A generalized motion centroid decomposition method based on local centroid and wave speed

Abstract

The application belongs to the technical field of fault diagnosis, and discloses a generalized motion centroid decomposition method based on local centroid and fluctuation rate. A signal extreme value set is obtained based on a vibration signal. Local centroids are calculated based on adjacent signal extreme values through a centroid solving formula, and a local centroid set is obtained by counting all local centroids in a time set. A slope set is obtained through formula calculation, and the slope set is traversed. A mapping feature point set is obtained based on the slope through a formula. A mean curve is generated by fitting all feature points through a cubic spline curve, and the mean curve is separated from an original signal and fitted to obtain an original separated extreme value curve. Local mean curve data obtained by repeating steps 1-4 for the original separated extreme value curve, until the standard deviation of the local mean curve meets the requirement, and a centroid decomposition signal is obtained by peeling the mean signal corresponding to the mean curve from the original signal. The cycle iteration is performed until the centroid decomposition signal is a monotonic function or a constant function.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology, and more specifically, to a method for decomposing a generalized center of mass based on local centroid and wave rate. Background Technology

[0002] With the acceleration of informatization, the demand for analysis and processing of complex signals in fields such as machinery and equipment is constantly increasing, and fault diagnosis of machinery and equipment is performed through the analysis of complex signals. In order to better meet these needs, various time-frequency domain analysis methods have been proposed, including Empirical Mode Decomposition (EMD), Local Feature Scale Decomposition (LCD), Local Mean Decomposition (LMD), and Global Empirical Mode Decomposition (EEMD). However, each of them has some problems and limitations, and the selection needs to be based on the specific application scenario.

[0003] To improve the limitations of these methods, especially to address the modal aliasing problem, the GMCD method was introduced. This method is based on the centroid and slope of the signal waveform and selects the optimal values ​​for signal extension to obtain a more accurate decomposition.

[0004] In view of this, the present invention provides a method for decomposing the generalized center of mass of motion based on the local center of mass and the wave rate. Summary of the Invention

[0005] To overcome the problems in the prior art, this invention proposes a generalized motion centroid decomposition method based on local centroid and wave rate, which comprehensively considers all data within the signal interval and improves upon the shortcomings of traditional integral formulas, such as long calculation time and the need for signal expressions, thus providing a new approach to limiting modal aliasing.

[0006] According to one aspect of the present invention, a method for decomposing a generalized center of mass based on a local center of mass and a wave rate is provided, comprising the following steps:

[0007] Step 1: Obtain the set of signal extrema based on the vibration signal;

[0008] Step 2: Based on the signal extremum set, calculate the local centroid using the centroid calculation formula based on adjacent signal extrema, and obtain the local centroid set by counting all local centroids within the time set;

[0009] Step 3: Calculate the slope set from the local centroid set using the formula, then iterate through the slope set to find the slope set that satisfies the condition... of ,make , and obtain in sequence The set of mapped feature points is obtained based on the slope using a formula.

[0010] Step 4: Use cubic spline curves to fit all feature points to generate a mean curve, separate the mean curve from the original signal and fit it to obtain the original separated extreme value curve;

[0011] Step 5: Using the local mean curve data obtained from the original extreme value curve in steps 1-4, determine whether the standard deviation of the local mean curve meets the preset standard value. If it does not meet the standard value, repeat steps 1-4 until the requirement is met, and then proceed to the next step, Step 6.

[0012] Step 6: Extract the mean signal corresponding to the mean curve from the original signal and obtain the centroid decomposition signal through the formula; repeat steps 1-5 on the centroid decomposition signal to obtain the local mean signal, and iterate until the centroid decomposition signal is a monotonic function or a constant function.

[0013] Step 7: GMCD can adaptively decompose the above centroid decomposition signal into a series of AM-FM signals, including... One intrinsic centroid function (ICF) and one residual component.

