CN113159139A - Damage state diagnosis method based on improved acoustic emission density clustering - Google Patents

Damage state diagnosis method based on improved acoustic emission density clustering Download PDF

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CN113159139A
CN113159139A CN202110358326.1A CN202110358326A CN113159139A CN 113159139 A CN113159139 A CN 113159139A CN 202110358326 A CN202110358326 A CN 202110358326A CN 113159139 A CN113159139 A CN 113159139A
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章欣
王康伟
沈毅
王艳
郭晓棠
张军
王军
赵成禹
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Abstract

The invention discloses a damage state diagnosis method based on improved acoustic emission density clustering, which is characterized in that acoustic emission features are fused and dimensionality reduced based on random neighborhood embedding, then the fused features are clustered and diagnosed through a density clustering algorithm, and parameters of the two are jointly optimized based on a genetic algorithm, so that crack signals contained in an acoustic emission feature set and corresponding damage states of the crack signals are finally diagnosed. The method adopts an unsupervised algorithm to explore the internal distribution rule and essential characteristics of acoustic emission signals in the steel degradation process, and comprises the steps of constructing a dimension reduction characteristic space through a random neighborhood embedding technology in manifold learning, improving a density clustering algorithm through a proposed internal evaluation target, autonomously optimizing the selection process of sensitive parameters of the algorithm, and enhancing the parameter robustness and anti-interference performance of the algorithm, so that the acoustic emission samples at different damage stages are automatically clustered.

Description

Damage state diagnosis method based on improved acoustic emission density clustering
Technical Field
The invention relates to a method for monitoring damage acoustic emission signals and diagnosing the state of the damage acoustic emission signals in a high-speed railway, in particular to a damage state diagnosis method based on improved acoustic emission density clustering.
Background
High speed railways are the economic industry of the legs of many countries with an average of over 30% total freight and 10% total passenger. In the detection and maintenance process of the high-speed railway system, the evaluation of the health state of the railway is very important. Although in practical application environments, acoustic emission events generated in the process from fatigue crack germination to propagation of wheels and steel rails are difficult to artificially demarcate the safety stages, in the degradation process, various fracture and failure mechanisms including micro crack germination, crack propagation and nucleation, crack instability and fracture and the like tend to be active in different health stages in sequence and are represented as main components in corresponding acoustic emission events, so that acoustic emission signal clusters or clusters with different waveforms and statistical characteristics are generated.
Clustering algorithms are generally more feasible in applications where a priori information is incomplete, such as lesion state monitoring. However, conventional segmentation clustering algorithms, hierarchical clustering and the like are only good at finding hypersphere data sets with balanced sample distribution, the processing results of the data sets with unbalanced samples, complex geometrical structures in characteristic spaces and serious noise interference are often poor, the density clustering algorithm ingeniously solves the three problems by constructing the concepts of density accessibility, connectivity and sample neighborhood, the robustness of the clustering algorithm on the interference factors is improved, and the result in the density clustering depends on two sensitive hyperspameters, namely neighborhood radius (epsilon) and neighborhood core points (Minpts). Both of them are difficult to estimate, although they depend on the sample prior distribution information; secondly, the density clustering has poor clustering effect on high-dimensional features, and the phenomenon of dimension disaster exists.
Disclosure of Invention
The invention provides a damage state diagnosis method based on improved acoustic emission density clustering, and aims to solve the problems that crack acoustic emission signals are automatically detected and a damage state is diagnosed by a density clustering method optimized by a genetic algorithm under the conditions that a large amount of noise exists in a railway field and the sample type distribution is unbalanced. Under the complex noise environment of the railway site, by combining the method provided by the invention, the acoustic emission signals are analyzed to realize the clustering analysis of the acoustic emission of the damage generated in the wheels and the railway in the environment, and the clustering type is used as the diagnosis result of the damage state, thereby providing further guidance for the diagnosis and maintenance of the railway health state.
