ranks digital number and the ranks digital number with all classes before all to differ so that each class of whole system process has unique ranks digital number.
Described step 1.3) in the distance that merges in the class that obtains and matrix A between each class remaining adopt below equation to calculate:
asi=α ami+(1-α)an*
Wherein, α is weight parameter, 0≤α≤1, asiRepresent the spacing between s class and i class, aniRepresent the spacing between n class and i class, amiRepresent the spacing between m class and i class.
Each sampled point of system is regarded as " characteristic vector " (or the characteristic point) of a state space, when system is in stable state, characteristic point fluctuation in certain interval, it is rendered as the higher-dimension Gauss distribution centered by a certain specified point.When system is in an interim state or when unstable state, state point will be disengaged from original Gauss distribution, and then presents other scattered distribution.This feature widely different of state between moment before and after when being in unstable state based on system, it is possible to carried out the detection of procedures system stable state by the difference degree between comparison system state characteristic vector.Here introducing clustering algorithm, in stable state detects, have significantly high similarity between steady state data, can be gathered in cluster is a class, there is very big-difference simultaneously, then can be assigned to different classifications between dynamic data point and steady state data.
Due to the characteristic of system, can only ensure that distributions time system is in stable state compares concentration, but if system is in fluctuation status, the fluctuation of its distribution is very big in state space.It is to say, while there is similarity between stable state sampled point, the similarity between dynamic sampling point is only small, in cluster result, the dynamic point in continuous time may be gathered at much different apoplexy due to endogenous wind.Therefore, it was the number that cannot determine the class that finally there are before cluster, adopts hierarchical clustering algorithm of the present invention based on these.
The invention has the beneficial effects as follows:
" big data " thought and technology are introduced in stable state detection by the present invention, and by comparing in data set the similarity degree between each sampled point, the temporal characteristics in combination with data carries out stable state detection, and proposes the method how determining cluster threshold value.
It is characteristic of the invention that the suitability is strong, and avoid and process the amount of calculation sharp increase phenomenon produced because of data dimension in data.
Accompanying drawing explanation
Fig. 1 is the flow chart of hierarchical clustering algorithm.
Fig. 2 is the flow chart of the inventive method threshold value selection course.
Fig. 3 is that the inventive method judges the flow chart of stable state in conjunction with sequential.
Fig. 4 is the input-output curve figure of embodiment 1 second order analogue system.
Fig. 5 is embodiment 1 second-order system state point cluster result figure.
Fig. 6 is that embodiment 1 clusters testing result figure.
Fig. 7 is the input-output curve figure of embodiment 2 second order analogue system.
Fig. 8 is the cluster result comparison diagram that embodiment 2 obtains when taking different threshold value.
Fig. 9 is the pending data and curves figure of embodiment 3 input.
Figure 10 is the cluster result in the 50th iteration of embodiment 3.
Figure 11 be in all 50 iteration of embodiment 3 in D 0 number and change profile figure.
Figure 12 is the part cluster result that embodiment 3 is representative.
Figure 13 is the stable state testing result figure of embodiment 3.
Detailed description of the invention
Below in conjunction with drawings and Examples, the invention will be further described.
The inventive method is applied particularly in the detection of procedures system stable state, as in figure 2 it is shown, there is following flow process: data point { d to be sortedi; first define the distance of point in its state space and between class distance metric form (due to the state point of procedures system in the state space that it is corresponding according to certain probability and aggregation extent random distribution, in the method for stable state detection, we select to use Euclidean distance to weigh).When weighing between class distance, our stable state of interest is a class in cluster result, and we will improve the aggregation extent of each class as far as possible, selects ultimate range more to meet above-mentioned requirements.
The input of algorithm: according to the system history data state point { d of time-sequencingi, wherein { diFor p dimension vector data, i=1,2,3 ..., N, N is sampled point number.
The output of algorithm: classification T, the T that each sampled point is corresponding is length is the one-dimensional sequence of N, i.e. sampled point class number sequence.Here class number only plays the other effect of region class, it does not have any physics and meaning numerically.
Step according to hierarchical clustering, following algorithm is iterated by calculating the distance between data set midpoint, and each step checks whether and reaches algorithm end condition, and algorithm terminates then output cluster result T.
