CN112257917B - Time sequence abnormal mode detection method based on entropy characteristics and neural network - Google Patents
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Abstract
The invention provides a time sequence abnormal mode detection method based on entropy characteristics and a neural network, which comprises the following steps: 1) Extracting a second-order differential rate sample entropy feature sequence from the time sequence in the training data set; 2) Training to generate an countermeasure network model to obtain a generator and a corresponding discriminator; 3) Calculating the abnormal score of the feature sequence and constructing a threshold value; 4) And carrying out abnormality judgment on the input data to be detected according to the threshold value. The method has the advantages that the characteristic extraction is carried out on the time sequence data by utilizing the differential rate sample entropy, so that the abnormal mode is more obvious; a new anomaly score calculation method is established, the accuracy and generalization of model identification are improved, and the model identification method has higher practicability and application value.
Description
Technical Field
The invention relates to prediction of a coal mine thermodynamic composite disaster, in particular to a time sequence abnormal mode detection method based on entropy characteristics and a neural network, and belongs to the field of emergency safety.
Background
Coal is used as main energy to occupy irreplaceable important position in the energy structure of China, the left area after the coal mine is mined is a goaf, ventilation in the goaf is poor, coal is more, and the coal is continuously oxidized to generate combustible gas so as to easily cause coal thermodynamic disasters such as spontaneous combustion, gas explosion and the like. The concentration change of the released combustible gas shows a certain rule along with the development of time, the inflection points of the monitoring data in different stages are effectively detected, and when the gas concentration is greatly changed, the abnormal mode can be considered to be entered, so that the possibility of disasters such as spontaneous combustion of coal is indicated. Different coal mine gases have different production contents, and if the size of the gas content value is used as a judging standard for disaster occurrence, a large error can be caused when the gas content value is applied to other coal mines, so that the detection of an abnormal mode can improve the generalization of disaster judgment, and a new idea is provided for the detection of coal composite disasters.
Along with research and penetration of artificial intelligence theory, a time sequence prediction method is applied to predict coal and gas to become a new trend, and the method is introduced into quantitative evaluation and analysis of coal and gas disasters and is combined with theory researches such as computer technology, support vector machines, artificial neural networks and the like to study, but the prediction methods are difficult to apply to complex data, have the problem of easy sinking into local minimum values, have the fitting phenomenon, have low accuracy and have large limitation.
With the improvement of information technology, the problem of abnormality detection in time series has become a recent research hotspot. Time series anomalies generally refer to a series of data that is significantly different from other data, and such anomalies do not refer to random deviations, but rather differences due to different mechanisms. The abnormal mode of the gas time sequence data is detected, so that a theoretical basis can be provided for the coal mine thermodynamic disasters. If the time sequence data has an abnormal mode, the change trend of the data is greatly changed, and the time sequence data can be used as a judging basis for disaster occurrence.
The prior art method (CN 201910809956.9) utilizes GAN to carry out anomaly detection on a time sequence, mainly builds an anomaly detection model by using an optimized GAN generator and a discriminator, and uses the generated residual error and discrimination loss output by the model as the judgment basis for judging anomaly data. However, most of the time sequence changes are not obvious, and the direct time sequence is used as input data of the GAN, so that the characteristics are not obvious enough; meanwhile, more effective judgment criteria are obtained by using the generated residual error and the discrimination loss output by the model, and how to improve the accuracy and universality of abnormal judgment is still to be researched.
