CN111122162A - Industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy - Google Patents

Industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy Download PDF

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CN111122162A
CN111122162A CN201911359880.0A CN201911359880A CN111122162A CN 111122162 A CN111122162 A CN 111122162A CN 201911359880 A CN201911359880 A CN 201911359880A CN 111122162 A CN111122162 A CN 111122162A
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周仁杰
王晓
万健
张纪林
张伟
蒋从锋
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Hangzhou Dianzi University
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Abstract

The invention discloses an industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy. The method can be used for describing the complexity of the time sequence from a plurality of time scales, and meanwhile, compared with the existing multi-scale Entropy (Multiscale Entropy) method, Composite Multiscale Entropy (Composite Multiscale Entropy) method and multi-scale fuzzy sample Entropy (FME), the method is obviously improved in the aspects of calculation stability and accuracy. The method can be used for judging and detecting the fault type of the industrial system and analyzing the time sequence complexity.

Description

Industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy
Technical Field
The invention relates to the field of system complexity research, relates to a method for depicting the complexity of an industrial system signal time sequence, and particularly relates to an industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy.
Background
The bearing vibration signal time sequence is an important high-dimensional data type and is a sequence formed by sampling values of a certain physical quantity of an objective object at different time points according to the time sequence. The complexity of quantitative analysis of a signal time series is a complex and important task for understanding the operation rule of a system. In order to analyze time series characteristics and distinguish between normal and chaotic behavior of a system, experts and scholars have proposed many methods to measure the complexity of a system signal many years ago.
The Multiscale Entropy (MSE) is used as a tool for describing the complexity of a bearing vibration signal time sequence, the Entropy theory and the Multiscale idea are combined for the first time, and the Multiscale Entropy is widely applied in various aspects since being proposed. The multi-scale Entropy was originally proposed based on the Sample Entropy proposed by Richman et al (Sample Entropy). The sample entropy can only be analyzed for a single time scale and does not reflect the inherent changes of long correlation time series well. The multi-scale entropy is proposed, the sample entropy can be calculated on different time scales for the same time sequence, and the complexity of the time sequence is revealed through the different time scales.
Although the multi-scale entropy is widely applied, when the time scale is large, the data sequence is shortened, and the variance of the entropy value is obviously increased, so that when the time series of different scale factors are calculated, the stability of the multi-scale entropy is obviously reduced, and the discrimination of different time series is reduced. Although the Composite Multiscale Entropy (CMSE) and Composite Multiscale Fuzzy Entropy (FME) proposed later solve the existing problems to some extent, the methods are still based on the traditional sample Entropy proposed by Richman, and the vector distance is calculated only according to the maximum absolute difference value of each corresponding component of two vectors, and the measurement mode has deviation when measuring the multidimensional vector distance. The multi-scale entropy and composite multi-scale entropy method adopts a non-zero one-to-one accumulation method when calculating the similarity of vectors in a specific time sequence, and the non-zero one-to-one characterization method cannot accurately characterize the similarity of two vectors in the time sequence. When the calculation is performed on a plurality of similar time series, the discrimination of the method is obviously reduced. Therefore, new methods for characterizing the signal time series of the industrial system and improving the fault detection level of the industrial system need to be found and researched.
Disclosure of Invention
The invention aims to provide an industrial system fault detection technology based on Euclidean distance multi-scale Fuzzy sample Entropy (EDM-Fuzzy) aiming at the defects of the traditional industrial system signal time sequence complexity characterization method. In the traditional multi-scale entropy calculation, for different embedding dimensions m, a method of maximum difference value of corresponding components of two vectors is adopted when calculating the similarity of time series, if the absolute distance of the two vectors is within an allowable similarity tolerance range, 1 is accumulated, otherwise, 0 is accumulated. The simple limitation makes the granularity of division too coarse when calculating the similarity of the time series, and the similar time series cannot be distinguished well. The invention adopts Euclidean distance to replace the maximum absolute difference value of corresponding components of two vectors and uses fuzzy function
Figure BDA0002336891510000021
The method replaces a 0-1 step function, solves the problem of 0-1 jump, improves the accuracy of the calculation of the matching degree between the templates, further improves the discrimination of different time sequences, and simultaneously enhances the calculation stability under a large time scale.
