CN113822257B - Abnormal point detection method based on combination of dimensionless features and virtual samples - Google Patents
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Abstract
The invention provides an abnormal point detection method based on combination of dimensionless characteristics and virtual samples, which comprises the steps of firstly extracting dimensionless parameters of vibration signals to reduce the influence of different devices on abnormal samples, then eliminating the scale influence before different characteristics through data standardization, then obtaining a certain number of virtual samples by applying a virtual sample technology to the support vectors of the abnormal samples, improving the number of training samples, training the models by utilizing a support vector machine, improving the popularization capability of the training models and improving the popularization capability of classification models. The method utilizes time domain dimensionless characteristic modeling to eliminate the scale influence of vibration data of different devices, and utilizes the sparsity of support vectors to carry out interpolation to obtain enough virtual samples, so that the probability distribution of the interpolated samples and the original samples is kept approximately consistent; the classification model is established based on the support vector machine, so that the method has good generalization performance on small sample learning, improves the robustness of abnormal vibration signal identification, and can be effectively used for real-time industrial monitoring.
Description
Technical Field
The invention relates to the technical field of measurement and testing, in particular to an abnormal point detection method based on combination of dimensionless features and virtual samples.
Background
Since the introduction of outlier mining (also commonly referred to as outlier detection and analysis) in 1980, there have been several alternations of aging, and in recent years, outlier mining (outlier mining) has become a significant research direction in the data mining technology field again. The abnormal point mining refers to a method for finding out a part of extremely small error information from the massive information data. With the complexity and the variability of the real world, the appearance of abnormal points in the complex heterogeneous data set has different reasons, wherein some abnormal points can be caused by data missing or wrong input and wrong measuring instruments, the abnormal points are called wrong data, and the data can be transformed and proposed by applying certain modes; the other causes of the outliers may be the data itself, and the outliers may also contain valuable information, and the outliers are often the central research content in the data mining. The significance of outlier mining is therefore no longer limited to earlier noise-removed data, but also to finding meaningful information that is potentially behind the data, and analyzing and understanding it. The abnormal points are small data which are stored in a mass data set, and although the existing data mining method is mature in classification or pattern learning, the special data mining task of the abnormal point mining is not perfect, so that the theory and the method for deeply discussing the abnormal point mining are very necessary. The outlier detection can be applied to various aspects such as climate change, gene mutation, etc. The abnormal point mining develops to date, and a plurality of classical methods such as density-based algorithm, clustering-based algorithm, distance-based algorithm and the like appear. Each algorithm has advantages and disadvantages, such as distance-based outlier mining determines whether an anomaly is present by k-neighborhood distance. The disadvantage is a strong dependence on the parameters. In density-based outlier mining, whether this data is an outlier is determined by the neighborhood of each data point. The disadvantage is that it does not scale well for sequence data and low density data objects. The abnormal point mining based on the deviation is to judge whether the abnormal point is an abnormal point by checking the main characteristics of the test data. The disadvantage is that the practical application is relatively few. In conclusion, there are so many classical methods for outlier detection, but none of them can perfectly solve this problem, so there is a need for reasonable improvement of these methods.
In the prior art, a rough set principle is used as abnormal point detection to clearly explain the mining process of abnormal data; in the algorithm, classification discussion is used as the basis of abnormal point analysis, and finally definition of abnormal attributes is given; an abnormal point detection method based on deviation.
