A Robust Method for Calculating Eigenvalues of Vibration Signals

Abstract

The present invention provides a robust method for calculating the eigenvalue of a vibration signal. The vibration signal X is subjected to short-time Fourier transform to obtain the short-time Fourier transform spectrum #imgabs0#. The mean spectrum Y is obtained by calculating column by column. According to the mean m of the mean spectrum Y Y and the standard deviation s Y A threshold T is set, and the local maximum method is used to obtain the local maximum points P in the mean spectrum Y that are greater than the threshold T, and the abnormal mutation signals are found. The vibration signals in the abnormal mutation signals are set as the mean value of the vibration signal X. According to the effective value calculation formula, the eigenvalue X of the vibration signal X after removing the abnormal mutation signals is estimated new of rms . The present invention uses the mean spectrum after short-time Fourier transform combined with the maximum value detection algorithm to identify the mutation region of the vibration signal, realizes the robustness of vibration data feature extraction, overcomes the eigenvalue mutation caused by external interference, and reduces the influence on the fault diagnosis result.

Description

Technical Field

[0001] The invention relates to the technical field of measurement and testing, and in particular to a robust vibration signal characteristic value calculation method. Background Art

[0002] Fault diagnosis technology based on vibration signal acquisition is an engineering science closely integrated with production practice and is the product of modern production development. With the application of modern science and technology on equipment, the structure of equipment is becoming more and more complex, the functions are becoming more and more perfect, and the degree of automation is becoming higher and higher. Due to the influence of many unavoidable factors, various faults will occur in the equipment, thereby reducing or losing the predetermined functions, and even causing serious or even catastrophic accidents. At present, due to the error of the measurer in reading or recording the data during the actual measurement, or because the detection instrument is subjected to random interference, these will cause the data to deviate and affect the feature extraction of the signal. As a data preprocessing method, data abnormal area recognition can identify the error information in the collected vibration data and ensure the correctness of the data before use as much as possible. Under the condition of limited fault data, the current data is used as much as possible to extract the real features to reduce the influence of the abnormal mutation area signal on the fault diagnosis effect. With the deepening of the research on abnormal data mining, many abnormal data mining algorithms have emerged in the field of fault diagnosis: such as detection methods based on hypothesis testing; detection methods based on linear model statistics; detection methods based on clustering; detection methods based on distance, etc.

[0003] There are many methods for detecting abnormal signal areas. Empirical mode decomposition (EMD) is an adaptive method for decomposing nonlinear and non-stationary signals proposed by Huang et al. Due to the adaptability of EMD, we can obtain potential processes with physical significance from complex data. The Hilbert-Huang transform (HHT) analysis method has good time-frequency aggregation characteristics. Starting from the local characteristic time scale of the data, the signal is decomposed into a finite number of intrinsic mode function (IMF) components of different characteristic scales through the EMD method. Since the local characteristic time scale of the abnormal mutation point reaction is small, that is, the interval between the two adjacent extreme points at the mutation is small, and the amplitude difference between the two adjacent maximum and minimum points is also much larger than that of the normal signal.

[0004] In a data sample, compared with other data, there may be inconsistencies in the general behavior or model of some data, and these data are outliers. Many data mining algorithms attempt to minimize the impact of outliers or eliminate them. Usually, outlier detection is also called deviation detection because outliers show significant deviations from the expected or common attribute values. Outlier detection is also called anomaly detection because outliers are far from other points on a scatter plot. Outlier detection is also called exception mining because, in a sense, outliers are exceptions.

[0005] With the increase in outlier mining methods and the in-depth study of them, the definitions of outliers have also increased, and generally can be divided into the following aspects:

[0006] (1) Outliers are usually noise data in the clustering process, and these data do not belong to any clustering cluster or small patterns within the cluster.

[0007] (2) Outliers are data objects with significant differences in behavior from the normal data in the dataset, and they do not belong to any clustering cluster nor are they noise data.

[0008] (3) Outliers are inconsistent with most data objects in the dataset, and they deviate significantly from other data objects in the dataset and do not conform to the general pattern or behavior of the data.

[0009] The outlier detection method based on wavelet analysis utilizes the multi-resolution analysis performance of wavelets to extract mutation information submerged in noise. However, the reasonable selection of wavelet bases is a difficult problem for this method.