The purpose of the invention is realized by the following technical scheme:
a damage state diagnosis method based on improved acoustic emission density clustering is characterized in that acoustic emission features are fused and dimensionality reduced based on random neighborhood embedding, then fused feature clustering diagnosis is performed through a density clustering algorithm, parameters of the two are jointly optimized based on a genetic algorithm, and finally crack signals contained in acoustic emission feature sets and corresponding damage states are diagnosed, and the method specifically comprises the following steps:
the method comprises the following steps: acquiring acoustic emission data S when monitoring the damage signal, wherein the acoustic emission data S comprises N sections of signals, and extracting an original acoustic emission characteristic of each section of acoustic emission signal in the S to form an original acoustic emission characteristic set C;
step two: setting evolution algebra i as 1 and nmaxRandomly initializing four parameters to be solved (fusing feature dimension d, complexity Perp, neighborhood core point number Minpts and neighborhood radius epsilon) and performingEach group of parameter solution binary codes are single individuals in a parent population, and the population contains l individuals;
step three: performing random neighborhood embedding optimization on the original acoustic emission feature set C based on the fusion feature dimension and complexity in the ith generation of parameters to obtain a fused acoustic emission feature set F under corresponding parameters;
step four: inputting the fused acoustic emission feature set F, neighborhood core points Minpts and neighborhood radius epsilon in the ith generation of parameters into a density clustering algorithm, and calculating the classification mode under the corresponding parameters by the density clustering algorithm according to the core points and connectivity definitions: comprising NCSet of individual classes CClusterID，ClusterID＝1,…,NCAnd a set of outlier noise points Nn；
Step five: evaluating the density clustering result of different individuals in the ith generation of population under corresponding parameters through the generalized contour coefficient, and calculating the generalized contour coefficient GSI (F) of different individuals in the ith generation of parent population;
step six: selecting and copying a parent population by taking the generalized contour coefficient of the population as a fitness function of the population, performing cross variation operation to obtain a child population, replacing the parent population with the child population, and recording a chemical algebra i as i + 1;
step seven: judging whether the evolution algebra reaches the maximum value nmaxIf not, returning to the third step; and if so, outputting the individual with the highest fitness in the population at the moment, and decoding the individual to obtain an optimal parameter solution and a density clustering result corresponding to the optimal parameter solution.
Compared with the prior art, the invention has the following advantages:
1. the method adopts an unsupervised algorithm to discover the internal distribution rule and essential characteristics of acoustic emission signals in the steel degradation process, comprises the steps of constructing a dimension reduction characteristic space through a random neighborhood embedding technology in manifold learning, improving a Density-Based Clustering of Applications with Noise, DBSCAN (distributed data area network) algorithm through a proposed internal evaluation target, autonomously optimizing the selection process of sensitive parameters of the algorithm and enhancing the parameter robustness and anti-interference performance of the algorithm, thereby realizing the automatic Clustering of acoustic emission samples at different damage stages.
2. The invention provides a damage state diagnosis method based on improved acoustic emission density clustering, which is used for evaluating a clustering effect through specific indexes from the perspective of an optimization method so as to obtain the optimal estimation of a hyperparameter. Meanwhile, the optimal dimension reduction feature after feature fusion is obtained based on the random neighborhood embedding technology optimized by the same index. Therefore, firstly, an internal clustering index-generalized contour coefficient capable of evaluating noise interference is provided. The index can be obtained by adding a proportion punishment term to the contour coefficient through a noise point set N in a data set CnThe index expression can be derived from the union of the single-element clusters considered as having no contour information. Therefore, the acoustic emission density clustering and damage state diagnosis method provided by the invention performs gradient optimization dimensionality reduction on the acoustic emission characteristic based on the random neighborhood embedding technology assuming the known parameters (complexity/fusion dimensionality) on the basis of the high-dimensional acoustic emission original characteristic to obtain the fusion characteristic; and then encoding key parameters of random neighborhood embedding and DBSCAN into an initial population through a genetic algorithm, carrying out density clustering on the fusion features to obtain clustering results, taking the generalized contour coefficients of the clustering results as fitness functions of the evaluation population, and carrying out cross and variation search in the population to ensure that the solution set evolves towards the direction with the maximum generalized contour coefficients, thereby obtaining the optimal fusion features and clustering parameters and obtaining the density clustering and autonomous diagnosis results of the damage state.
