Wind tunnel balance calibration formula coefficient evaluation method and system

Abstract

The invention discloses a wind tunnel balance calibration formula coefficient evaluation method and system, and belongs to the technical field of wind tunnel test and measurement. The system comprises a user login module, a parameter configuration module, a calibration coefficient estimation and evaluation module and a report output module. And the calibration coefficient estimation and evaluation module comprises a data reading sub-module, a data analysis sub-module and a data calculation sub-module. According to the invention, uncertainty evaluation is introduced into the balance calibration formula coefficient, and the uncertainty is transmitted to the measurement value of the wind tunnel balance force / torque through the balance calibration formula coefficient, so that the uncertainty of the measurement value dynamically changes along with the actually applied load value, and the balance calibration result is directly transmitted to the wind tunnel force measurement test site. On the basis that the wind tunnel balance calibration formula coefficient is calculated through the least square method, the estimated value of the wind tunnel balance calibration formula coefficient is calculated through Monte Carlo sampling and statistical analysis, and the risk that errors are too large due to single calculation is avoided. According to the invention, the evaluation result can be output in a report form.

Description

Technical Field

[0001] This invention relates to a method and system for evaluating the coefficients of a wind tunnel balance calibration formula, belonging to the fields of wind tunnel testing technology and measurement technology. Background Technology

[0002] The core of wind tunnel force measurement testing is simulating the forces acting on an aircraft model in airflow, a complex process involving multiple stages. In wind tunnel force measurement testing, the wind tunnel balance captures the aerodynamic forces (lift, drag, side forces) and moments (roll moment, yaw moment, pitch moment) experienced by the model in the airflow. Accurate force and moment data are the direct basis for verifying the rationality of the test design and optimizing the aerodynamic layout, significantly reducing the cost and risk of actual aircraft testing.

[0003] To ensure the quality of wind tunnel balance measurement data, the balance needs to be calibrated in a laboratory environment before use to determine the measurement error and uncertainty. Currently, balance calibration is performed according to the requirements of GJB 2244A-2011 "Wind Tunnel Balance Strain Specification". Since the balance output is a strain voltage after applying a load, the specification proposes using a balance calibration formula to convert the load and strain voltage into the force or torque value measured by the balance. The specific balance calibration formula is as follows (ignoring third-order terms):

[0004]

[0005] Where i represents the balance component, i = 1, 2, ..., N, ΔU i The voltage signal output for the i-th component load; P j The load is the j-th component that interferes with the i-th component; a i For the i-th component load principal term coefficient, These are first-order interference correction coefficients. These are second-order squared term interference correction coefficients or cross-interference correction coefficients, with a total of N*L terms, where L=(N 2 +3N) / 2.

[0006] Currently, GJB 2244A only uses the least squares method to calculate the coefficient values ​​of the N*L terms in one step, but it does not provide an evaluation method for these coefficient values, i.e., a method for calculating the uncertainty of the coefficient values. In wind tunnel balance laboratory calibration, the force / torque value of the wind tunnel balance is calculated based on the calculated coefficient values ​​using the aforementioned balance calibration formula. Then, combined with the uncertainty introduced by the balance calibration device, the uncertainty introduced by repeatability, and the comprehensive loading error, the uncertainty of the wind tunnel balance calibration can be calculated. However, for the same wind tunnel balance, this uncertainty is under full-scale conditions. Considering that in actual applications, the comprehensive loading load on the balance often cannot reach its full scale, this uncertainty cannot accurately reflect the balance's performance under actual working conditions, thus affecting the reasonable judgment and accurate evaluation of the balance's measurement accuracy. Furthermore, it will affect the effective transmission of the uncertainty introduced by the wind tunnel balance force / torque measurement at the wind tunnel force measurement test site. Summary of the Invention