[0014] Preferably, the set of signal extrema is labeled as The corresponding time set is marked as ;

[0015] in, Set of signal extrema Length, ;No. Signal extreme values The corresponding time point is .

[0016] Preferably, a set of local centroids is obtained. The specific steps include:

[0017] In the interval Internal data fitted with respect to the time variable Local centroid equation For time variables The equation obtained by differentiation ;

[0018] definition For time points and The number of data points between them, the time set of adjacent extreme points and the corresponding data set are ,in ;

[0019] right and Perform centroid operations on adjacent data within the array, then rewrite the code after traversing the entire array. and The value inside;

[0020] Repeat the above steps until... and There is only one data point left, denoted as: and ;

[0021] By traversing all time intervals, we obtain the local centroid set. .

[0022] Preferably, the slope calculation formula is as follows:

[0023] ;

[0024] in, No. A local centroid signal; No. A local centroid signal; No. The time point corresponding to each local centroid signal; No. The time point corresponding to each local centroid signal.

[0025] Preferably, the coordinates of the centroid are obtained based on the slope, and the coordinates of the feature points are calculated based on the linear equation.

[0026] Preferably, the formula for separating the mean curve from the original signal and fitting it to obtain the original separated extreme value curve is as follows:

[0027] ;

[0028] in: The mean curve, To collect the original signal of the rolling bearing vibration operation by the sensor, This is the original separation extreme value curve.

[0029] Preferably, the AM-FM signal includes One intrinsic centroid function (ICF) and one residual component, the specific formula is as follows:

[0030] ;

[0031] in: For the first An intrinsic centroid function (ICF), ; For the first A residual component.

[0032] The technical effects and advantages of the generalized motion centroid decomposition method based on local centroid and wave rate of the present invention are as follows:

[0033] This invention, based on end-point data processing and feature point extraction methods, achieves signal decomposition and accurate fault location identification. It overcomes the shortcomings of traditional centroid formulas that rely on predictive signal expressions and employs slope-based data processing at the ends to reduce the impact of end-point effects. The method yields fewer components with higher similarity and more prominent fault frequencies, which helps reduce spurious components and effectively improves diagnostic efficiency and accuracy. Attached Figure Description

[0034] Figure 1 This is a flowchart of the generalized motion center of mass decomposition method of the present invention;

[0035] Figure 2 Time-domain waveforms of inner and outer ring faults;

[0036] Figure 3 The diagram shows the EMD decomposition, where (a) represents the EMD component set diagram; and (b) represents the frequency diagram corresponding to IMF1.

[0037] Figure 4 Here is the LMD decomposition diagram, where: (a) represents the LMD component set diagram; (b) represents the frequency diagram corresponding to PF1;

[0038] Figure 5 The diagram shows the LCD component set diagram, where (a) represents the LCD component set diagram and (b) represents the frequency diagram corresponding to ISC1.

[0039] Figure 6 The diagram shows the decomposition of GMCD, where (a) represents the GMCD component set diagram and (b) represents the frequency diagram corresponding to ICF1. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Example 1

[0042] Please see Figure 1-6 As shown in this embodiment, a generalized motion centroid decomposition method based on local centroid and wave rate is described, which uses sensors to collect vibration signals during the operation of a rolling bearing. The steps include:

[0043] Step 1: Based on vibration signals Obtain the set of signal extrema The set of signal extrema is marked as The corresponding time set is marked as ;

[0044] in, Set of signal extrema Length, ;in For the first The signal extreme value, the th signal extreme value, The time points corresponding to the extreme values ​​of the signals are: ;

[0045] It should be noted here that the set of signal extrema... The extreme values ​​of a signal can be either maximum or minimum. Therefore, for ease of subsequent calculations, the maximum values ​​are denoted as the maximum set. The corresponding time set is The minimum values ​​of the signal are denoted as the minimum value set. The corresponding time set is .

