Gear dynamic stress measurement data outlier rejection method under small sample

Abstract

The application provides a gear dynamic stress measurement data outlier elimination method under a small sample, comprising the following steps: step 1, determining a gear dynamic stress measurement position and a number requirement; step 2, determining a vibration excitation order of the gear dynamic stress measurement data; step 3, classifying and arranging the gear dynamic stress measurement data; step 4, preliminarily screening abnormal data based on a quartile range algorithm; step 5, determining a statistical characteristic value of the dynamic stress test data; and step 6, finally determining the abnormal data based on a Grubbs criterion method. The method can effectively reduce the influence of gross errors on the mean value and standard deviation of small sample data, improve the identification reliability of abnormal data, and improve the accuracy of gear fatigue risk assessment; the method is fast and convenient, easy to be programmed, improves work efficiency, and is helpful to reduce the cost of manpower and financial resources.

Description

Technical Field

[0001] This invention relates to the field of aero-engine technology, specifically to a method for eliminating outliers in gear dynamic stress measurement data under small sample sizes. Background Technology

[0002] With the improvement of engine performance and weight reduction design, the traveling wave resonance problem of thin-walled lightweight gears under high-speed and heavy-load conditions has become prominent. Gear dynamic stress measurement has become an important test for aero-engines, and test data analysis and processing is a crucial step that directly affects fatigue failure risk assessment. Due to the limited space in the gear layout and the low survival rate of the gear patches in high-concentration oil mist environments, the sample size of gear dynamic stress measurement data is small. Factors such as patch position deviation and strain gauge microstructure distortion in high-speed, high-oil-mist environments can cause abrupt changes in test data, resulting in numerical anomalies. These anomalies lead to gross errors, manifesting as excessively high or low values. If these data are conservatively assessed as normal, it leads to a waste of manpower and resources for structural improvements; if they are easily deleted, false conclusions are drawn, and inaccurate fatigue risk assessments can lead to failures. Therefore, identifying and eliminating abnormal data is a crucial part of measurement data analysis and processing.

[0003] In engineering, abnormal values ​​are typically identified by examining the location of strain gauge patches and the microstructure of strain gauges. However, this process is lengthy, complex, and tedious, resulting in a significant workload. Furthermore, human intervention during the inspection process can be detrimental, making it difficult to achieve effective results. Mathematical statistical identification methods, on the other hand, are fast, convenient, and save considerable manpower and economic costs, making them a reliable means of identification. Currently, commonly used data anomaly detection methods include the Païta criterion, the Chauvenet criterion, the Grubbs criterion, and the Dixon criterion (Q-test). The Païta criterion is suitable for large data samples, while the Chauvenet criterion requires repeated testing, increasing costs. The latter three methods are suitable for small samples, but when using different methods to identify abnormal data with small samples, it is difficult to obtain consistent results. Relying solely on one method is not highly reliable; therefore, it is necessary to use multiple identification methods in combination, tailored to specific industries and objects, to improve the accuracy of abnormal data identification. Summary of the Invention

[0004] In view of this, the present invention provides a method for removing outliers from gear dynamic stress measurement data with a small sample size, so as to improve the reliability of outlier identification.

[0005] This invention provides the following technical solution: a method for removing outliers from gear dynamic stress measurement data with a small sample size, comprising:

[0006] Step 1: Determine the required locations and number of gear dynamic stress measurements;

[0007] Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data;

[0008] Step 3: Classify and organize the gear dynamic stress measurement data;

[0009] Step 4: Initially screen for abnormal data based on the interquartile range algorithm;

[0010] Step 5: Determine the statistical characteristic values ​​of the dynamic stress test data;

[0011] Step 6: Identify outlier data based on the Grubbs criterion.

[0012] Compared with the prior art, the beneficial effects that the above-mentioned at least one technical solution adopted by the present invention can achieve include at least the following: the method can effectively reduce the impact of gross errors on the mean and standard deviation of small sample data, improve the reliability of abnormal data identification, and improve the accuracy of gear fatigue risk assessment; the method is fast, convenient, easy to program, improves work efficiency, and helps to reduce human and financial costs. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram showing the position and number of patches according to an embodiment of the present invention;

[0015] Figure 2 This is a flowchart illustrating an embodiment of the present invention.

[0016] The attached diagram is labeled as follows: 1. Gear; 2. Patch. Detailed Implementation

[0017] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0018] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] like Figure 1 and Figure 2 As shown, this embodiment of the invention provides a method for removing outliers from gear dynamic stress measurement data with a small sample size, specifically including the following steps:

[0020] Step 1: Determine the required locations and number of gear dynamic stress measurements.