[0007] To address the problem of effectively transmitting uncertainties introduced by wind tunnel balance force / torque measurements in wind tunnel force testing, the present invention aims to provide a method and system for evaluating wind tunnel balance calibration formula coefficients. This method and system can calculate the estimated values ​​and corresponding uncertainties of the wind tunnel balance calibration formula coefficients, incorporating the uncertainties into the calibration formula coefficients. This allows the system to directly calculate the estimated values ​​and corresponding uncertainties of the wind tunnel balance calibration formula coefficients and output the evaluation results in report form, thereby improving the accuracy and efficiency of wind tunnel balance calibration formula coefficient evaluation.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] This invention discloses a method for evaluating the calibration formula coefficients of a wind tunnel balance. It fully considers the factor that the uncertainty of the measured force / torque in a wind tunnel force measurement test should change with the actual applied load value. Uncertainty assessment is introduced into the balance calibration formula coefficients, and the uncertainty is transferred to the measured force / torque value of the wind tunnel balance through these coefficients. This allows the measurement uncertainty to dynamically change with the actual applied load value, achieving direct transmission of the balance calibration results to the wind tunnel force measurement test site. Based on the least squares method for calculating the wind tunnel balance calibration formula coefficients, this invention utilizes Monte Carlo sampling and statistical analysis to calculate the estimated values ​​of the coefficients, avoiding the risk of excessive errors introduced by a single calculation. Furthermore, this invention also provides a wind tunnel balance calibration formula coefficient evaluation system, which can directly calculate the estimated values ​​of the wind tunnel balance calibration formula coefficients and their corresponding uncertainties, and output the evaluation results in report form, improving the accuracy and efficiency of wind tunnel balance calibration formula coefficient evaluation.

[0010] This invention discloses a method for evaluating the coefficients of a wind tunnel balance calibration formula, comprising the following steps:

[0011] Step 1: Given the data, which includes an R-row N-column load data table after zero-point load correction, an R-row N-column voltage data table after zero-point voltage correction and bridging, a data table showing the distribution characteristics and standard deviation of each of the R-row N-column load data, and a data table showing the distribution characteristics and standard deviation of each of the R-row N-column voltage data.

[0012] Based on the distribution characteristics and standard deviation of the load data and the voltage data, the Monte Carlo sampling method is used to sample the load data and voltage data M times, respectively obtaining M load data tables with R rows and N columns and M corresponding voltage data tables with R rows and N columns.

[0013] Step 2: Based on the balance calibration model formula in GJB 2244A, substitute the data from each sampled load data table and its corresponding voltage data table into the formula. For each of the N components of the balance, a system of linear algebraic equations can be obtained, and each system of linear algebraic equations contains R equations. Specifically, the calculation method is as follows.

[0014] For the m-th component of the balance, we have

[0015]

[0016] in,

[0017] F mr The load data on the left side of the rth equation in the linear equation system corresponding to the mth component of the balance corresponds to the data in the rth row and mth column of the load data table.

[0018] ΔU mr For the voltage data on the right side of the corresponding r-th equation, the voltage data in the r-th row and m-th column of the voltage data table is used.

[0019] a mr The load principal term coefficient for the m-th component on the right-hand side of the corresponding r-th equation;

[0020] The vector is composed of the other component loads that interfere with the m-th component of the balance, which are on the right-hand side of the corresponding r-th equation.

[0021] For corresponding A vector composed of first-order interference correction coefficients;

[0022] The vector is composed of the product of the loads that disturb the m-th component of the balance on the right side of the corresponding r-th equation.

[0023] For corresponding A vector composed of second-order squared term interference correction coefficients or cross-interference correction coefficients.

[0024] and The vector expressions are as follows:

[0025]

[0026] in,

[0027] P m-1,r For the load data of the (m-1)th component that interferes with the m-th component of the balance in the r-th equation, the corresponding data in the (r-th)th row and (m-1)th column of the load data table;

[0028] For P in the r-th equation m-1,r The first-order disturbance coefficient corresponding to the component load;

[0029] P 1r ·P Nr P is the product of the first load and the Nth load that disturb the m-th component of the balance. 1r The data in the r-th row and 1-th column of the corresponding load data table, P Nr The data in the r-th row and N-th column of the corresponding load data table;

[0030] For P in the r-th equation 1r ·P Nr Cross-interference correction factor corresponding to the load product.

