CN104111109B - A kind of vibration condition recognition methods based on different order statistic and support vector machine - Google Patents
A kind of vibration condition recognition methods based on different order statistic and support vector machine Download PDFInfo
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Abstract
The invention discloses a kind of vibration condition recognition methods based on different order statistic and support vector machine, its step is as follows: (1) is by the vibration data of vibration measurement device collection machinery system and carry out segmentation to vibration data respectively, go average pre-service; (2) calculate Third-order cumulants and the fourth order cumulant of every section of vibration data after pre-service, it can be used as two proper vectors; Estimate fractional lower-order statistics-characteristic exponent α and the dispersion coefficient γ of the rear every segment data of process, as two other proper vector; (3) with above-mentioned 4 proper vectors for foundation, utilize the vibrational state of support vector machine to mechanical system make classification and judge; Advantage of the present invention is under the concept of non-Gaussian signal process, high-order statistic in feature extracting method and fractional lower-order statistics two class statistical method are combined, extract vibration signal characteristics more comprehensively, overcome traditional performance degradation problem occurred based on second-order statistics metering method system under non-gaussian condition.
Description
Technical Field
The invention belongs to the field of mechanical engineering, relates to a mechanical vibration state identification method, and particularly relates to a mechanical vibration state identification method based on different-order statistics and a support vector machine.
Background
Under severe working environment, gears, bearings, rotors and the like in a mechanical system are easy to break down, so that the whole machine is damaged and even serious accidents happen. The vibration monitoring system monitors a mechanical system in real time and accurately identifies the vibration state of the mechanical system, and is very important for ensuring the safety of the mechanical system.
The process of identifying the operating state of a mechanical system by means of a vibration signal is generally divided into three steps. Firstly, data acquisition is carried out, and related vibration data (such as acceleration and the like) capable of reflecting the running state of mechanical equipment is acquired through instruments such as a sensor, a data acquisition instrument and the like; secondly, extracting features, namely extracting or highlighting mechanical feature information hidden in the vibration data by adopting a proper method; the third step is state identification, and vibration data of different states are identified through some intelligent classifiers (such as a support vector machine).
The traditional rolling bearing fault feature extraction method generally uses second-order statistics as an analysis tool, but the second-order statistics can only reflect the features of Gaussian signals, can not extract non-Gaussian features of the signals, and has poor noise and interference suppression effects.
Therefore, in order to extract the features of the signal, higher order statistics must be used. Thus, in non-gaussian signals, high-order moments and high-order cumulants, particularly third-order and fourth-order statistics, dominate the feature extraction.
In recent years, researchers have focused on fractional order statistics, where Alpha-stable distributions have wider applicability than gaussian distributions, and fractional order moments or fractional order statistics are important means for feature extraction when the distributions are non-gaussian. Considering four parameters in Alpha stable distribution, position parameteraCan be zeroed by means of mean value removal, and the symmetric coefficientsFor fault signals, they are also generally approximately zero, so that only the characteristic index remains for a valid characteristic parameterAnd coefficient of dispersion。
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a mechanical system vibration state identification method based on different order statistics and a support vector machine. The method fully utilizes the high-order statistic and the fractional low-order statistic of the data as the feature vector, avoids the defect that the feature vector is formed by single statistic, and overcomes the problem of performance degradation of the second-order statistic under the non-Gaussian condition.
The technical scheme of the invention comprises the following steps:
step (1), data acquisition and pretreatment:
acquiring vibration data by a mechanical vibration measuring device at a sampling frequency which is not less than 10 times of the characteristic frequency of the system, and segmenting and averaging the acquired vibration data;
calculating 4 kinds of feature vectors in the step (2):
A. calculating skewness feature vectors and kurtosis feature vectors:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and respectively calculating the third order statistic and the fourth order statistic of each section of vibration data in the system, namely skewness, according to the obtained vibration data of each sectionDegree of harmonyWherein i is the number of the ith vibration data,is the skewness value corresponding to the ith vibration data,taking the kurtosis value corresponding to the ith section of vibration data, wherein i is more than or equal to 1 and less than or equal to N, and taking N calculation results as two feature vectors, namely a skewness feature vector and a kurtosis feature vector;
B. calculating a characteristic index characteristic vector and a dispersion coefficient characteristic vector:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and performing parameter estimation on each section of vibration data by using a logarithm method to obtain two parameters representing fraction low order statistics, namely characteristic indexesAnd coefficient of dispersionThus obtaining N calculation results as the other two feature vectors, namely feature index feature vector and dispersion coefficient feature vector;
and (3) selecting a radial basis kernel function, selecting an optimal parameter penalty factor by adopting cross validation, and training the whole training set by using a support vector machine algorithm to obtain a support vector machine model so as to finish the classification of vibration data and the vibration state identification of a mechanical system.
The pre-processing of the mean value removal of each section of vibration data is calculated by adopting the following formula (1):
（1）
wherein,represents a mathematical expectation;
i is more than or equal to 1 and less than or equal to N;
i is more than or equal to 1 and less than or equal to N.