The invention specifically comprises the following steps:
step 1, signal data of an industrial system in a normal working state and different types of fault states are acquired through signal acquisition equipment;
step 2, corresponding an original signal to a time sequence { x (i) | i ═ 1, 2., N } under each state type, wherein the i sequence has numerical values at a certain time, and N represents the length of the time sequence; performing coarse-grained transformation (tau is a positive integer) on the time sequence { x (i) | i ═ 1, 2.. times, N }, by using a scale factor tau to form a plurality of coarse-grained vectors
Figure BDA0002336891510000022
Figure BDA0002336891510000023
Finally, tau new signal time sequences with the coarse graining length p are obtained, wherein the k-th new signal time sequence has the following specific transformation formula:
Figure BDA0002336891510000024
step 3, carrying out vector reconstruction with embedding dimension m on the kth new signal time sequence with coarse graining length p to obtain the k-th new signal time sequence
Figure BDA0002336891510000025
To
Figure BDA0002336891510000026
Wherein
Figure BDA0002336891510000027
Figure BDA0002336891510000028
The specific formula is as follows:
Figure BDA0002336891510000031
the invention translates the time sequence vector of the new signal, and the translation distance is the average value of the m-dimensional vectors. The purpose of this is to more accurately calculate the similarity between two vectors in the case where the two vectors are similar but where the new signal waveform is masked.
Step 4, calculating the Euclidean distance fuzzy sample entropy of the kth new signal time sequence under the scale factor tau by using the reconstructed vector:
4.1 any two initial directionsM-dimensional signal time series with different quantities
Figure BDA0002336891510000032
And
Figure BDA0002336891510000033
the distance between
Figure BDA0002336891510000034
The specific formula for the euclidean distance of the two reconstructed vectors is as follows:
Figure BDA0002336891510000035
the present invention uses Euclidean distance to replace the vector distance defined by the maximum absolute difference value of each corresponding component of two vectors used by other methods. In the traditional method, the maximum absolute difference value of each corresponding component of two vectors is defined as the distance between the two vectors, namely the absolute difference value of only one pair of components represents the difference between all components of the two vectors, and the method has obvious one-sidedness. The Euclidean distance is adopted to define the distance between the two vectors, which means that the difference of all components of the two vectors can be reflected, the one-sidedness of the traditional method is overcome, the distance between the two signal vectors can be more comprehensively and accurately described, and a foundation is laid for improving the accuracy and stability of vector similarity calculation later. The invention overcomes the defect that the distance between two signal vectors is calculated only according to the maximum absolute difference value of each corresponding component of the two vectors, and improves the accuracy of calculating the distance between the two signal vectors.
4.2 given a threshold r, r ═ 0.15 × SD, SD is the standard deviation of the original sequence { x (i) |1 ≦ i ≦ N }; by fuzzy functions
Figure BDA0002336891510000036
Computing
Figure BDA0002336891510000037
And
Figure BDA0002336891510000038
similarity between them
Figure BDA0002336891510000039
The formula is as follows:
Figure BDA00023368915100000310
Figure BDA0002336891510000041
the invention adopts fuzzy function
Figure BDA0002336891510000042
Instead of a 0-1 step function, the similarity of two vectors is characterized. The measure of the 0-1 step function between the two m-dimensional vector sequences is that if the distance between the two m-dimensional vector sequences is within an allowable range, the similarity is 1, and if the distance is not within the allowable range, the similarity is 0, so that the inaccuracy and instability of the matching degree of the two m-dimensional vector sequences are greatly increased. While the fuzzy function
Figure BDA0002336891510000043
Then there is a continuous definition of the distance d between the two m-dimensional vectors from 0 to plus infinity, and therefore there is a continuous definition of the similarity between the two vectors from 0-1, which can more accurately depict the similarity between the two vectors.