[0031] Additionally, when m = 1, we have

[0032]

[0033] When m = N, we have

[0034]

[0035] Each of the above linear algebraic equation systems is an overdetermined system of equations;

[0036] Therefore, for each load data table and its corresponding voltage data table, N overdetermined equations can be obtained. For M load data tables and their corresponding voltage data tables, a total of M*N overdetermined equations can be obtained, that is, M groups, each group with N overdetermined equations.

[0037] Step 3: For each component, solve the N overdetermined algebraic equations using the least squares method to obtain the N*L coefficient values ​​corresponding to the N components in the balance calibration model formula (L=(N2 +3N) / 2); Iterate through the M components, solve the system of equations using the least squares method, and finally obtain the N*L coefficient values ​​of the M groups;

[0038] Step 4: Based on the Monte Carlo measurement uncertainty assessment method in JJF 1059.2, perform statistical analysis on the obtained M groups of N*L coefficient values ​​to obtain the estimated values ​​of N*L coefficients and the corresponding uncertainties.

[0039] This invention discloses a wind tunnel balance calibration formula coefficient evaluation system, implemented based on the aforementioned wind tunnel balance calibration formula coefficient evaluation method. The wind tunnel balance calibration formula coefficient evaluation system includes modules for user login, parameter configuration, calibration coefficient estimation and evaluation, and report output. The calibration coefficient estimation and evaluation module includes sub-modules for data reading, data analysis, and data calculation.

[0040] The user login module is mainly used to implement user authentication.

[0041] The parameter configuration module is mainly used by users to fill in information such as the balance model, evaluation date, and the name of the evaluator.

[0042] The calibration coefficient estimation and evaluation module mainly implements the estimation of the coefficients of the wind tunnel balance calibration formula and the calculation of the corresponding uncertainties. The data reading submodule is mainly used to read the load data after zero-point correction and the voltage data after bridging, as well as the distribution characteristics and standard deviation data corresponding to the load and voltage data. The data analysis submodule is mainly used to implement Monte Carlo sampling and data storage of the load and voltage data. The data calculation submodule is mainly used to perform the calculations in steps three and four, calculating the estimated values ​​of the wind tunnel balance calibration formula coefficients and the corresponding uncertainties.

[0043] The report output module is mainly used to output report information and evaluation results. Report information includes the wind tunnel balance model, evaluation date, and the name of the evaluator. Evaluation results include the estimated values ​​of the wind tunnel balance calibration formula coefficients and the uncertainty of these estimates.

[0044] Beneficial effects:

[0045] 1. The present invention discloses a method and system for evaluating the calibration formula coefficients of a wind tunnel balance. By constructing an estimated value of the calibration formula coefficients of the wind tunnel balance and a method for calculating the corresponding uncertainty of the estimated value, the uncertainty is introduced into the calibration formula coefficients of the balance. This enables the uncertainty of the force / torque measured by the balance to change dynamically with the actual applied load, solving the problem that the uncertainty introduced by the force / torque measured by the wind tunnel balance is difficult to effectively transmit in the wind tunnel force measurement test site. Furthermore, it can output a report based on the calculation and evaluation results.

[0046] 2. This invention discloses a method and system for evaluating the calibration formula coefficients of a wind tunnel balance. Considering that in practical applications of balances, the comprehensive load often fails to reach the full scale, and that traditional wind tunnel balance force measurement uses the fixed uncertainty at full scale as the measurement accuracy, which cannot accurately reflect the balance's performance under actual working conditions, this invention introduces uncertainty into the calibration formula coefficients of the wind tunnel balance. Based on the distribution characteristics and standard deviation of load and voltage data, Monte Carlo sampling and overdetermined equations are constructed to estimate the calibration formula coefficients and evaluate the uncertainty of the estimated values. This allows the balance force / torque to change according to the actual applied load, promoting reasonable judgment and accurate evaluation of the balance measurement accuracy. Furthermore, it facilitates the effective transmission of the uncertainty introduced by the wind tunnel balance force / torque measurement at the wind tunnel force measurement test site, accelerating the evaluation of wind tunnel aerodynamic coefficients.