The abnormal points in the data set are judged by the concentration degree of the data objects in the data set in each area, and the data objects far away from the concentrated area are determined as abnormal data. Currently, there are two main techniques for detecting an abnormal point based on a deviation: OLAP data cube techniques and sequencing techniques. This technique is an algorithm for detecting abnormal data based on a deviation. The visualization mode can be more convenient for users to use, and the unit value under a certain calibration can be further analyzed according to the requirements of the users. Algorithms that detect outliers based on depth can also handle datasets that do not have a distribution that follows a certain rule. The principle is that the probability that data points in a shallow layer become abnormal points is greater than that of data in a deeper layer, so that the algorithm can save the step of detecting the abnormal points of the data object in the deeper layer, and the calculation efficiency is greatly improved. In a cluster-based outlier detection method, data objects with the same characteristics are clustered together as much as possible to form clusters one after another, and the greatest dissimilarity between clusters is required. The purpose of outlier detection is to find data objects that deviate from other data objects, while the purpose of clustering is to find data that is closely related to those data objects, so it seems that the clustering method and the outlier detection method are opposite, but with improvement, the clustering method has been applied in data mining for outlier detection because most algorithms for detecting outlier data based on clustering are very small in complexity, so such outlier detection methods generally have high efficiency. The abnormal points detected by the density-based abnormal point detection algorithm are more comprehensive, and the density-based abnormal data detection method can be used for analyzing a data set with uneven density distribution. The principle is that the abnormal degree of the calculated data is judged by measuring certain density of the calculated data and the neighborhood data.
All attribute values of the data are considered in the rough set algorithm during abnormal point detection, so that the efficiency is low when a data set with multi-dimensional attributes is detected; the bias-based outlier detection algorithm, when using this technique, requires that for all subsets, the degree of difference of the previous subset from this subset needs to be known. However, in the actual outlier detection case, the dataset is mostly high dimensional and has multiple attributes, and it is difficult to determine the main features of the dataset. Therefore, when the deviation-based abnormal point detection is used, it is often difficult to measure the deviation degree of the data by selecting an appropriate degree of dissimilarity, so the deviation-based abnormal point detection method is often only used in scientific theory research and rarely appears in the actual abnormal point detection case. Depth-based outlier detection methods can also be used to process data points having a multidimensional space. However, as the dimension increases [54], the complexity of detection increases greatly, greatly affecting the efficiency of outlier detection, and therefore, depth-based outlier detection methods are generally only applied in the lower dimension space, and are generally rarely used for datasets with high dimension spaces. In the cluster anomaly point detection algorithm, because the accuracy of the clustering algorithm is greatly influenced by the selection of the clustering specification, a proper clustering algorithm needs to be selected according to actual conditions. The density-based outlier detection method requires knowledge of the probability distribution of the sample, which is difficult in practical applications.
Disclosure of Invention
The invention aims to solve the problems of low robustness, poor real-time performance and the like of the traditional abnormal point detection method, and provides an abnormal point detection method based on combination of dimensionless characteristics and virtual samples.
The invention provides an abnormal point detection method based on combination of dimensionless characteristics and virtual samples, which comprises the following steps:
s1, dimensionless feature extraction: separately extracting normal signal sample sets
And abnormal signal sample set
Obtaining a normal signal dimensionless feature set by the dimensionless feature variable of each signal sample
And abnormal signal dimensionless feature set
Wherein, P is the number of normal signal samples, Q is the number of abnormal signal samples, and L is the signal length of each signal sample;
the types of the dimensionless characteristic variables comprise time domain skewness, time domain kurtosis, time domain peak value factors, time domain margin factors, time domain waveform factors and time domain pulse indexes;
s2, preprocessing data: dimensionless feature set for normal signals
And abnormal signal dimensionless feature set
Respectively carrying out scale normalization on each dimensionless characteristic variable to obtain a normal signal normalization sample set
And abnormal signal normalization sample set
；
S3, obtaining a support vector: normalizing a normal signal to a set of samples
And abnormal signal normalization sample set
Establishing a classification model by using a linear support vector machine and acquiring a support vector;
s4, obtaining a virtual sample set: normalization sample set for judging abnormal signals
Whether the support vector of (a) is sparse in k neighbors: if yes, obtaining virtual samples by using an interpolation method, and if not, obtaining virtual samples by using an extrapolation method, wherein the virtual samples form a virtual sample set
Where k is an odd number and R is the number of virtual samples;
s5, training and establishing a final classification model: normalizing a normal signal to a set of samples
Set of normalized samples of abnormal signals
And virtual sample set
Establishing a final classification model using a linear support vector machine
；
S6, detecting a sample to be detected: inputting the sample to be tested into the final classification model
And detecting and judging whether the vibration signal is an abnormal vibration signal.
