Adaptive multivariate calibration method for wind tunnel balance

Abstract

The invention belongs to the technical field of wind tunnel tests, and discloses a self-adaptive multivariate calibration method for a wind tunnel balance. The calibration method is based on a multi-point force application body shafting balance calibration system, and loads are divided into a basic group load, an improved group load and a comprehensive group load. After basic group load loading is completed, a calibration formula with low precision is preliminarily fitted, then comprehensive group load is applied, a measured value is calculated according to the calibration formula, units with poor balance inspection precision are analyzed item by item, interference items with large errors are obtained, corresponding improved group load is re-compiled for the interference items, and the balance inspection precision is improved. The calibration value range of the improved group load is wider, the steps are denser, the group load loading is improved again, the calibration formula is continuously fitted, and the steps are repeated to carry out automatic iterative loading and continuously improve the accuracy of the calibration formula until the accuracy error of the calibration formula is smaller than a preset accuracy error value. The balance calibration method and the balance calibration system have practical engineering value.

Description

Technical Field

[0001] The invention belongs to the technical field of wind tunnel testing, and in particular relates to an adaptive multivariate calibration method for a wind tunnel balance. Background Art

[0002] A wind tunnel balance is essentially a multi-dimensional force sensor. Balance calibration involves applying a load to the balance using a ground-based static calibration device, collecting the corresponding voltage output, and fitting a balance calibration matrix that correlates the load and voltage output. This matrix is ​​then used to inversely calculate the forces and moments exerted by the airflow on the model during the wind tunnel test. Conventional force balances typically have six components, measuring three forces and three moments.

[0003] The balance calibration process typically involves first compiling a load table, then applying the load according to the load table, and finally performing curve fitting between the load and the corresponding voltage value to obtain the balance calibration formula matrix. Based on the loading method, balance calibration can be divided into unit calibration and multivariate calibration. When using the unit calibration method, the balance calibration coefficient is generally calculated using the least squares method. When using the multivariate calibration method, after all items in the load group (the number of items is greater than the number of components) have been loaded, a multivariate linear regression calculation is performed. The corresponding balance calibration formula matrix is ​​obtained by analyzing the relationship between the load and the corresponding voltage output value. Furthermore, when a large amount of loading data is required and a large number of iterations are required, a neural network algorithm can also be used.

[0004] Specifically, the balance calibration process typically involves first loading the balance according to the load table, collecting the corresponding voltage values, and then fitting a balance formula based on the load-voltage relationship. The calibration formula for a conventional six-component balance should include 96 coefficients: 1 principal term coefficient, 5 primary interference coefficients, 6 quadratic interference coefficients, 6 cubic interference coefficients, 15 quadratic cross-interference coefficients, 6 primary asymmetric interference coefficients, 51 quadratic asymmetric interference coefficients, and 6 tertiary asymmetric interference coefficients. Currently, asymmetry and cubic interference coefficients are generally not considered in the balance calibration formula matrix, resulting in 27 coefficients for each component. For a conventional six-component balance, a 6×27 matrix is ​​used as the final balance calibration formula matrix. The calibration coefficients are generally calculated using the least squares method. When using the unit calibration method, one coefficient is calculated for each calibration item. After completing the unit and cross-term loading calibration, the coefficients are combined to form the balance calibration formula matrix. When the unit calibration method is used, after completing all items of the load group (the number of items is greater than the number of components), a multiple linear regression calculation is performed to obtain the corresponding balance calibration formula matrix.

[0005] Wind tunnel balance calibration systems can be divided into body-axis wind tunnel balance calibration systems and earth-axis wind tunnel balance calibration systems according to the loaded coordinate axis system. The body-axis wind tunnel balance calibration system has a complex structure and high cost because of the reset mechanism. However, the advantage of the body-axis wind tunnel balance calibration system is that the number of interference items in the balance calibration formula matrix is ​​significantly reduced, the interference value is also significantly reduced, and the balance measurement accuracy is higher. Therefore, the body-axis calibration system is usually used. However, because the body-axis calibration system requires a reset operation every time a step value is loaded when performing unit or multivariate calibration, the overall efficiency is not high. Moreover, the formula can only be fitted after all calibration items are loaded, which is time-consuming and costly.