[0046] Step 2: Based on the set of signal extrema The local centroid is calculated based on the adjacent signal extrema using the centroid solution formula. Statistical analysis of all local centroids within the time set Obtain the set of local centroids ;

[0047] Obtain the set of local centroids The specific steps include:

[0048] In the interval Internal data fitted with respect to the time variable Local centroid equation , For time variables The equation obtained by differentiation ;

[0049] It should be noted that step 2 aims to determine the centroid between adjacent extreme values. Specifically, it can be understood that since there are multiple data points between adjacent extreme values ​​(e.g., the first extreme value and the second extreme value), the centroid is calculated by comprehensively considering all the data points between the extreme values. In other words, a centroid can be calculated within each extreme value interval. For example, the set consists of multiple data points, and the centroid can be understood as a coordinate, such as (1, 2) which means x = 2 when t = 1.

[0050] The number of extreme value intervals is determined by the extreme points of two adjacent signals; that is, the intervals extracted in step 1 are... If there are multiple extreme values ​​of a signal, then two adjacent extreme values ​​form an extreme value interval. Each extreme point corresponds to a A range of extreme values, The corresponding extreme value intervals are obtained by solving the problem. The coordinates of the centroids, therefore, are related to the local centroid set. There is no conflict; It is the mean value reflecting the monotonic changes of the local signal. Considering that calculating the fitting equation and integration is extremely time-consuming, and taking into account the characteristics of the current high acquisition frequency, the calculation formula for the centroid is optimized. The idea that the arithmetic mean of two points is the center of the line segment formed by those two points, and that point is also the centroid of that line segment, is analogous to the process of solving for the signal centroid.

[0051] Specific examples: Assuming For time points and The number of data points between them, the time set of adjacent extreme points and the corresponding data set are ,in .

[0052] right and Centroid operation is performed on adjacent data within the array. Specifically, this can be obtained by solving formula (1). After traversing the entire array, the operation is rewritten. and Repeat the above operation for the value inside, until... and There is only one data point left, denoted as: and Traverse all intervals to obtain the set of local centroids. .

[0053] (1)

[0054] Step 3: Obtain the set of mapped feature points Set the local centroids The slope set is obtained by calculating using formula (2). Slope set Traversing the set of slopes Finding of ,make The same method was used to obtain ;

[0055] The formula for calculating the slope is as follows:

[0056] (2)

[0057] The specific slope calculation is as follows:

[0058]

[0059] It should be noted here that: calculating the centroid point ( , ) and the center of mass ( , The slope between intervals is Since n-1 centroids are calculated in step 2, we obtain them sequentially. And denote the set of slopes as .

[0060] Calculate the slope From the slope Select with The slope with the smallest difference ,because Then it is believed The curve waveform in the interval and The slope with the highest similarity is found at the endpoint. Considering the large amount of data at the endpoints (i.e., many data points between the first data point and the first extreme point of the signal), unprocessed slopes would suffer from endpoint effects. Based on the above analysis, the slope with the highest similarity is determined, therefore, the slope is... By analogy .

[0061] Calculate the slope From the slope Select with The slope with the smallest difference ,because Then it is believed The waveform of the curve in the interval and The slope with the highest similarity is found at the endpoints. Considering the large amount of data at the endpoints (i.e., many data points between the last extreme point and the last data point of the signal), unprocessed slopes would suffer from endpoint effects. Based on the above analysis, the slope with the highest similarity is determined, therefore, the slope is... By analogy .

[0062] In summary, regarding the slope and The calculation yields the slope set. .

[0063] The point is obtained through formula (3). .

[0064] The formula for calculating feature points is as follows:

[0065]

[0066] (3)

[0067] For example, based on the above formula (2), k1 is calculated to obtain the coordinates of the first centroid (t1, x1), and a straight line equation formula (3) y = k1*(t-t1) + x1 is obtained.

