Mahalanobis distance-based fuselage assembly process optimization method and storage medium

Abstract

The invention discloses a mahalanobis distance-based fuselage assembly process optimization method and a storage medium. The method comprises the steps of 1, measuring three-dimensional space coordinates of all horizontal measurement points on each manufactured fuselage; 2, for each fuselage, calculating the distance between every two horizontal measurement points by using the three-dimensional space coordinates of the horizontal measurement points as a deformation actual measurement index W; making a difference between the deformation actual measurement index W and the design theoretical value T, and calculating a difference vector; step 3, according to the difference vector, establishing a generalized covariance matrix as a data stability index; 4, calculating an inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; 5, establishing a mahalanobis distance and an average mahalanobis distance for evaluating the assembly deformation according to the inverse matrix and the difference vector; step 6, establishing a Mahalanobis distance limit value through a statistical method to form a fuselage assembly process evaluation index; and step 7, optimizing the assembly process according to the fuselage assembly process evaluation index, the mahalanobis distance and the average mahalanobis distance.

Description

Technical Field

[0001] This invention relates to, but is not limited to, the field of aircraft component assembly technology, and particularly to a method for optimizing fuselage assembly processes and a storage medium based on Mahalanobis distance. Background Technology

[0002] Modern aircraft fuselages generally employ large, thin-walled cylindrical structures. To determine which stage of the assembly process of this thin-walled, weak-rigidity, large-opening structure resulted in what type of deformation, it is necessary to measure the spatial coordinates of horizontal measurement points at multiple assembly stages. This reflects the assembly offset of the thin-walled, weak-rigidity, large-opening structure and allows for error tracing. Traditional fuselage assembly process optimization methods compare the spatial coordinates of measured horizontal measurement points at multiple assembly stages with theoretical coordinates, optimizing the process with the greatest discrepancy. However, this approach focuses only on a single deviation, neglecting the interrelationships between different indicators, failing to identify potential assembly quality problems, and hindering optimization of critical process stages.

[0003] In statistics, Mahalanobis distance is an effective method for describing the distance between distributions. By establishing an index that considers the correlation between assembly indicators, and optimizing the fuselage assembly process, Mahalanobis distance can account for the relationship between various deformation indicators during fuselage assembly, and is unaffected by dimensions, thus eliminating interference from correlations between variables. This method can identify potential problems and systematic deviations in the assembly quality of multiple fuselages and multiple process stages. It identifies process stages affecting the final assembly quality of the fuselage and proposes further optimization methods, avoiding the trial-and-error approach of traditional methods in a large number of assembly stages. This facilitates the development of effective quality control measures, improves assembly efficiency, and is a highly efficient optimization method. Summary of the Invention

[0004] This invention provides a fuselage assembly process optimization method and storage medium based on Mahalanobis distance. This method can identify potential problems and systematic deviations in the assembly quality of multiple fuselages and multiple process steps. It identifies process steps that affect the final assembly quality of the fuselage and proposes further optimization methods. This avoids the trial-and-error approach of traditional methods in a large number of assembly steps, facilitates the formulation of effective quality control measures, and improves assembly efficiency. It is a highly efficient optimization method.

[0005] The technical solution of this invention is as follows: In a first aspect, embodiments of the present invention provide a method for optimizing fuselage assembly processes based on Mahalanobis distance, comprising: Step 1: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Step two: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector by taking the subtraction. Step 3: Establish a generalized covariance matrix as a data stability indicator; Step four: Calculate the inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; Step 5: Establish the Mahalanobis distance and average Mahalanobis distance used to evaluate the deformation; Step 6: Establish Mahalanobis distance limits using statistical methods to form evaluation indicators for fuselage assembly processes; Step 7: Optimize the assembly process based on the fuselage assembly process evaluation indicators.