[0010] There are some new methods in the research of outlier detection based on statistics. For example, to gain a deeper understanding of the overall characteristics of the data, it is necessary to first analyze the dispersion of the data, that is, analyze the data variation index. By studying the variation index, understand the distribution of the data, and then discover outliers in the data. Standard deviation, range, mean difference, interquartile range, and coefficient of variation are all commonly used data variation indices. If the value of the variation index is large, it indicates large variation and wide data dispersion; if the value of the variation index is small, it indicates small variation and dense data. However, most data in practice are multi-dimensional, so it is necessary to perform outlier detection in a multi-dimensional space. And most of the outlier detection methods based on statistics are for single attributes, and the detection effect for multi-dimensional data is not very ideal. In addition, this method can only detect whether the signal is abnormal, but cannot detect the abnormal region of the signal.

[0011] The distance-based outlier detection method is an inclusion and extension of the statistical idea. When the data set does not satisfy any specific distribution model, or when the spatial dimension is relatively high, the algorithm can effectively detect outliers. The disadvantage of this method is that it uses a unified distance standard for all data, while in reality, the data is likely to have sparse and dense parts, and different distance standards should be used between them.

[0012] The deviation-based outlier detection method is easy to operate and has good computational performance. However, this method has an overly idealized assumption of the existence of outliers and complicates the definition of the dissimilarity function, which is caused by its lack of understanding of the characteristics of the data. Therefore, the deviation-based outlier detection method does not work well for complex data in practice.

[0013] The density-based outlier detection algorithm needs to define the minimum number of neighbors and the radius of the neighborhood in advance. The selection of these two parameters seriously affects the final detection result. Summary of the Invention

[0014] The present invention is to solve the effectiveness of estimating the characteristics of abnormal vibration signals, reduce the interference of abnormal vibration on the calculation of characteristic values, identify the signal jump region through short-time Fourier transform combined with the outlier monitoring principle, set the data in the abnormal region to the mean value of the original signal, and calculate the effective value of the corrected signal, which can improve the robustness of the signal characteristic value estimation and reduce the false alarm rate of fault diagnosis.

[0015] The present invention provides a robust method for calculating the characteristic value of vibration signals, including the following steps:

[0016] S1. Short-time Fourier transform: Perform short-time Fourier transform on the vibration signal X to obtain the short-time Fourier transform spectrum

[0017] S2. Obtain the mean spectrum: Calculate the mean spectrum Y by column for the short-time Fourier transform spectrum ;

[0018] S3. Obtain the mean and standard deviation of the mean spectrum: Calculate the mean m Y and the standard deviation σ Y ;

[0019] S4. Obtain local maximum points: Set the threshold T according to the mean m Y and the standard deviation σ Y and use the local maximum method to obtain the local maximum points P in the mean spectrum Y that are greater than the threshold T;

[0020] S5. Obtain the abnormal mutation signal region: In the vibration signal X, with the local maximum point P as the center, extend the length of the abnormal point interval range parameter tol to the left and right respectively. The region obtained is the abnormal mutation signal region. The signal in the abnormal mutation signal region is the abnormal mutation signal. Set the vibration signal in the abnormal mutation signal to the mean value of the vibration signal X to obtain the vibration signal X after removing the abnormal mutation signal. new ;

[0021] S6. Obtain the eigenvalue after removing the abnormal mutation signal: Estimate the eigenvalue X of the vibration signal X after removing the abnormal mutation signal according to the effective value calculation formula. new of rms .

[0022] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S1, the vibration signal X = [x1, x2, x3..., x L , where L is the length of the vibration signal X.

[0023] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S1, the following parameters are set before performing the short-time Fourier transform: the moving window size window, the overlapping length overlap of two adjacent frames of signals, the short-time Fourier transform data length nfft, and the abnormal point interval range length parameter tol.

[0024] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S1, M = fix(nfft / 2)+1, where fix represents rounding down.

[0025] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S1, N = fix((L - overlap) / (window - overlap)).

[0026] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S1, the method of short-time Fourier transform is as follows: The vibration signal at a certain moment t of the vibration signal X is x(t). Select a time-frequency localization window function g(t). Assume that the window function g(t) is stationary within a short time interval. Move the window function g(t) and calculate the spectra at different moments according to the following formula

[0027]

[0028] In a robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, the spectra at different moments constitute the short-time Fourier transform spectrum.

[0029] A robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S2, the mean spectrum Y is: Y = [y1, y2, y3..., y N .

[0030] A robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S4, the threshold T is:

[0031] T = m Y + α * σ Y , where a is the abnormal point monitoring threshold.