[0068] By setting t1=T1, the corresponding y1 coordinate can be obtained;

[0069] Step 4: Fit all feature points using cubic spline curves Generate the mean curve The mean curve is obtained through formula (4). From the original signal The original extreme value curves were obtained by separating and fitting the original curves. ;

[0070] (4)

[0071] Step 5: Original Separation Extreme Curve Local mean curve data obtained through steps 1-4 Determine the local mean curve Is the standard deviation less than the original separation extreme value curve? If the standard deviation is 0.5, repeat steps 1-4 above until the requirement is met, then proceed to step 6.

[0072] Step 6: Plot the mean curve Corresponding mean signal The centroid decomposition signal is obtained by stripping the original signal using formulas (5) and (6). Decompose the centroid signal Repeat steps 1-5 to obtain the local mean signal. loop iteration Next, until the first Centroid decomposition signal It is a monotonic function or a constant function.

[0073] (5)

[0074] (6)

[0075] Step 7: GMCD can decompose the above centroid into signals. Adaptively decomposed into a series of AM-FM signals, including AM-FM signals. One intrinsic centroid function (ICF) and one residual component, as shown in Equation (7). Appendix Figure 1 This shows the flowchart of the GMCD algorithm.

[0076] (7)

[0077] in: For the first An intrinsic centroid function (ICF), ; For the first A residual component.

[0078] Example 2

[0079] Taking the LDK UER204 type experimental bearing as an example, the experimental bearing model was selected from the rolling bearing accelerated life test dataset of Xi'an Jiaotong University. The LDK UER204 type bearing corresponds to the inner and outer ring failures. The sampling frequency was set to 25600Hz, the experimental rotational frequency was 35Hz, and the rotational speed was 2100 rpm. 1000 data points were selected for analysis. The green and red vertical lines represent the theoretical inner ring failure frequency, respectively. The frequency multiplication factor, theoretical outer ring fault frequency frequency multiplication, Figure 2 The time-domain waveforms for inner and outer ring faults are shown.

[0080] Numerous studies have shown that fault signals are high-frequency signals, while the signal frequencies obtained through time-frequency domain analysis are distributed from high to low frequencies, with the highest frequency in the first component and the lowest frequency in the last component. If there are too many components, over-decomposition can occur, causing the fault frequency to be split across multiple components, ultimately making it impossible to accurately extract the fault signal and easily leading to misjudgment. The evaluation criterion for endpoint effects is similarity; the higher the similarity, the smaller the impact of endpoint effects. Compared to other methods, the GMCD method shows improvements in both fault information extraction and endpoint effect suppression.

[0081] The fault signal was processed by EMD to obtain 8 components and by LCD to obtain 11 components. The later components had low similarity to the fault signal and were false components. Therefore, this paper only selected the first 6 components for display.

[0082] LMD decomposition yields 5 components, while GMCD decomposition yields 4 components. The more components obtained, the more diluted the effective fault signals contained in the components become, leading to over-decomposition and ultimately causing misjudgment of faults.

[0083] Figure 3 (b) Remarkably prominent, and The amplitude at each location is approximately 0.3. and The other harmonics are not particularly prominent.

[0084] Figure 4 (b) and Figure 5 (b) It stands out, and Other frequency multipliers and None of the multipliers are particularly prominent.

[0085] Figure 6 (b) , Peaks appeared at all points, while near... A peak also appeared at that point. , , and Peaks of varying amplitudes appeared at all locations.

[0086] Table 1 shows that the similarity of the first component obtained by EMD and LCD is less than 0.2, while the similarity of LMD is 0.23 and the similarity of GMCD is 0.27. This is confirmed by the correlation spectrum diagram; compared to EMD, LCD, and LMD, the corresponding fault frequency obtained by GMCD is more prominent. The components obtained by the above methods all transition from high-frequency to low-frequency signals, while fault information generally resides within high-frequency signals. The larger the value, the more fault information it contains. Although the similarity of subsequent low-frequency components is high, it cannot reflect the fault characteristics.