[0006] Specifically, step one includes: Step 1-1: Control the environmental factors at the machine assembly site: temperature less than 35 degrees Celsius; relative humidity less than 85%; no vibration sources within a 20m × 20m radius around the tooling; Steps 1-2: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Specifically, step two includes: Step 2-1: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector. D = W - T ; Step 2-2: Calculate the lower tolerance LSL and upper tolerance USL according to the aircraft design requirements; Specifically, step three includes: Step 3-1, Calculate standardized data :

[0007] in, D The vector representing the difference between the measured and theoretical values ​​of deformation; LSL represents the lower tolerance deviation; USL represents the upper tolerance deviation. Step 3-2: Solve for the determinant of the generalized covariance matrix. As an indicator of data stability; among which, For standardized data The covariance matrix; Specifically, step four includes: Step 4-1: Calculate the covariance matrix of the difference vector between the measured and theoretical deformation values. ; Step 4-2: Solve for the covariance matrix using the Moore-Penrose method in matrix theory. The pseudo-inverse matrix; Specifically, step five includes: Step 5-1, for the statistical... i The deformation measurement indicators for each process are used to establish a deformation evaluation based on Mahalanobis distance: ; In the formula, For the first statistical i The Mahalanobis distance index for deformation in each process; D This is the vector of differences between the measured and theoretical values ​​of deformation. Step 5-2, for the statistical first... i The measured deformation index for each process was used to calculate the average Mahalanobis distance:

[0008] In the formula, The average Mahalanobis distance; n This refers to the total number of times the fuselage was used for statistical purposes; Specifically, step six includes: Step 6-1: Based on the fact that Mahalanobis distance follows a chi-square distribution, calculate the inverse cumulative distribution function and obtain the quantile at the 85% cumulative probability as the Mahalanobis distance limit. ul ; Step 6-2, according to the exponential decay model, the evaluation index for the computer body assembly process is:

[0009] In the formula, For the first i The average Mahalanobis distance of the measured deformation index of each process; For the first i Each process has a Mahalanobis distance limitation; Specifically, step seven has the following requirements: Based on the fuselage assembly process evaluation indicators, the assembly process with the lowest assembly quality evaluation indicators is identified, and the process is optimized.

[0010] In a second aspect, embodiments of the present invention provide a computer-readable storage medium, including: a memory and a processor; The memory is used to store computer-readable programs; The processor is configured to implement, when executing a computer-readable program, the fuselage assembly process optimization method based on Mahalanobis distance as described above.

[0011] The beneficial effects of this invention are as follows: This invention establishes a fuselage assembly process optimization method and storage medium based on Mahalanobis distance. This assembly process optimization method can consider the relationship between various deformation indicators during fuselage assembly and is unaffected by dimensions, thus eliminating interference from correlations between variables. This method can identify potential problems and systematic deviations in assembly quality across multiple fuselage sorties and multiple process stages. It identifies process stages affecting the final fuselage assembly quality and proposes further optimization methods, avoiding the trial-and-error approach of traditional methods across numerous assembly stages. This facilitates the development of effective quality control measures, improves assembly efficiency, and is a highly efficient optimization method. Attached Figure Description

[0012] Figure 1 This is a flowchart of a fuselage assembly process optimization method based on Mahalanobis distance proposed in this invention; Figure 2 The fuselage section and its horizontal measurement point in step one of this invention; Figure 3 This refers to the Mahalanobis distance scores of the 10 aircraft in step six of this invention. The numbers in the diagram are explained as follows: 1. Fuselage section; 2. First fuselage level measurement point; 3. Second fuselage level measurement point; 4. Third fuselage level measurement point; 5. Fourth fuselage level measurement point; 6. Fifth fuselage level measurement point; 7. Sixth fuselage level measurement point. Detailed Implementation

[0013] As explained in the background section, traditional methods for evaluating the assembly quality of aircraft fuselage sections judge assembly quality by comparing the deviation between measured and theoretical values. This approach has three main problems: First, existing methods focus only on the deviation of individual indicators, neglecting the interrelationships and systemic issues between different indicators, potentially overlooking certain assembly quality problems. Second, they cannot deeply analyze the causes of deviations under the combined effect of multiple factors, making it difficult to identify fundamental process problems. Third, data processing efficiency is low; comparing a large number of parameters one by one is inefficient and may miss key information or patterns. Therefore, a comprehensive evaluation method is needed that considers the correlation between indicators, can identify potential assembly quality problems or systemic deviations, can identify data patterns and trends, help locate problems in key process steps, provide a basis for production process optimization, facilitate the development of effective assembly quality control measures for fuselage section 1, and improve assembly efficiency and quality.