Disclosure of Invention
The invention aims to realize a time sequence abnormal mode detection method based on entropy characteristics and a neural network. The method of the invention is divided into 4 stages: extracting a second-order differential rate sample entropy feature sequence from the time sequence in the training data set; training to generate an countermeasure network model to obtain a generator and a corresponding discriminator; calculating the abnormal score of the feature sequence and constructing a threshold value; and carrying out abnormality judgment on the input data to be detected according to the threshold value. Specifically, the method of the present invention comprises the steps of:
A. extracting a second-order differential rate sample entropy feature sequence from a time sequence in a training data set, wherein the method is concretely realized as follows:
A1. dividing the training data set into two sets, namely a training data set 1 and a training data set 2;
the training data set 1 is all normal data, and the training data set 2 comprises normal data and abnormal data;
A2. for training data set 1 time series
Segmentation is performed by sliding the window size W and the step size d through the method 1 to obtain a sequence segment set W with the length L, wherein the ith time sequence segment is marked as s i ；
s i ＝[x 1+(i-1)d ,x 2+(i-1)d ,…,x 1+(i-1)d+w ](1)
Said T train Representing the number of time series of training data sets, 1 xT train Representing a training dataset time series dimension;
A3. performing differential rate operation on each sequence segment in the sequence segment set W to obtain a second-order differential rate sequence of all the sequence segments, wherein the second-order differential rate sequence is specifically realized as follows:
A3.1. for sequence segment s i Calculating a second-order differential rate sequence G= { G by using the method 2 1 ,g 2 ,…,g w′ -and find its standard deviation std;
the said process
E-order difference value for u time point, +.>
The e-level difference value is the u-1 time point;
A3.2. dividing a second-order differential rate sequence with w 'data points by taking m time sequence data points as one sub-segment, and marking the total w' -m+1 sub-sequence segments as K2 i ＝{q 1 ,q 2 ,…,q w′-m+1 }；
A4. Sample entropy feature extraction is carried out on the second-order differential rate sequences of all the sequence segments, so that the second-order differential rate sample entropy feature sequences of all the sequence segments are obtained, and the method is concretely realized as follows:
A4.1. calculation of arbitrary two subsequence fragments q a And q b Distance D [ q ] a ,q b ]The distance is determined by the maximum difference of the corresponding position elements in the two sub-sequence segments;
A4.2. calculation of the subsequence fragment q a The similarity probability with other subsequence segments is obtained through a formula 3, the duty ratio of the subsequence segments with the distance between the subsequence segments smaller than a threshold value is obtained through a formula 4, and the average similarity probability of the second-order differential rate sequence is obtained;
r is a similarity threshold;
A4.3. according to steps A4.1-A4.2, the average similarity probability B is recalculated by taking m+1 as the length of the subsequence m+1 (r) obtaining a second-order differential rate sample entropy feature SE through a formula 5;
A5. carrying out segment average pretreatment on the differential rate sample entropy sequence to obtain the differential rate sample entropy sequence, wherein the method is specifically realized as follows:
A5.1. from X t (t=1, 2..t-w), and removing a sequence segment S of length w t ＝{X t ,X t+1 ,...,X w+t-1 } 1×t Summing according to formula 6, and then averaging according to formula 7;
sum t ＝X t +X t +1...X w+t-1 (6)
sum t ＝sum t /w; (7)
A5.2. Repeating the step A4.1, taking t-w sequence segments out, and adding sum t Composing a new differential rate sample entropy sequence S t '＝{sum 1 ,sum 2 ,…,sum t-w } 1×t ；
B. Training and generating an countermeasure network model to obtain a generator and a corresponding discriminator, wherein the method is concretely realized as follows:
B1. random sampling noise data z= { Z i I=1, 2, …, n, where n corresponds to the number of samples. The generator model G is a plurality of LSTM memory units, the number of the memory units is set, Z is input into the generator model G, and reconstructed sample sequence data G (Z) is generated;
B2. entropy sequence S of new differential rate sample t The' and the generated reconstructed sample sequence data G (Z) are input into a built discriminator model D;
B3. updating model parameters by using a random gradient descent algorithm according to the value of the loss function, updating parameters of a discriminator firstly, and then updating parameters of a generator by using an Adam optimization algorithm according to noise data;