[0047] 3. The present invention discloses a method and system for evaluating the calibration formula coefficients of a wind tunnel balance. By calculating the estimated value of the calibration formula coefficients of the wind tunnel balance and the corresponding uncertainty of the estimated value, the uncertainty is introduced into the calibration formula coefficients of the balance. This enables the uncertainty of the force / torque measured by the wind tunnel balance to change dynamically with the actual applied load, thereby improving the estimation of the measurement performance or accuracy of the wind tunnel balance in conventional force measurement tests in wind tunnels, reducing test costs, and accelerating the accurate evaluation of the aerodynamic coefficients at the site of conventional force measurement tests in wind tunnels. Attached Figure Description

[0048] Figure 1 A flowchart of a method for evaluating the coefficients of a wind tunnel balance calibration formula.

[0049] Figure 2 This is a schematic diagram of the architecture and process of a wind tunnel balance calibration formula coefficient evaluation system. Detailed Implementation

[0050] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0051] Example 1:

[0052] Taking the six-component wind tunnel balance used in the conventional force measurement test of the FL-62 wind tunnel as an example, such as Figure 1 As shown in this embodiment, a method for evaluating the coefficients of a wind tunnel balance calibration formula is disclosed. The specific implementation steps are as follows:

[0053] Step 1: Given the documents obtained from the six-component wind tunnel balance calibration laboratory, including a 144x6 load data table after zero-point load correction and a 144x6 voltage data table after zero-point voltage correction and bridging, along with data tables showing the distribution characteristics and standard deviations of the 144x6 load data and the 144x6 voltage data, respectively. Based on the distribution characteristics and standard deviations of the load and voltage data, a Monte Carlo sampling method is used to sample the load and voltage data 100,000 times, resulting in 100,000 144x6 load data tables and 100,000 corresponding 144x6 voltage data tables.

[0054] Step 2: Substitute the data from each load data table and its corresponding voltage data table obtained in Step 1 into the balance calibration model formula. For each of the six components of the balance, a system of linear algebraic equations can be obtained. Each system of linear algebraic equations contains 144 equations. Specifically, the calculation process is as follows.

[0055] For the m-th component of the balance, we have

[0056]

[0057] in,

[0058] F mr The load data on the left side of the rth equation in the linear equation system corresponding to the mth component of the balance corresponds to the data in the rth row and mth column of the load data table.

[0059] ΔU mr For the voltage data on the right side of the corresponding r-th equation, the voltage data in the r-th row and m-th column of the voltage data table is used.

[0060] a mr The load principal term coefficient for the m-th component on the right-hand side of the corresponding r-th equation;

[0061] The vector is composed of the other component loads that interfere with the m-th component of the balance, which are on the right-hand side of the corresponding r-th equation.

[0062] For corresponding A vector composed of first-order interference correction coefficients;

[0063] The vector is composed of the product of the loads that disturb the m-th component of the balance on the right side of the corresponding r-th equation.

[0064] For corresponding A vector composed of second-order squared term interference correction coefficients or cross-interference correction coefficients.

[0065] and The vector expressions are as follows:

[0066]

[0067]

[0068] in,

[0069] N = 6, R = 144;

[0070] P m-1,r For the load data of the (m-1)th component that interferes with the m-th component of the balance in the r-th equation, the corresponding data in the (r-th)th row and (m-1)th column of the load data table;

[0071] For P in the r-th equation m-1,r The first-order disturbance coefficient corresponding to the component load;

[0072] P 1r ·P Nr P is the product of the first load and the Nth load that disturb the m-th component of the balance. 1r The data in the r-th row and 1-th column of the corresponding load data table, P Nr The data in the r-th row and N-th column of the corresponding load data table;

[0073] For P in the r-th equation 1r ·P Nr Cross-interference correction factor corresponding to the load product.