The invention relates to an abnormal point detection method based on dimensionless characteristic and virtual sample, which is used as an optimal mode,
in step S1, the calculation formula of the time domain skewness is:
；
the time-domain kurtosis is calculated by the formula:
；
time domain crest factor:
；
the calculation formula of the time domain margin factor is as follows:
；
the time domain form factor is calculated as:
；
the calculation formula of the time domain pulse index is as follows:
；
wherein the content of the first and second substances,x(n)is a normal sample signal or an abnormal sample signal containing n sampling points, L isx(n)The length of the signal of (a) is,
is the average value of x (n),σ x is composed ofx(n)Standard deviation of (d);
the invention relates to an abnormal point detection method based on dimensionless characteristic and virtual sample, which is used as an optimal mode,
in step S2, the formula of the scale normalization is:
wherein the content of the first and second substances,
is the mean value of the dimensionless characteristic variables,
is the standard deviation of the dimensionless characteristic variable.
According to the abnormal point detection method based on the dimensionless feature and the virtual sample, which is disclosed by the invention, as a preferable mode, in the step S3 and the step S5, a support vector is obtained through an SVM algorithm.
As a preferred mode, in step S3, the specific use method of the linear support vector machine is as follows:
the training sample set is
In which
Normalizing a set of samples for a normal signal
Or abnormal signal normalization sample set
The sample of (a) is selected,
is that
The label of the corresponding category of the user,
i =1, …, n, then the optimal hyperplane separating the samples correctly is:
then
，
Wherein
Is the variable of the amount of relaxation,
。
in the method for detecting an abnormal point based on combination of dimensionless features and virtual samples according to the present invention, as a preferred embodiment, in step S5,
normalizing sample sets for normal signals
Or abnormal signal normalization sample set
Or virtual sample set
The sample of (1).
The invention relates to an abnormal point detection method based on dimensionless characteristic and virtual sample, which is used as an optimal mode,
the method for solving the optimal hyperplane comprises the following steps:
wherein C is a penalty factor, C > 0;
the dual form is:
wherein α is a Lagrange multiplier.
The invention relates to an abnormal point detection method based on dimensionless characteristic and virtual sample, which is used as an optimal mode,
the optimal classification surface is as follows:
wherein the content of the first and second substances,
for the optimal solution of Lagrange multipliers,
is an offset.
The abnormal point detection method based on combination of dimensionless features and virtual samples is used as an optimal selection mode, and the penalty factor C is automatically obtained through 5-fold cross validation of a training set.
In the method for detecting an abnormal point based on combination of dimensionless features and virtual samples according to the present invention, as a preferred embodiment, in step S4, k is 5.
The invention aims to utilize time domain dimensionless characteristics, obtain a support vector corresponding to an abnormal vibration signal through a support vector machine, construct a virtual sample in a mode of interpolating or extrapolating the support vector, improve the sample capacity, and identify the abnormal vibration signal according to a classification model constructed by the support vector machine, so as to better serve related fields of fault diagnosis, health management and the like of equipment.
Dimensionless feature extraction
Given signal
In the form of a time-domain sequence,
extracting 6 time domain dimensionless features: definition of
Mean value
Standard deviation of
。
Data preprocessing: scale normalization (data normalization)
Data standardization (normalization) processing is a basic work of data mining, different evaluation indexes often have different dimensions and dimension units, the condition can affect the result of data analysis, and in order to eliminate the dimension influence among the indexes, the data standardization processing is needed to solve the comparability among the data indexes. After the raw data are subjected to data standardization processing, all indexes are in the same order of magnitude, and the method is suitable for comprehensive comparison and evaluation.