[0021] Strain gauges should be preferentially installed on flat areas near areas with high gear stress or fatigue crack initiation to facilitate installation and effective monitoring of maximum vibration stress. The recommended number of installations is 6-10, which facilitates statistical analysis as strain gauges may be damaged. Multiple installations should be placed at multiple locations with similar structural characteristics, ensuring that the radial height and installation direction of each strain gauge remain consistent. Figure 1 As shown, the patch feature is located between the two teeth, close to the tooth root, and the patch angle is circumferential, maintaining consistent radial height.

[0022] Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data.

[0023] When using strain gauges to directly measure the vibration stress at critical locations of gears, the acquired signals are the results of analysis in the gear's dynamic coordinate system. The vibration modes of a specific pitch diameter are only excited by a specific excitation order. The gear pitch diameter vibration excitation at this time is as follows:

[0024] k=mz±n (1)

[0025] In the formula, k is the gear excitation order, z is the number of gear teeth, n is the number of gear traveling wave resonance pitch diameters, n≥2, +n represents the rear traveling wave, -n represents the front traveling wave, m is the excitation harmonic, and the value m=1 represents the first-order excitation harmonic, and so on.

[0026] Step 3: Categorize and organize the gear dynamic stress measurement data.

[0027] Since the vibration mode of a gear with a specific pitch diameter is only excited by a specific excitation order, there are two key parameters for the analysis of the test results: the excitation order and its corresponding dynamic strain. According to formula (1), the excitation order and the corresponding dynamic strain of the resonance point in the commonly used operating speed range of the engine are sorted out. Figure 1 The results of compiling the dynamic stress data at eight measuring points at the characteristic locations shown under a specific excitation order are shown in Table 1. The dynamic strain data in Table 1 are compiled from the original test data source [x]. i ], where [x i [A set of dynamic stress data under a specific excitation order collected at a certain measuring point location.]

[0028] Table 1. Example of classifying and organizing dynamic stress data for a certain gear.

[0029]

[0030] Step 4: Initially screen for possible abnormal data based on the interquartile range (IQR) algorithm.

[0031] The initial screening strategy is based on the interquartile range (IQR) algorithm to initially screen for possible outliers. The specific method is as follows:

[0032] Determine the interquartile range (IQR): For the original data source [x i Sort the data points from smallest to largest to obtain the first quartile Q1 and the third quartile Q3. At this point, the interquartile range IQR = Q3 - Q1.

[0033] Determine the detection coefficient k: take k = 1.0~1.5;

[0034] Determine the upper and lower limits of outliers in the preliminary screening data: lower limit L = Q1 - k * IQR, upper limit U = Q3 + k * IQR.

[0035] Identifying initial outlier data: When any raw data x i When the value is greater than U or less than L, it is initially identified as an outlier and placed in the suspected outlier data source [y]. i The remaining normal data sources are [z] i ].

[0036] Step 5: Determine the statistical characteristic values ​​of the dynamic stress test data.

[0037] Theoretically, dynamic stress data for gears with the same patch placement position and angle should be identical. However, operator errors during patch placement lead to inconsistent patch placement positions, and the machining quality at each tooth along the circumferential direction is not entirely consistent, resulting in some dispersion in the dynamic stress data. Directly using a test data source that may contain gross errors [x] iCalculating statistical characteristic values ​​for dynamic stress test data may amplify this dispersion. Therefore, the following steps are used to construct:

[0038] First, based on normal data sources [z i The sample mean av and standard deviation S of the normal test data are calculated as the statistical characteristic parameters of the dynamic stress test data. The calculation formula is as follows:

[0039] (2)

[0040] (3)

[0041] In the formula: j is the normal data source [z i The number of samples, and These are normal data sources [z] i Sort in ascending order and Location data, For normal data sources [z i Sort in ascending order The location data above is used to represent the statistical median, z. i This represents the i-th normal data point.

[0042] Secondly, based on the original data source of the test [x] i ] Calculate the sample mean av of the original test data. x and standard deviation S x As a statistical characteristic value reference parameter for dynamic stress test data, the calculation formula is as follows:

[0043] (4)

[0044] (5)

[0045] In the formula: ζ represents the original data source for the test [x i Total number of samples.

[0046] Finally, the statistical characteristic values ​​of the dynamic stress test data are determined. When the raw data may contain gross errors, it may amplify the dispersion of the raw data. In this case, the following formula must be satisfied:

[0047] (6)

[0048] In the formula: α is the statistical significance level, which is generally taken as 0.05. For statistics Distribution value.

[0049] When formula (6) is satisfied, the statistical standard deviation S of the dynamic stress test data is determined. eq =S; conversely, S eq =S x .

[0050] Furthermore, the statistical average value of the dynamic stress test data is determined by the following formula:

[0051] (7)

[0052] In the formula: α is the statistical significance level, which is generally taken as 0.05. To calculate the t-distribution value.

[0053] When formula (7) is satisfied, the statistical average value of the dynamic stress test data is determined. =av; conversely =av x .