[0014] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0015] Example 1 This invention provides a method for optimizing fuselage assembly processes based on Mahalanobis distance, comprising: Step 1: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Step two: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector by taking the subtraction. Step 3: Establish a generalized covariance matrix as a data stability indicator; Step four: Calculate the inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; Step 5: Establish the Mahalanobis distance and average Mahalanobis distance used to evaluate the deformation; Step 6: Establish Mahalanobis distance limits using statistical methods to form evaluation indicators for fuselage assembly processes; Step 7: Optimize the assembly process based on the fuselage assembly process evaluation indicators.

[0016] Specifically, step one includes: Step 1-1: Control the environmental factors at the machine assembly site: temperature less than 35 degrees Celsius; relative humidity less than 85%; no vibration sources within a 20m × 20m radius around the tooling; Steps 1-2: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Specifically, step two includes: Step 2-1: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector. D = W - T ; Step 2-2: Calculate the lower tolerance LSL and upper tolerance USL according to the aircraft design requirements; Specifically, step three includes: Step 3-1, Calculate standardized data :

[0017] in, D The vector representing the difference between the measured and theoretical values ​​of deformation; LSL represents the lower tolerance deviation; USL represents the upper tolerance deviation. Step 3-2: Solve for the determinant of the generalized covariance matrix. As an indicator of data stability; among which, For standardized data The covariance matrix; Specifically, step four includes: Step 4-1: Calculate the covariance matrix of the difference vector between the measured and theoretical deformation values. ; Step 4-2: Solve for the covariance matrix using the Moore-Penrose method in matrix theory. The pseudo-inverse matrix; Specifically, step five includes: Step 5-1, for the statistical... i The deformation measurement indicators for each process are used to establish a deformation evaluation based on Mahalanobis distance: ; In the formula, For the first statistical i The Mahalanobis distance index for deformation in each process; D This is the vector of differences between the measured and theoretical values ​​of deformation. Step 5-2, for the statistical first... i The measured deformation index for each process was used to calculate the average Mahalanobis distance:

[0018] In the formula, The average Mahalanobis distance; n This refers to the total number of times the fuselage was used for statistical purposes; Specifically, step six includes: Step 6-1: Based on the fact that Mahalanobis distance follows a chi-square distribution, calculate the inverse cumulative distribution function and obtain the quantile at the 85% cumulative probability as the Mahalanobis distance limit. ul ; Step 6-2, according to the exponential decay model, the evaluation index for the computer body assembly process is:

[0019] In the formula, For the first i The average Mahalanobis distance of the measured deformation index of each process; For the first i Each process has a Mahalanobis distance limitation; Specifically, step seven has the following requirements: Based on the fuselage assembly process evaluation indicators, the assembly process with the lowest assembly quality evaluation indicators is identified, and the process is optimized.

[0020] Example 2 like Figure 1-3As shown, a method for optimizing fuselage assembly process based on Mahalanobis distance includes the following steps: Step 1: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. For example, the horizontal measurement points include the first fuselage horizontal measurement point 2, the second fuselage horizontal measurement point 3, the third fuselage horizontal measurement point 4, the fourth fuselage horizontal measurement point 5, the fifth fuselage horizontal measurement point 6, and the sixth fuselage horizontal measurement point 7. The embodiments of this application do not specifically limit the horizontal measurement points.

[0021] Step two: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector by taking the subtraction. Step 3: Establish a generalized covariance matrix as a data stability indicator; Step four: Calculate the inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; Step 5: Establish the Mahalanobis distance and average Mahalanobis distance for evaluating assembly deformation; Step 6: Establish Mahalanobis distance limits using statistical methods to form evaluation indicators for fuselage assembly processes; Step 7: Optimize the assembly process based on the fuselage assembly process evaluation indicators.