B4. saving model parameters, repeating the steps B1-B3 for cyclic iteration, and finally obtaining a trained generator model G which can generate a normal time sequence and a corresponding discriminant model D;
C. calculating the anomaly score of the feature sequence and constructing a threshold, wherein the anomaly score is specifically realized as follows:
C1. using time sequences in training dataset 2
Repeating steps A2-A5, and extracting features to obtain new feature sequence->
C2. Will randomly sample noise data Z val Is input into a training completion generator G to generate a reconstructed sample G (Z val ) Calculating the generation anomaly score R of the input sample by using the generation error score The method is concretely realized as follows:
C2.1. for a reconstructed sample of length n G (Z val ) New feature sequence with training dataset 2
The elements in the absolute error E of (2) are sequenced from small to large to obtain sequenced absolute error E i ′＝{e′ 1 ,e′ 2 ,…,e′ n Sequence and absolute error E i ′＝{e′ 1 ,e′ 2 ,…,e′ n An average value M;
C2.2. will E' i The extracted element is compared with the average value M, and E 'is taken out' i In { e' k ,e′ k+1 ,…,e′ n -data elements larger than the average value M, the number n-k+1; initializing a weight sequence W i ′＝{w′ 1 ,w′ 2 ,…,w′ n } T ,w′ 1～n-2 =0, set x' n Corresponding weight w' n Is lambda, x' n-1 Corresponding weight w' n-1 For 1-lambda, update weight sequence W i ' size of element in W is defined as W by 8 i ' update;
C2.3. using updated weight sequences W i 'and ordered sample E' i Calculating the generated anomaly score R of the training sample set 2 through a method 9 score ；
R score ＝E i ′·W i ' A (9)
C3. Generating a sample and a new feature sequence by using D output of the discriminator trained in the step B
Calculating the similarity probability P of the number of the abnormal scores D score 1-P;
C4. using the discrimination anomaly score D score And generating an anomaly score R score The anomaly score O is calculated by means of the method 10, and a threshold is established according to the training data set 2, specifically implemented as follows:
O＝W D ×D score +W G ×R score (10)
The W is D And W is G Generating weights of the anomaly scores for the discrimination anomaly scores and the samples respectively;
C4.1. training data set
The maximum abnormal score and the minimum abnormal score in the result are used as the maximum boundary and the minimum boundary, the maximum abnormal score and the minimum abnormal score are divided averagely, and the abnormal score of the q-th training data set 2 is calculated through a formula 11;
C4.2. the abnormal score corresponding to the maximum F1 score is used as a threshold value, and the calculation mode of F1 is shown as formula 12;
the Pre is the proportion of positive samples predicted to be positive in all samples predicted to be positive, and the Rec is the proportion of positive samples predicted to be positive in all positive samples; TP is a positive sample predicted to be positive by the model; FP is the negative sample predicted to be positive by the model; FN is positive samples predicted negative by the model;
D. the method comprises the steps of carrying out abnormality judgment on input data to be detected according to a threshold value, and specifically realizing the following steps:
D1. inputting a time series of data sets to be detected
Repeating the steps A1-A5, and extracting entropy features of the differential rate sample to obtain a new time sequence +.>
D2. Repeating steps C1-C4, and
inputting the data into a trained generation countermeasure network, and calculating an anomaly score O of the data to be detected by using a formula 10 real ；
D3. Anomaly score O obtained by calculation real C, comparing the data with the threshold value calculated in the step C, if the abnormal score is larger than the threshold value, judging that the data to be detected contains an abnormal mode, otherwise, judging that the data to be detected does not contain the abnormal mode.
The method has the advantages that the characteristic extraction is carried out on the time sequence data by utilizing the differential rate sample entropy, so that the abnormal mode is more obvious; a new anomaly score calculation method is established, the accuracy and generalization of time sequence anomaly mode detection are improved, and the method has higher practicability and application value.
Drawings
Fig. 1: overall flow chart for abnormal pattern detection
Detailed Description
The present invention will be further described as an embodiment by performing CO time-series prediction on experimental data and performing a description of a time-series abnormal pattern detection method based on a differential rate entropy feature and a generation countermeasure network according to a time-series data amount, an input-output dimension, and the like, with reference to the accompanying drawings.
