A fusion uncertainty evaluation method suitable for complex measurement systems

Abstract

The application discloses a fusion uncertainty evaluation method suitable for a complex measurement system and relates to the technical field of measurement data processing. B / P The method comprises the following steps: obtaining original measurement data and establishing a multi-stage measurement model; dividing the model into a front-stage, a nonlinear and a rear-stage uncertainty propagation section; performing double-component modeling on input variables B 、 P ; performing GUM analytical propagation on the front-stage section; performing Monte Carlo propagation on the nonlinear section and counting outputs of two components respectively; performing GUM analytical synthesis on the rear-stage section to obtain an estimated value of a target output variable, B / P a component standard uncertainty and a synthesized standard uncertainty; and connecting the three sections through interlayer transmission information to form a fusion uncertainty propagation chain. B / P The application can accurately propagate the uncertainty in the nonlinear link while retaining double-component engineering expression, and is suitable for a complex measurement system such as a wind tunnel force measurement system.

Description

Technical Field

[0001] This invention relates to the field of measurement data processing technology, and in particular to a method for evaluating the fusion uncertainty of complex measurement systems. Background Technology

[0002] Measurement uncertainty is used to quantitatively characterize the dispersion of the measured value. It is an important basis for evaluating the quality of measurement results, comparing different measurement schemes, and making compliance judgments. For cases where the measurement model is relatively simple and can be effectively linearized around the estimated input values, the standard uncertainty of the output quantity can usually be calculated using the sensitivity coefficient and the uncertainty propagation law, following the basic principles of the Guide to the Expression of Uncertainty in Measurement (GUM). This type of method is computationally efficient, provides clear results, and facilitates tracing the contribution of each input quantity to the uncertainty of the output quantity.

[0003] However, complex measurement systems such as multi-axis load measurement, three-dimensional coordinate measurement, multi-sensor pose measurement, and flow and thermal parameter measurement typically involve processing steps including calibration conversion, attitude correction, matrix transformation, coordinate transformation, inversion calculation, normalization, and multivariate coupling. The uncertainty of the input quantity propagates step-by-step along the multi-stage measurement model, and some processing steps exhibit significant nonlinearity. If a uniform first-order linearization propagation is applied to the entire multi-stage measurement model, it may not fully reflect the impact of nonlinearity and variable coupling on the output distribution.

[0004] The Monte Carlo Method (MCM) generates random samples based on the probability distribution of input quantities and propagates these random samples directly through the measurement model, making it suitable for handling complex nonlinear models. Documents such as JCGM 101:2008 provide a basic framework for probability distribution propagation using the Monte Carlo method. Existing techniques also include methods for calculating combined uncertainty using Monte Carlo statistical simulation. However, uniformly implementing Monte Carlo propagation on a complete measurement model involving numerous measurement processing steps, multiple output quantities, and multiple operating conditions typically requires a large computational load and makes it difficult to maintain the categorical uncertainty expression used in complex engineering experiments over the long term.

[0005] In engineering tests such as wind tunnel tests, structural tests, and multi-component force measurements, sources of uncertainty are typically categorized into deviation limits. B Component and precision limits P Quantity. B The components mainly reflect the sources of uncertainty with systematic characteristics, such as instrument readings, calibration, installation, and correction models. PThe components mainly reflect sources of uncertainty with random characteristics, such as repeated measurement discreteness and short-term random fluctuations. B / P Two-component representation can clearly reflect the impact of different types of uncertainty on measurement results, facilitating experimental data quality evaluation and engineering applications. However, existing complete Monte Carlo propagation methods typically incorporate all types of uncertainty into a single joint propagation, making it difficult to directly retain the results. B / P Independent propagation results of the two components.

[0006] Therefore, a fusion uncertainty assessment method suitable for complex measurement systems is needed. Based on the propagation characteristics of each processing stage in a multi-stage measurement model, analytical propagation based on the GUM concept is used in the uncertainty propagation sections of the pre- and post-stages, while MCM probability distribution propagation is used in the nonlinear uncertainty propagation section. Furthermore, different propagation methods are connected through inter-stage information transfer. B Components and P The components are modeled, propagated, and classified separately, thus forming a GUM-MCM-GUM fusion evaluation mechanism suitable for multi-stage nonlinear measurement models. Summary of the Invention