The set of primitive features is normalized to a data set with a mean value of 0 and a variance of 1, and the normalization formula is as follows:
wherein the content of the first and second substances,
、
mean and standard deviation of the raw feature set, respectively.
Model training: support vector machine
A Support Vector Machine (SVM) is a commonly used qualitative analysis algorithm. It is a general machine learning algorithm established by Vapnik et al on the basis of statistical learning theory and the principle of Structural Risk Minimization (SRM). It seeks the best compromise between the complexity of the model and the learning ability, based on the limited sample information, in order to obtain the best generalization ability. The basic principle is as follows:
hypothesis training sample set
Wherein
For the (i) th sample,
is that
I.e. the category information corresponding to the ith sample. It is noted as a binary problem
. If the training samples are linearly separable or nearly linearly separable, an optimal hyperplane must be found to correctly separate the two types of samples and maximize the separation of the two types of samples from the hyperplane. The optimal hyperplane is set as:
the hyperplane correctly separates the two types of samples meaning:
wherein
Is an introduced relaxation variable, there are:
namely solving the optimization problem:
wherein
Is a penalty factor that controls the degree to which erroneous samples are penalized. Introducing Lagrange multipliers
The above optimization problem is changed to its dual form (quadratic programming problem):
the optimal classification surface is as follows:
wherein the content of the first and second substances,
is the optimal solution to the quadratic programming problem described above,
is an offset.
For the nonlinear classification problem, a support vector machine utilizes nonlinear transformation to map linear indivisible data in an input space to a high-dimensional feature space, and a linear discriminant function is constructed in the high-dimensional space to realize the nonlinear classification in an original space. The inner product in the high-dimensional space can be represented by a kernel function, commonly used kernel functions include an RBF kernel, a polynomial kernel, a Sigmoid kernel and the like, and then a corresponding optimization objective function is changed into:
accordingly, the optimal classification surface becomes
And (4) carrying out voting decision on the decomposition of the multi-classification problem into a plurality of two-classification problems.
Virtual sample generation
In fault diagnosis analysis, obtaining sufficient training samples often requires a large expenditure of manpower and material resources. Therefore, how to improve the generalization ability of the traditional learner under the condition of a small amount of training data becomes a topic worthy of research. The learning problem in the case where training sample data is small is called a small sample learning problem. In order to improve the learning ability on the small sample problem, many excellent methods such as semi-supervised learning, active learning, and direct-push learning strategies have been developed in recent years. A common feature of these methods is that a large number of unlabeled samples are required as learning aids, which is sometimes difficult to satisfy. In 1994, Poggio and Vetter proposed the idea of virtual sampling. The virtual sample is a part of reasonable samples in a sample space for generating a problem to be researched by combining the existing training samples by utilizing the prior knowledge in the research field under the condition of unknown sample probability distribution functions. Nguyen et al propose a boundary Over-sampling (BOS) method to generate virtual samples based on interpolation or extrapolation of support vectors, the basic idea being as follows:
1. for original training samples, extracting support vectors of few types of samples by using SVM algorithm
2. And judging whether the obtained support vector of each low-class sample is sparse in the corresponding k (k is an odd number) neighbor or not. If the sparse is obtained, an interpolation method is adopted to obtain a virtual sample, otherwise, an extrapolation method is adopted to obtain the virtual sample, and compared with the SMOTE method, the BOS method carries out interpolation or extrapolation on the support vector.