Further, the third order statistic and the fourth order statistic, i.e., skewnessDegree of harmonyValue of (A)Calculating according to the following formula (2) to formula (3):
（2）
（3）
wherein,the skewness value corresponding to the ith section of vibration data is represented, i is more than or equal to 1 and less than or equal to N;
the kurtosis value corresponding to the ith section of vibration data is, i is more than or equal to 1 and less than or equal to N;
forming a sequence for the vibration data after the ith section is subjected to mean value removal;
nis the above sequenceLength of (d);
is the above sequenceStandard deviation of (2).
Further, the characteristic indexAnd coefficient of dispersionThe value of (c) is calculated according to the following formula (4) to formula (7):
due to the fact thatIs a standard symmetryThe position parameters of the stably distributed random variables after the pretreatment in the step (1)Symmetric parameterWhen the standard is symmetricalWhen the steadily distributed random variables have finite negative order moments, becauseSatisfies the following formula (4):
（4），
wherein,is composed ofIs/are as follows(ii) an expectation of the absolute value of the central moment of order;
is a characteristic index;
is in fractional order;
is the dispersion coefficient;
satisfying the following formula (5):
（5），
wherein,is a gamma function;
is only thatAnda function of, and a random variableIrrelevant;
after the concept of a negative order moment is introduced,in thatIs continuously treated, order，Is composed ofA moment generating function ofAnd satisfy(ii) a From the characteristics of the moment generating functionThe first moment of (a) is as in equation (6), i.e.:
（6），
wherein Euler constantC e =0.577212566；
Due to the fact thatSatisfies the following formula (7):
（7），
wherein,is composed ofThe variance of (a);
the characteristic index can be obtained according to the formula (7)Substituting into equation (6) to obtain the dispersion coefficientThe value is obtained.
The method of the invention has the following beneficial effects:
(1) the high-order statistic represented by skewness and kurtosis avoids the defects that the traditional second-order statistic cannot extract non-Gaussian characteristics of signals and the anti-noise effect is poor, and the signal processing effect is improved.
(2) By a characteristic indexAnd coefficient of dispersionThe represented fractional low-order statistic is an important means for signal analysis under the condition of non-Gaussian distribution signal noise, particularly, when a vibration signal of a mechanical system has strong pulse characteristics, the signal shows extremely strong nonlinear and non-stationary characteristics, the traditional Gaussian distribution cannot meet the fitting requirement of the probability density of the signal, and the Alpha stable distribution can better reflect the real vibration state of the mechanical system.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The following describes the method of the present invention in detail by taking the status recognition process of the rolling bearing as an example, with reference to fig. 1, so as to better understand the technical solution of the present invention.
The state identification process of the rolling bearing is as follows:
the method comprises the following steps of (1) measuring vibration data of the rolling bearing in different states for a period of time, wherein the different states are a normal state, an inner ring fault, an outer ring fault, a roller fault (deep) and a roller fault (shallow), the vibration data can be acceleration signals or other various vibration related data, and the sampling frequency of the mechanical vibration measuring device is 12 times of the system characteristic frequency.
The acceleration signal is first segmented, for example, the acceleration signal data may be divided into 30 segments (corresponding to 30 repeated experiments), each segment of data length includes at least 10 rotation cycles, 30 × 5=150 sets of data are obtained for the signals in five states, and then the averaging process is performed on each segment of data.
The mean value removing pretreatment of each section of vibration data is calculated by adopting the following formula (1):
（1）
wherein,represents a mathematical expectation;
i is more than or equal to 1 and less than or equal to N;
i is more than or equal to 1 and less than or equal to N.
The time average approximation can be used instead of the statistical average in the actual calculation process.
Calculating 4 kinds of feature vectors in the step (2):
A. calculating skewness feature vectors and kurtosis feature vectors:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and respectively calculating the third-order cumulant and the fourth-order cumulant of each section of vibration data in the system, namely skewness, according to the obtained vibration data of each sectionDegree of harmonyWherein i is the number of the ith vibration data,is the skewness value corresponding to the ith vibration data,taking the N calculation results as two feature vectors, namely a skewness feature vector and a kurtosis feature vector, respectively, wherein i is more than or equal to 1 and less than or equal to N, and the kurtosis value corresponding to the ith section of vibration data;
B. calculating a characteristic index characteristic vector and a dispersion coefficient characteristic vector:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and performing parameter estimation on each section of vibration data by using a logarithm method to obtain two parameters representing fraction low order statistics, namely characteristic indexesAnd coefficient of dispersionRepeating the process to obtain N calculation results as another two feature vectors, namely a feature index feature vector and a dispersion coefficient feature vector;
and (3) selecting a radial basis kernel function, selecting an optimal parameter penalty factor by adopting cross validation, and training the whole training set by using a support vector machine algorithm to obtain a support vector machine model so as to finish the classification of vibration data and the vibration state identification of a mechanical system.