4.3 statistical degree of match between vectors, note
Figure BDA00023368915100000414
Figure BDA0002336891510000044
4.4 for all
Figure BDA0002336891510000045
Average and record as
Figure BDA0002336891510000046
Figure BDA0002336891510000047
4.5 increasing the embedding dimension to m +1 and repeating the above steps 3-4.4 to calculate the matching degree between vectors, and recording as
Figure BDA0002336891510000048
And for all
Figure BDA0002336891510000049
Average and record as
Figure BDA00023368915100000410
Figure BDA00023368915100000411
Figure BDA00023368915100000412
4.6 Euclidean distance sample fuzzy entropy defining the kth new signal time series:
Figure BDA00023368915100000413
step 5, updating the k value, recovering the embedding dimension to m, repeating the steps 3-4.6, and solving the Euclidean distance sample fuzzy entropy of the next new signal time sequence until solving the Euclidean distance sample fuzzy entropy of all the tau new signal time sequences;
step 6, averaging the Euclidean distance fuzzy sample entropies of all the tau new signal time sequences to finally obtain the Euclidean distance fuzzy sample entropies of the original time sequence under the scale tau:
Figure BDA0002336891510000051
step 7, updating the value of the scale factor tau, returning to the step 2, solving the Euclidean distance fuzzy sample entropy of the next scale factor until the requirement of the number of the scale factors is met, and finally obtaining the Euclidean distance multi-scale fuzzy sample entropy, namely a group of Euclidean distance fuzzy sample entropy values under a plurality of different scale factors;
step 8, the Euclidean distance multi-scale fuzzy sample entropy is used as the input of a forward and backward propagation neural network, the neural network is set to be a four-layer topological structure, the number of input layer points is equal to the number of scale factors, each point corresponds to the Euclidean distance fuzzy sample entropy of each scale factor, and the number of hidden layers is 30 points; the output layer outputs vector values corresponding to each type of mark under different bearing state types of the system; and finally, identifying the fault signal of the industrial system.
The invention has the beneficial effects that: the invention provides a signal time sequence complexity calculation method-Euclidean Distance multi-scale Fuzzy sample Entropy (EDM-Fuzzy). Euclidean distance multi-scale fuzzy sample entropy uses Euclidean distance to replace the maximum value of the difference value of each corresponding component of two vectors, and uses a new fuzzy function
Figure BDA0002336891510000052
To replace the 0-1 step function and thereby depict the state information of the signal time series with great accuracy. Entropy values on different scales are calculated by combining the Euclidean distance multi-scale fuzzy sample entropy with the Euclidean distance and the fuzzy function, the complexity of signals is measured from different time scales, the discrimination of different types of signal time sequences is further improved, and meanwhile, the calculation stability under the large time scale is enhanced. And then the accuracy of the fault type detection of the industrial system is greatly improved, and different types of faults can be detected by using the entropy as the fault characteristic.
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FIG. 1 is a flow chart of entropy calculation of Euclidean distance multi-scale fuzzy samples;
FIG. 2 is a coarse grain transformation flow diagram;
FIG. 3 is a vector matching illustration;
FIG. 4 is a fuzzy function illustration;
FIG. 5 is a diagram of an artificial neural network construction.
Detailed Description
The invention is described in further detail below with reference to the figures and methods of practice.
The implementation process of the invention on bearing fault diagnosis is described by referring to the execution steps of FIG. 1:
the industrial system fault detection method based on the Euclidean distance multi-scale fuzzy sample entropy comprises the following steps:
step 1, acquiring an original vibration signal time sequence (with the length of about 48000 data points) of a bearing under different state types through a bearing vibration signal acquisition device, and cutting the original vibration signal time sequence into a group of 2000-point subsequences (one group of which comprises about 240 subsequences);
the bearing vibration signal acquisition device comprises a 2 horsepower motor, a torque sensor, a power meter and an electronic control device.
The collected bearing state types are divided into six types, namely a normal state, a ball bearing fault, an inner ring fault, an outer ring 3 o ' clock fault, an outer ring 6 o ' clock fault and an outer ring 12 o ' clock fault.