[0006] Currently, there is an urgent need to develop an adaptive multivariate calibration method for wind tunnel balances targeting the body-axis balance calibration system. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a self-adaptive multivariate calibration method for a wind tunnel balance, so as to overcome the defects of the prior art.

[0008] The adaptive multivariate calibration method for a wind tunnel balance of the present invention comprises the following steps: A. Prepare the calibration load of the balance; B. Carry out foundation group load loading; C. Perform linear fitting; D. Perform tare weight calculation; E. Perform nonlinear fitting; F. Perform iterative calculations; G. Perform accuracy calculations; H. Conduct error analysis; I. Repeat the process of increasing group load, error analysis and iteration.

[0009] Furthermore, the step A comprises the following steps: A1. Prepare the basic group load; A1.1 Prepare the unit items in the basic group load; According to the design load of the balance, determine the calibration loads of the six components of the balance, X, Y, Z, Mx, My, and Mz. X is the drag component, Y is the lift component, Z is the side force component, Mz is the rolling moment component, My is the yaw moment component, and Mz is the pitching moment component. The calibration load takes 80% to 120% of the design range and is loaded in nine steps of 0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, and 0%. After each component is loaded with positive and negative values, a loading array of 12 unit items is obtained. A1.2 Prepare the combination items in the basic group load; According to the calibration load of the balance, the 6 components of the balance are Select 15 positive combinations of YMz+, YX+, YMx+, YZ+, YMy+, MzX+, MzMx+, MzZ+, MzMy+, XMx+, XZ+, XMy+, MxZ+, MxMy+ and ZMy+, and the corresponding 15 negative combinations of YMz-, YX-, YMx-, YZ-, YMy-, MzX-, MzMx-, MzZ-, MzMy-, XMx-, XZ-, XMy-, MxZ-, MxMy- and ZMy-; A2. Prepare to increase group load; A2.1 Compile the unit items in the enhanced group load; The loading steps in A1.1 are The calibration range is encrypted and increased at the same time, so that the calibration load is loaded in 19 steps of 0%, 12.5%, 25%, 37.5%, 50%, 62.5%, 75%, 87.5%, 100%, 125%, 100%, 87.5%, 75%, 62.5%, 50%, 37.5%, 25%, 12.5%, and 0%; A2.2 Prepare the combination items in the enhanced group load; The loading steps in A1.2 are Encryption: expand the five steps of the basic group load (0%, 50%, 100%, 50%, 0%) to nine steps (0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, 0%), and at the same time expand the two positive and negative direction combination items of a unit item to four combination items; A3. Prepare comprehensive group loads; A comprehensive group load is compiled in accordance with the requirements of full range coverage, uniform distribution, and positive and negative symmetry. The comprehensive group load is used to verify the accuracy error of the balance calibration formula.

[0010] Furthermore, the step B comprises the following steps: B1. Determine the reference reading: Collect the voltage value arrays of the six components at the four states of the balance roll angle of 0°, 90°, 180°, and 270°. Average the four voltage value arrays to obtain an average voltage value array. The average voltage value array is the reference voltage for balance calibration. , , representing the voltage readings of X, Y, Z, Mx, My and Mz elements respectively; B2. Complete the loading of the unit items and combination items of the basic group load according to the balance calibration specifications, and obtain the calibration array including the load value and the corresponding voltage value. , , ; and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

[0011] Furthermore, the step C comprises the following steps: C1. Perform data preprocessing: Subtract the zero-point load value from the balance loading step values ​​in the plus or minus 12 unit items and the plus or minus 30 combined items to obtain the net value added. C2. Perform multiple regression calculation to obtain the corresponding calibration coefficient. The calculation formula is: ; in, The applied load value Quantity, The applied load value Quantity; is the loading step voltage value of each unit of the balance, is the initial value of each unit of the balance; is the coefficient of the first term, when When is the main coefficient, When Quantity pair The first-order interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component; , , ; 、 and The six components representing the X, Y, Z, Mx, My and Mz elements of the balance; C3. Perform formula conversion; calculate the 27 coefficients corresponding to each unit of the balance and form a 27×6 matrix. First, convert the main coefficient of each unit into conduct Transformation, then multiply the first and second interference coefficients by the new main coefficient , and finally transpose the whole to get a 6×27 matrix.