[0007] The technical solution of this invention to solve the above-mentioned technical problems is to provide a method for evaluating the fusion uncertainty of complex measurement systems, comprising the following steps: Step 1: Obtain raw measurement data to characterize the physical quantities of the object being measured and establish a multi-stage measurement model; Step 2: Divide the multi-stage measurement model into at least one pre-stage uncertainty propagation segment, at least one nonlinear uncertainty propagation segment, and at least one post-stage uncertainty propagation segment. The preceding uncertainty propagation section is located upstream of the nonlinear uncertainty propagation section, and the subsequent uncertainty propagation section is located downstream of the nonlinear uncertainty propagation section. The nonlinear uncertainty propagation section includes at least one nonlinear propagation sub-model. Step 3: Identify the input quantities and their uncertainty sources in the preceding uncertainty propagation segment, the nonlinear uncertainty propagation segment, and the subsequent uncertainty propagation segment, and divide the uncertainty of each input quantity into deviation limits. B Component and precision limits P Components, and respectively determine the estimated value of the input quantity, B Component standard uncertainty P Component standard uncertainty and corresponding probability distribution; Step 4: In the preceding uncertainty propagation section, a preceding analytical propagation method based on the Guide to Measurement Uncertainty (GUM) is adopted. This method utilizes one or a combination of sensitivity coefficients, uncertainty propagation laws, and analytical calculations to obtain intermediate quantity estimates as inputs to the nonlinear uncertainty propagation section. B Component standard uncertainty P The standard uncertainty of the components and their corresponding probability distributions form the information transmitted between the preceding layers. Step 5: Based on the inter-layer transfer information from the preceding layers, perform [further steps] in the nonlinear uncertainty propagation section. B Components and P Each component generates a random sample, and these random samples are then input into the nonlinear propagation sub-model for Monte Carlo propagation to obtain the results. B Component propagation output sample set and P Component propagation outputs the sample set; Step 6, respectively for the... B Component propagation output sample set and the P Statistical analysis is performed on the component propagation output sample set to obtain the output quantity of the nonlinear uncertainty propagation segment. B Component propagation estimate P Component propagation estimate B Component standard uncertainty and P Component standard uncertainty, and according to the stated B Component propagation estimate and the P The component propagation estimate determines the segment output estimate of the output of the nonlinear uncertainty propagation segment, forming the subsequent inter-layer transmission information; Step 7: Input the inter-level transfer information and the uncertainty information of other input quantities in the subsequent uncertainty propagation section into the subsequent uncertainty propagation section, and propagate and synthesize them separately using the subsequent analytical propagation method based on the GUM concept. B Components and P Components, to obtain an estimate of the target output quantity, B Component standard uncertainty P Component standard uncertainty and combined standard uncertainty; The pre-stage analytical propagation based on the GUM concept, the Monte Carlo propagation in the nonlinear uncertainty propagation section, and the post-stage analytical propagation based on the GUM concept are interconnected through the inter-layer information transfer between the pre-stage and post-stage stages, forming a fused uncertainty propagation chain.

[0008] Furthermore, in step 1, a multi-stage measurement model is established based on the original measurement data and the data processing relationships of the complex measurement system. The complex measurement system comprises multiple series, parallel, or coupled measurement processing steps, and at least one measurement processing step includes nonlinear function operations, variable coupling, matrix transformation, coordinate transformation, iterative calculation, inversion calculation, or piecewise calculation.

[0009] Further, in step 2, the nonlinear propagation sub-model is determined according to at least one of the following conditions: Includes trigonometric functions, exponential functions, logarithmic functions, or non-integer power functions; Multiplication, division, or coupling operations involving two or more uncertain inputs that have a non-negligible nonlinear effect on the output distribution; Includes operations on coordinate transformation matrices, rotation matrices, or multi-component matrices; It includes iterative, inversion, optimization, or implicit solution processes; or it is designated as a measurement processing step that uses probability distribution propagation according to preset rules.

[0010] Furthermore, in step 3, the deviation limit B The component is determined by at least one of the following: instrument indication error, calibration error, installation error, environmental correction error, model correction error, and geometric dimension error; the accuracy limit is... P The component is determined by at least one of repeated measurement discreteness, short-term random fluctuations, and data acquisition noise.

[0011] Furthermore, when the first i The deviation limit of each input quantity is And the conversion factor corresponding to its probability distribution is At that time, its B The standard uncertainty of the component is: ; When the i The repeated measures sample standard deviation of the input quantities is: s i The number of repeated measurements is n i At that time, its P The standard uncertainty of the component is: .