[0074] Additionally, when m = 1, we have

[0075]

[0076] When m = N, we have

[0077]

[0078] Each of the above linear algebraic equation systems is an overdetermined system of equations;

[0079] Therefore, for each load data table and its corresponding voltage data table, 6 sets of overdetermined equations can be obtained. For 100,000 load data tables and their corresponding voltage data tables, a total of 100,000 * 6 sets of overdetermined equations can be obtained, that is, 100,000 groups, with 6 sets of overdetermined equations in each group.

[0080] Step 3: For the 6 overdetermined equations in each component, solve them by least squares to obtain 6*27 coefficient values ​​corresponding to the 6 components of the wind tunnel balance in the balance calibration model formula; iterate through 100,000 components and solve the equations by least squares in each case to finally obtain 100,000 sets of 6*27 coefficient values.

[0081] Step 4: Based on the Monte Carlo measurement uncertainty assessment method in JJF 1059.2, statistical analysis was performed on the 100,000 sets of 6*27 coefficient values ​​obtained, and the mean and standard deviation of each coefficient value were calculated. Finally, the estimated values ​​of the 6*27 coefficients in the wind tunnel 6-component balance calibration formula and the corresponding uncertainties were obtained, as shown in Tables s1 and s2 below.

[0082] Table s1 Estimated values ​​of coefficients for the calibration formula of the 6-component balance in the wind tunnel.

[0083]

[0084] Table s2 Uncertainty of Estimated Coefficients for Wind Tunnel Six-Component Balance Calibration Formula

[0085]

[0086] The estimated values ​​of the 6*27 coefficients and their corresponding uncertainties in the wind tunnel 6-component balance calibration formula are mainly applied to the wind tunnel balance force measurement stage during wind tunnel force measurement tests. This is achieved by substituting the applied load, the strain voltage output by the balance, and the estimated values ​​of the 6*27 coefficients into the following formula.

[0087]

[0088] The force / torque value of the balance can then be calculated.

[0089] The above formula is a measurement model. It distributes the uncertainties of the load applied to each component of the wind tunnel balance, the uncertainty of the strain voltage output by the balance, and the corresponding uncertainties of the estimated values ​​of 6*27 coefficients, to calculate the uncertainty of the force / torque measured by the balance. This uncertainty dynamically changes with the actual applied load value, rather than being a fixed uncertainty corresponding to the full scale of the wind tunnel balance.

[0090] Comparative Example 1:

[0091] In existing conventional wind tunnel force measurement tests, the wind tunnel balance force measurement process only uses a 144-row, 6-column load data table corrected for zero-point load and a 144-row, 6-column voltage data table corrected for zero-point voltage and after bridging. The data is substituted into the wind tunnel balance calibration formula to obtain a set of 6*27 coefficients. This is a single-point calculation and does not introduce the calculation of uncertainty.

[0092] Furthermore, currently only the uncertainty of the wind tunnel balance at full scale is used as the uncertainty of its force / torque measurement, which is a fixed value. The uncertainty of the balance force measurement does not change dynamically with the actual load applied by the balance. This uncertainty cannot accurately reflect the performance of the balance under actual working conditions, thus affecting the reasonable judgment and accurate evaluation of the balance measurement accuracy.