Scheme flow
In order to effectively identify the abnormal vibration signal and improve the subsequent fault diagnosis effect, the method firstly calculates six dimensionless characteristics of the time domain signal and then carries out scale normalization (data standardization) preprocessing on the characteristics to eliminate the scale influence among all characteristic indexes. Based on the characteristics, a support vector machine is utilized to train two types of signals (normal signals and abnormal signals) and establish a classification hyperplane and a support vector: and carrying out corresponding interpolation and extrapolation operation on each support vector in the abnormal signal according to whether the support vector is sparse in k neighbors to generate a certain number of virtual samples, constructing a new training set by using the original samples and the newly generated virtual samples, and carrying out training by using a support vector machine again to obtain a machine learning final training model. After the signal to be predicted is subjected to dimensionless feature extraction and scale normalization preprocessing, a corresponding prediction result (whether the signal is an abnormal signal or not) is automatically given according to the training model.
The specific scheme flow is as follows: assume that there are two types of signals: set of normal signal samples
(wherein there are
Normal signals, each signal of length L); set of abnormal signal samples
(wherein there are
An abnormal signal, each signal of length L), in general
：
The signal
Has a length of
，
1. Separately computing normal signal sample sets
And abnormal signal sample set
Six dimensionless characteristic variables of each signal: compressing an original normal signal sample set and an abnormal signal sample set from L characteristics into 6 characteristics, namely:
and
2. respectively carrying out scale normalization (data standardization) processing on each characteristic of the two types of signal sample sets in the step 1 to obtain
And
3. and (3) establishing a classification model for the two types of sample sets in the step (2) by using a linear support vector machine (selecting hyper-parameters based on 5-fold cross validation) and obtaining support vectors.
4. To pair
Judging whether each support vector is sparse in 5 fields: if the sparse is obtained, the virtual sample is obtained by adopting an interpolation method, otherwise, the virtual sample is obtained by adopting an extrapolation method. The constructed virtual sample set is
(obtaining R virtual anomaly samples in total)
5. According to the new sample set
And establishing a final classification model by using a linear support vector machine (selecting hyper-parameters based on 5-fold cross validation)
。
Utilizing the classification model in step 5 for the signal sample to be predicted
And predicting whether the sample is an abnormal vibration signal in real time.
The invention has the following advantages:
(1) the method utilizes time domain dimensionless feature modeling, eliminates the scale influence of different equipment vibration data, and improves the robustness and the popularization of subsequent models;
(2) the method utilizes the sparsity of the support vector to carry out interpolation to obtain enough virtual samples, so that the probability distribution of the interpolated samples and the original samples is kept approximately consistent;
(3) the method establishes a classification model based on a support vector machine, and the machine learning algorithm has good generalization performance on small sample learning;
(4) the method mainly involves two parameters: a support vector K is adjacent to a parameter, and the parameter is insensitive to a prediction model result; the linear support vector machine punishment parameter C is automatically obtained through 5-fold cross validation of the training set, so that the whole process of the method is insensitive to parameter selection, and the robustness of abnormal vibration signal identification is improved;
(5) the method relates to algorithms such as linear interpolation, support vector machine, dimensionless feature extraction and the like in the calculation process, has small calculation amount, meets the requirement of on-line processing, and can be effectively applied to real-time industrial monitoring situations such as fault diagnosis, equipment health management and the like.