[0012] Furthermore, in step 5, within the nonlinear uncertainty propagation region, for B Components and P Each component is subjected to at least one million Monte Carlo samplings; each B During component propagation, P The component remains at its center value or is not introduced. P Component random perturbation; each time P During component propagation, BThe component remains at its center value or is not introduced. B The components are subject to random perturbation.

[0013] Furthermore, in step 5, let the stated B The component propagation output sample set is The above P The component propagation output sample set is , Then calculate separately B Component propagation estimate , P Component propagation estimate and the corresponding sample standard deviation , , and according to Determine the output estimate for the section.

[0014] Furthermore, in step 7, the post-stage analytical propagation method based on the GUM concept, according to the sensitivity coefficient of the target output to each input, applies the following to each input: B Component standard uncertainty and P The component standard uncertainties are summed and combined to obtain the target output quantity. B Component standard uncertainty and P Component standard uncertainty ,according to Obtain the composite standard uncertainty based on the preset coverage factor. according to Obtain the expanded uncertainty of the target output and output the estimated value of the target output. B Component standard uncertainty P At least one of component standard uncertainty, combined standard uncertainty, and expanded uncertainty.

[0015] Furthermore, the complex measurement system is a wind tunnel force measurement test system; the inputs of the wind tunnel force measurement test system include at least the balance output voltage signal, model attitude angle, total pressure, static pressure, and model geometric parameters; the target outputs include at least one of the drag coefficient, lift coefficient, side force coefficient, roll moment coefficient, yaw moment coefficient, and pitch moment coefficient; the pre-stage uncertainty propagation section includes balance calibration conversion and attitude angle correction; the nonlinear uncertainty propagation section includes the coordinate transformation of the load from the balance axis system through the model axis system to the wind axis system; and the post-stage uncertainty propagation section includes dynamic pressure calculation, aerodynamic coefficient normalization calculation involving model geometric parameters, and aerodynamic coefficient uncertainty synthesis.

[0016] This invention divides the multi-stage measurement model of a complex measurement system into a pre-stage GUM analytical section, a nonlinear MCM probability propagation section, and a post-stage GUM analytical section. It utilizes inter-level information transfer in the pre-stage and post-stage stages to achieve seamless integration of the three propagation mechanisms. This avoids the problem of significant propagation deviations in the nonlinear stages caused by a single GUM linearization method, and overcomes the computational burden and difficulty in preserving data from a unified Monte Carlo simulation of the entire model. B / P The shortcomings of the two-component engineering expression method; at the same time, through the deviation limit B Component and precision limits P The components are independently modeled, randomly sampled along different paths, and statistically analyzed. This approach accurately reflects the differential impact of various uncertainty sources on the output distribution during highly nonlinear processes such as coordinate transformation and matrix transformation. Furthermore, it naturally outputs results widely accepted in the engineering field during subsequent analytical synthesis. B Component standard uncertainty P The component standard uncertainty and combined standard uncertainty significantly improve the accuracy, computational efficiency and interpretability of uncertainty assessment for complex measurement systems, providing a fusion assessment scheme that combines theoretical rigor and engineering practicality for complex tests such as wind tunnel force measurement and multiaxial load measurement. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the fusion uncertainty assessment method applicable to complex measurement systems according to the present invention. Figure 2 The graph shows the variation of the combined standard uncertainty of aerodynamic coefficients at different angles of attack. Detailed Implementation

[0019] This invention proposes a method for evaluating the fusion uncertainty of complex measurement systems, aiming to design a method for evaluating the fusion uncertainty of complex measurement systems.

