CN104111109B - A kind of vibration condition recognition methods based on different order statistic and support vector machine - Google Patents

Abstract

The invention discloses a mechanical vibration state recognition method based on statistics of different orders and a support vector machine. The steps are as follows: (1) collect vibration data of the mechanical system through a vibration measurement device, and segment and remove the vibration data respectively. Mean preprocessing; (2) Calculate the third-order cumulant and fourth-order cumulant of each vibration data after preprocessing, and use them as two eigenvectors; estimate the fractional low-order statistic of each segment of data after processing-characteristic index α and dispersion coefficient γ, as the other two eigenvectors; (3) based on the above 4 eigenvectors, use support vector machine to classify and judge the vibration state of the mechanical system; Under the concept of feature extraction, the combination of high-order statistics and fractional low-order statistics in the feature extraction method can extract vibration signal features more comprehensively, and overcome the performance degradation of the traditional method based on second-order statistics under non-Gaussian conditions. question.

Description

A Mechanical Vibration State Recognition Method Based on Different Order Statistics and Support Vector Machine

technical field

The invention belongs to the field of mechanical engineering and relates to a mechanical vibration state recognition method, in particular to a mechanical vibration state recognition method based on statistics of different orders and a support vector machine.

Background technique

In the harsh working environment, gears, bearings, rotors, etc. in the mechanical system are prone to failure, resulting in damage to the whole machine or even serious accidents. Real-time monitoring of the mechanical system and accurate identification of its vibration state are very important to ensure the safety of the mechanical system.

The process of identifying the operating state of a mechanical system through vibration signals is generally divided into three steps. The first is data acquisition, through sensors and data acquisition instruments and other instruments to obtain relevant vibration data (such as acceleration, etc.) Mechanical feature information; the third step is state identification, through some intelligent classifiers (such as support vector machines) to identify vibration data in different states.

Traditional rolling bearing fault feature extraction methods generally use second-order statistics as an analysis tool, but second-order statistics can only reflect the characteristics of Gaussian signals, and cannot extract non-Gaussian features of signals, and the effect of suppressing noise and interference is poor.

Therefore, in order to extract the characteristics of the signal, it is necessary to use higher order statistics. Thus, in non-Gaussian signals, higher-order moments and higher-order cumulants, especially third-order and fourth-order statistics, occupy a high position in feature extraction.

Fractional low-order statistics have attracted the attention of researchers in recent years. Alpha stable distribution has wider applicability than Gaussian distribution. Fractional low-order moments or fractional low-order statistics are important means of feature extraction for non-Gaussian distributions. Considering the four parameters in the Alpha stable distribution, the position parameter a can be zeroed by removing the mean, and the symmetric coefficient For the fault signal, it is also approximately equal to zero in general, so the only effective characteristic parameters are the characteristic index and dispersion coefficient .

Contents of the invention

Aiming at the deficiencies of the prior art, the technical problem to be solved by the present invention is to propose a method for identifying the vibration state of a mechanical system based on different order statistics and a support vector machine. This method makes full use of the high-order statistics and fractional low-order statistics of the data as feature vectors, avoids the disadvantage of using a single statistic to form a feature vector, and overcomes the performance degradation of the second-order statistics under non-Gaussian conditions.

Technical scheme of the present invention comprises the following steps:

Step (1) Data collection and preprocessing:

The vibration data is collected by the mechanical vibration measurement device at a sampling frequency not lower than 10 times the system characteristic frequency, and the collected vibration data is segmented and averaged;

Step (2) Calculate 4 kinds of eigenvectors:

A. Calculate the skewness eigenvector and kurtosis eigenvector:

N segments of vibration data are obtained after segmentation and averaging, where N is greater than or equal to 1. According to the obtained vibration data of each segment, the third-order statistics and fourth-order statistics of each segment of vibration data in the system are respectively calculated, that is, the skewness and kurtosis , where i is the number of the i-th vibration data, is the skewness value corresponding to the i-th vibration data, is the kurtosis value corresponding to the i-th vibration data, 1≤i≤N, and the N calculation results are used as two eigenvectors, namely the skewness eigenvector and the kurtosis eigenvector;

B. Calculate the characteristic index eigenvector and dispersion coefficient eigenvector:

N segments of vibration data are obtained after segmenting and averaging, where N is greater than or equal to 1, and the logarithmic method is used to estimate the parameters of each segment of vibration data, and two parameters representing the low-order statistics of the score are obtained, namely the characteristic index and dispersion coefficient , so as to obtain N calculation results as the other two eigenvectors, namely the characteristic index eigenvector and the dispersion coefficient eigenvector;

Step (3) Select the radial basis kernel function, use cross-validation to select the best parameter penalty factor, and use the support vector machine algorithm to train the entire training set to obtain the support vector machine model, so as to complete the classification of vibration data and the vibration state of the mechanical system identify.

