Method for eliminating abnormal value of gear dynamic stress measurement data under small sample

Abstract

The invention provides a method for eliminating abnormal values of gear dynamic stress measurement data under a small sample. The method comprises the following steps: step 1, determining gear dynamic stress measurement positions and number requirements; 2, determining the vibration excitation order of the gear dynamic stress measurement data; step 3, classifying and sorting the gear dynamic stress measurement data; step 4, preliminarily screening abnormal data based on a quartile algorithm; 5, determining a statistical characteristic value of the dynamic stress test data; and step 6, finally determining 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 recognition reliability of abnormal data, and improve the accuracy of gear fatigue risk assessment; the method is rapid and convenient, is easy to program, improves the working efficiency, and facilitates the reduction of manpower and financial costs.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engines, and in particular to a method for eliminating abnormal values ​​in gear dynamic stress measurement data under a small sample size. Background Art

[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 aircraft engines. Test data analysis and processing is a key link, which directly affects fatigue failure risk assessment. In a narrow space layout, the number of gear patches is small, and the patch survival rate is low in a high-concentration oil mist environment, which makes the sample size of gear dynamic stress measurement data small. Factors such as patch position deviation and strain gauge tissue alienation in a high-speed and high-oil mist environment may cause test data mutations and produce numerical anomalies. Numerical anomalies lead to gross errors. These measurement data appear to be too large or too small. If they are classified as normal data and the fatigue risk is conservatively assessed, it will lead to a waste of manpower and financial resources for structural improvements. If they are easily deleted, false conclusions will be obtained, and inaccurate fatigue risk assessment will lead to failures. Therefore, identifying and eliminating abnormal data is an important part of measurement data analysis and processing.

[0003] In engineering, abnormal values ​​are often identified by reviewing the patch position and strain gauge structure. However, this inspection process is long, complex, and labor-intensive, and can also introduce sabotage, making it difficult to be effective. Identification methods based on mathematical statistics are fast and convenient, saving significant manpower and economic costs, and are also a reliable means of identification. Currently, commonly used data anomaly detection methods include the Paǔta criterion, the Chauvenet criterion, the Grubbs criterion, the Dixon criterion (Q test), and the Dixon criterion (Q test). The Paǔta criterion is suitable for large data samples, while the Chauvenet criterion requires repeated testing, which increases costs. The latter three methods are suitable for small sample sizes. However, when using different methods to identify abnormal data in small sample sizes, it is difficult to obtain consistent results. Reliability is limited by using a single method. It is necessary to apply multiple identification methods across specific industries and applications to improve the accuracy of abnormal data identification. Summary of the Invention

[0004] In view of this, the present invention provides a method for eliminating outliers in gear dynamic stress measurement data under small sample conditions, so as to improve the reliability of abnormal data identification.

[0005] The present invention provides the following technical solution: a method for eliminating outliers in gear dynamic stress measurement data under a small sample, comprising: Step 1: Determine the gear dynamic stress measurement position and number requirements; Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data; Step 3: Classify and organize the gear dynamic stress measurement data; Step 4: Preliminary screening of abnormal data based on the interquartile range algorithm; Step 5: Determine the statistical characteristic value of the dynamic stress test data; Step 6: Finally determine the abnormal data based on the Grubbs criterion method.

[0006] Compared with the existing technology, the beneficial effects that can be achieved by at least one of the above-mentioned technical solutions adopted in the present invention include at least: this method can effectively reduce the impact of gross errors on the mean and standard deviation of small sample data, improve the reliability of identifying abnormal data, and improve the accuracy of gear fatigue risk assessment; this method is fast and convenient, easy to program, improves work efficiency, and helps to reduce manpower and financial costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0008] Figure 1 Schematic diagram of patch positions and numbers according to an embodiment of the present invention; Figure 2 It is a flowchart of an embodiment of the present invention.

[0009] Reference numerals in the figure: 1, gear; 2, patch. DETAILED DESCRIPTION

[0010] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0011] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the features in the following embodiments and embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative work are within the scope of protection of this application.

[0012] like Figure 1 and Figure 2 As shown, an embodiment of the present invention provides a method for eliminating abnormal values ​​in gear dynamic stress measurement data under a small sample, which specifically includes the following steps: Step 1: Determine the gear dynamic stress measurement locations and number requirements.