[0032] A robust vibration signal eigenvalue calculation method according to the present invention, as a preferred embodiment, in step S6, the effective value calculation formula is:

[0033]

[0034] In view of the particularity of the abnormal region detection of vibration signals in complex industrial processes, the present invention proposes a new method for abnormal region detection. The method first performs a short-time Fourier transform on the original vibration signal, then calculates its average spectrum at each time scale, and then identifies the local maximum points of the average spectrum according to the pre-given parameters. The region near the local maximum points is the abnormal region of the original signal, and the eigenvalue of the original signal is calculated according to the identified abnormal region. The specific technical solution includes the following contents:

[0035] Short-time Fourier transform

[0036] Short-time Fourier transform (STFT: ShortTime FourierTransform): Given a signal x(t), select a time-frequency localization window function. Assume that the analysis window function g(t) is stationary (pseudo-stationary) within a short time interval, and move the window function (usually taking the "Hamming window") to calculate the spectra at different times as follows:

[0037]

[0038] In the original vibration signal, some signals are background noise, and the mutation region contains high-frequency and low-frequency information. When the above signal is subjected to STFT, its time-frequency distribution will be concentrated in the region where the signal mutates.

[0039] σ X Principle

[0040] Standard Deviation is most commonly used as a measure of the degree of statistical distribution in probability statistics. The standard deviation is defined as the square root of the arithmetic mean of the squared deviations of the standard values of all units in the population from their mean. It reflects the degree of dispersion among individuals within a group. The standard deviation can be regarded as a measure of uncertainty. By determining whether the sampled values conform to the predicted values, it is decided whether the vibration signal is an abnormal sample. The standard deviation of the measured values plays a decisive role: If the measured average is too far from the predicted value (while comparing with the value of the standard deviation), then the measured value and the predicted value are considered to be in contradiction. Because if the measured values all fall outside a certain numerical range, it can be reasonably inferred whether the predicted value is correct.

[0041] Let the original vibration signal X = [x1, x2, x3..., x L contain L sampling points: Calculate the mean m of the signal X X as:

[0042]

[0043] Then the unbiased standard deviation σ of the signal X x is:

[0044]

[0045] σ x Principle: The probability that the numerical distribution is in (m x - σ x , m x + σ x ) is 0.6526; 2σ x Principle: The probability that the numerical distribution is in (m x - 2σ x , m x + 2σ x ) is 0.9544; 3σ x Principle: The probability that the numerical distribution is in (m x - 3σ x , m x + 3σ x ) is 0.9974; where in the normal distribution, σ x represents the standard deviation, and m X represents the mean of the vibration signal X = [x1, x2, x3..., x L . Due to the basic idea of "small probability events" and hypothesis testing, "small probability events" usually refer to events with a probability of occurrence less than 5%, and it is considered that such events are almost impossible to occur in a single trial. Thus, it can be seen that X falls within (m x - 3σ x , m x + 3σ x) The probability other than this is less than three-thousandths. In practical problems, the corresponding event is often considered not to occur, and basically the interval (m x -3σ x , m x +3σ x ) can be regarded as the actual possible value interval of the random variable X.

[0046] Estimation of the effective value of the vibration signal

[0047] In the analysis of vibration signals, the characteristics of effective value calculation are usually utilized:

[0048] The purpose of the present invention is to utilize the mean spectrum after short-time Fourier transform combined with the maximum value detection algorithm to identify the mutation region of the vibration signal, realize the robustness of vibration data feature extraction, overcome the mutation of eigenvalue caused by external interference, and reduce the influence on the fault diagnosis result.

[0049] In order to effectively estimate the characteristics of abnormal vibration signals and reduce the interference of abnormal vibration on the calculation of eigenvalues, the present invention identifies the signal jump region through short-time Fourier transform combined with the principle of outlier monitoring, sets the data in the abnormal region to the mean value of the original signal, and calculates the effective value of the corrected signal, which can improve the robustness of signal eigenvalue estimation and reduce the false alarm rate of fault diagnosis.

[0050] (Assume the signal length is L = 2048 and the sampling frequency is 2.56 KHz): X = [x1, x2, x3..., x L . In practical applications of short-time Fourier transform, its discrete form is usually considered: Given short-time Fourier transform parameters: window (size of the moving window), overlap (length of overlap between adjacent two frames of signals), nfft (length of Fourier transform data), given outlier monitoring threshold α, outlier interval range length parameter tol:

[0051] Calculate the short-time Fourier transform spectrum of signal X according to parameters window, overlap, and nfft where M = fix(nfft / 2)+1, fix means rounding down; N = fix((L - overlap) / (window - overlap));

[0052] For Calculate the mean spectrum by columns: Y = [y1, y2, y3..., y N ;