The overall flow chart of the method is shown in fig. 1. The method comprises the following steps: 1) Extracting a second-order differential rate sample entropy feature sequence from the time sequence in the training data set; 2) Training to generate an countermeasure network model to obtain a generator and a corresponding discriminator; 3) Calculating the abnormal score of the feature sequence and constructing a threshold value; 4) And carrying out abnormality judgment on the input data to be detected according to the threshold value. The invention is further described in the following steps, in connection with examples:
A. extracting a second-order differential rate sample entropy feature sequence from a time sequence in a training data set, wherein the method is concretely realized as follows:
A1. selecting experimental data, wherein a research object is a one-dimensional time sequence of CO gas concentration, selecting a training data set, dividing the training data set into two sets, and respectively marking the two sets as a training data set 1 and a training data set 2;
the training data set 1 is all normal data, and the training data set 2 comprises normal data and abnormal data;
A2. setting the sliding window size of a sequence section to be 10 for a training data set 1 which is all normal data, and segmenting the training data set by sliding with the step length of 1;
A3. performing differential rate operation on each sequence segment in the sequence segment set to obtain a second-order differential rate sequence of all the sequence segments, wherein the second-order differential rate sequence is specifically realized as follows:
A3.1. for 348 pieces of data in total of CO gas concentration sequence, the formula is utilized
The second-order differential rate sequence of 345 partial data is obtained, and G= { G is shown in table 2 1 ,g 2 ,…,g w′ And its standard deviation std was found to be 0.11, part of the data is as follows:
A3.2. dividing a second-order differential rate sequence with 345 data points by taking 6 time sequence data points as one sub-segment, and marking the total 340 sub-sequence segments as K2 i ＝{q 1 ,q 2 ,…,q w′-m+1 Partial data is as follows:
A4. sample entropy feature extraction is carried out on the second-order differential rate sequences of all the sequence segments, so as to obtain second-order differential rate sample entropy feature sequences of all the sequence segments, and the method is concretely realized as follows;
A4.1. calculating the second-order differential rate sample entropy characteristic of each sequence segment, and finally obtaining a complete second-order differential rate sample entropy sequence, wherein partial data are as follows:
A5. carrying out segment average pretreatment on the differential rate sample entropy sequence to obtain the differential rate sample entropy sequence, wherein the method is specifically realized as follows:
A5.1. from X t (t=1, 2..t-w), and removing a sequence segment S of length w t ＝{X t ,X t+1 ,...,X w+t-1 } 1×t Summing and then averaging;
A5.2. repeating the step A4.1, taking t-w sequence segments out, and adding sum t Composition of a novel sequence S t '＝{sum 1 ,sum 2 ,…,sum t-w } 1×t The partial data are as follows:
B. training and generating an countermeasure network model to obtain a generator and a corresponding discriminator, wherein the method is concretely realized as follows:
B1. random sampling noise data z= { Z i I=1, 2, …, n }, where n is 330. The generator model is a plurality of LSTM memory units, the number of the memory units is set, Z is input into the built generator model, and reconstructed sample sequence data G (Z) is generated;
B2. entropy S of new differential rate sample t The' and the generated reconstructed sample sequence data G (Z) are input into the constructed discriminant model D, and part of the parameter data are as follows:
B3. updating model parameters by using a random gradient descent algorithm according to the value of the loss function, updating parameters of a discriminator firstly, and then updating parameters of a generator by using an Adam optimization algorithm according to noise data;
B4. saving model parameters, returning to B2 for 1000 times of cyclic iteration, setting the learning rate to 0.1, and finally obtaining a trained generator model G and a trained discriminant model D;
C. calculating the anomaly score of the feature sequence and constructing a threshold, wherein the anomaly score is specifically realized as follows:
C1. first repeating steps A2-A5 for a time series of training data sets 2 comprising normal data and abnormal data
Extracting features to obtain new feature sequence->
The partial data are as follows:
C2. using the discrimination anomaly score D score And sample generation anomaliesScore R score Calculating an anomaly score O;
C2.1. training data set
The maximum anomaly score and the minimum anomaly score in the result are used as the maximum and minimum boundaries, and the maximum anomaly score and the minimum anomaly score are divided evenly to obtain the anomaly score of the training data set 2 of the q-th section
C2.2. The maximum F1 score is 0.8916, and the corresponding anomaly score O is used as a threshold value to obtain a threshold value of 0.375;
D. the method comprises the steps of carrying out abnormality judgment on input data to be detected according to a threshold value, and specifically realizing the following steps:
D1. inputting time series samples of a data set to be detected
Repeating the steps A2-A5, and extracting entropy features of differential rate samples to obtain a new time sequence +.>
The partial data are as follows:
D2. repeating steps C1-C4, and
inputting the data into a trained generation countermeasure network, and calculating an anomaly score O of an actual data sample real 0.572;
D3. anomaly score O obtained by calculation real C, comparing the abnormal score with the threshold value calculated in the step C, and judging that the sample is an abnormal sample if the abnormal score is larger than the threshold value, wherein the actual processing result of the whole sample is as follows:
the method realizes a time sequence abnormal mode detection method based on the difference rate entropy characteristics and the generation countermeasure network, and can detect whether the sequence section contains an abnormal mode, thereby achieving the purpose of providing a judgment basis for occurrence of coal mine thermodynamic disasters; a new anomaly score calculation method is established, the accuracy and generalization of model identification are improved, and the model identification method has higher application value.
Finally, it should be noted that the examples are disclosed for the purpose of aiding in the further understanding of the present invention, but those skilled in the art will appreciate that: various alternatives and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the disclosed embodiments, but rather the scope of the invention is defined by the appended claims.