[0013] Prioritize the placement of strain gauges on flat areas near gears with high stress or fatigue cracks to facilitate placement and effective monitoring of maximum vibration stress. The recommended number of patches is 6 to 10. This is for ease of statistical analysis, as strain gauges may be damaged. Multiple patches should be placed at multiple locations with the same characteristic structure. The radial height and direction of each strain gauge should be kept consistent, such as Figure 1 As shown, the characteristic position of the patch is between the two teeth and close to the tooth root, and the patch angle is circumferential, keeping the radial height consistent.

[0014] Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data.

[0015] When using strain gauges to directly measure the vibration stress at the critical position of the gear, the collected signal is the analysis result under the dynamic coordinate of the gear. The mode of the gear's specific pitch diameter vibration is only excited by a specific excitation order. At this time, the gear pitch diameter vibration excitation is as follows: k=mz±n (1) Where k is the gear excitation order, z is the number of gear teeth, n is the gear traveling wave resonance pitch number, n ≥ 2, +n represents the backward traveling wave, -n represents the forward traveling wave, m is the excitation harmonic, and the value m = 1 represents the first-order excitation harmonic, and so on.

[0016] Step 3: Classify and organize the gear dynamic stress measurement data.

[0017] 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 in the analysis of the test results, namely the excitation order and its corresponding dynamic strain. According to formula (1), the excitation order and the corresponding dynamic strain of the resonance point within the common operating speed range of the engine are sorted out. Figure 1 The dynamic stress data of eight measuring points at the characteristic position shown in Table 1 under a specific excitation order are sorted as follows. The dynamic strain data in Table 1 are sorted as the original data source of the test [x i ], where [x i ] is a set of dynamic stress data collected at a certain measuring point under a specific excitation order.

[0018] Table 1 Example of classification and arrangement of dynamic stress data of a gear

[0019] Step 4: Preliminary screening of possible abnormal data based on the interquartile range (IQR) algorithm.

[0020] The initial screening strategy is to preliminarily screen possible abnormal data based on the interquartile range (IQR) algorithm. The specific method is as follows: Determine the interquartile range IQR: i ] Sort the data points from small to large to obtain the first quartile Q1 and the third quartile Q3. At this time, the interquartile range IQR=Q3-Q1; Determine the detection coefficient k: take k=1.0~1.5; Determine the upper and lower limits of outliers for the preliminary screening data: lower limit L = Q1-k*IQR, upper limit U = Q3+k*IQR.

[0021] Determine preliminary abnormal data: When any original data x i When it is greater than U or less than L, the value is initially screened as an abnormal value and placed in the suspected abnormal data source [y i ], the remaining normal data sources are [z i ].

[0022] Step 5: Determine the statistical characteristic values ​​of the dynamic stress test data.

[0023] Theoretically, the dynamic stress data of a group of gears with the same patch position and patch angle are the same. However, the patch position is not completely consistent due to the operation error of the patch operator. At the same time, the processing quality of each tooth along the circumference of the gear is not completely consistent, which leads to a certain dispersion of the dynamic stress data at that location. If the original test data source [x i ] Calculating the statistical eigenvalues ​​of dynamic stress test data may magnify this dispersion. Therefore, it is constructed by the following steps: First, according to the normal data source [z i ], calculate the sample mean value av and standard deviation S of the normal test data as the statistical characteristic value benchmark parameters of the dynamic stress test data, and the calculation formula is as follows: (2) (3) Where: j is the normal data source [z i ], and They are normal data sources [z i ] Sort by order from smallest to largest and Location data, For normal data source [z i ] Sort by order from smallest to largest The data of the location, the above data is used to represent the statistical median, z i is the i-th normal data.

[0024] Secondly, according to the test original data source [x i ], calculate the sample average value av of the test original data x and standard deviation S x , as the statistical characteristic value reference parameter of dynamic stress test data, the calculation formula is as follows: (4) (5) Where: ζ is the original data source for testing [x i ]Total number of samples.

[0025] Finally, determine the statistical characteristic value of the dynamic stress test data. When the original data may contain gross errors, the dispersion of the original data may be magnified, and the following formula is satisfied at this time: (6) Where: α is the statistical significance level, generally set to 0.05, For statistics Distribution value.

[0026] When formula (6) is satisfied, the statistical standard deviation S of the dynamic stress test data is determined eq =S; otherwise S eq =S x .

[0027] Furthermore, the statistical mean value of the dynamic stress test data is determined by the following formula: (7) Where: α is the statistical significance level, generally set to 0.05, is the statistical t distribution value.

[0028] When formula (7) is satisfied, the statistical mean value of the dynamic stress test data is determined =av; otherwise =av x .

[0029] Step 6: Finalize abnormal data based on Grubbs criterion method.

