CN111122162B - Industrial system fault detection method based on Euclidean distance multi-scale fuzzy sample entropy - Google Patents
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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
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 problems existing in the past are solved to some extent by Composite Multiscale Entropy (CMSE) and Composite Multiscale Fuzzy Entropy (FME), these 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 of each corresponding component of two vectors, and the measurement mode has a 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 corresponding components of two vectorsMethod of maximum absolute difference and using fuzzy functionThe 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:
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:
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.
4.1 m-dimensional Signal time series with any two different initial vectorsAndthe distance betweenThe specific formula for the euclidean distance of the two reconstructed vectors is as follows:
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 functionsComputingAndsimilarity between themThe formula is as follows:
the invention adopts fuzzy functionInstead of a 0-1 step function, the similarity of two vectors is characterized. The measure of the 0-1 step function between two m-dimensional vector sequences is that if the distance between the two m-dimensional vector sequences is within an allowable range, the similarity is1, and if the similarity 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 functionThen 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.
4.5 increasing the embedding dimension to m +1 and repeating the above steps 3-4.4 to calculate the matching degree between vectors, and recording asAnd for allAverage and record as
4.6 Euclidean distance sample fuzzy entropy defining the kth new signal time series:
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 is provided withThe beneficial effects are 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 functionTo 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.
Drawings
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:
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.
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:
4.1 m-dimensional Signal time series with any two different initial vectorsAndthe distance betweenThe specific formula for the euclidean distance of the two reconstructed vectors is as follows:
the invention uses Euclidean distance to define the distance between two vectors, and replaces the vector distance defined by the maximum absolute difference value of each corresponding component of the two vectors used by other methods. 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 functionsComputingAndsimilarity between them The formula is as follows:
the invention adopts a fuzzy function when calculating the similarity of two vectorsInstead 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. The fuzzy function adopted by the invention is smoothed from 0-1, the similarity can be defined by the method under the condition that 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 functionThe vector distance d is continuously defined from 0 to positive infinity, so the accuracy of vector similarity calculation is greatly improvedAnd stability.
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 asAnd for allAverage and record as
4.6 Euclidean distance fuzzy sample entropy defining the kth new signal time series:
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 neural network which propagates forward and backward, and sets an input layer as 20 points, namely each point corresponds to each group of data from 1 to 1 in scale factorThe Euclidean distance fuzzy sample entropy value corresponding to 20 is 30 points, the hidden layer is provided with 6 points on the output layer, and the 6 points correspond to the vector value of each type of mark in 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%)
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 functionsThe 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 distanceThe 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 on a scale factor tau, wherein tau is a positive integer, on a time sequence { x (i) | i ═ 1, 2., N }, and forming a plurality of coarse-grained numerical points
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:
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 sequenceToWherein
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 vectorsAndthe distance betweenThe specific formula for the euclidean distance of the two reconstructed vectors is as follows:
4.2, setting a threshold r, wherein the value of r is 0.15 multiplied by SD, and SD is the standard deviation of an original sequence { x (i) |1 ≦ i ≦ N }; by fuzzy functionsComputingAndsimilarity between them The formula is as follows:
4.5 will inlayIncreasing the input dimension to m +1, repeating the steps 3-4.4 to calculate the matching degree between vectors, and recording asAnd for allAverage and record as
4.6 Euclidean distance fuzzy sample entropy defining the kth new signal time series:
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:
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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