[0012] Furthermore, the step D comprises the following steps: D1. Tare weight refers to the sum of the loading device load and the counterweight load during loading. The corresponding voltage value is the loading zero point and the reference reading. The difference between D2. Collect the 42 groups of loading zero points of unit items and combination items to form a loading zero point group , where the reference reading As the first row of initial readings, then iterate according to the implicit formula of the balance to obtain 42 tare load groups corresponding to the zero point of loading , the calculation formula is: ; Where, For the balance Calculated values ​​of component loads, and Calculate for When , the load values ​​of the remaining 5 components of the balance; is the initial load value, is the main coefficient, for Quantity pair The first-order interference coefficient of the component; for Quantity pair The first-order asymmetric interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component, When is the quadratic interference coefficient; When is the quadratic cross-term interference coefficient; , , ; 、 and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

[0013] Furthermore, the step E comprises the following steps: E1. Load the zero point group in D2 The values ​​in are restored to the corresponding unit items or load groups of the combined items to obtain the benchmark readings. The actual load value includes the load value and tare weight. The actual load value and the corresponding voltage value are combined into a new calibration array; E2. Repeat steps C2 to C3 to get a new round of balance calculation formula matrix ; E3. The new round of balance calculation formula matrix and D2's loading zero group Perform a new round of tare weight calculation according to the D2 calculation method to obtain a new round of tare weight load group, and perform a corresponding difference calculation with the previous round of tare weight load group.

[0014] Furthermore, the step F comprises the following steps: If the difference between the new tare load group and the previous tare load group is greater than the preset iterative convergence standard, the balance calibration formula matrix does not converge. Repeat steps D to E until the difference meets the iterative convergence standard. The iterative calculation ends and the obtained balance calculation formula matrix is The performance is stable and meets the calibration specifications.

[0015] Furthermore, the step G comprises the following steps: G1. Load the balance integrated group; G2. Using the Matrix The calibration coefficient is calculated according to the implicit formula of the balance to obtain the measured value of the balance, and the test standard deviation is calculated by comparing the measured value with the theoretical value. : ; in, is the difference between the measured value and the theoretical value; is the number of loading items for the comprehensive group load; G3. Set the experimental standard deviation of each unit Divide it by the maximum calibration value to obtain the calibration accuracy value. If the accuracy error of each unit is less than the preset accuracy error value, the balance calibration is completed; otherwise, error analysis is performed.

[0016] Furthermore, the step H comprises the following steps: H1. Calculate the relative error; use the maximum calibration value of each unit as input and enter it into the balance calculation formula matrix in E3. , multiply the coefficients, where the coefficient of the first interference term of Mz on Y is , then the maximum value of the primary interference of Mz on Y is : ; get The relative error for the Y element is : ; H2. According to H1, calculate the 27 coefficients of each of the 6 units of the balance in turn to obtain the relative error group ; H3. Screening to obtain relatively large errors; in the relative error group Among the 27 coefficients, select the largest coefficient that is greater than the preset accuracy error value.

[0017] Furthermore, the step I comprises the following steps: I1. Select the load group corresponding to the largest coefficient in the load group. If YMz has the largest interference on X, select the four cross terms +Y+Mz, +Y-Mz, -Y+Mz, and -Y-Mz in the load group for load calibration. I2. Replace the original calibration array with the collected data of the four cross items Repeat D~H to get the corresponding items in the new formula matrix And the corresponding experimental standard deviation value ; I3. Perform error analysis again. If the accuracy error of the relatively large error term is less than the preset accuracy error value, stop calibration and obtain the final balance calibration formula for the relatively large error term. I4. If the accuracy error of the relatively large error item is greater than the preset accuracy error value, return to H, continue to filter the relatively large error items, and increase the group load again. If the accuracy error is still greater than the preset accuracy error value, the step value of the corresponding unit item or combination item is increased by 2 n The method is encrypted again and returns to step D until the accuracy error is less than the preset accuracy error value.