[0053] Calculate the mean and standard deviation of the mean spectrum Y: m Y , σ Y ;

[0054] Calculate the threshold T = mY +α*σ Y , use the local maximum method to find the local maximum points in sequence Y that are greater than T, denoted as P;

[0055] With point P as the center, extend tol length to the left and right respectively. Then the signals in this interval are abnormal mutation signals. Let the signals in this interval be the mean value of the original signals, denoted as X new ;

[0056] Estimate the eigenvalue after removing the abnormal mutation signals according to the effective value calculation formula: X rms ;

[0057] The present invention has the following advantages:

[0058] (1) Utilize the time-frequency locality characteristics of the short-time Fourier transform to extract the mutation characteristics in the signal, which can effectively handle real-time online data acquisition analysis and fault diagnosis processing, and improve the robustness of data cleaning.

[0059] (2) This method has a fast processing speed, is suitable for online processing, and can be effectively applied to real-time monitoring scenarios such as fault diagnosis and equipment health management. Description of the Drawings

[0060] Figure 1 It is a flowchart of a robust vibration signal eigenvalue calculation method;

[0061] Figure 2 It is an abnormal vibration signal diagram of Embodiment 2 of a robust vibration signal eigenvalue calculation method;

[0062] Figure 3 It is a short-time Fourier transform spectrogram of Embodiment 2 of a robust vibration signal eigenvalue calculation method;

[0063] Figure 4 It is a short-time Fourier transform mean spectrogram of a robust vibration signal eigenvalue calculation method;

[0064] Figure 5 It is a schematic diagram of the abnormal area jump signal of Embodiment 2 of a robust vibration signal eigenvalue calculation method. Detailed Embodiments

[0065] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0066] Embodiment 1

[0067] As Figure 1 shown, a robust vibration signal eigenvalue calculation method includes the following steps:

[0068] S1, Short-time Fourier transform: Perform short-time Fourier transform on the vibration signal X to obtain the short-time Fourier transform spectrum

[0069] The vibration signal X = [x1, x2, x3..., x L , where L is the length of the vibration signal X. Before performing the short-time Fourier transform, set the following parameters: moving window size window, overlapping length overlap between two adjacent frames of signals, short-time Fourier transform data length nfft, and abnormal point interval range length parameter tol. M = fix(nfft / 2)+1, where fix represents rounding down, and N = fix((L - overlap) / (window - overlap));

[0070] The method of short-time Fourier transform is as follows: The vibration signal at a certain moment t of the vibration signal X is x(t). Select a time-frequency localization window function g(t). Assume that the window function g(t) is stationary within a short time interval. Move the window function g(t) and calculate the spectra at different moments according to the following formula

[0071] The spectra at different moments constitute the short-time Fourier transform spectrum

[0072] S2, Obtain the mean spectrum: Calculate the mean spectrum Y column by column for the short-time Fourier transform spectrum Y = [y1, y2, y3..., y N ;

[0073] S3, Obtain the mean and standard deviation of the mean spectrum: Calculate the mean m Y and standard deviation σ Y of the mean spectrum Y;

[0074] S4, Obtain local maximum points: Set the threshold T according to the mean m Y and standard deviation σ Y , and use the local maximum method to obtain the local maximum points P in the mean spectrum Y that are greater than the threshold T;

[0075] The threshold T is

[0076] T = m Y +α*σ Y , where a is the abnormal point monitoring threshold;

[0077] S5. Obtain the abnormal mutation signal region: In the vibration signal X, with the local maximum point P as the center, extend the length of the abnormal point interval range parameter tol to the left and right respectively. The region obtained is the abnormal mutation signal region. The signal in the abnormal mutation signal region is the abnormal mutation signal. Set the vibration signal in the abnormal mutation signal as the mean value of the vibration signal X to obtain the vibration signal X after removing the abnormal mutation signal. new ;

[0078] S6. Obtain the eigenvalue after removing the abnormal mutation signal: Estimate the eigenvalue X of the vibration signal X after removing the abnormal mutation signal according to the effective value calculation formula. new of rms ;

[0079] The effective value calculation formula is:

[0080]

[0081] Embodiment 2

[0082] As Figure 1 shown, a robust vibration signal eigenvalue calculation method. In this example, real-time data is collected using the "Intelligent Operation and Maintenance Big Data Cloud Platform" of Aerospace Intelligence Control (Beijing) Monitoring Technology Co., Ltd. for the abnormal vibration signal X (as Figure 2 shown, the number of sampling points is 2048), and the sampling frequency is 2560 Hz. Window = 128, overlap = 100, nfft = 128, and the given abnormal point monitoring threshold a = 1, and the abnormal point interval range parameter tol = 200.