3. The method can be used for acoustic emission data sets with unbalanced sample distribution or noise interference, automatic clustering diagnosis does not need any priori knowledge training, traditional clustering parameters such as Minpts, Eps, clustering category number and the like do not need to be preset, heuristic search efficiency is high by means of a genetic algorithm, an optimization function is not limited, the clustering problem of the acoustic emission samples is truly and autonomously clustered and diagnosed by optimizing the provided internal clustering index, and the method can be used for diagnosing and analyzing damage and noise signals acquired on a railway site; and the clustering method provided by the invention can still achieve the purposes of accurately detecting the crack signals and judging the damage states of the crack signals under the conditions that the sample distribution is unbalanced and the wheel track noise signals are far more than the crack signals.
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FIG. 1 is a flow chart of a method for improved acoustic emission density clustering based damage status diagnosis according to the present invention;
FIG. 2 is a graph of crack signatures used in the present invention;
FIG. 3 is a diagram of a wheel-track noise signal employed in the present invention;
FIG. 4 is a result of clustering acoustic emission data when the number of noise samples is 100 according to the present invention;
FIG. 5 is a comparison of the clustering effect of the method of the present invention and the hierarchical clustering and hierarchical density clustering algorithm under different noise interferences.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a damage state diagnosis method based on improved acoustic emission density clustering, which comprises the following seven steps: and extracting an original characteristic C from the acoustic emission data S of the collected damage signal. And (2) randomly generating and coding according to the parameters to be solved (including the parameters of random neighborhood embedding, namely fusion characteristic dimension d and complexity Perp, and density clustering parameters, namely Minpts and epsilon) to obtain an initial population, and then performing gradient descent optimization of random neighborhood embedding according to the parameters of the generated population to obtain the fused characteristics. And inputting the initial density clustering parameters and the fused features as a density clustering algorithm, and calculating a set of core points, boundary points and outlier noise points of the fused feature space to obtain a clustering result. Then based on a genetic algorithm, evaluating the fitness of all individuals in the parent population by using the generalized contour coefficient, selecting and copying the population according to the individual fitness, obtaining an offspring population after cross mutation operators as an i +1 th generation parent population, and repeating iteration until the evolution algebra reaches the maximum value nmaxOutputting the optimal solution and the corresponding clustering result, and performing the optimal operation on the algorithm according to the clustering resultAnd (5) final evaluation. As shown in fig. 1, the specific implementation steps are as follows:
the method comprises the following steps: and acquiring acoustic emission data S when the damage signal is monitored, wherein the acoustic emission data S comprises N sections of signals, and extracting the original acoustic emission characteristics of each section of acoustic emission signal in the S to form an original acoustic emission characteristic set C.
The acoustic emission data multi-dimensional original features specifically include: the acoustic emission method comprises the following steps that wavelet packet coefficient energy ratio, wavelet packet entropy, peak value, absolute mean value, root mean square, kurtosis, skewness, peak value factor, waveform factor, impulse factor and margin factor are included in an original acoustic emission characteristic set, the original acoustic emission characteristic set comprises N samples, and each sample is characterized by d0。
Step two: setting evolution algebra i as 1 and nmaxRandomly initializing parameters to be solved and carrying out binary coding to obtain parent population; the initial parent population comprises l individuals, each individual is composed of chromosomes obtained by randomized parameter coding, and four parameters to be solved in the chromosomes specifically comprise: 1) parameters of random neighborhood embedding: fusing a feature dimension d and complexity Perp; 2) density clustering parameters: neighborhood core points Minpts and neighborhood radius ε.
Step three: and (4) carrying out random neighborhood embedding on the original acoustic emission feature set C to obtain a corresponding fused acoustic emission feature set F under the ith generation of parameters. The specific operation comprises the following steps:
(1) calculating x between high-dimensional samples in the original acoustic emission feature set under the condition of corresponding ith generation parameters d and Perpi，xjConditional similarity of (1):
Figure BDA0003004484160000071
wherein, σ is the estimated variance of the samples in the original acoustic emission feature set, and the estimated value is determined by Perp; its high dimensional feature symmetric similarity is pij＝(pj|i+pi|j)/2；
(2) Then calculating corresponding sample f in fused acoustic emission feature seti,fjLow dimensional feature symmetry similarity of (2):
Figure BDA0003004484160000072
(3) according to high-dimensional feature symmetry similarity pijSimilarity q with low dimensional feature symmetryijThe Kullback-Leibler (KL) divergence measures the difference in distribution between the two, and the KL divergence of the two is calculated as follows:
Figure BDA0003004484160000073
(4) taking KL divergence as an optimization target of random neighborhood embedding, and setting KL divergence convergence range as e0When KL (p | | q) is less than or equal to e0And considering that the KL divergence is converged, and performing gradient optimization on the target to obtain a fused acoustic emission feature set F under the corresponding initial parameters.