[0054] Step 6: Identify outlier data based on the Grubbs criterion.

[0055] Using the statistical characteristic values ​​of the dynamic stress test data obtained in step 5, the inspection observations of suspected abnormal data sources [yi] are calculated one by one based on the Grubbs criterion method. The calculation formula is as follows:

[0056] (8)

[0057] In the formula: y i This is the i-th suspected abnormal data.

[0058] Calculate the test coefficient k jy The formula is as follows:

[0059] (9)

[0060] In the formula: α is the statistical significance level, which is recommended to be 0.005. To calculate the Grubbs distribution value.

[0061] When k jy If the value is greater than 1, it is considered abnormal data; otherwise, it is considered normal.

[0062] Once data is identified as abnormal, it will be removed.

[0063] This invention proposes a method for outlier removal in gear dynamic stress measurement data with small sample sizes. It initially screens for potential outliers using the interquartile range (IQR) algorithm, then utilizes the remaining normal dataset to obtain reliable mathematical statistical patterns in the test data. Finally, it performs a final screening of the initially screened outliers using the Grubbs criterion method. This method effectively reduces the impact of gross errors on the mean and standard deviation of small sample data, improves the reliability of outlier identification, and further enhances the accuracy of gear fatigue risk assessment. The comparison results with using only the Grubbs method are shown in Table 2. Table 2 shows that this method can effectively identify gross errors with large numerical deviations, while using only the Grubbs criterion is difficult to identify outliers. Furthermore, after later decomposition and inspection, the strain gauge A-9 showed a large error in its patch position, while the larger value of A-4 was due to abnormal strain gauge microstructure, consistent with the data anomaly analysis in this paper.

[0064] Table 2 Comparison Results

[0065]

[0066] In a specific embodiment, the following steps are included:

[0067] Step 1: Determine the required locations and number of gear dynamic stress measurements.

[0068] Through gear resonance analysis, the resonant mode within the operating speed range exhibits higher stress at the midpoint between two teeth, close to the tooth root. This area is also relatively flat; therefore, it was selected as the location for the strain gauge patch. The circumferential stress is highest at this location, thus the patch placement direction was determined to be circumferential. Due to the potential for strain gauge damage, and for ease of statistical analysis, the number of strain gauge patches at this location was determined to be eight. Figure 1 As shown, the patch feature is located between the two teeth, close to the tooth root, and the patch angle is circumferential, maintaining consistent radial height.

[0069] Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data.

[0070] The number of teeth on the gear in the implementation case is 38. Resonance analysis revealed that there is a 3-pitch forward traveling wave resonance excited by the first harmonic of the meshing frequency. According to formula (1), the excitation order is determined to be 35.

[0071] Step 3: Categorize and organize the gear dynamic stress measurement data.

[0072] Since the vibration mode of a specific pitch diameter gear is only excited by a specific excitation order, there are two key parameters for the analysis of the test results: the excitation order and its corresponding dynamic strain. According to formula (1), the excitation order and the corresponding dynamic strain of the resonance point in the commonly used operating speed range of the engine are organized as shown in Table 1. The dynamic strain data in Table 1 are organized as the original test data source [x] i], where [x i [A set of dynamic stress data under a specific excitation order collected at a certain measuring point location.]

[0073] Step 4: Initially screen for possible abnormal data based on the interquartile range (IQR) algorithm.

[0074] The initial screening strategy is based on the interquartile range (IQR) algorithm to initially screen for possible outliers. The specific method is as follows:

[0075] Determine the interquartile range (IQR): For the original data source [x i Sort the data points from smallest to largest as shown in Table 3. The first quartile Q1 = 81 and the third quartile Q3 = 94 are obtained. At this time, the interquartile range IQR = Q3 - Q1 = 13.

[0076] Determine the detection coefficient k: In this example, k = 1.25;

[0077] Determine the upper and lower limits of outliers in the preliminary screening data: lower limit L = Q1 - k * IQR = 64.75, upper limit U = Q3 + k * IQR = 110.25.

[0078] Identifying initial outlier data: When any raw data x i When the value is greater than U or less than L, it is initially identified as an outlier and placed in the potentially abnormal data source [y]. i ]=[55,116], the remaining normal data sources are [z i = [75,81,86,90,91,92,94,95].

[0079] Table 3. Determination of the interquartile range (IQR) of dynamic stress data for a certain gear.

[0080]

[0081] Step 5: Determine the statistical characteristic values ​​of the dynamic stress test data.

[0082] Based on normal data source [z i According to formulas (2) and (3), the statistical characteristic value benchmark parameters are calculated, and av=90.5 and S=7.4 are obtained.

[0083] Based on the original data source of the test [x i According to formulas (4) and (5), the statistical characteristic value reference parameter is calculated to obtain av. x =86.9, S x =17.6.