The de-meaning preprocessing of each section of vibration data is calculated using the following formula (1):

(1)

in, represents the mathematical expectation;

is the sequence composed of the vibration data collected in the i-th section, 1≤i≤N;

It is a sequence composed of the vibration data after the i-th segment has been de-averaged, 1≤i≤N.

Further, the third-order statistics and fourth-order statistics, that is, skewness and kurtosis The value of is calculated according to the following formula (2) ~ formula (3):

(2)

(3)

in, is the skewness value corresponding to the vibration data of the i segment, 1≤i≤N;

is the kurtosis value corresponding to the i-th segment vibration data, 1≤i≤N;

is the sequence formed by the vibration data after the i-th segment has been averaged;

n is the above sequence length;

for the above sequence standard deviation of .

Further, the characteristic index and dispersion coefficient The value of is calculated according to the following formula (4) ~ formula (7):

because a standard symmetry The random variable of stable distribution, after the preprocessing in the step (1), its position parameter , the symmetry parameter , when the standard symmetry When a random variable with a stable distribution has finite negative moments, due to Satisfy the following formula (4):

(4),

in, for of The expectation of the absolute value of the order central moment;

is the characteristic index;

is fractional order;

is the dispersion coefficient;

Satisfies the following formula (5):

(5),

in, is the gamma function;

only and function, and the random variable irrelevant;

After introducing the concept of negative moments, exist continuous, let , for The moment generating function of , then , and satisfy ;According to the characteristics of the moment generating function, we can get The first-order moment of is as formula (6), that is:

(6),

Among them, Euler's constant C _e =0.577212566;

because Satisfy the following formula (7):

(7),

in, for Variance;

According to the formula (7), the characteristic index can be obtained , substituted into formula (6) to get the dispersion coefficient value.

The beneficial effect that the inventive method has is:

(1) The high-order statistics represented by skewness and kurtosis avoid the defects that the traditional second-order statistics cannot extract non-Gaussian features of the signal and have poor anti-noise effects, and improve the effect of signal processing.

(2) With characteristic index and dispersion coefficient The fractional low-order statistic represented by the representative is an important means of signal analysis under the condition of non-Gaussian distribution signal noise, especially when the vibration signal of the mechanical system has strong pulse characteristics, it will show strong nonlinear and non-stationary characteristics. The traditional Gaussian At this time, the distribution can no longer meet the fitting requirements of the signal probability density, and the Alpha stable distribution can better reflect the real vibration state of the mechanical system.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Detailed ways

The implementation method of the present invention will be specifically described below with reference to the accompanying drawing 1, taking the state recognition process of a rolling bearing as an example, so as to better understand the technical solution of the present invention.

The state identification process of rolling bearings is as follows:

Step (1) Measure the vibration data of the rolling bearing in different states for a period of time, namely normal state, inner ring fault, outer ring fault, roller fault (deep) and roller fault (shallow). The vibration data can be For acceleration signals or other various vibration-related data, the sampling frequency of the mechanical vibration measurement device is 12 times the system characteristic frequency.

First, the acceleration signal is processed in segments. For example, the acceleration signal data can be divided into 30 segments (equivalent to 30 repeated experiments), and the length of each segment of data must contain at least 10 rotation cycles. For the signals in five states, 30 can be obtained. *5=150 sets of data, and then remove the mean value for each piece of data.

The following formula (1) is used to calculate the average value of each vibration data:

(1)

in, represents the mathematical expectation;

is the sequence composed of the vibration data collected in the i-th section, 1≤i≤N;

It is a sequence composed of the vibration data after the i-th segment has been de-averaged, 1≤i≤N.

In the actual calculation process, the time average can be used to approximate the statistical average.

Step (2) Calculate 4 kinds of eigenvectors:

A. Calculate the skewness eigenvector and kurtosis eigenvector:

N segments of vibration data are obtained after segmentation and averaging, where N is greater than or equal to 1. According to the obtained vibration data of each segment, the third-order cumulant and fourth-order cumulant of each segment of vibration data in the system are respectively calculated, that is, the skewness and kurtosis , where i is the number of the i-th vibration data, is the skewness value corresponding to the i-th vibration data, is the kurtosis value corresponding to the vibration data of the i-th segment, 1≤i≤N, and the N calculation results are respectively used as two eigenvectors, namely the skewness eigenvector and the kurtosis eigenvector;

B. Calculate the characteristic index eigenvector and dispersion coefficient eigenvector:

N segments of vibration data are obtained after segmenting and averaging, where N is greater than or equal to 1, and the logarithmic method is used to estimate the parameters of each segment of vibration data, and two parameters representing the low-order statistics of the score are obtained, namely the characteristic index and dispersion coefficient , repeating this process to obtain N calculation results as the other two eigenvectors, namely the characteristic index eigenvector and the dispersion coefficient eigenvector;

Step (3) Select the radial basis kernel function, use cross-validation to select the best parameter penalty factor, and use the support vector machine algorithm to train the entire training set to obtain the support vector machine model, so as to complete the classification of vibration data and the vibration state of the mechanical system identify.