Drawings
FIG. 1 is a flow chart of a method for detecting an abnormal point based on dimensionless features in combination with virtual samples;
fig. 2 is a graph of the first 5 spectra of a normal sample a1 in an embodiment 2 of an abnormal point detection method based on dimensionless features in combination with virtual samples;
fig. 3 is a graph of the first 5 spectra of an abnormal sample a2 in the abnormal point detection method based on dimensionless features combined with virtual samples in example 2;
fig. 4 is five spectrograms before feature time domain dimensionless features of a normal sample a1 in the embodiment of an abnormal point detection method based on dimensionless features combined with virtual samples;
fig. 5 is a graph of five spectra before an abnormal point detection method based on dimensionless feature combined with a virtual sample, in example 2, an abnormal sample a2 feature time domain dimensionless feature;
FIG. 6 is five spectrograms before normalization of a normal sample A1 time domain dimensionless feature scale in an embodiment 2 of a method for detecting an abnormal point based on dimensionless feature combined with a virtual sample;
FIG. 7 is a graph of five spectra before normalization of an abnormal sample A2 time domain dimensionless feature scale in the abnormal point detection method based on dimensionless feature combined with a virtual sample in embodiment 2;
fig. 8 is a PCA feature distribution diagram of a normal sample a1 and an abnormal sample a2 in the abnormal point detection method based on dimensionless features in combination with virtual samples of embodiment 2;
fig. 9 is a PCA feature distribution diagram of virtual samples of the normal sample a1, the abnormal sample a2, and the abnormal sample in embodiment 2 of the abnormal point detection method based on dimensionless features in combination with the virtual samples.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Example 1
As shown in fig. 1, a method for detecting an abnormal point based on dimensionless features in combination with virtual samples includes the following steps:
s1, dimensionless feature extraction: separately extracting normal signal sample sets
And abnormal signal sample set
Obtaining a normal signal dimensionless feature set by the dimensionless feature variable of each signal sample
And abnormal signal dimensionless feature set
Wherein, P is the number of normal signal samples, Q is the number of abnormal signal samples, and L is the signal length of each signal sample;
the types of the dimensionless characteristic variables comprise time domain skewness, time domain kurtosis, time domain peak value factors, time domain margin factors, time domain waveform factors and time domain pulse indexes;
the calculation formula of the time domain skewness is as follows:
；
the time-domain kurtosis is calculated by the formula:
；
time domain crest factor:
；
the calculation formula of the time domain margin factor is as follows:
；
the time domain form factor is calculated as:
；
the calculation formula of the time domain pulse index is as follows:
；
wherein the content of the first and second substances,x(n)is a normal sample signal or an abnormal sample signal containing n sampling points, L isx(n)The length of the signal of (a) is,
is the average value of x (n),σ x is composed ofx(n)Standard deviation of (d);
s2, preprocessing data: dimensionless feature set for normal signals
And abnormal signal dimensionless feature set
Respectively carrying out scale normalization on each dimensionless characteristic variable to obtain a normal signal normalization sample set
And abnormal signal normalization sample set
；
The scale normalization formula is:
wherein the content of the first and second substances,
is the mean value of the dimensionless characteristic variables,
is a dimensionless characteristicStandard deviation of the variables;
s3, obtaining a support vector: normalizing a normal signal to a set of samples
And abnormal signal normalization sample set
Establishing a classification model by using a linear support vector machine and acquiring a support vector;
obtaining a support vector through an SVM algorithm;
the specific use method of the linear support vector machine is as follows:
the training sample set is
Wherein
Normalizing sample sets for normal signals
Or abnormal signal normalization sample set
The sample of (a) is selected,
is that
The label of the corresponding category of the user,
i =1, …, n, then the optimal hyperplane separating the samples correctly is:
then
，
Wherein
Is the variable of the amount of relaxation,
；
the method for solving the optimal hyperplane comprises the following steps:
wherein C is a penalty factor, C > 0;
the dual form is:
wherein α is a Lagrange multiplier;
the optimal classification surface is as follows:
wherein the content of the first and second substances,
for the optimal solution of Lagrange multipliers,
is an offset; the penalty factor C is automatically obtained through 5-fold cross validation of the training set;
s4, obtaining a virtual sample set: normalization sample set for judging abnormal signals
Whether the support vector of (a) is sparse in k neighbors: if so, useObtaining virtual samples by interpolation method, if not, obtaining virtual samples by extrapolation method, the virtual samples forming virtual sample set
Where k is an odd number and R is the number of virtual samples; k is 5
S5, training and establishing a final classification model: normalizing a normal signal to a set of samples
Set of normalized samples of abnormal signals
And virtual sample set
Establishing a final classification model using a linear support vector machine
；
Obtaining a support vector through an SVM algorithm;
the specific use method of the linear support vector machine is as follows:
the training sample set is
Wherein
Normalizing sample sets for normal signals
Or abnormal signal normalization sample set
Or virtual sample set
In (1)The sample is taken from the sample container,
is that
The label of the corresponding category of the user,
then the optimal hyperplane that correctly separates the samples is:
then
，
Wherein
Is the variable of the amount of relaxation,
。
the method for solving the optimal hyperplane comprises the following steps:
wherein C is a penalty factor, C > 0;
the dual form is:
wherein α is a Lagrange multiplier;
the optimal classification surface is as follows:
wherein the content of the first and second substances,
for the optimal solution of Lagrange multipliers,
is an offset; the penalty factor C is automatically obtained through 5-fold cross validation of the training set;
s6, detecting a sample to be detected: inputting the sample to be tested into the final classification model
And detecting and judging whether the vibration signal is an abnormal vibration signal.