Data object owing to analyzing is the time series according to Time alignment, when system is in stable state within a period of time, and its spatial distribution also Relatively centralized.Hence with the timing of data, meeting following two conditions, be namely regarded as stable state: 1) data acquisition sampling point is continuous in time；2) similarity of data acquisition sampling point significantly high (namely data are gathered an apoplexy due to endogenous wind by clustering algorithm).
Stable state is obtained by cluster result, it needs to be determined that the threshold value of cluster, and judge stable minimum time interval T, under selected threshold value δ, when in a period of time that length is not less than T, the state point of system is gathered in same class, namely illustrate that in this period, system is in stable state.The determination of minimum time interval T can according to the time response of system object, below main choosing and the threshold value impact on algorithm of cluster threshold value δ is discussed.
In the process of cluster calculation, data acquisition system to be clustered has N number of sample, data are aggregated to gradually from N class the clustering tree matrix Z of process record N*3 of 1 class, wherein Zi1The first kind sequence number of two apoplexy due to endogenous wind, Z is merged when recording the i-th step clusteri2The Equations of The Second Kind sequence number of two apoplexy due to endogenous wind, Z is merged when recording the i-th step clusteri3The distance between two classes is merged when recording the i-th step cluster.Therefore acquisition optimum cluster threshold value is and finds a line in Z, as the end line of algorithm output, wherein Zi3It is threshold value.Here we take the mode that the result of every a line is enumerated to obtain optimal threshold.
Additionally the innovation of the present invention is in that to adopt the rational quantizating index of appointment to find rational threshold value to be calculated, and concrete principle is: TkEnumerate, for kth time, the cluster result obtained, use its Difference Terms D=diff (Tk) weigh overall Clustering Effect, along with threshold value reduces, in D, the number of 0 element is gradually reduced, ordinary circumstance is such as (1)～(9), and in D, the number of 0 reduces in slower trend, but when a class stable state is split off out, result there will be system point in a period of time frequently switch between two classes, this will make the number of 0 in D sharply reduce, accordingly, it would be desirable to undertaken enumerating by cluster result until the threshold value enumerated too little to stable state identification meaningless time stop.Find out the maximum step of number change of in wherein D 0, be the suitable stable state threshold value that the termination step that cluster threshold value reduces, the threshold value of its correspondence namely current data cluster are required, it is determined that the flow chart of threshold value such as 3.
Embodiments of the invention are as follows:
Embodiment 1
Embodiment 1 is for a second order single-input single-output system, adopting the input after the inventive method simulation process and output as shown in Figure 4, simulation time length is 100s, and the sampling interval is 0.1s, Fig. 4 (a) represents input variable curve, and Fig. 4 (b) represents output variable curve.
In embodiment 1 variable no noise added, can see from the curve of Fig. 4, system is in stable state in the incipient stage (t=0～300), produce a slope in the input of t=300 place to adjust, system enters transitive state, when t=600 rear slopes signal ended, output also tends to stable final system and enters another stable state.Due to no noise added, the system mode extent of polymerization when stable state is very high, the method that wouldn't adopt above-mentioned algorithms selection threshold value here, and direct labor selects an only small threshold value t=0.01, and data are clustered, and the result obtained is as shown in Figure 5.
Curve from Fig. 4 can be seen that, in whole process, system has two different steady statues, and in Fig. 5 cluster result, the data point category label being in same stable state is consistent, it can be seen that Fig. 5 exists the part of two sections of levels, corresponding with the two of system equilibrium transport on the time.
The result of cluster illustrates state point distance in space, it is judged that whether system is in stable state needs the timing in conjunction with data.When system is in stable state within a period of time, then the data in this section of time interval will be gathered same class because similarity is high.In turn can as steady-state criterion, being all clustered that algorithm gathers when all data in one section of continuous time τ is a class, then the system that is considered as is in stable state.Wherein the length τ of time period determines according to the time response of institute's object of study, takes the unit-step response regulating time that τ=2t*, t* are system here.
Therefore the system stability result obtained is as shown in Figure 6, Fig. 6 (a) represents second-order system status number strong point cluster result, Fig. 6 (b) represents the final stable state testing result of system, in steady result, 1 represents stable, 0 represents instability, result can be seen that, system is approximately near t=300 and departs from from first stable state, enter transition state, it is again introduced into stable state when close to t=700, contrast input and output, although input just finishes ramp signal and enters stable when t=600, but output y experienced by the adjustment of a period of time later and just settles out.