[0018] The present invention is a self-adaptive multivariate calibration method for a wind tunnel balance, based on a multi-point force-applying body axis balance calibration system capable of simultaneous loading, and divides the loading loads into three groups: a basic group load, an enhanced group load, and a comprehensive group load. After completing the loading of the basic group load, a calibration formula with lower precision is preliminarily fitted, and then the comprehensive group load is applied. The measurement value is calculated according to the calibration formula, and the units with poor balance inspection precision are analyzed item by item to obtain interference items with larger errors. Then, the interference items are re-compiled into corresponding enhanced group loads, and the calibration value range of the enhanced group load is wider and the steps are denser. The enhanced group load is loaded again, and after the enhanced group load loading is completed, data processing is performed again, and the error of the calibration process is known at any time. The calibration formula is continuously fitted, and the automatic iterative loading is repeated in this way to continuously improve the accuracy of the calibration formula. When the accuracy of the calibration formula reaches the advanced indicators of industry standards, the calibration is terminated, and a high-precision balance calibration formula is finally obtained.

[0019] The adaptive multivariate calibration method for wind tunnel balances of the present invention can adapt to various balances with different interference coefficients without the need for human intervention. The calculation method is based on the traditional multivariate regression classical framework, the mathematical model is robust, the calculation method is mature, and the calibration efficiency can be improved while ensuring the calibration quality, and it has practical engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The figure is a flow chart of the adaptive multivariate calibration method for a wind tunnel balance according to the present invention. DETAILED DESCRIPTION

[0021] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0022] The wind tunnel balance in this embodiment is a six-component rod-type balance. Essentially, it is a six-dimensional force sensor used to measure forces and corresponding moments in three spatial directions. Its measurement principle involves attaching resistive strain gauges to the balance body. The small deformations produced by the balance under load cause resistance changes in the strain gauges, which are then converted into voltage changes via a Wheatstone bridge circuit. Balance calibration involves applying a standard force (torque) to the balance, measuring the corresponding voltage changes, and fitting a load-voltage relationship matrix. In this embodiment, six load components were applied to the balance (see Table 1). Multiple linear regression was then used to calculate the final relationship matrix (see Table 2). The experimental standard deviation of this relationship matrix was then calculated using comprehensive group loading data, resulting in an accuracy error of 0.129% (see Table 3).

[0023] like Figure 1 As shown, the adaptive multivariate calibration method for a wind tunnel balance of this embodiment includes the following steps: A. Prepare the calibration load of the balance; B. Carry out foundation group load loading; C. Perform linear fitting; D. Perform tare weight calculation; E. Perform nonlinear fitting; F. Perform iterative calculations; G. Perform accuracy calculations; H. Conduct error analysis; I. Repeat the process of increasing group load, error analysis and iteration.