Example 2
As shown in fig. 1, a method for detecting an abnormal point based on dimensionless features in combination with virtual samples includes the following steps:
assume that there are two types of signals: set of normal signal samples
(wherein there are
Normal signals, each signal having a length of L); set of abnormal signal samples
(wherein there are
An abnormal signal, each signal of length L), in general
：
The signal
Has a length of
，
；
1. Separately computing normal signal sample sets
And abnormal signal sample set
Six dimensionless characteristic variables of each signal: compressing an original normal signal sample set and an abnormal signal sample set from L characteristics into 6 characteristics, namely:
and
；
2. respectively carrying out scale normalization (data standardization) processing on each characteristic of the two types of signal sample sets in the step 1 to obtain
And
；
3. establishing a classification model for the two types of sample sets in the step 2 by using a linear support vector machine (selecting hyper-parameters based on 5-fold cross validation) and obtaining support vectors;
4. to pair
Judging whether each support vector is sparse in 5 fields: if the sparse is obtained, the virtual sample is obtained by adopting an interpolation method, otherwise, the virtual sample is obtained by adopting an extrapolation method. After construction of the memorySet of virtual samples as
(R virtual anomaly samples were obtained altogether);
5. according to the new sample set
And establishing a final classification model by using a linear support vector machine (selecting hyper-parameters based on 5-fold cross validation)
；
6. Utilizing the classification model in step 5 for the signal sample to be predicted
And predicting whether the sample is an abnormal vibration signal in real time.
The example adopts an intelligent operation and maintenance big data cloud platform of a space flight intelligence control (Beijing) monitoring technology Limited company to acquire real-time data, and respectively acquires normal vibration data A1 (1200, sampling points 2048), abnormal data A2 (100, sampling points 2048) and sampling frequency 2560 Hz, wherein sample information is shown in a table 1
Table 1: sample information
The specific situation is as follows:
1. five spectra before the normal signal sample A1 are shown in FIG. 2, and five spectra before the abnormal signal sample A2 are shown in FIG. 3.
2. Extracting 6 time domain dimensionless features from the normal and abnormal signals: time domain skewness, time domain kurtosis, time domain peak factor, time domain margin factor, time domain form factor, time domain pulse index, five samples before the extraction of the two kinds of signal characteristics are respectively shown in fig. 4 and fig. 5.
3. In order to overcome the influence of different scales of each feature on the classification result, the two types of samples are subjected to scale normalization, as shown in fig. 6 and 7. Compared with fig. 4 and 5, the distribution of each characteristic of the sample after the scale normalization is more concentrated.
4. PCA feature extraction for original normal samples (1200) and abnormal samples (100) is shown in fig. 8: due to the unbalanced distribution of the normal samples and the abnormal samples, the classification line can misclassify more abnormal samples into normal sample regions. After generating virtual samples for the support vectors in the abnormal signals, as shown in fig. 9, the classification lines obtained by retraining better separate the normal signals from the abnormal signals.