[0083] 1. Calculate the short-time Fourier transform spectrum of the signal sample X according to the parameters window, overlap, and nfft (as Figure 3 shown)

[0084] 2. Calculate the mean spectrum by column for : Y = [y1, y2, y3..., y 69 (as Figure 4 shown)

[0085] 3. Calculate (as Figure 4 shown) the mean value and its standard deviation of the mean spectrum Y: m Y , σ Y

[0086] 4. Given the threshold T = m Y + σ Y , use the local maximum method to find the local maximum points in the sequence Y that are greater than T, denoted as P ((as Figure 4 shown) two points shown)

[0087] 5. With point P as the center, extend tol = 200 lengths to the left and right respectively. Then the signal in this interval is an abnormal mutation signal (as Figure 5 shown), and let the signal in this interval be the mean value of the original signal, denoted as X new ;

[0088] 6. According to the effective value calculation formula, the effective value of the original data X is: 13.3715. After removing the abnormal mutation signal, the eigenvalue of X new is: 2.404. Through the abnormal point detection algorithm, the influence of abnormal points on the estimation of the vibration signal eigenvalue is effectively reduced, avoiding the misjudgment of the fault diagnosis result by this signal.

[0089] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent replacements or changes, should be covered by the protection scope of the present invention.

Claims

1. A robust method for calculating the eigenvalue of vibration signals, characterized in that: Including the following steps: S1. Short-time Fourier transform: Perform short-time Fourier transform on the vibration signal X to obtain the short-time Fourier transform spectrum S2. Obtain the mean spectrum: For the short-time Fourier transform spectrum Calculate the mean spectrum Y column by column; S3. Obtain the mean and standard deviation of the mean spectrum: Calculate the mean m of the mean spectrum Y Y and the standard deviation σ Y ; S4. Obtain local maximum points: According to the mean value m Y and the standard deviation σ Y set a threshold T, and use the local maximum method to obtain local maximum points P in the mean spectrum Y that are greater than the threshold T; S5. Obtain the abnormal mutation signal region: With the local maximum point P as the center in the vibration signal X, the regions extending left and right by the length of the abnormal point interval range parameter tol are the abnormal mutation signal regions. The signals in the abnormal mutation signal regions are abnormal mutation signals. Set the vibration signal in the abnormal mutation signals as the mean value of the vibration signal X to obtain the vibration signal Xnew after removing the abnormal mutation signals; S6. Obtain the eigenvalue after removing the abnormal mutation signals: Estimate the eigenvalue Xrms of the vibration signal Xnew after removing the abnormal mutation signals according to the effective value calculation formula; The effective value calculation formula is:

2. A robust method for calculating the eigenvalue of a vibration signal according to claim 1, wherein: In step S1, the vibration signal X = [x1, x2, x3..., x L , where L is the length of the vibration signal X.

3. A robust vibration signal eigenvalue calculation method according to claim 2, characterized in that: In step S1, set the following parameters before performing the short-time Fourier transform: moving window size window, overlapping length overlap of adjacent two frames of signals, short-time Fourier transform data length nfft, and abnormal point interval range length parameter tol.

4. A robust vibration signal eigenvalue calculation method according to claim 3, characterized in that: In step S1, M = fix(nfft / 2)+1, where fix represents rounding down.

5. A robust method for calculating vibration signal eigenvalues according to claim 4, characterized in that: In step S1, N = fix((L - overlap) / (window - overlap)).

6. A robust vibration signal eigenvalue calculation method according to claim 5, characterized in that: In step S1, the method of short-time Fourier transform is as follows: the vibration signal at a certain moment t of the vibration signal X is x(t). A window function g(t) with time-frequency localization is selected. It is assumed that the window function g(t) is stationary within a short time interval. The window function g(t) is moved, and the spectra at different moments are calculated according to the following formula 7. A robust vibration signal eigenvalue calculation method according to claim 6, characterized in that: The spectra at each different moment constitute the short-time Fourier transform spectrum 8. A robust method for calculating vibration signal eigenvalue according to claim 1, characterized in that: In step S2, the mean spectrum Y is: Y = [y1, y2, y3..., y N .

9. A robust method for calculating vibration signal eigenvalue according to claim 1, characterized in that: In step S4, the threshold T is: T = m Y + α * σ Y , where α is the abnormal point monitoring threshold.

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