[0024] Furthermore, the step A comprises the following steps: A1. Prepare the basic group load; A1.1 Prepare the unit items in the basic group load; According to the design load of the balance, determine the calibration loads of the six components of the balance, X, Y, Z, Mx, My, and Mz. X is the drag component, Y is the lift component, Z is the side force component, Mz is the rolling moment component, My is the yaw moment component, and Mz is the pitching moment component. The calibration load takes 80% to 120% of the design range and is loaded in nine steps of 0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, and 0%. After each component is loaded with positive and negative values, a loading array of 12 unit items is obtained. A1.2 Prepare the combination items in the basic group load; According to the calibration load of the balance, the 6 components of the balance are A total of 15 positive combination items are selected from the combination method, including YMz+, YX+, YMx+, YZ+, YMy+, MzX+, MzMx+, MzZ+, MzMy+, XMx+, XZ+, XMy+, MxZ+, MxMy+ and ZMy+, and the corresponding 15 negative combination items are YMz-, YX-, YMx-, YZ-, YMy-, MzX-, MzMx-, MzZ-, MzMy-, XMx-, XZ-, XMy-, MxZ-, MxMy- and ZMy-; for example: for the YMz+ combination: the combination item Y takes 50%~80% of the calibration load value, and when calibrating YMz+, Y is always kept constant, and the combined item Mz is loaded according to five steps of 0%, 50%, 100%, 50% and 0%; A2. Prepare to increase group load; A2.1 Compile the unit items in the enhanced group load; The loading steps in A1.1 are The calibration range is encrypted and increased at the same time, so that the calibration load is loaded in 19 steps of 0%, 12.5%, 25%, 37.5%, 50%, 62.5%, 75%, 87.5%, 100%, 125%, 100%, 87.5%, 75%, 62.5%, 50%, 37.5%, 25%, 12.5%, and 0%; A2.2 Prepare the combination items in the enhanced group load; The loading steps in A1.2 are Encryption: expand the five steps of the basic group load (0%, 50%, 100%, 50%, 0%) to nine steps (0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, 0%), and expand the two positive and negative direction combination items of a unit item to four combination items; for example, expand YMz+ and YMz- to four combination values ​​of YMz+, YMz-, Y-Mz+, and Y-Mz-, and load them separately; A3. Prepare comprehensive group loads; A comprehensive group load is compiled in accordance with the requirements of full range coverage, uniform distribution, and positive and negative symmetry. The comprehensive group load is used to verify the accuracy error of the balance calibration formula.

[0025] Furthermore, the step B comprises the following steps: B1. Determine the reference reading: Collect the voltage value arrays of the six components at the four states of the balance roll angle of 0°, 90°, 180°, and 270°. Average the four voltage value arrays to obtain an average voltage value array. The average voltage value array is the reference voltage for balance calibration. , , representing the voltage readings of X, Y, Z, Mx, My and Mz elements respectively; B2. Complete the loading of the unit items and combination items of the basic group load according to the balance calibration specifications, and obtain the calibration array including the load value and the corresponding voltage value. , , ; and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

[0026] Furthermore, the step C comprises the following steps: C1. Perform data preprocessing: Subtract the zero-point load value from the balance loading step values ​​in the plus or minus 12 unit items and the plus or minus 30 combined items to obtain the net value added. C2. Perform multiple regression calculation to obtain the corresponding calibration coefficient. The calculation formula is: ; in, The applied load value Quantity, The applied load value Quantity; is the loading step voltage value of each unit of the balance, is the initial value of each unit of the balance; is the coefficient of the first term, when When is the main coefficient, When Quantity pair The first-order interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component; , , ; 、 and The six components representing the X, Y, Z, Mx, My and Mz elements of the balance; C3. Perform formula conversion; calculate the 27 coefficients corresponding to each unit of the balance and form a 27×6 matrix. First, convert the main coefficient of each unit into conduct Transformation, then multiply the first and second interference coefficients by the new main coefficient , and finally transpose the whole to get a 6×27 matrix.

[0027] Furthermore, the step D comprises the following steps: D1. Tare weight refers to the sum of the loading device load and the counterweight load during loading. The corresponding voltage value is the loading zero point and the reference reading. The difference between D2. Collect the 42 groups of loading zero points of unit items and combination items to form a loading zero point group , where the reference reading As the first row of initial readings, then iterate according to the implicit formula of the balance to obtain 42 tare load groups corresponding to the zero point of loading , the calculation formula is: ; Where, For the balance Calculated values ​​of component loads, and Calculate for When , the load values ​​of the remaining 5 components of the balance; is the initial load value, is the main coefficient, for Quantity pair The first-order interference coefficient of the component; for Quantity pair The first-order asymmetric interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component, When is the quadratic interference coefficient; When is the quadratic cross-term interference coefficient; , , ; 、 and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

[0028] Furthermore, the step E comprises the following steps: E1. Load the zero point group in D2 The values ​​in are restored to the corresponding unit items or load groups of the combined items to obtain the benchmark readings. The actual load value includes the load value and tare weight. The actual load value and the corresponding voltage value are combined into a new calibration array; E2. Repeat steps C2 to C3 to get a new round of balance calculation formula matrix ; E3. The new round of balance calculation formula matrix and D2's loading zero group Perform a new round of tare weight calculation according to the D2 calculation method to obtain a new round of tare weight load group, and perform a corresponding difference calculation with the previous round of tare weight load group.