[0087] Table 1 Evaluation Indicators for EMD, LMD, LCD, and GMCD Methods

[0088]

[0089] In summary, the EMD, LMD, and LCD decomposition methods all diagnose inner ring faults, with a prominent amplitude at the first octave of the inner ring fault frequency, while the outer ring fault frequency is submerged. Therefore, all of the above methods suffer from mode aliasing, failing to accurately determine the location of bearing faults. In contrast, the GMCD method accurately highlights the inner and outer ring fault frequencies in multi-fault diagnosis.

[0090] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0091] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0092] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for decomposing the generalized center of mass of motion based on local center of mass and wave rate, characterized in that, Includes the following steps: Step 1: Obtain the set of signal extrema based on the vibration signal; Step 2: Based on the signal extremum set, calculate the local centroid using the centroid calculation formula based on adjacent signal extrema, and obtain the local centroid set by counting all local centroids within the time set; Step 3: Calculate the slope set from the local centroid set using the slope calculation formula. The slope set is: ; The formula for calculating the slope is as follows: , ; in, No. A local centroid signal; No. A local centroid signal; No. The time point corresponding to each local centroid signal; No. The time point corresponding to each local centroid signal; Traverse the set of slopes, starting from the slope Select with The slope with the smallest difference Select the one that satisfies of ,make ; Traverse the set of slopes, from the slope Select with The slope with the smallest difference Select the one that satisfies of Regarding the slope Obtained by analogy , The slope is obtained by formulating the set of mapped feature points. Step 4: Use cubic spline curves to fit all feature points to generate a mean curve, separate the mean curve from the original signal and fit it to obtain the original separated extreme value curve; Step 5: Using the local mean curve data obtained from the original extreme value curve in steps 1-4, determine whether the standard deviation of the local mean curve meets the preset standard value. If it does not meet the standard value, repeat steps 1-4 until the requirement is met, and then proceed to the next step, Step 6. Step 6: Extract the mean signal corresponding to the mean curve from the original signal and obtain the centroid decomposition signal through the formula; repeat steps 1-5 on the centroid decomposition signal to obtain the local mean signal, and iterate until the centroid decomposition signal is a monotonic function or a constant function. Step 7: Adaptively decompose the above centroid decomposition signal into a series of AM-FM signals, including... One intrinsic centroid function and one residual component.

2. The method for decomposing the generalized center of mass of motion based on local centroid and wave rate according to claim 1, characterized in that, The set of signal extrema is labeled as The corresponding time set is marked as ; in, Set of signal extrema Length, ;No. Signal extreme values The corresponding time point is .

3. The method for decomposing the generalized center of mass of motion based on local center of mass and wave rate according to claim 2, characterized in that, Obtain the set of local centroids The specific steps include: In the interval Internal data fitted about the time variable Local centroid equation For time variables The equation obtained by differentiation ; definition For time points and The number of data points between them, the time set of adjacent extreme points and the corresponding data set are ,in ; right and Perform centroid operations on adjacent data within the array, then rewrite the code after traversing the entire array. and The value inside; Repeat the above steps until... and There is only one data point left, denoted as: and ; By traversing all time intervals, we obtain the local centroid set. .

4. The method for decomposing the generalized center of mass of motion based on local centroid and wave rate according to claim 3, characterized in that, The coordinates of the centroid are obtained based on the slope, and the coordinates of the feature points are calculated based on the linear equation.

5. The method for decomposing the generalized center of mass of motion based on local center of mass and wave rate according to claim 4, characterized in that, The formula for separating the mean curve from the original signal and fitting it to obtain the original separated extreme value curve is: ； in: The mean curve, To collect the original signal of the rolling bearing vibration operation by the sensor, This is the original separation extreme value curve.

6. The method for decomposing the generalized center of mass of motion based on local center of mass and wave rate according to claim 5, characterized in that, AM-FM signals include The intrinsic centroid function ICF and one residual component are defined by the following formulas: ； in: For the first An intrinsic centroid function ICF, ; For the first A residual component.

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