[0020] The fusion uncertainty assessment method for complex measurement systems proposed in this invention will be described below in specific embodiments: Example 1: A method for evaluating the fusion uncertainty of complex measurement systems includes the following steps: Step 1: Obtain raw measurement data to characterize the physical quantities of the object being measured and establish a multi-stage measurement model; Step 2: Divide the multi-stage measurement model into at least one pre-stage uncertainty propagation segment, at least one nonlinear uncertainty propagation segment, and at least one post-stage uncertainty propagation segment. The preceding uncertainty propagation section is located upstream of the nonlinear uncertainty propagation section, and the subsequent uncertainty propagation section is located downstream of the nonlinear uncertainty propagation section. The nonlinear uncertainty propagation section includes at least one nonlinear propagation sub-model. Step 3: Identify the input quantities and their uncertainty sources in the preceding uncertainty propagation segment, the nonlinear uncertainty propagation segment, and the subsequent uncertainty propagation segment, and divide the uncertainty of each input quantity into deviation limits. B Component and precision limits P Components, and respectively determine the estimated value of the input quantity, B Component standard uncertainty P Component standard uncertainty and corresponding probability distribution; Step 4: In the preceding uncertainty propagation section, a preceding analytical propagation method based on the Guide to Measurement Uncertainty (GUM) is adopted. This method utilizes one or a combination of sensitivity coefficients, uncertainty propagation laws, and analytical calculations to obtain intermediate quantity estimates as inputs to the nonlinear uncertainty propagation section. B Component standard uncertainty P The standard uncertainty of the components and their corresponding probability distributions form the information transmitted between the preceding layers. Step 5: Based on the inter-layer transfer information from the preceding layers, perform [further steps] in the nonlinear uncertainty propagation section. B Components and P Each component generates a random sample, and these random samples are then input into the nonlinear propagation sub-model for Monte Carlo propagation to obtain the results. B Component propagation output sample set and P Component propagation outputs the sample set; Step 6, respectively for the... B Component propagation output sample set and the P Statistical analysis is performed on the component propagation output sample set to obtain the output quantity of the nonlinear uncertainty propagation segment. B Component propagation estimate P Component propagation estimate B Component standard uncertainty and P Component standard uncertainty, and according to the stated B Component propagation estimate and the PThe component propagation estimate determines the segment output estimate of the output of the nonlinear uncertainty propagation segment, forming the subsequent inter-layer transmission information; Step 7: Input the inter-level transfer information and the uncertainty information of other input quantities in the subsequent uncertainty propagation section into the subsequent uncertainty propagation section, and propagate and synthesize them separately using the subsequent analytical propagation method based on the GUM concept. B Components and P Components, to obtain an estimate of the target output quantity, B Component standard uncertainty P Component standard uncertainty and combined standard uncertainty; The pre-stage analytical propagation based on the GUM concept, the Monte Carlo propagation in the nonlinear uncertainty propagation section, and the post-stage analytical propagation based on the GUM concept are interconnected through the inter-layer information transfer between the pre-stage and post-stage stages, forming a fused uncertainty propagation chain.

[0021] Furthermore, in step 1, a multi-stage measurement model is established based on the original measurement data and the data processing relationships of the complex measurement system. The complex measurement system comprises multiple series, parallel, or coupled measurement processing steps, and at least one measurement processing step includes nonlinear function operations, variable coupling, matrix transformation, coordinate transformation, iterative calculation, inversion calculation, or piecewise calculation.

[0022] Further, in step 2, the nonlinear propagation sub-model is determined according to at least one of the following conditions: Includes trigonometric functions, exponential functions, logarithmic functions, or non-integer power functions; Multiplication, division, or coupling operations involving two or more uncertain inputs that have a non-negligible nonlinear effect on the output distribution; Includes operations on coordinate transformation matrices, rotation matrices, or multi-component matrices; It includes iterative, inversion, optimization, or implicit solution processes; or it is designated as a measurement processing step that uses probability distribution propagation according to preset rules.

[0023] Furthermore, in step 3, the deviation limit B The component is determined by at least one of the following: instrument indication error, calibration error, installation error, environmental correction error, model correction error, and geometric dimension error; the accuracy limit is... P The component is determined by at least one of repeated measurement discreteness, short-term random fluctuations, and data acquisition noise.

[0024] Furthermore, when the first i The deviation limit of each input quantity is And the conversion factor corresponding to its probability distribution is At that time, its B The standard uncertainty of the component is: ; When the i The repeated measures sample standard deviation of the input quantities is: s i The number of repeated measurements is n i At that time, its P The standard uncertainty of the component is: .

[0025] Furthermore, in step 5, within the nonlinear uncertainty propagation region, for B Components and P Each component is subjected to at least one million Monte Carlo samplings; each B During component propagation, P The component remains at its center value or is not introduced. P Component random perturbation; each time P During component propagation, B The component remains at its center value or is not introduced. B The components are subject to random perturbation.

[0026] Furthermore, in step 5, let the stated B The component propagation output sample set is The above P The component propagation output sample set is , Then calculate separately B Component propagation estimate , P Component propagation estimate and the corresponding sample standard deviation , , and according to Determine the output estimate for the section.