[0029] Furthermore, the iterative calculation of F comprises the following steps: If the difference between the new tare load group and the previous tare load group is greater than the preset iterative convergence standard, the balance calibration formula matrix does not converge. Repeat steps D to E until the difference meets the iterative convergence standard. The iterative calculation ends and the obtained balance calculation formula matrix is The performance is stable and meets the calibration specifications.

[0030] Furthermore, the step G comprises the following steps: G1. Load the balance integrated group; G2. Using the Matrix The calibration coefficient is calculated according to the implicit formula of the balance to obtain the measured value of the balance, and the test standard deviation is calculated by comparing the measured value with the theoretical value. : ; in, is the difference between the measured value and the theoretical value; is the number of loading items for the comprehensive group load; G3. Set the experimental standard deviation of each unit Divide it by the maximum calibration value to obtain the calibration accuracy value. If the accuracy error of each unit is less than the preset accuracy error value, the balance calibration is completed; otherwise, error analysis is performed.

[0031] Furthermore, the step H comprises the following steps: H1. Calculate the relative error; use the maximum calibration value of each unit as input and enter it into the balance calculation formula matrix in E3. , multiply the coefficients, where the coefficient of the first interference term of Mz on Y is , then the maximum value of the primary interference of Mz on Y is : ; get The relative error for the Y element is : ; H2. According to H1, calculate the 27 coefficients of each of the 6 units of the balance in turn to obtain the relative error group ; H3. Screening to obtain relatively large errors; in the relative error group Among the 27 coefficients, select the largest coefficient that is greater than the preset accuracy error value.

[0032] Furthermore, the step I comprises the following steps: I1. Select the load group corresponding to the largest coefficient in the load group. If YMz has the largest interference on X, select the four cross terms +Y+Mz, +Y-Mz, -Y+Mz, and -Y-Mz in the load group for load calibration. I2. Replace the original calibration array with the collected data of the four cross items Repeat D~H to get the corresponding items in the new formula matrix And the corresponding experimental standard deviation value ; I3. Perform error analysis again. If the accuracy error of the relatively large error term is less than the preset accuracy error value, stop calibration and obtain the final balance calibration formula for the relatively large error term. I4. If the accuracy error of the relatively large error item is greater than the preset accuracy error value, return to H, continue to filter the relatively large error items, and increase the group load again. If the accuracy error is still greater than the preset accuracy error value, the step value of the corresponding unit item or combination item is increased according to The method is encrypted again and returns to step D until the accuracy error is less than the preset accuracy error value.

[0033] Table 1 Calibration raw data of the six-component beam balance ,

[0034] Table 2 Coefficients of the calibration formula matrix for a six-component beam balance

[0035] Table 3 Calculation of calibration accuracy of rod-type six-component balance ,

[0036] (Note: The voltage values ​​in the odd-numbered rows in the table are zero-point readings, and the voltage values ​​in the even-numbered rows are after loading).

[0037] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the description and implementation methods. For those familiar with the art, all features disclosed in the present invention, or all steps in the disclosed methods or processes, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for adaptive multivariate calibration of a wind tunnel balance, characterized in that: The following steps are involved: A. Prepare the calibration load of the balance; B. Carry out foundation group load loading; C. Perform linear fitting; D. Perform tare weight calculation; E. Perform nonlinear fitting; F. Perform iterative calculations; G. Perform accuracy calculations; H. Conduct error analysis; I. Repeat the process of increasing group load, error analysis and iteration.