[0022] Step 1: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Step 1-1: Control the environmental factors at the machine assembly site: temperature less than 35 degrees Celsius; relative humidity less than 85%; no vibration sources within a 20m × 20m radius around the tooling; Steps 1-2: According to the aircraft design requirements, use a laser tracker to measure and record the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage of each aircraft. Step two: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector by taking the subtraction. Step 2-1: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector. D = W - T The difference vector calculated for the first fuselage is as follows:

[0023] Step 2-2: Calculate the lower tolerance LSL and upper tolerance USL according to the aircraft design requirements. In this embodiment, both the lower tolerance LSL and upper tolerance USL are taken as 0.5mm. Step 3: Establish a generalized covariance matrix as a data stability indicator; Step 3-1, Calculate standardized data :

[0024] in, D The vector represents the difference between the measured and theoretical values ​​of deformation; LSL represents the lower tolerance deviation; USL represents the upper tolerance deviation; in this embodiment, the following is calculated:

[0025] Step 3-2: Solve for the determinant of the generalized covariance matrix. As an indicator of data stability; among which, For standardized data The covariance matrix; in this embodiment, the covariance matrix is ​​calculated. The value is much smaller than the order of magnitude of the measured data, indicating that the calculation results are stable; Step four: Calculate the inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; Step 4-1: Calculate the covariance matrix of the difference vector between the measured and theoretical deformation values. ;

[0026] Step 4-2: Using the Moore-Penrose method in matrix theory, this embodiment utilizes a Python program or the commercial software SPSS to solve the covariance matrix. The pseudo-inverse matrix;

[0027] Step 5: Establish the Mahalanobis distance and average Mahalanobis distance for evaluating assembly deformation; Step 5-1: For the measured deformation index of the first process, establish a deformation evaluation based on Mahalanobis distance as follows: ; In the formula, The Mahalanobis distance index for the deformation of the first process in the statistical analysis; D This is the vector of differences between the measured and theoretical deformation values. In this embodiment, the Mahalanobis distance index of the deformation in the first process is calculated to be 4.28 using a Python program or the commercial software SPSS. Step 5-2, for the statistical first... i The measured deformation index for each process was used to calculate the average Mahalanobis distance:

[0028] In the formula, The average Mahalanobis distance; n To determine the total number of fuselage frame operations, this embodiment uses n=10. The Mahalanobis distance index for the first process is calculated to be 3.87 using a Python program or the commercial software SPSS. Step 6: Establish Mahalanobis distance limits using statistical methods to form evaluation indicators for fuselage assembly processes; Step 6-1: Based on the fact that Mahalanobis distance follows a chi-square distribution, calculate the inverse cumulative distribution function using a Python program or commercial software SPSS, and obtain the quantile at the 85th percentile of the cumulative probability as the Mahalanobis distance limit. ul =4.04.

[0029] Step 6-2, according to the exponential decay model, the evaluation index for the computer body assembly process is:

[0030] In the formula, The average Mahalanobis distance of the measured deformation index for the first process; For the first process's Mahalanobis distance limitation, this embodiment calculates the fuselage assembly process evaluation index results, such as... Figure 3 As shown; Step 7: Optimize the assembly process based on the fuselage assembly process evaluation indicators.

[0031] Based on the fuselage assembly process evaluation indicators, the assembly process with the lowest assembly quality evaluation indicators is identified, and the process is optimized.

[0032] In summary, this invention discloses a fuselage assembly process optimization method based on Mahalanobis distance. It includes the following steps: measuring the three-dimensional spatial coordinates of all horizontal measurement points on each manufactured fuselage using a laser tracker; calculating the distance between two horizontal measurement points using their three-dimensional spatial coordinates; establishing a generalized covariance matrix as a data stability index; calculating the inverse matrix of the covariance matrix by solving the pseudo-inverse matrix; establishing Mahalanobis distance and mean Mahalanobis distance for evaluating assembly deformation; establishing Mahalanobis distance limits using statistical methods to form fuselage assembly process evaluation indicators; and optimizing the assembly process based on these evaluation indicators. This assembly process optimization method considers the relationships between various deformation indicators during fuselage assembly and is unaffected by dimensions, eliminating interference from correlations between variables. This method can identify the assembly quality in multiple fuselage sorties and multiple process stages, identify process stages affecting the final fuselage assembly quality, and propose further optimization methods. It avoids the trial-and-error approach of traditional methods in numerous assembly stages, improving assembly efficiency and representing a highly efficient optimization method.