Step four: inputting initial parameters (Minpts and epsilon) and the fused acoustic emission feature set F into a density clustering algorithm, calculating a core point set, a boundary point set and an outlier noise point set corresponding to the fused acoustic emission feature set through the definition of core points and connectivity of the density clustering algorithm, and outputting a clustering division result F of the density clustering algorithm ({ C)ClusterID}∪Nn)，ClusterID＝1,…,NCI.e. dividing F into a total of NCSet of individual classes CClusterIDAnd an outlier noise set Nn。
Step five: evaluating the density clustering results under different parameters in the same population through the generalized contour coefficients, and calculating the generalized contour coefficients GSI (F) of different individuals in the parent population, wherein the calculation mode of the GSI (F) is as follows:
Figure BDA0003004484160000081
wherein N is the total number of samples of the fused acoustic emission feature set F, and N isnFor clustering outliers NnTotal number of samples of (a); a, (i), b (i) are samples f with ClusterID as class in feature set respectivelyiOf intra-class similarity and inter-class similarityEvaluating the formula, wherein the calculation formula is as follows:
Figure BDA0003004484160000082
wherein n isClusterIDTotal number of samples for a subset of classes ClusterID, njTotal number of samples for subset of category j.
Step six: taking the generalized contour coefficient of the population individuals as a fitness function of the population individuals, setting the selection probability of the individuals according to a roulette algorithm based on the population individual fitness function, carrying out selection and copying operations on the parent population, carrying out cross variation operation to obtain the offspring population, replacing the parent population with the offspring population, and recording a conversion algebra i as i + 1.
Step seven: judging whether the evolution algebra reaches the maximum value nmaxIf not, returning to the third step; and if so, outputting the individual with the highest fitness in the population at the moment, decoding the individual to obtain an optimal parameter solution and obtaining a corresponding density clustering result.
Example (b):
the method comprises the following steps: and acquiring acoustic emission data S when the damage signal is monitored, wherein the acoustic emission data S comprises N sections of signals, and extracting the original acoustic emission characteristics of each section of acoustic emission signal in the S to form an original acoustic emission characteristic set C.
The crack signal adopted in the embodiment is a crack signal acquired by a tensile experiment, the sampling rate of the acoustic emission signal is 5MHz, the signal comprises 2048 sampling points, the duration is 0.4096 milliseconds, the waveform example of the signal is shown in fig. 2, and all the signals can be sequentially divided into three healthy stages of crack germination, propagation and fracture by using yield strength and ultimate strength according to the characteristics of the material. And meanwhile, acquiring wheel-track noise acoustic emission signals generated when the train runs at the speed of 55km/h on a railway site, wherein the acquisition setting is the same as that of a stretching experiment, and the waveform of the noise signals is shown in figure 3. In the embodiment, in order to verify the robustness of the method to noise, random tests are adopted, 100 samples are taken from three stages of crack germination, propagation and fracture at random, and labels are given as 1, 2 and 3; subsequent noise on wheel and rail100 x beta samples are taken from the acoustic signal, beta is gradually increased and is an integer between 1 and 10, a label is given as-1, and the clustering result when the noise interference is increased can be seen by adjusting the increase of beta, and the robustness of the method for the noise interference and the unbalanced distribution is improved. In summary, the total number of acoustic emission samples is N ═ 3+ β × 100, and β ≧ 10 ≧ 1. Extracting original features of each acoustic emission signal, wherein the extracted feature categories comprise time domain features, frequency domain features and time-frequency features; the specific characteristic names are wavelet packet coefficient energy ratio, wavelet packet entropy, peak value, absolute mean value, root mean square, kurtosis, skewness, peak value factor, waveform factor, pulse factor and margin factor, and the original characteristic dimension is d0＝15。
Step two: setting evolution algebra i equal to 1 and nmaxRandomly initializing four parameters to be solved (fusion feature dimension d, complexity Perp, neighborhood core points Minpts and neighborhood radius epsilon) and binary coding each group of parameters into a single individual in a parent population, wherein the population contains 40 individuals in total.