Claims (6)
1. A time sequence abnormal mode detection method based on entropy characteristics and a neural network comprises the following steps:
A. extracting a second-order differential rate sample entropy feature sequence from a time sequence in a training data set, wherein the method is concretely realized as follows:
A1. dividing the training data set into two sets, namely a training data set 1 and a training data set 2;
the training data set 1 is all normal data, and the training data set 2 comprises normal data and abnormal data;
A2. for training data set 1 time series
Segmenting by sliding with a window size W and a step size d to obtain a sequence segment set W with a length L, wherein the ith time sequence segment is marked as s i The calculation formula is as follows:
s i ＝[x 1+(i-1)d ,x 2+(i-1)d ,…,x 1+(i-1)d+w ]
said T train Representing the number of time series of training data sets, 1 xT train Representing a training dataset time series dimension;
A3. performing differential rate operation on each sequence segment in the sequence segment set W to obtain a second-order differential rate sequence of all the sequence segments;
A4. sample entropy feature extraction is carried out on the second-order differential rate sequences of all the sequence segments, so that the second-order differential rate sample entropy feature sequences of all the sequence segments are obtained;
A5. carrying out sectional average pretreatment on the differential rate sample entropy sequence to obtain a differential rate sample entropy sequence;
B. training and generating an countermeasure network model to obtain a generator and a corresponding discriminator, wherein the method is concretely realized as follows:
B1. random sampling noise data z= { Z i I=1, 2, …, n }, where n corresponds to the number of samples, the generator model G is a plurality of LSTM memory cells, and the number of memory cells is set, Z is input into the generator model G, generating reconstructed sample sequence data G (Z);
B2. entropy sequence S of new differential rate sample t The' and the generated reconstructed sample sequence data G (Z) are input into a built discriminator model D;
B3. updating model parameters by using a random gradient descent algorithm according to the value of the loss function, updating parameters of a discriminator firstly, and then updating parameters of a generator by using an Adam optimization algorithm according to noise data;
B4. saving model parameters, repeating the steps B1-B3 for cyclic iteration, and finally obtaining a trained generator model G which can generate a normal time sequence and a corresponding discriminant model D;
C. calculating the anomaly score of the feature sequence and constructing a threshold, wherein the anomaly score is specifically realized as follows:
C1. using time sequences in training dataset 2
Repeating the steps A2-A5, extracting the characteristics to obtain a new characteristic sequence/>
C2. Will randomly sample noise data Z val Is input into a training completion generator G to generate a reconstructed sample G (Z val ) Calculating the generation anomaly score R of the input sample by using the generation error score ；
C3. Generating a sample and a new feature sequence by using D output of the discriminator trained in the step B
Calculating the similarity probability P of the number of the abnormal scores D score 1-P;
C4. using the discrimination anomaly score D score And generating an anomaly score R score The anomaly score O is calculated, a threshold value is established according to the training data set 2, and a calculation formula is as follows:
O＝W D ×D score +W G ×R score
the W is D And W is G Generating weights of the anomaly scores for the discrimination anomaly scores and the samples respectively;
D. the method comprises the steps of carrying out abnormality judgment on input data to be detected according to a threshold value, and specifically realizing the following steps:
D1. inputting a time series of data sets to be detected
Repeating the steps A1-A5, and extracting entropy features of the differential rate sample to obtain a new time sequence +.>
D2. Repeating steps C1-C4, and
inputting the data into a trained generation countermeasure network, and calculating an anomaly score O of the data to be detected by using a formula 10 real ；
D3. Anomaly score O obtained by calculation real C, comparing the data with the threshold value calculated in the step C, if the abnormal score is larger than the threshold value, judging that the data to be detected contains an abnormal mode, otherwise, judging that the data to be detected does not contain the abnormal mode.