5. The prediction accuracy of the final training model for the normal sample points of the samples is 98%, and the prediction accuracy for the abnormal samples is 99% as shown in table 1.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (9)
1. An abnormal point detection method based on combination of dimensionless characteristics and virtual samples is characterized in that: the method comprises the following steps:
s1, dimensionless feature extraction: separately extracting normal signal sample sets
And abnormal signal sample set
Obtaining a normal signal dimensionless feature set by the dimensionless feature variable of each signal sample
And abnormal signal dimensionless feature set
Wherein, P is the number of normal signal samples, Q is the number of abnormal signal samples, L is the signal length of each signal sample, N is a normal signal identifier, and O is an abnormal signal identifier;
the types of the dimensionless characteristic variables comprise time domain skewness, time domain kurtosis, time domain peak value factors, time domain margin factors, time domain waveform factors and time domain pulse indexes;
the calculation formula of the time domain skewness is as follows:
；
the time domain kurtosis is calculated by the following formula:
；
time domain crest factor:
；
the calculation formula of the time domain margin factor is as follows:
；
the time domain form factor is calculated as:
；
the time domain pulse index is calculated by the following formula:
；
wherein the content of the first and second substances,x(n)is a normal sample signal or an abnormal sample signal containing n sampling points, L isx(n)The length of the signal of (a) is,
is the average value of x (n),σ x is composed ofx(n)Standard deviation of (d);
s2, preprocessing data: set of dimensionless features for the normal signal
And said anomaly signal dimensionless feature set
Respectively carrying out scale normalization on each dimensionless characteristic variable to obtain a normal signal normalization sample set
And abnormal signal normalization sample set
；
S3, obtaining a support vector: normalizing the normal signal by a set of samples
And the abnormal signal normalization sample set
Establishing a classification model by using a linear support vector machine and acquiring a support vector;
s4, obtaining a virtual sample set: judging the abnormal signal normalization sample set
Whether the support vector of (a) is sparse in k neighbors: if yes, obtaining virtual samples by using an interpolation method, and if not, obtaining virtual samples by using an extrapolation method, wherein the virtual samples form a virtual sample set
Where k is an odd number and R is a dummy patternThe number of books;
s5, training and establishing a final classification model: normalizing the normal signal by a set of samples
The set of normalized samples of the anomaly signal
And the set of virtual samples
Establishing a final classification model using a linear support vector machine
；
S6, detecting a sample to be detected: inputting the sample to be tested into the final classification model
And detecting and judging whether the vibration signal is an abnormal vibration signal.
2. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 1, wherein: in step S2, the formula of the scale normalization is:
wherein the content of the first and second substances,
is the mean value of the dimensionless characteristic variables,
is the standard deviation of the dimensionless characteristic variable.
3. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 1, wherein: in steps S3 and S5, a support vector is acquired by an SVM algorithm.
4. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 3, wherein: in step S3, the specific use method of the linear support vector machine is as follows:
the training sample set is
Wherein
Normalizing a set of samples for the normal signal
Or the abnormal signal normalization sample set
The sample of (a) is selected,
is that
The label of the corresponding category of the user,
i =1, …, n, then the optimal hyperplane separating the samples correctly is:
then
，
Wherein
Is the variable of the amount of relaxation,
。
5. the abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 4, wherein: in the step S5, in the step S,
normalizing a set of samples for the normal signal
Or the abnormal signal normalization sample set
Or the set of virtual samples
The sample of (1).
6. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 5, wherein:
the method for solving the optimal hyperplane comprises the following steps:
wherein C is a penalty factor, C>0，
Is the introduced relaxation variable;
the dual form is:
wherein α is a Lagrange multiplier.
7. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 6, wherein:
the optimal classification surface is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for the optimal solution of Lagrange multipliers,
is an offset.
8. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 6, wherein: and the penalty factor C is automatically obtained through 5-fold cross validation of the training set.
9. The abnormal point detection method based on the dimensionless feature combined with the virtual sample as claimed in claim 1, wherein: in step S4, k is 5.
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