[0033] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

[0034] The parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A method for optimizing fuselage assembly process based on Mahalanobis distance, characterized in that, Includes the following steps: Step 1: According to the aircraft design requirements, use a laser tracker to measure the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage. Step two: For each fuselage, calculate the distance between every two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W Deformation measured index W Compared with the design theoretical value T Calculate the difference vector by taking the subtraction. Step 3: Based on the difference vector, establish the generalized covariance matrix as a data stability index; Step 4: Calculate the inverse of the covariance matrix by solving for the pseudo-inverse matrix; Step 5: Based on the inverse matrix and the difference vector, establish the Mahalanobis distance and the average Mahalanobis distance used to evaluate assembly deformation; Step 6: Establish Mahalanobis distance limits using statistical methods to form evaluation indicators for fuselage assembly processes; Step 7: Optimize the assembly process based on the fuselage assembly process evaluation indicators, Mahalanobis distance, and average Mahalanobis distance.

2. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 1, characterized in that, Step one includes: Step 1-1: Control the environmental factors at the machine assembly site: temperature less than 35 degrees Celsius; relative humidity less than 85%; no vibration sources around the tooling; Steps 1-2: According to the aircraft design requirements, use a laser tracker to measure the three-dimensional spatial coordinates of all horizontal measurement points on the manufactured fuselage.

3. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 1, characterized in that, Step two includes: Step 2-1: For each fuselage, calculate the distance between two horizontal measurement points using the three-dimensional spatial coordinates of the horizontal measurement points, and use this distance as the actual deformation measurement index. W , and the design theoretical value T Calculate the difference vector. D = W - T ; Step 2-2: Calculate the lower tolerance LSL and upper tolerance USL according to the aircraft design requirements.

4. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 4, characterized in that, Step three includes: Step 3-1, Calculate standardized data : in, D The vector representing the difference between the measured and theoretical values ​​of deformation; LSL represents the lower tolerance deviation; USL represents the upper tolerance deviation. Step 3-2: Solve for the determinant of the generalized covariance matrix. As an indicator of data stability; among which, For standardized data The covariance matrix.

5. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 4, characterized in that, Step four includes: Step 4-1: Calculate the covariance matrix of the difference vector between the measured and theoretical deformation values. ; Step 4-2: Solve for the covariance matrix using the Moore-Penrose method in matrix theory. The pseudo-inverse matrix.

6. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 4, characterized in that, Step five includes: Step 5-1, for the statistical... i The deformation measurement indicators for each process are used to establish a deformation evaluation based on Mahalanobis distance: ； In the formula, For the first statistical i The Mahalanobis distance index for deformation in each process; D This is the vector of differences between the measured and theoretical values ​​of deformation. Step 5-2, for the statistical first... i The measured deformation index for each process was used to calculate the average Mahalanobis distance: In the formula, The average Mahalanobis distance; n This refers to the total number of times the fuselage has been used in the statistics.

7. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 2, characterized in that, Step six includes: Step 6-1: Based on the fact that Mahalanobis distance follows a chi-square distribution, calculate the inverse cumulative distribution function and obtain the quantile at the 85% cumulative probability as the Mahalanobis distance limit. ul ; Step 6-2, according to the exponential decay model, the evaluation index for the computer body assembly process is: In the formula, For the first i The average Mahalanobis distance of the measured deformation index of each process; For the first i Each process has a Mahalanobis distance limit.

8. The method for optimizing fuselage assembly process based on Mahalanobis distance according to claim 2, characterized in that, Step seven has the following requirements: Based on the fuselage assembly process evaluation indicators, the assembly process with the lowest assembly quality evaluation indicators is identified, and the process is optimized.

9. A computer-readable storage medium, characterized in that, include: Memory and processor; The memory is used to store computer-readable programs; The processor is configured to implement, when executing a computer-readable program, the fuselage assembly process optimization method based on Mahalanobis distance as described in any one of claims 1 to 8.

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