Embodiment 2
Embodiment 2 adds noise and emulates, and the single-input single-output systematic procedure used based on embodiment 1 further illustrates threshold value and chooses process, add the analogue system input and output of noise as shown in Figure 7, Fig. 7 (a) represents input variable curve, and Fig. 7 (b) represents output variable curve:
Can be seen that in Fig. 7, system, in the interval of time t=0～300, is in a stable state, and then input u produces a slope change, and through transition state after a while, system enters another one stable state.In whole status of processes space, the state point aggregation extent of two stable states is higher, and transitive state point then ratio is relatively decentralized.Choosing of threshold value takes descending order to enumerate, and along with reducing of cluster threshold value, the intensity within each class is more and more higher.When proceed to jth step, threshold value narrows down to and to a certain degree then the class point originally belonging to same stable state can be separated into multiclass, it is believed that threshold value now is the too little expectation beyond us, continue to zoom out threshold value also it is not necessary that.Now, the threshold value that back and jth-1 step reach is currently suitable value.
The single-input single-output second-order system of embodiment 2 carries out enumerating front 12 steps of cluster as shown in Figure 8: as can be seen from Figure 8, in Fig. 8 (1), threshold value is bigger, data only be divide into two classes by algorithm, in Fig. 8 (2)～Fig. 8 (9), middle data in an interim state are constantly separated under the driving of algorithm.When cluster threshold value reduces, the extent of polymerization in each class is more and more higher, and the result of the present invention is more accurate.But in Fig. 8 (10), when t is 700～1000, the state point of system originally belongs to same class, but after this step threshold value reduces, many points are therefrom stripped out, and two classes being separated out are interlaced with each other in time sequencing.If this two class being all considered as the stable state of system, Fig. 8 (10) representing, during this period of time system switches continually between two stable states, and this is non-existent in natural procedures system to be absent from transitive state.
It is thus regarded that, the state in Fig. 8 (10) has reached the limit that threshold value reduces, and rational distance threshold size should take threshold value that in Fig. 8 (9), result is corresponding as final threshold value.
Embodiment 3:
Embodiment 3 be applied in real process produce historical data, employ certain power plant 60MW unit boiler data and carry out data experiments.Data specifically include that boiler load instruction, generated output, coal input quantity, intake, each some soda pop temperature of measuring, pressure etc., totally 180 tie up.Choosing wherein 10000 point data uses above-mentioned clustering algorithm to carry out stable state detection.Variable change situation main in this period is as shown in Figure 9:
As seen from Figure 9, in the time period studied, system loading has bigger twice adjustment, generally creates the data of 3 sections of stable states in interval.Main steam temperature and main steam pressure have bigger fluctuation, only even do not see the fluctuation situation of system from vapor (steam) temperature curve.Below the state point that all of for system variable forms is clustered, according to the method above selecting threshold value, selecting total iterations is 50 times, data experiments proves result such as Figure 10 of the 50th time, cannot obtain useful message from result, therefore here stop continuing iteration, in the D finally obtained 0 number and change such as Figure 11, Figure 11 (a) represents in 50 iteration the number distribution of in D 0, and Figure 11 (b) represents in 50 iteration the situation of change of 0 number in D.
Embodiment is when 16 step, and in D, the number of 0 element is undergone mutation, and in order to more intuitively arrive the change of cluster, the representative iteration result of selected part is as shown in Figure 12.Can be seen that in Figure 12, when iteration is from the 16th step to 17 step, the point in 0～2000 time period is split into two classes, and the picture on cluster result coincide with the sudden change of 0 element number in D, also illustrate that the reasonability of the inventive method.
According to the result that cluster obtains, suitable time span is selected to carry out stable state detection, the characteristic according to industrial object, it is believed that when system remains stable in 500 sampled points, then it is believed that system is in stable state.In the cluster result of embodiment, adopt in cluster result be not less than in 500 interval to cluster a little number all identical, then think that system is in steady statue, obtain the stable state detection output result of system accordingly as shown in figure 13, Figure 13 (c) wherein 1 expression is stable, and 0 represents instability.
The final visible present invention has its significant technique effect, the stable state detection suitability is strong, it is to avoid process the amount of calculation sharp increase phenomenon produced in data because of data dimension.
Above-described embodiment is not the restriction for the present invention, and the present invention is not limited only to above-described embodiment, as long as meeting application claims, belongs to protection scope of the present invention.