[0093] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating the coefficients of a wind tunnel balance calibration formula, characterized in that: Includes the following steps: Step 1: Given the data, which includes an R-row N-column load data table after zero-point load correction, an R-row N-column voltage data table after zero-point voltage correction and bridging, a data table showing the distribution characteristics and standard deviation of each of the R-row N-column load data, and a data table showing the distribution characteristics and standard deviation of each of the R-row N-column voltage data. Based on the distribution characteristics and standard deviation of the load data and the distribution characteristics and standard deviation of the voltage data, the Monte Carlo sampling method is used to sample the load data and voltage data M times to obtain M load data tables with R rows and N columns and M corresponding voltage data tables with R rows and N columns, respectively. Step 2: Based on the balance calibration model formula in GJB 2244A, substitute the data from each sampled load data table and its corresponding voltage data table into the formula. For each of the N components of the balance, obtain the corresponding linear algebra equation system. Each linear algebra equation system contains R equations, and the calculation method is as follows. For the m-th component of the balance, we have in, F mr The load data on the left side of the rth equation in the linear equation system corresponding to the mth component of the balance corresponds to the data in the rth row and mth column of the load data table. ΔU mr For the voltage data on the right side of the corresponding r-th equation, the voltage data in the r-th row and m-th column of the voltage data table is used. a mr The load principal term coefficient for the m-th component on the right-hand side of the corresponding r-th equation; The vector is composed of the other component loads that interfere with the m-th component of the balance, which are on the right-hand side of the corresponding r-th equation. For corresponding A vector composed of first-order interference correction coefficients; The vector is composed of the product of the loads that disturb the m-th component of the balance on the right side of the corresponding r-th equation. For corresponding A vector composed of second-order squared term interference correction coefficients or cross-interference correction coefficients; and The vector expressions are as follows: in, P m-1,r For the load data of the (m-1)th component that interferes with the m-th component of the balance in the r-th equation, the corresponding data in the (r-th)th row and (m-1)th column of the load data table; For P in the r-th equation m-1,r The first-order disturbance coefficient corresponding to the component load; P 1r ·P Nr P is the product of the first load and the Nth load that disturb the m-th component of the balance. 1r The data in the r-th row and 1-th column of the corresponding load data table, P Nr The data in the r-th row and N-th column of the corresponding load data table; For P in the r-th equation 1r ·P Nr Cross-interference correction factor corresponding to the load product; Additionally, when m = 1, we have When m = N, we have Each of the above linear algebraic equation systems is an overdetermined system of equations; For each load data table and its corresponding voltage data table, N sets of overdetermined equations are obtained. Then, for M load data tables and their corresponding voltage data tables, a total of M*N sets of overdetermined equations are obtained, that is, M groups, each group having N sets of overdetermined equations. Step 3: For each component, solve the N overdetermined algebraic equations using the least squares method to obtain the N*L coefficient values ​​corresponding to the N components in the balance calibration model formula (L=(N 2 +3N) / 2); Iterate through the M components, and solve the system of equations using the least squares method to obtain the N*L coefficient values ​​of the M groups; Step 4: Based on the Monte Carlo measurement uncertainty assessment method in JJF 1059.2, perform statistical analysis on the obtained M groups of N*L coefficient values ​​to obtain the estimated values ​​of N*L coefficients and the corresponding uncertainties.

2. A system for implementing the method as described in claim 1, characterized in that: It includes modules for user login, parameter configuration, calibration coefficient estimation and evaluation, and report output; the calibration coefficient estimation and evaluation module includes sub-modules for data reading, data analysis, and data calculation. The user login module is mainly used to implement user authentication. The parameter configuration module is mainly used by users to fill in information such as the balance model, evaluation date, and the name of the evaluator. The calibration coefficient estimation and evaluation module mainly realizes the estimation of the coefficients of the wind tunnel balance calibration formula and the calculation of the uncertainty corresponding to the estimated value; the data reading submodule is mainly used to read the load data after zero-point correction and the voltage data after bridging, and to read the distribution characteristics and standard deviation data of the load data and voltage data; the data analysis submodule is mainly used to realize the Monte Carlo sampling and data storage of load data and voltage data; the data calculation submodule is mainly used to realize the calculations in steps three and four, and to calculate the estimated value of the wind tunnel balance calibration formula coefficient and the uncertainty of the estimated value. The report output module is mainly used to output report information and evaluation results; the report information includes the wind tunnel balance model, evaluation date, and name of the evaluator; the evaluation results include the estimated value of the wind tunnel balance calibration formula coefficient and the uncertainty of the estimated value.

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