2. The method for detecting abnormal patterns of time series based on entropy features and neural network as claimed in claim 1, wherein the differential rate operation is performed on each sequence segment in the sequence segment set W to obtain a second-order differential rate sequence of all sequence segments, which is specifically implemented as follows:
A3.1. for sequence segment s i Calculate its second order differential rate sequence g= { G 1 ,g 2 ,…,g w′ And solving the standard deviation std, wherein the calculation formula is as follows:
the said process
E-order difference value for u time point, +.>
The e-level difference value is the u-1 time point;
A3.2. dividing a second-order differential rate sequence with w 'data points by taking m time sequence data points as one sub-segment, and marking the total w' -m+1 sub-sequence segments as K2 i ＝{q 1 ,q 2 ,…,q w′-m+1 }。
3. The method for detecting abnormal modes of time series based on entropy features and neural network as claimed in claim 1, wherein the sample entropy feature extraction is performed on the second order differential rate sequences of all the sequence segments to obtain the second order differential rate sample entropy feature sequences of all the sequence segments, and the specific implementation steps are as follows:
A4.1. calculation of arbitrary two subsequence fragments q a And q b Distance D [ q ] a ,q b ]The distance is composed of two sub-componentsDetermining the maximum difference value of the corresponding position element in the sequence segment;
A4.2. calculation of the subsequence fragment q a The average similarity probability of the second-order differential rate sequence is used as a second-order differential rate sample entropy by using the ratio of the subsequence segments with the distance between the subsequence segments smaller than the threshold value as the similarity probability of the rest subsequence segments, and the calculation formula is as follows:
r is a similarity threshold;
A4.3. according to steps A4.1-A4.2, the average similarity probability B is recalculated by taking m+1 as the length of the subsequence m+1 (r), second-order differential rate sample entropy feature SE, the calculation mode is:
4. the method for detecting abnormal patterns of time series based on entropy features and neural network as claimed in claim 1, wherein the step of performing segment average pretreatment on the differential rate sample entropy sequence to obtain the differential rate sample entropy sequence is specifically implemented as follows:
A5.1. from X t (t=1, 2..t-w), and removing a sequence segment S of length w t ＝{X t ,X t+1 ,...,X w+t-1 } 1×t Summing and then averaging, wherein the calculation formula is as follows:
sum t ＝X t +X t +1...X w+t-1
sum t ＝sum t /w；
A5.2. repeating the step A4.1, taking t-w sequence segments out, and adding sum t Composing a new differential rate sample entropy sequence S t '＝{sum 1 ,sum 2 ,…,sum t-w } 1×t 。
5. The method for detecting abnormal patterns in time series based on entropy features and neural network as claimed in claim 1, wherein the noise data Z is randomly sampled val Is input into a training completion generator G to generate a reconstructed sample G (Z val ) Calculating the generation anomaly score R of the input sample by using the generation error score The method is concretely realized as follows:
C2.1. for a reconstructed sample of length n G (Z val ) New feature sequence with training dataset 2
The elements in the absolute error E of (2) are sequenced from small to large to obtain sequenced absolute error E i ′＝{e′ 1 ,e′ 2 ,…,e′ n Sequence and find the absolute error E' i ＝{e′ 1 ,e′ 2 ,…,e′ n An average value M;
C2.2. will E' i The extracted element is compared with the average value M, and E 'is taken out' i In { e' k ,e′ k+1 ,…,e′ n -data elements larger than the average value M, the number n-k+1; initializing a weight sequence W i ′＝{w′ 1 ,w′ 2 ,…,w′ n } T ,w′ 1～n-2 =0, set x' n Corresponding weight w' n Is lambda, x' n-1 Corresponding weight w' n-1 For 1-lambda, update weight sequence W i The size of the element in' is calculated as:
C2.3. using updated weight sequences W i 'and ordered sample E' i Calculating the generation anomaly score R of the training sample set 2 score The calculation formula is as follows:
R score ＝E i ′·W i ′。
6. the method for detecting a time-series abnormal pattern based on entropy features and neural network according to claim 1, wherein the discrimination abnormality score D is used score And generating an anomaly score R score The anomaly score O is calculated by means of the method 10, and a threshold is established according to the training data set 2, specifically implemented as follows:
C4.1. training data set
The maximum anomaly score and the minimum anomaly score in the result are used as the maximum boundary and the minimum boundary, the maximum anomaly score and the minimum anomaly score are divided averagely, the anomaly score of the q-th section training data set 2 is calculated, and the calculation formula is as follows:
C4.2. the anomaly score corresponding to the maximum F1 score is used as a threshold value, and the calculation formula of F1 is as follows:
the Pre is the proportion of positive samples predicted to be positive in all samples predicted to be positive; rec is the proportion of positive samples predicted to be positive in all positive samples, TP is the positive sample predicted to be positive by the model; FP is the negative sample predicted to be positive by the model; FN is positive samples predicted negative by the model.
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