[0027] Furthermore, in step 7, the post-stage analytical propagation method based on the GUM concept, according to the sensitivity coefficient of the target output to each input, applies the following to each input: B Component standard uncertainty and P The component standard uncertainties are summed and combined to obtain the target output quantity. B Component standard uncertainty and P Component standard uncertainty ,according to Obtain the composite standard uncertainty based on the preset coverage factor. according to Obtain the expanded uncertainty of the target output and output the estimated value of the target output. B Component standard uncertainty P At least one of component standard uncertainty, combined standard uncertainty, and expanded uncertainty.

[0028] Furthermore, the complex measurement system is a wind tunnel force measurement test system; the inputs of the wind tunnel force measurement test system include at least the balance output voltage signal, model attitude angle, total pressure, static pressure, and model geometric parameters; the target outputs include at least one of the drag coefficient, lift coefficient, side force coefficient, roll moment coefficient, yaw moment coefficient, and pitch moment coefficient; the pre-stage uncertainty propagation section includes balance calibration conversion and attitude angle correction; the nonlinear uncertainty propagation section includes the coordinate transformation of the load from the balance axis system through the model axis system to the wind axis system; and the post-stage uncertainty propagation section includes dynamic pressure calculation, aerodynamic coefficient normalization calculation involving model geometric parameters, and aerodynamic coefficient uncertainty synthesis.

[0029] Example 2: A method for evaluating the fusion uncertainty of complex measurement systems, such as Figure 1 As shown, it includes the following steps: Step 1: Establish a multi-stage measurement model for wind tunnel force measurement tests; Step 2: Determine the propagation segment in the multi-stage measurement model; Step 3, perform the input quantities of the multi-stage measurement model. B / P Modeling of two-component uncertainty; Step 4: Analytical propagation based on the GUM concept is adopted in the uncertainty propagation section of the preceding stage; Step 5, in the nonlinear uncertainty propagation section, respectively... B Components and P The components undergo Monte Carlo propagation; Step 6, for the nonlinear uncertainty propagation section B Components and P The data after component sampling and propagation are statistically analyzed to determine the output of the nonlinear uncertainty propagation section and the inter-layer information transmitted in the subsequent stages. Step 7: In the subsequent uncertainty propagation section, analytical propagation and uncertainty synthesis based on the GUM concept are adopted.

[0030] Furthermore, step 1 includes the following steps: Step 1.1: Determine the raw input quantities, intermediate quantities for measurement and processing, and target output quantities for the wind tunnel force measurement test. The raw input quantities shall include at least: (1) Balance output voltage signal vector ; (2) Model attitude angle measurements; (3) Total pressure output by the pressure sensor and static pressure ; (4) Model reference area S ; (5) Model reference span ; (6) Model reference chord length ; The torque reference point translation, support disturbance correction, or other additional corrections.

[0031] The intermediate quantities for the measurement processing include at least: (1) Load vector of balance axis system ; (2) Corrected model attitude angle vector ; (3) Wind axis load vector ; (4) Wind tunnel test dynamic pressure .

[0032] The target output is an aerodynamic coefficient vector: ; In the formula, The drag coefficient, The lift coefficient, This is the lateral force coefficient. This is the rolling moment coefficient. This is the yaw moment coefficient. This is the pitching moment coefficient.

[0033] Step 1.2: Establish measurement sub-models for each measurement and processing stage based on the data processing flow of the wind tunnel force measurement test. (1) Establish a balance calibration conversion model. Based on the balance calibration results, convert the balance output voltage signal vector... Converted to balance shaft system load vector : ; in: ; In the formula, These represent the force components in the three directions of the balance axis system. These are the torque components in the three directions of the balance axis system; This refers to the balance calibration conversion model established based on the balance calibration coefficients, calibration matrix, or calibration fitting model.

[0034] (2) Establish an attitude angle correction model. Based on the angle sensor measurements, model installation angle, airflow deflection angle, and other attitude correction values, determine the angle vector used for load coordinate transformation: ; In the formula, For the angle of attack, Sideslip angle, Correct the model's mounting angle, airflow deflection angle, or other attitude angles.

[0035] (3) Establish the load coordinate transformation model. The loads of the balance axis system are sequentially transformed to the model axis system and the wind axis system. The load coordinate transformation model is expressed as: ; Further expressed as: ; In the formula, This represents the load vector of the wind shaft system. This is the load transformation matrix from the balance axis system to the model axis system. This is the load transformation matrix from the model shaft system to the wind shaft system. This is for torque reference point translation, support disturbance correction, or other additional load correction items.

[0036] The load coordinate transformation model includes trigonometric functions, rotation matrices, matrix multiplication, and the coupling between load components and attitude angles, and belongs to the nonlinear propagation sub-model in this embodiment.