The specific process of identifying the state of the rolling bearing by using the intelligent classifier of the support vector machine is as follows:
firstly, preparing a data set according to a format required by a software package of a support vector machine, particularly a data format required by the software package; secondly, selecting a radial basis function as a kernel function, and training by using the existing data to form a data model; then selecting an optimal penalty factor and a nuclear parameter by adopting a cross validation method, taking 30 groups of data under each state type as a training sample set, and training the whole training set to obtain a support vector machine model; and finally, the obtained model can be used for predicting vibration data and classifying and identifying states.
In conclusion, the mechanical system vibration state identification method based on different-order statistics and the support vector machine can effectively overcome the defects of weak noise resistance, unstable calculation result, inaccurate state identification result and the like of the traditional low-order statistics, and has high identification accuracy and precision.
The embodiments described above are only preferred embodiments of the invention and are not exhaustive of the possible implementations of the invention. Any obvious modifications to the above would be obvious to those of ordinary skill in the art, but would not bring the invention so modified beyond the spirit and scope of the present invention.
Claims (4)
1. A mechanical vibration state identification method based on different-order statistics and a support vector machine is characterized by comprising the following steps:
step (1), data acquisition and pretreatment:
acquiring vibration data by a mechanical vibration measuring device at a sampling frequency which is not less than 10 times of the characteristic frequency of the system, and segmenting and averaging the acquired vibration data;
calculating 4 kinds of feature vectors in the step (2):
A. calculating skewness feature vectors and kurtosis feature vectors:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and respectively calculating the third order statistic and the fourth order statistic of each section of vibration data in the system, namely skewness, according to the obtained vibration data of each sectionDegree of harmonyWherein i is the number of the ith vibration data,is the skewness value corresponding to the ith vibration data,taking the kurtosis value corresponding to the ith section of vibration data, wherein i is more than or equal to 1 and less than or equal to N, and taking N calculation results as two feature vectors, namely a skewness feature vector and a kurtosis feature vector;
B. calculating a characteristic index characteristic vector and a dispersion coefficient characteristic vector:
obtaining N sections of vibration data after segmentation and mean value removal, wherein N is more than or equal to 1, and performing parameter estimation on each section of vibration data by using a logarithm method to obtain two parameters representing fraction low order statistics, namely characteristic indexesAnd coefficient of dispersionThus obtaining N calculation results as the other two feature vectors, namely feature index feature vector and dispersion coefficient feature vector;
and (3) selecting a radial basis kernel function, selecting an optimal parameter penalty factor by adopting cross validation, and training the whole training set by using a support vector machine algorithm to obtain a support vector machine model so as to finish the classification of vibration data and the vibration state identification of a mechanical system.
2. The method for recognizing mechanical vibration state based on different order statistics and support vector machine according to claim 1, characterized in that: the pre-processing of the mean value removal of each section of vibration data is calculated by adopting the following formula (1):
（1）
wherein,represents a mathematical expectation;
i is more than or equal to 1 and less than or equal to N;
i is more than or equal to 1 and less than or equal to N.
3. The method for identifying mechanical vibration state based on different order statistics and support vector machine according to claim 1 or 2, characterized in that: the third order statistic and the fourth order statistic, i.e., skewnessDegree of harmonyThe value of (c) is calculated according to the following formula (2) to formula (3):
（2）
（3）
wherein,the skewness value corresponding to the ith section of vibration data is represented, i is more than or equal to 1 and less than or equal to N;
the kurtosis value corresponding to the ith section of vibration data is, i is more than or equal to 1 and less than or equal to N;
forming a sequence for the vibration data after the ith section is subjected to mean value removal;
nis the above sequenceLength of (d);
is the above sequenceStandard deviation of (2).
4. The method for recognizing mechanical vibration state based on different order statistics and support vector machine according to claim 3, characterized in that: the characteristic indexAnd coefficient of dispersionThe value of (c) is calculated according to the following formula (4) to formula (6):
due to the fact thatIs a standard symmetryThe position parameters of the stably distributed random variables after the pretreatment in the step (1)Symmetric parameterWhen the standard is symmetricalWhen the steadily distributed random variables have finite negative order moments, becauseSatisfies the following formula (4):
（4），
wherein,is composed ofIs/are as follows(ii) an expectation of the absolute value of the central moment of order;
is a characteristic index;
is in fractional order;
is the dispersion coefficient;
satisfying the following formula (5):
（5），
wherein,is a gamma function;
is only thatAnda function of, and a random variableIrrelevant;
after the concept of a negative order moment is introduced,in thatIs continuously treated, order，Is composed ofA moment generating function ofAnd satisfy(ii) a From the characteristics of the moment generating functionThe first moment of (a) is as in equation (6), i.e.:
（6），
wherein Euler constantC e =0.577212566；
Due to the fact thatSatisfies the following formula (7):
（7），
wherein,is the variance of Y;
the characteristic index can be obtained according to the formula (7)Substituting into equation (6) to obtain the dispersion coefficientThe value is obtained.
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| CN102829974A (en) * | 2012-08-07 | 2012-12-19 | 北京交通大学 | LMD (local mean decomposition) and PCA (principal component analysis) based rolling bearing state identification method |
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