Step 2, each original vibration signal subsequence segmented under each state type corresponds to a time sequence { x (i) | i ═ 1, 2.. and N }, wherein the i sequence has numerical values at a certain moment, N represents the length of the time sequence, and N ═ 2000; the time sequence { x (i) | i ═ 1, 2., N } is subjected to coarse-grained transformation with scale factor τ (τ is a positive integer, and τ in this embodiment is set from 1 to 20), and coarse-grained vectors are formed as shown in fig. 2, and coarse-grained vectors are formed
Figure BDA0002336891510000061
Figure BDA0002336891510000062
Finally, tau new signal time sequences with the coarse graining length p are obtained, wherein the k-th new signal time sequence has the following specific transformation formula:
Figure BDA0002336891510000063
step 3, carrying out vector reconstruction with embedding dimension m on the kth new signal time sequence with coarse graining length p to obtain the k-th new signal time sequence
Figure BDA0002336891510000064
To
Figure BDA0002336891510000065
Wherein
Figure BDA0002336891510000066
Figure BDA0002336891510000067
The specific formula is as follows:
Figure BDA0002336891510000068
step 4, calculating Euclidean distance sample fuzzy entropy of the kth new signal time sequence under the scale factor tau by using the reconstructed vector:
4.1 m-dimensional Signal time series with any two different initial vectors
Figure BDA0002336891510000071
And
Figure BDA0002336891510000072
the distance between
Figure BDA0002336891510000073
The specific formula for the euclidean distance of the two reconstructed vectors is as follows:
Figure BDA0002336891510000074
the inventionThe Euclidean distance is used for defining the distance between the two vectors, and the vector distance defined by the maximum absolute difference value of each corresponding component of the two vectors used by other methods is replaced. The similarity between two vibration signal vectors can be more accurately described by defining the vector distance based on the Euclidean distance, so that the accuracy of the vector similarity is improved. The defect that the distance between two vibration signal vectors is calculated only according to the maximum absolute difference value of each corresponding component of the two vectors is overcome, and the accuracy of distance characterization of the two vibration signal vectors is improved. Calculation of the distance between two vectors is shown in FIG. 3, assuming x1,x2,x3,x4,x5A time sequence of new signals. When m is 2, (x)2,x3) And (x)4,x5) For two vectors, the traditional method uses the maximum absolute difference max { | x of each corresponding component of the two vectors2-x4|,|x3-x5Defines two vectors (x)2,x3) And (x)4,x5) The distance of (2) is equivalent to representing the difference between all components of two vectors by the absolute difference of only one pair of components, and has obvious one-sidedness. In addition, the traditional method adopts a step function when calculating the similarity of two vectors, and assumes that the maximum absolute difference value of each corresponding component of the two vectors is r + Δ r, because a given threshold value is exceeded, the vector similarity is defined as 0 at this time, but Δ r is a minimum value and is far smaller than r, so the definition of the vector similarity greatly reduces the accuracy and stability of the calculation of the vector similarity. The Euclidean distance is adopted to define the distance between the two vectors, which means that the difference of all components of the two vectors can be reflected, so that the vector distance defined based on the Euclidean distance has better comprehensiveness. The Euclidean distance can define the distance between two vectors in any range, when the two vectors are completely the same, the Euclidean distance between the two vectors is 0, and when the two vectors only have a slight difference, the distance between the two vectors is a minimum value close to 0.