[0030] Using the statistical characteristic values ​​of the dynamic stress test data obtained in step 5, the inspection observation values ​​of the suspected abnormal data sources [yi] are calculated one by one based on the Grubbs criterion method. The calculation formula is as follows: (8) Where: y i is the i-th suspected abnormal data.

[0031] Calculate the test coefficient k jy , the formula is as follows: (9) Where: α is the statistical significance level, which is recommended to be 0.005. is the statistical Grubbs distribution value.

[0032] When k jy If it is greater than 1, it is considered abnormal data, otherwise it is normal.

[0033] Once the data is determined to be abnormal, it will be eliminated.

[0034] This paper proposes a method for removing outliers from gear dynamic stress measurement data using a small sample size. This method uses the interquartile range (IQR) algorithm to initially screen for possible outliers. The remaining normal data set is then used to determine reliable mathematical statistical patterns for the test data. Finally, each of these potentially outliers is screened using the Grubbs criterion. This method effectively reduces the impact of gross errors on the mean and standard deviation of small sample data, improves the reliability of identifying outliers, and further enhances the accuracy of gear fatigue risk assessment. Table 2 shows that this method effectively identifies gross errors with large numerical deviations, whereas the Grubbs criterion alone struggles to identify outliers. Subsequent analysis of this data reveals a large error in the patch position of strain gauge A-9, while the larger value of A-4 is due to the structural anomaly of this strain gauge, consistent with the data anomalies analyzed in this paper.

[0035] Table 2 Comparison results

[0036] In a specific embodiment, the following steps are included: Step 1: Determine the gear dynamic stress measurement locations and number requirements.

[0037] Through gear resonance analysis, the stress of the resonance mode within the working speed range is larger at the tooth root between the two teeth, and this area is relatively flat. This area is selected as the patch position. The stress along the circumferential direction of this area is the largest, so the patch direction is determined to be circumferential. Since the strain gauge may be damaged, the number of patches at this area is determined to be 8 for the convenience of statistical analysis. Figure 1 As shown, the characteristic position of the patch is between the two teeth and close to the tooth root, and the patch angle is circumferential, keeping the radial height consistent.

[0038] Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data.

[0039] The number of teeth of the gear in the implementation case is 38. The resonance analysis found that there are three-pitch radial forward wave resonances caused by the first-order harmonic excitation of the meshing frequency. According to formula (1), the excitation order is determined to be 35.

[0040] Step 3: Classify and organize the gear dynamic stress measurement data.

[0041] Since the vibration mode of the gear with a specific pitch diameter is only excited by a specific excitation order, there are two key parameters in the test result analysis, namely the excitation order and its corresponding dynamic strain. According to formula (1), the excitation order of the resonance point within the common operating speed range of the engine and the corresponding order of dynamic strain are sorted as shown in Table 1. The dynamic strain data in Table 1 are sorted as the original data source of the test [x i ], where [x i ] is a set of dynamic stress data collected at a certain measuring point under a specific excitation order.

[0042] Step 4: Preliminary screening of possible abnormal data based on the interquartile range (IQR) algorithm.

[0043] The initial screening strategy is to preliminarily screen possible abnormal data based on the interquartile range (IQR) algorithm. The specific method is as follows: Determine the interquartile range IQR: i ] are sorted from small to large, as shown in Table 3, and the first quartile Q1=81 and the third quartile Q3=94 of the data points are obtained. At this time, the interquartile range IQR=Q3-Q1=13; Determine the detection coefficient k: in this example, k=1.25; Determine the upper and lower limits of outliers for the preliminary screening data: lower limit L = Q1-k*IQR=64.75, upper limit U = Q3+k*IQR=110.25.

[0044] Determine preliminary abnormal data: When any original data x i When it is greater than U or less than L, the value is initially screened as an abnormal value and placed in the data source [y i ]=[55,116], the remaining normal data sources are [z i ]=[ 75,81,86,90,91,92,94,95].

[0045] Table 3 Determination of the interquartile range (IQR) of the dynamic stress data of a gear

[0046] Step 5: Determine the statistical characteristic values ​​of the dynamic stress test data.

[0047] According to normal data sources [z i], according to formula (2) and formula (3), the statistical eigenvalue benchmark parameters are calculated, and av=90.5 and S=7.4 are obtained.

[0048] According to the test original data source [x i ], according to formula (4) and formula (5), calculate the statistical characteristic value reference parameters and get av x =86.9, S x =17.6.