[0084] Based on formula (6), test the original data source [x] iTotal number of samples ζ=8 =39.1> =14.1, therefore the statistical standard deviation of the dynamic stress test data is Seq=7.4.

[0085] Based on formula (7), test the original data source [x] i Total number of samples ζ=8 =1.4< =1.9, determine the statistical average value of the dynamic stress test data. =86.9.

[0086] Step 6: Identify outlier data based on the Grubbs criterion.

[0087] Using the statistical characteristic values ​​of the dynamic stress test data obtained in step 5, the abnormal data sources [y] are calculated one by one based on the Grubbs criterion method. i The inspection observations are shown in Table 4.

[0088] Table 4. Inspection results based on the Grubbs criterion.

[0089]

[0090] As shown in Table 4, the data for strains A-9 and A-4 are outliers, and these two data should be removed.

[0091] The above description is merely a specific embodiment of this application, but the scope of protection of this application 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 this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for outlier rejection of gear dynamic stress measurement data under small sample, characterized in that, The application relates to a gear dynamic stress test method and device. Step 1, determining gear dynamic stress measurement position and number requirement; Step 2, determining vibration excitation order of gear dynamic stress measurement data; Step 3, classifying and arranging gear dynamic stress measurement data; Step 4, preliminarily screening abnormal data based on quartile range algorithm; Step 5, determining statistical characteristic value of dynamic stress test data; Step 6, finally determining abnormal data based on Grubbs criterion method; The step 2 is specifically by formula k JL =mz±n The vibration excitation order of the gear is calculated, wherein k JL is the gear excitation order, z is the gear teeth, n is the gear wave resonance pitch number, and m is the excitation harmonic. The step 3 is specifically: selecting an excitation order, classifying and arranging gear dynamic stress measurement data corresponding to the excitation order, and obtaining test original data source under the excitation order; The step 4 is specifically: The test original data source is sorted from small to large to obtain the first quartile Q1 and the third quartile Q3 in the data points, and the quartile range IQR=Q3-Q1 is calculated; the detection coefficient k, the upper limit L of the preliminarily screened data abnormal value and the lower limit U of the preliminarily screened data abnormal value are determined, wherein L=Q1-k*IQR and U=Q3+k*IQR; when any data value in the test original data source is greater than U or smaller than L, the data value is preliminarily screened as an abnormal value at this moment, and the abnormal value is put into the preliminarily screened abnormal data source, and the remaining normal data is put into the normal data source; The step 5 is specifically: according to normal data source, calculating sample average value av and standard deviation S of normal test data; according to test original data source, calculating sample average value av and standard deviation S of test original data x ; determining statistical standard deviation and statistical average value of dynamic stress test data x ; The step 6 is specifically: according to The data in the preliminary screening abnormal data source is calculated one by one, wherein, G i is the inspection observation value of the preliminary screening abnormal data source, is the statistical average value of the dynamic stress test data, Seq is the statistical standard variance of the dynamic stress test data, y i is the i th abnormal data; according to The inspection coefficient is calculated, wherein, is the statistical Grubbs distribution value; when k jy > 1, it is determined that the corresponding data is abnormal data, and the data is removed; the above step 6 is repeated until all data in the preliminary screening abnormal data source is verified and the final normal data source is obtained; whether the gear dynamic stress meets the use requirement is evaluated according to the final normal data source.

2. The small sample pinion dynamic stress measurement data outlier rejection method of claim 1, wherein, The calculation of the sample average av and the standard deviation S of the normal test data is specifically: The sample average of normal test data is ; The standard deviation of the normal test data is ; j is the number of samples from the normal data source. and The order after sorting normal data sources from smallest to largest and Location data, The order after sorting normal data sources from smallest to largest Location data, z i This represents the i-th normal data point.

3. The small sample pinion dynamic stress measurement data outlier rejection method of claim 2, wherein, The sample mean av of the test raw data is calculated x and the standard deviation S x Specifically: The sample average of the test raw data is ; The standard deviation of the test raw data is ; where ζ is the total number of samples of the test raw data source, x i is any data of the test raw data source.

4. The small sample pinion dynamic stress measurement data outlier rejection method of claim 3, wherein, The determination of the statistical standard deviation and the statistical average of the dynamic stress test data is specifically: When the condition is satisfied , the statistical standard deviation of the dynamic stress test data is the standard deviation of the normal test data; when the condition is not satisfied , the statistical standard deviation of the dynamic stress test data is the standard deviation of the test original data; wherein, α is a statistical significance level, , the statistical distribution value; When the condition is satisfied , the statistical average of the dynamic stress test data is the statistical average of the normal test data; when the condition is not satisfied , the statistical average of the dynamic stress test data is the statistical average of the test original data, a t-distribution value is calculated.

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