Claims (6)
1. the systematic steady state detection algorithm based on hierarchical clustering, it is characterised in that:
STEP1 generates clustering tree:
1.1) comprised to the industrial data { d of N number of sampled point one period of continuous time in intervali, i=1,2,3 ..., N, in set, sampled point is as class, diRepresent the industrial data of class；
1.2) calculate all distances between class between two, obtain the matrix of N × NIn matrix A, the element of p row q row is designated as apq, apqRepresent class dpWith class dqBetween distance, app=0；
1.3) the class spacing minima a in matrix A is foundmnNamely m class and the n-th class are two classes that current distance is nearest, m class and the n-th class are merged into a new class, m row in puncture table A, n row, m arrange and n row, the class of current residual is adopted step 1.2 again with merging the new class obtained) identical mode calculates class spacing, it is thus achieved that the matrix A after renewal；
1.4) step 1.2 is repeated)～1.3) be iterated, until matrix A becomes the matrix of 1 × 1, record m, n and a in each iterative processmn, constitute expression matrix Z, the m of N × 3 of hierarchical clustering tree, n and amnThe first, second, third columns value respectively as matrix Z；
STEP2 threshold value is chosen:
For expression matrix Z, calculate cluster result reasonability value D_zero (k) obtaining each time successively to the order of first time iterative numerical by last iterative numerical, asked for calculate by each calculated cluster result reasonability value D_zero (k) and obtain final threshold value, with z3kAs final threshold value to industrial data { diCarry out cluster calculation, it is thus achieved that final cluster result sequence T；
STEP3 combines sequential and judges stable state:
Element T in final cluster result sequence TiIf meeting the following conditions, then it is assumed that the system between m-th sampled point to the m+l-1 sampled point is in stable state:
Ti=c, i=m, m+1, m+2 ..., m+l-1
Wherein, TiFor the cluster result that the i-th sampled point in final cluster result sequence T is corresponding, c represents result constant, l=τ/Ts, τ is above-mentioned time span threshold value, TsSampling time interval for data.
2. a kind of systematic steady state detection algorithm based on hierarchical clustering according to claim 1, it is characterized in that: described step 1.3) the middle end merged in the matrix A after the new class obtained is placed in renewal, in described matrix A, the ranks digital number of remaining class remains unchanged, and the ranks rank-numeral merging the new class obtained adopts new ranks digital number and the ranks digital number with all classes before all to differ.
3. a kind of systematic steady state detection algorithm based on hierarchical clustering according to claim 1, it is characterized in that: described step 1.3) in merge in the class that obtains and matrix A between each class remaining distance calculation as follows, class after note m class and the merging of n class is numbered s, i class is any sort except s class, then the distance calculating s class and i class has:
asi=α ami+(1-α)αni
Wherein, α is weight parameter, 0≤α≤1, asiRepresent the spacing between s class and i class, aniRepresent the spacing between n class and i class, amiRepresent the spacing between m class and i class.
4. a kind of systematic steady state detection algorithm based on hierarchical clustering according to claim 1, it is characterised in that: described step STEP2 calculates every time and calculates all in the following ways: with current lowest distance value amnFor threshold value to industrial data { diCarrying out cluster calculation, the cluster result sequence obtained is Tk, k represents iteration ordinal number, cluster result sequence TkIt is the integer sequence of 1 × N, calculates and ask for cluster result sequence TkDifference sequence D, calculate in difference sequence D the number of zero as cluster result reasonability value D_zero (k).
5. a kind of systematic steady state detection algorithm based on hierarchical clustering according to claim 1, it is characterized in that: described step STEP2 is asked for by each calculated cluster result reasonability value D_zero (k) calculating and obtains final threshold value particularly as follows: be made up of cluster result reasonability value sequence D_zero each calculated cluster result reasonability value D_zero (k), calculate the difference sequence asking for cluster result reasonability value sequence D_zero, therefrom find the sequence number j at difference value maximum in difference sequence and place thereof, and with Z3jAs final threshold value.
6. a kind of systematic steady state detection algorithm based on hierarchical clustering according to claim 1, it is characterised in that: described step STEP2 is calculated, to the order of first time iterative numerical, the centre time iterative numerical referring to first time iterative numerical or the k=N/2 calculating k=1 by last iterative numerical successively.
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