The specific process of using the intelligent classifier of the support vector machine to identify the state of the rolling bearing is as follows:

Firstly, the data set should be prepared according to the format required by the support vector machine software package, especially the data format required by the software package; secondly, the radial basis function should be selected as the kernel function, and the existing data should be used for training to form a data model; The cross-validation method selects the best penalty factor and kernel parameters, takes 30 sets of data in each state type as the training sample set, and trains the entire training set to obtain the support vector machine model; finally, the obtained model can be used for vibration Data prediction and status classification identification.

To sum up, the vibration state identification method of mechanical system based on different order statistics and support vector machine provided by the present invention can effectively avoid traditional low-order statistics with weak anti-noise ability, unstable calculation results, and inaccurate state identification results. And other defects, with high recognition accuracy and precision.

The implementation manners described above are only preferred embodiments of the present invention, rather than an exhaustive list of feasible implementations of the present invention. For those skilled in the art, any obvious changes made without departing from the principle and spirit of the present invention should be considered to be included in the protection scope of the claims of the present invention.

Claims (4)

1. A mechanical vibration state recognition method based on different order statistics and support vector machine, is characterized in that comprising the steps: Step (1) Data collection and preprocessing: The vibration data is collected by the mechanical vibration measurement device at a sampling frequency not lower than 10 times the system characteristic frequency, and the collected vibration data is segmented and averaged; Step (2) Calculate 4 kinds of eigenvectors: A. Calculate the skewness eigenvector and kurtosis eigenvector: N segments of vibration data are obtained after segmentation and averaging, where N is greater than or equal to 1. According to the obtained vibration data of each segment, the third-order statistics and fourth-order statistics of each segment of vibration data in the system are respectively calculated, that is, the skewness and kurtosis , where i is the number of the i-th vibration data, is the skewness value corresponding to the i-th vibration data, is the kurtosis value corresponding to the i-th vibration data, 1≤i≤N, and the N calculation results are used as two eigenvectors, namely the skewness eigenvector and the kurtosis eigenvector; B. Calculate the characteristic index eigenvector and dispersion coefficient eigenvector: N segments of vibration data are obtained after segmenting and averaging, where N is greater than or equal to 1, and the logarithmic method is used to estimate the parameters of each segment of vibration data, and two parameters representing the low-order statistics of the score are obtained, namely the characteristic index and dispersion coefficient , so as to obtain N calculation results as the other two eigenvectors, namely the characteristic index eigenvector and the dispersion coefficient eigenvector; Step (3) Select the radial basis kernel function, use cross-validation to select the best parameter penalty factor, and use the support vector machine algorithm to train the entire training set to obtain the support vector machine model, so as to complete the classification of vibration data and the vibration state of the mechanical system identify. 2. A mechanical vibration state identification method based on statistics of different orders and support vector machines according to claim 1, characterized in that: the preprocessing of the average value of each vibration data is calculated by the following formula (1) : (1) in, represents the mathematical expectation; is the sequence composed of the vibration data collected in the i-th section, 1≤i≤N; It is a sequence composed of the vibration data after the i-th segment has been de-averaged, 1≤i≤N. 3. A kind of mechanical vibration state recognition method based on different order statistics and support vector machine according to claim 1 or 2, is characterized in that: described third-order statistics and fourth-order statistics, namely skewness and kurtosis The value of is calculated according to the following formula (2) ~ formula (3): (2) (3) in, is the skewness value corresponding to the vibration data of the i segment, 1≤i≤N; is the kurtosis value corresponding to the i-th segment vibration data, 1≤i≤N; is the sequence formed by the vibration data after the i-th segment has been averaged; n is the above sequence length; for the above sequence standard deviation of . 4. a kind of mechanical vibration state recognition method based on different order statistics and support vector machine according to claim 3, is characterized in that: described feature index and dispersion coefficient The value of is calculated according to the following formula (4) ~ formula (6): because a standard symmetry The random variable of stable distribution, after the preprocessing in the step (1), its position parameter , the symmetry parameter , when the standard symmetry When a random variable with a stable distribution has finite negative moments, due to Satisfy the following formula (4): (4), in, for of The expectation of the absolute value of the order central moment; is the characteristic index; is fractional order; is the dispersion coefficient; Satisfies the following formula (5): (5), in, is the gamma function; only and function, and the random variable irrelevant; After introducing the concept of negative moments, exist continuous, let , for The moment generating function of , then , and satisfy ;According to the characteristics of the moment generating function, we can get The first-order moment of is as formula (6), that is: (6), Among them, Euler's constant C _e =0.577212566; because Satisfy the following formula (7): (7), in, is the variance of Y; According to the formula (7), the characteristic index can be obtained , substituted into formula (6) to get the dispersion coefficient value.