2. The adaptive multivariate calibration method for a wind tunnel balance according to claim 1, characterized in that: Described step A comprises the following steps: A1. Prepare the basic group load; A1.1 Prepare the unit items in the basic group load; According to the design load of the balance, determine the calibration loads of the six components of the balance, X, Y, Z, Mx, My, and Mz. X is the drag component, Y is the lift component, Z is the side force component, Mz is the rolling moment component, My is the yaw moment component, and Mz is the pitching moment component. The calibration load takes 80% to 120% of the design range and is loaded in nine steps of 0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, and 0%. After each component is loaded with positive and negative values, a loading array of 12 unit items is obtained. A1.2 Prepare the combination items in the basic group load; According to the calibration load of the balance, the 6 components of the balance are Select 15 positive combinations of YMz+, YX+, YMx+, YZ+, YMy+, MzX+, MzMx+, MzZ+, MzMy+, XMx+, XZ+, XMy+, MxZ+, MxMy+ and ZMy+, and the corresponding 15 negative combinations of YMz-, YX-, YMx-, YZ-, YMy-, MzX-, MzMx-, MzZ-, MzMy-, XMx-, XZ-, XMy-, MxZ-, MxMy- and ZMy-; A2. Prepare to increase group load; A2.1 Compile the unit items in the enhanced group load; The loading steps in A1.1 are The calibration range is encrypted and increased at the same time, so that the calibration load is loaded in 19 steps of 0%, 12.5%, 25%, 37.5%, 50%, 62.5%, 75%, 87.5%, 100%, 125%, 100%, 87.5%, 75%, 62.5%, 50%, 37.5%, 25%, 12.5%, and 0%; A2.2 Prepare the combination items in the enhanced group load; The loading steps in A1.2 are Encryption: expand the five steps of the basic group load (0%, 50%, 100%, 50%, 0%) to nine steps (0%, 25%, 50%, 75%, 100%, 75%, 50%, 25%, 0%), and at the same time expand the two positive and negative direction combination items of a unit item to four combination items; A3. Prepare comprehensive group loads; A comprehensive group load is compiled in accordance with the requirements of full range coverage, uniform distribution, and positive and negative symmetry. The comprehensive group load is used to verify the accuracy error of the balance calibration formula.

3. The adaptive multivariate calibration method for a wind tunnel balance according to claim 2, characterized in that: Described step B comprises the following steps: B1. Determine the reference reading: Collect the voltage value arrays of the six components at the four states of the balance roll angle of 0°, 90°, 180°, and 270°. Average the four voltage value arrays to obtain an average voltage value array. The average voltage value array is the reference voltage for balance calibration. , , representing the voltage readings of X, Y, Z, Mx, My and Mz elements respectively; B2. Complete the loading of the unit items and combination items of the basic group load according to the balance calibration specifications, and obtain the calibration array including the load value and the corresponding voltage value. , , ; and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

4. The adaptive multivariate calibration method for a wind tunnel balance according to claim 3, characterized in that: Described step C comprises the following steps: C1. Perform data preprocessing: Subtract the zero-point load value from the balance loading step values ​​in the plus or minus 12 unit items and the plus or minus 30 combined items to obtain the net value added. C2. Perform multiple regression calculation to obtain the corresponding calibration coefficient. The calculation formula is: ； in, The applied load value Quantity, The applied load value Quantity; is the loading step voltage value of each unit of the balance, is the initial value of each unit of the balance; is the coefficient of the first term, when When is the main coefficient, When Quantity pair The first-order interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component; , , ; 、 and The six components representing the X, Y, Z, Mx, My and Mz elements of the balance; C3. Perform formula conversion; calculate the 27 coefficients corresponding to each unit of the balance and form a 27×6 matrix. First, convert the main coefficient of each unit into conduct Transformation, then multiply the first and second interference coefficients by the new main coefficient , and finally transpose the whole to get a 6×27 matrix.