The coding length of each chromosome individual adopted in this embodiment is 46, wherein the neighborhood radius is a continuous variable, the corresponding coding length of this embodiment is 25, and the highest retrieval precision is 1 × 10-7For the other three integer variables, seven-bit binary coding is adopted, and the retrieval range is [1,100 ]]。
Step three: decoding fusion characteristic dimension d and complexity Perp in the ith generation of individual parameters, estimating the similarity between high-dimensional samples of an original acoustic emission characteristic set and the similarity between low-dimensional samples of a fused acoustic emission characteristic set according to a random neighborhood embedding technology, calculating KL divergence between the high-dimensional samples and the low-dimensional samples, reducing the KL divergence by a gradient method to optimize the fused acoustic emission characteristic set, and setting the KL divergence convergence range to be less than or equal to e0＝1×10-5And obtaining a fused acoustic emission feature set F which is closest to the original acoustic emission feature set distribution under the corresponding parameters.
Step four: decoding Minpts and epsilon in the ith generation individual parameters, inputting the Minpts and epsilon and the fused acoustic emission feature set F into a density clustering algorithm, defining through core points and connectivity of the density clustering algorithm,calculating a core point set, a boundary point set and an outlier noise point set in the acoustic emission feature set after corresponding fusion, and outputting a clustering division result F ({ C) of a density clustering algorithmClusterID}∪Nn)，ClusterID＝1,…,NCI.e. dividing F into a total of NCSet of individual classes CClusterIDAnd an outlier noise set NnIn the present embodiment, the total number of cluster categories NC＝3。
Step five: evaluating the density clustering results under different parameters in the same population through the generalized contour coefficients, and calculating the generalized contour coefficients GSI (F) of different individuals in the parent population, wherein the calculation mode of the GSI (F) is as follows:
Figure BDA0003004484160000101
wherein N is the total number of samples of the fused acoustic emission feature set F, and N isnFor clustering outliers NnTotal number of samples of (a); a, (i), b (i) are samples f with ClusterID as class in feature set respectivelyiThe evaluation formula of the intra-class similarity and the inter-class similarity is as follows:
Figure BDA0003004484160000111
wherein n isClusterIDIs the total number of samples with the category of the subset of ClusterID, | | | | is a function of the Euclidean distance, njTotal number of samples for subset of category j.
Step six: taking the generalized contour coefficient of the population individuals as a fitness function of the population individuals, setting the selection probability of the individuals according to a roulette algorithm based on the population individual fitness function, carrying out selection and copying operations on the parent population, carrying out cross variation operation to obtain the offspring population, replacing the parent population with the offspring population, and recording a conversion algebra i as i + 1.
Step seven: judging whether the evolution algebra reaches the maximum value nmaxIn this embodiment, nmaxIf not, returning to the third step; if it isIf the result is reached, outputting the individual with the highest fitness in the population at this time, decoding the individual to obtain an optimal parameter solution and a density Clustering result corresponding to the optimal parameter solution, under the interference of 100 noise Points, and based on the Clustering result of the invention, as shown in fig. 4, simultaneously evaluating and comparing the optimal Clustering result obtained by the invention when beta is more than or equal to 10 and more than or equal to 1 with the Clustering result of an Hierarchical Clustering method (AHC) and an Hierarchical density Clustering method (optical to Identify the Clustering Structure, OPTICS). In this embodiment, the evaluation indexes include clustering accuracies Acc and F1The fractions are respectively as follows:
Figure BDA0003004484160000112
wherein the content of the first and second substances,
Figure BDA0003004484160000113
total number of samples, n, representing the real label as class i and the simultaneous clustering result as class jiAnd n'jRespectively representing the total number of samples with label category i and the total number of samples with clustering result category j. The clustering result evaluation index changes under the noise interference of different proportions are shown in fig. 5, and the comparison shows that the method can obtain higher clustering accuracy, the range of the clustering accuracy is between 0.928 and 0.986, which is much higher than that of the two comparison methods, the influence of the noise interference and the sample set imbalance phenomenon on the clustering result is smaller, and the method has higher robustness.