4.2 given a threshold r, r is 0.15 × SD, SD is the standard deviation of the original sequence { x (i) |1 ≦ i ≦ N }, r is typically set to 0.15; by fuzzy functions
Figure BDA0002336891510000075
Computing
Figure BDA0002336891510000076
And
Figure BDA0002336891510000077
similarity between them
Figure BDA0002336891510000078
Figure BDA0002336891510000079
The formula is as follows:
Figure BDA00023368915100000710
Figure BDA00023368915100000711
the invention adopts a fuzzy function when calculating the similarity of two vectors
Figure BDA00023368915100000712
Instead of a 0-1 step function. The traditional method adopts a 0-1 step function when calculating the similarity of two vectors, if the distance between the two vectors is within an allowable range, the similarity of the two vectors is 1, and if the distance is not within the allowable range, the similarity is 0. If each of the respective maximum absolute differences of the two vectors is r + Δ r, the vector similarity is defined as 0 since a given threshold r is exceeded, and if each of the respective maximum absolute differences of the two vectors is r- Δ r, the vector similarity is defined as 1 since the given threshold r is not exceeded. However, Δ r is a minimum value, which is much smaller than r, meaning that a slight change of the vector distance around the threshold will cause a 0-1 jump of the vector similarity, and therefore, the definition of the vector similarity by the step function greatly reduces the accuracy and stability of the vector similarity calculation. While the fuzzy function employed in the present invention is smoothed from 0-1, such a methodThe method can also define the similarity when the similarity of the two vectors is extremely small, and the fuzzy function is shown by a dotted line in figure 4. The solid line part in fig. 4 represents a step function, and the similarity between two vectors in the allowable range r is defined as 1, and the similarity not in the allowable range r is defined as 0. Such similarity definition method greatly reduces the accuracy of vector similarity calculation, and the fuzzy function
Figure BDA0002336891510000081
The vector distance d is continuously defined from 0 to positive infinity, so that the accuracy and the stability of vector similarity calculation are greatly improved.
4.3 statistical degree of match between vectors, note
Figure BDA0002336891510000082
Figure BDA0002336891510000083
4.4 for all
Figure BDA0002336891510000084
Average and record as
Figure BDA0002336891510000085
Figure BDA0002336891510000086
4.5 increasing the embedding dimension to m +1, repeating the above steps 3-4.4 to calculate the matching degree between vectors, and recording as
Figure BDA0002336891510000087
And for all
Figure BDA0002336891510000088
Average and record as
Figure BDA0002336891510000089
Figure BDA00023368915100000810
Figure BDA00023368915100000811
4.6 Euclidean distance fuzzy sample entropy defining the kth new signal time series:
Figure BDA0002336891510000091
step 5, updating the k value, recovering the embedding dimension to m, repeating the steps 3-4.6, and solving the Euclidean distance fuzzy sample entropy of the next new signal time sequence until solving the Euclidean distance sample fuzzy entropies of all the tau new signal time sequences;
step 6, averaging the Euclidean distance fuzzy sample entropies of all the tau new signal time sequences to finally obtain the Euclidean distance fuzzy sample entropies of the original time sequence under the scale tau:
Figure BDA0002336891510000092
step 7, updating the value of the scale factor tau, returning to the step 2, solving the Euclidean distance fuzzy sample entropy of the next scale factor until the requirement of the number of the scale factors is met, and finally obtaining the Euclidean distance multi-scale fuzzy sample entropy, namely a group of Euclidean distance fuzzy sample entropy values under a plurality of different scale factors;
step 8, constructing a bearing fault detection model
The Euclidean distance multi-scale fuzzy sample entropy is used as the input of a forward and backward propagation neural network, the neural network is set to be of a four-layer topological structure, wherein the input layer is tau points, each point corresponds to the Euclidean distance fuzzy sample entropy of each scale factor, and the hidden layer is 30 points; the output layer outputs vector values corresponding to each type of mark under different bearing state types; and finally, identifying a bearing fault signal and detecting the fault. The method comprises the following specific steps:
1) in order to improve the generalization of the data, the data set described in step 1 needs to be randomly divided. The data are divided into 30% of training data, 35% of verification data and 35% of test data.
2) Training process:
the bearing fault detection model adopts a four-layer structure forward and backward propagation neural network, an input layer is set to be 20 points, namely each point corresponds to an Euclidean distance fuzzy sample entropy value corresponding to each group of data from 1 to 20 in a scale factor, a hidden layer is set to be 30 points, 6 points are arranged on the output layer, and the 6 points correspond to vector values of each type of mark under different states: normal state flags are [1,0,0,0,0,0]Ball bearing failure flag is [0,1,0,0]Inner ring fault flag is [0,0,1,0,0,0]And the outer ring fault 3 o' clock is marked as [0,0,0,1,0,0]And the outer ring fault 6 o' clock is marked as [0,0,0,0,1,0 ]]And the outer ring fault 12 o' clock is marked as [0,0,0,0,0,1 ]]. The artificial neural network is shown in fig. 5. During data training, the target mean variance is 0, the learning rate is 0.001, and the minimum gradient is 10-7The maximum number of iterations is 1000. The construction of the artificial neural network is shown in fig. 5. Such experiments are one-time experiments, and the mode of dividing each experiment is random division. 200 experiments were performed for the entire experiment. And obtaining a bearing fault detection model after 200 experiments.