5. The adaptive multivariate calibration method for a wind tunnel balance according to claim 4, characterized in that: Described step D comprises the following steps: D1. Tare weight refers to the sum of the loading device load and the counterweight load during loading. The corresponding voltage value is the loading zero point and the reference reading. The difference between D2. Collect the 42 groups of loading zero points of unit items and combination items to form a loading zero point group , where the reference reading As the first row of initial readings, then iterate according to the implicit formula of the balance to obtain 42 tare load groups corresponding to the zero point of loading , the calculation formula is: ； Where, For the balance Calculated values ​​of component loads, and Calculate for When , the load values ​​of the remaining 5 components of the balance; is the initial load value, is the main coefficient, for Quantity pair The first-order interference coefficient of the component; for Quantity pair The first-order asymmetric interference coefficient of the component; for Quantity and Quantity pair The quadratic interference coefficient of the component, When is the quadratic interference coefficient; When is the quadratic cross-term interference coefficient; , , ; 、 and Represent the six components of the balance: X, Y, Z, Mx, My, and Mz.

6. The adaptive multivariate calibration method for a wind tunnel balance according to claim 5, characterized in that: The step E comprises the following steps: E1. Load the zero point group in D2 The values ​​in are restored to the corresponding unit items or load groups of the combined items to obtain the benchmark readings. The actual load value includes the load value and tare weight. The actual load value and the corresponding voltage value are combined into a new calibration array; E2. Repeat steps C2 to C3 to get a new round of balance calculation formula matrix ; E3. The new round of balance calculation formula matrix and D2's loading zero group Perform a new round of tare weight calculation according to the D2 calculation method to obtain a new round of tare weight load group, and perform a corresponding difference calculation with the previous round of tare weight load group.

7. The adaptive multivariate calibration method for a wind tunnel balance according to claim 6, characterized in that: Described step F comprises the following steps: If the difference between the new tare load group and the previous tare load group is greater than the preset iterative convergence standard, the balance calibration formula matrix does not converge. Repeat steps D to E until the difference meets the iterative convergence standard. The iterative calculation ends and the obtained balance calculation formula matrix is The performance is stable and meets the calibration specifications.

8. The adaptive multivariate calibration method for a wind tunnel balance according to claim 7, characterized in that: Described step G comprises the following steps: G1. Load the balance integrated group; G2. Using the Matrix The calibration coefficient is calculated according to the implicit formula of the balance to obtain the measured value of the balance, and the test standard deviation is calculated by comparing the measured value with the theoretical value. : ； in, is the difference between the measured value and the theoretical value; is the number of loading items for the comprehensive group load; G3. Set the experimental standard deviation of each unit Divide it by the maximum calibration value to obtain the calibration accuracy value. If the accuracy error of each unit is less than the preset accuracy error value, the balance calibration is completed; otherwise, error analysis is performed.

9. The adaptive multivariate calibration method for a wind tunnel balance according to claim 8, characterized in that: Described step H comprises the following steps: H1. Calculate the relative error; use the maximum calibration value of each unit as input and enter it into the balance calculation formula matrix in E3. , multiply the coefficients, where the coefficient of the first interference term of Mz on Y is , then the maximum value of the primary interference of Mz on Y is : ； get The relative error for the Y element is : ； H2. According to H1, calculate the 27 coefficients of each of the 6 units of the balance in turn to obtain the relative error group ; H3. Screening to obtain relatively large errors; in the relative error group Among the 27 coefficients, select the largest coefficient that is greater than the preset accuracy error value.

10. The adaptive multivariate calibration method for a wind tunnel balance according to claim 9, characterized in that: Described step 1 comprises the following steps: I1. Select the load group corresponding to the largest coefficient in the load group. If YMz has the largest interference on X, select the four cross terms +Y+Mz, +Y-Mz, -Y+Mz, and -Y-Mz in the load group for load calibration. I2. Replace the original calibration array with the collected data of the four cross items Repeat D~H to get the corresponding items in the new formula matrix And the corresponding experimental standard deviation value ; I3. Perform error analysis again. If the accuracy error of the relatively large error term is less than the preset accuracy error value, stop calibration and obtain the final balance calibration formula for the relatively large error term. I4. If the accuracy error of the relatively large error item is greater than the preset accuracy error value, return to H, continue to filter the relatively large error items, and increase the group load again. If the accuracy error is still greater than the preset accuracy error value, the step value of the corresponding unit item or combination item is increased according to The method is encrypted again and returns to step D until the accuracy error is less than the preset accuracy error value.

Images