Claims (7)

1. A damage state diagnosis method based on improved acoustic emission density clustering is characterized by comprising the following steps:
the method comprises the following steps: acquiring acoustic emission data S when monitoring the damage signal, wherein the acoustic emission data S comprises N sections of signals, and extracting an original acoustic emission characteristic of each section of acoustic emission signal in the S to form an original acoustic emission characteristic set C;
step two: setting evolution algebra i as 1 and nmaxRandomly initializing fusion feature dimension d, complexity Perp, neighborhood core point number Minpts,Neighborhood radius epsilon four parameters to be solved and binary coding each group of parameters into a single individual in a parent population, wherein the population contains l individuals;
step three: performing random neighborhood embedding optimization on the original acoustic emission feature set C based on the fusion feature dimension and complexity in the ith generation of parameters to obtain a fused acoustic emission feature set F under corresponding parameters;
step four: inputting the fused acoustic emission feature set F and neighborhood core points Minpts and neighborhood radius epsilon in the ith generation parameter into a density clustering algorithm, and calculating a classification mode under the corresponding parameter by the density clustering algorithm according to the core points and connectivity definition: comprising NCSet of individual classes CClusterID，ClusterID＝1,…,NCAnd a set of outlier noise points Nn；
Step five: evaluating the density clustering result of different individuals in the ith generation of population under corresponding parameters through the generalized contour coefficient, and calculating the generalized contour coefficient GSI (F) of different individuals in the ith generation of parent population;
step six: selecting and copying a parent population by taking the generalized contour coefficient of the population as a fitness function of the population, performing cross variation operation to obtain a child population, replacing the parent population with the child population, and recording a chemical algebra i as i + 1;
step seven: judging whether the evolution algebra reaches the maximum value nmaxIf not, returning to the third step; and if so, outputting the individual with the highest fitness in the population at the moment, and decoding the individual to obtain an optimal parameter solution and a density clustering result corresponding to the optimal parameter solution.
2. The method of claim 1, wherein the raw acoustic emission features comprise: wavelet packet coefficient energy ratio, wavelet packet entropy, peak, absolute mean, root mean square, kurtosis, skewness, peak factor, form factor, pulse factor, and margin factor.
3. The damage state based on improved acoustic emission density clustering of claim 1The diagnostic method is characterized in that the original acoustic emission feature set C comprises N samples, and the feature dimension of each sample is d0。
4. The damage status diagnosis method based on improved acoustic emission density clustering according to claim 1, wherein the third step comprises the following steps:
(1) calculating x between high-dimensional samples in the original acoustic emission feature set under the condition of corresponding ith generation parameters d and Perpi，xjConditional similarity of (1):
Figure FDA0003004484150000021
wherein, sigma is the estimated variance of the samples in the original acoustic emission feature set, and the symmetric similarity of the high-dimensional features is pij＝(pj|i+pi|j)/2；
(2) Calculating a corresponding sample f in the fused acoustic emission characteristic seti,fjLow dimensional feature symmetry similarity of (2):
Figure FDA0003004484150000022
(3) according to high-dimensional feature symmetry similarity pijSimilarity q with low dimensional feature symmetryijThe KL divergence of (A) measures the difference in distribution between the two;
(4) taking KL divergence as an optimization target of random neighborhood embedding, and setting KL divergence convergence range as e0When KL (p | | q) is less than or equal to e0And considering that the KL divergence is converged, and performing gradient optimization on the target to obtain a fused acoustic emission feature set F under the corresponding initial parameters.
5. The method according to claim 4, wherein the KL divergence is calculated as follows:
Figure FDA0003004484150000031
6. the method of claim 1, wherein the generalized contour coefficients gsi (f) are calculated as follows:
Figure FDA0003004484150000032
wherein N is the total number of samples of the fused acoustic emission feature set F, and N isnFor clustering outliers NnTotal number of samples of (a); a, (i), b (i) are samples f with ClusterID as class in feature set respectivelyiThe intra-class similarity and the inter-class similarity of (2).
7. The method for diagnosing damage status based on improved acoustic emission density clustering according to claim 1, wherein the calculation formulas of a (i), b (i) are as follows:
Figure FDA0003004484150000033
wherein n isClusterIDTotal number of samples for a subset of classes ClusterID, njTotal number of samples for subset of category j.
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