3) And detecting and analyzing the unknown bearing fault. And (3) preprocessing any number of bearing fault time sequences of unknown types according to the step 1 to obtain a subsequence with the length of 2000. And respectively carrying out Euclidean distance fuzzy sample entropy value calculation on each preprocessed time subsequence to obtain a group of Euclidean distance fuzzy sample entropy data under 20 different scale factors (the scale factors are from 1 to 20) in the step 7. The set of data reflects the entropy characterization exhibited by the bearing subsequence for scale factors from 1 to 20. The type of the bearing fault can be analyzed according to the entropy characteristics of the bearing time series. Inputting 20 points on an input layer of the artificial neural network, namely each point corresponds to an Euclidean distance fuzzy sample entropy value of a bearing subsequence corresponding to a scale factor from 1 to 20, and outputting 6 points on an output layer through training of the artificial neural network, wherein the 6 points correspond to bearing fault types. The types of bearing faults are distinguished through the detection model. The Euclidean distance multi-scale fuzzy sample entropy test result is in a pair with the traditional multi-scale entropy and composite multi-scale entropy test result shown in Table 1. Wherein MSE represents multi-scale entropy, CMSE represents composite multi-scale entropy, FME represents traditional fuzzy sample entropy, and EDMFuzzy represents Euclidean distance multi-scale fuzzy sample entropy. The data in the table are the accuracy results of the bearing fault type detection analysis.
TABLE 1MSE, CMSE, FME and EDMFuzzy bearing failure detection accuracy (× 100%)
Figure BDA0002336891510000101
The results in the table show that the bearing fault detection method based on the Euclidean distance multi-scale fuzzy sample entropy is superior to other methods in the aspect of detection accuracy of all fault types. Namely, the Euclidean distance multi-scale fuzzy sample entropy of the bearing time sequence is calculated according to the steps, and the characteristics of the bearing fault can be more effectively reflected. In the conventional entropy calculation method used for bearing fault detection, when the calculation is carried out on a bearing time sequence, the discrimination is obviously reduced, and the characteristics among different bearing faults cannot be well discriminated. In other methods for calculating entropy values (including multi-scale entropy, composite multi-scale entropy and multi-scale fuzzy sample entropy), the distance and the difference between vectors cannot be comprehensively measured only according to the maximum absolute difference value of each corresponding component of two vectors when the distance of the bearing time sequence is calculated for different matching lengths m. And a 0-1 step function is adopted when calculating the vector similarity. The two defects enable the classification granularity of other entropy methods to be too coarse when the similarity of the bearing time series is calculated, and similar bearing fault types cannot be well distinguished. The Euclidean distance multi-scale fuzzy sample entropy provided by the invention creatively adopts the Euclidean distance to measure the distance of the vector, and can more comprehensively describe the distance and the difference of the sequence. Innovatively introducing new fuzzy functions
Figure BDA0002336891510000111
The fuzzy function has continuous definition in the range from 0 to positive infinity of the vector distance d, so that the accuracy and the stability of vector similarity calculation are greatly improved. In summary, the present invention innovatively defines the distance between vectors by Euclidean distance, and innovatively uses new fuzzy function based on the Euclidean distance
Figure BDA0002336891510000112
The vector similarity is calculated, the accuracy and stability of calculation of the distance and the similarity between different time sequences are greatly improved, the discrimination of the bearing faults of different types is further improved in the aspect of detecting and distinguishing the bearing faults of different types, meanwhile, the stability of calculation under large scale is enhanced, and finally, the accuracy and stability of bearing fault detection and diagnosis are improved.