[0049] According to formula (6), the original data source [x i ]The total number of samples ζ=8, =39.1> =14.1, and the statistical standard deviation Seq of the dynamic stress test data is determined to be 7.4.

[0050] According to formula (7), the original data source [x i ]The total number of samples ζ=8, =1.4< =1.9, determine the statistical mean value of dynamic stress test data =86.9.

[0051] Step 6: Finalize abnormal data based on Grubbs criterion method.

[0052] Using the statistical characteristic values ​​of the dynamic stress test data obtained in step 5, the abnormal data sources [y i ] inspection observation values, and the inspection results are shown in Table 4. Table 4 Inspection results based on the Grubbs criterion method

[0053] As shown in Table 4, the data of strains A-9 and A-4 are abnormal data, so these two data are eliminated.

[0054] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions, characterized in that: include: Step 1: Determine the gear dynamic stress measurement position and number requirements; Step 2: Determine the vibration excitation order of the gear dynamic stress measurement data; Step 3: Classify and organize the gear dynamic stress measurement data; Step 4: Preliminary screening of abnormal data based on the interquartile range algorithm; Step 5: Determine the statistical characteristic value of the dynamic stress test data; Step 6: Finally determine the abnormal data based on the Grubbs criterion method.

2. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 1 is characterized in that: The step 2 is specifically performed by formula k JL =mz±n Calculate the vibration excitation order of the gear, where k JL is the gear excitation order, z is the number of gear teeth, n is the gear traveling wave resonance pitch number, and m is the excitation harmonic.

3. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 2, characterized in that: The step 3 specifically includes: selecting an excitation order, classifying and arranging the gear dynamic stress measurement data corresponding to the excitation order, and obtaining the original data source of the test under the excitation order.

4. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 3 is characterized in that: The step 4 is specifically as follows: Sort the original data source of the test from small to large, obtain the first quartile Q1 and the third quartile Q3 of the data points, and calculate the interquartile range IQR=Q3-Q1; Determine the detection coefficient k, the upper limit L of the abnormal value of the preliminary screening data, and the lower limit U of the abnormal value of the preliminary screening data, where L=Q1-k*IQR, U=Q3+k*IQR; When any data value in the original data source is greater than U or less than L, the data value is preliminarily screened as an abnormal value and placed in the preliminary screening abnormal data source, and the remaining normal data is placed in the normal data source.

5. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 4, characterized in that: The step 5 is specifically as follows: Based on the normal data source, calculate the sample mean av and standard deviation S of the normal test data; According to the original data source of the test, calculate the sample average value av of the original data of the test x and standard deviation S x ; Determine the statistical standard deviation and statistical mean of dynamic stress test data.

6. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 5, characterized in that: The calculation of the sample mean av and standard deviation S of the normal test data is specifically as follows: The sample average of normal test data is ; The standard deviation of normal test data is ; j is the number of samples of normal data source, and The order after sorting the normal data sources from small to large is and Location data, The order after sorting the normal data source from small to large Position data, z i is the i-th normal data.

7. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 6, characterized in that: The calculation test raw data sample average value av x and standard deviation S x Specifically: The sample mean of the original test data is ; The standard deviation of the original test data is ; Among them, ζ is the total number of samples of the original data source for testing, x i Any data from the original data source for testing.

8. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 7, characterized in that: The statistical standard deviation and statistical mean value of the dynamic stress test data are determined as follows: When satisfied When the statistical standard deviation of the dynamic stress test data is the standard deviation of the normal test data; when When , the statistical standard deviation of the dynamic stress test data is the standard deviation of the original test data; where α is the statistical significance level, For statistics distribution value; When satisfied When the statistical mean of the dynamic stress test data is the statistical mean of the normal test data; when When , the statistical mean value of the dynamic stress test data is the statistical mean value of the original test data, is the statistical t distribution value.

9. The method for eliminating abnormal values ​​in gear dynamic stress measurement data under small sample conditions according to claim 8, characterized in that: The step 6 is specifically as follows: according to Calculate the data in the initial screening of abnormal data sources one by one, where G i To preliminarily screen out abnormal data sources, check observations. is the statistical mean value of the dynamic stress test data, Seq is the statistical standard deviation of the dynamic stress test data, y i is the i-th abnormal data; according to Calculate the test coefficient, where is the statistical Grubbs distribution value; When k jy When it is greater than 1, the corresponding data is judged as abnormal data and is eliminated; Repeat step 6 above until all data in the initial screening of abnormal data sources are verified and the final normal data source is obtained; Evaluate whether the gear dynamic stress meets the use requirements based on the final normal data source.

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