Claims (1)

1. The industrial system fault detection method based on the Euclidean distance multi-scale fuzzy sample entropy is characterized by comprising the following steps of:
step 1, acquiring original signals under different state types through industrial system signal acquisition equipment;
step 2, corresponding an original signal to a time sequence { x (i) | i ═ 1, 2., N } under each state type, wherein the i sequence corresponds to a numerical value at a certain moment, and N represents the length of the time sequence; performing coarse-grained transformation (tau is a positive integer) on the time sequence { x (i) | i ═ 1, 2.. so, N }, by using a scale factor tau to form a plurality of coarse-grained numerical points
Figure FDA0002336891500000011
Figure FDA0002336891500000012
Finally, tau new signal time sequences with the coarse graining length p are obtained, wherein the k-th new signal time sequence has the following specific transformation formula:
Figure FDA0002336891500000013
step 3, carrying out vector reconstruction with embedding dimension m on the kth new signal time sequence with coarse graining length p to obtain the k-th new signal time sequence
Figure FDA0002336891500000014
To
Figure FDA0002336891500000015
Wherein
Figure FDA0002336891500000016
Figure FDA0002336891500000017
The specific formula is as follows:
Figure FDA0002336891500000018
step 4, calculating the Euclidean distance fuzzy sample entropy of the kth new signal time sequence under the scale factor tau by using the reconstructed vector:
4.1 m-dimensional Signal time series with any two different initial vectors
Figure FDA0002336891500000019
And
Figure FDA00023368915000000110
the distance between
Figure FDA00023368915000000111
The specific formula for the euclidean distance of the two reconstructed vectors is as follows:
Figure FDA00023368915000000112
4.2, a threshold r is given, wherein r generally takes a value of 0.15 × SD, and SD is the standard deviation of an original sequence { x (i) |1 ≦ i ≦ N }; by fuzzy functions
Figure FDA0002336891500000021
Computing
Figure FDA0002336891500000022
And
Figure FDA0002336891500000023
similarity between them
Figure FDA0002336891500000024
The formula is as follows:
Figure FDA0002336891500000025
Figure FDA0002336891500000026
4.3 statistical degree of match between vectors, note
Figure FDA0002336891500000027
Figure FDA0002336891500000028
4.4 for all
Figure FDA0002336891500000029
Average and record as
Figure FDA00023368915000000210
Figure FDA00023368915000000211
4.5 increasing the embedding dimension to m +1, repeating the above steps 3-4.4 to calculate the matching degree between vectors, and recording as
Figure FDA00023368915000000212
And for all
Figure FDA00023368915000000213
Average and record as
Figure FDA00023368915000000214
Figure FDA00023368915000000215
Figure FDA00023368915000000216
4.6 Euclidean distance fuzzy sample entropy defining the kth new signal time series:
Figure FDA00023368915000000217
step 5, updating the k value, recovering the embedding dimension to m, repeating the steps 3-4.6, and solving the Euclidean distance fuzzy sample entropy of the next new signal time sequence until solving the Euclidean distance fuzzy sample entropies of all the tau new signal time sequences;
step 6, averaging the Euclidean distance fuzzy sample entropies of all the tau new signal time sequences to finally obtain the Euclidean distance fuzzy sample entropies of the original time sequence under the scale tau:
Figure FDA00023368915000000218
step 7, updating the value of the scale factor tau, returning to the step 2, solving the Euclidean distance fuzzy sample entropy of the next scale factor until the requirement of the number of the scale factors is met, and finally obtaining the Euclidean distance multi-scale fuzzy sample entropy, namely a group of Euclidean distance fuzzy sample entropy values under a plurality of different scale factors;
step 8, the Euclidean distance multi-scale fuzzy sample entropy is used as the input of a forward and backward propagation neural network, the neural network is set to be a four-layer topological structure, the number of input layer points is equal to the number of scale factors, each point corresponds to the Euclidean distance fuzzy sample entropy of each scale factor, and the number of hidden layers is 30 points; the output layer outputs vector values corresponding to each type of mark under different state types of the system; and finally, identifying the fault signal and detecting the fault of the industrial system.
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