[0037] (4) Establish a dynamic pressure measurement model. Based on the total pressure, static pressure, and corresponding pressure correction parameters, establish a dynamic pressure measurement model: ; in: ; In the formula, For total pressure, For static pressure, q For dynamic pressure, This is a dynamic pressure calculation model established based on the relationship of wind tunnel flow field parameters.

[0038] (5) Establish a normalized aerodynamic coefficient model. Calculate the aerodynamic coefficients based on the wind shaft load, dynamic pressure, and model geometric parameters: ; in: ; The normalized matrix can be represented as: ; Step 1.3: Connect the various measurement sub-models according to the propagation sequence of the measurement information to form a multi-stage measurement model for the wind tunnel force measurement test: ; in: ; This results in a complete multi-stage measurement model, from the original measurements to the aerodynamic coefficients.

[0039] Furthermore, step 2 includes the following steps: Step 2.1: Analyze the functional form, variable coupling relationship and uncertainty propagation characteristics of each processing step, including balance calibration conversion, attitude angle correction, load coordinate transformation, dynamic pressure calculation and aerodynamic coefficient normalization. Step 2.2, the process of converting the load from the balance axis system to the wind axis system is determined as a nonlinear uncertainty propagation sub-model; Furthermore, the nonlinear uncertainty propagation sub-model is as follows: ; Since the transformation matrix is ​​related to the angle of attack, sideslip angle and installation correction angle, and includes trigonometric functions, matrix operations and multi-load component coupling, it is not suitable to use only a fixed sensitivity coefficient for propagation. Therefore, it is determined to be the nonlinear uncertainty propagation sub-model in this embodiment.

[0040] Step 2.3: The balance calibration and attitude angle correction located upstream of the load coordinate transformation model are determined as the pre-stage uncertainty propagation segment; Step 2.4, the process of transferring the load from the balance axis system to the wind axis system is defined as the nonlinear uncertainty propagation section; Step 2.5 defines the dynamic pressure calculation, the normalized calculation involving model geometric parameters, and the aerodynamic coefficient uncertainty synthesis as the subsequent uncertainty propagation section.

[0041] Furthermore, step 3 includes the following steps: Step 3.1: Identify the input quantities and their uncertainty sources in the preceding uncertainty propagation section, the nonlinear uncertainty propagation section, and the subsequent uncertainty propagation section, as shown in Table 1.

[0042] Table 1: ; Step 3.2 identifies the sources of uncertainty, including instrument indication error, balance calibration error, model installation error, angle correction error, airflow deflection angle correction error, and other sources with systematic characteristics. B Quantity; Step 3.3 identifies the sources of uncertainty, including repeated measurement discreteness, short-term random fluctuations, data acquisition noise, and other uncertainties with random characteristics, as follows: P Quantity; Step 3.4: Based on the statistical characteristics of each source of uncertainty, determine... B Components and P The probability distribution type and probability distribution parameters corresponding to the components, wherein the probability distribution includes at least one of normal distribution, uniform distribution, triangular distribution, arcsine distribution and empirical distribution; Step 3.5: Determine the estimated values ​​of each input quantity, and assign them accordingly. B Components and P Components are converted to standard uncertainty; Furthermore, when the first i The deviation limit of each input quantity is The conversion factor corresponding to its probability distribution is At that time, the input quantity B The standard uncertainty of the component is: ; When the i The repeated measures sample standard deviation of the input quantities is: The number of repeated measurements is At that time, the input quantity P The standard uncertainty of the component is: .

[0043] Furthermore, step 4 includes the following steps: Step 4.1, calculate the intermediate quantity estimate. Input the balance output voltage signal into the balance calibration conversion model to obtain the estimated value of the balance shaft load: ; Input the original attitude angle, model mounting angle, and airflow deflection correction value into the attitude angle correction model to obtain the corrected attitude angle estimate: ; The intermediate quantity of the propagation section of the preceding uncertainty is expressed as: ; Step 4.2, determine the sensitivity coefficient. For the first... j intermediate quantity and the i Each pre-stage input Determine the sensitivity coefficient: ; The sensitivity coefficient is obtained through analytical differentiation or numerical calculation; Step 4.3, propagate separatelyB Components and P Quantity Based on each input quantity B Component standard uncertainty, calculation of intermediate quantities of B Component standard uncertainty: ; Based on each input quantity P Component standard uncertainty, calculation of intermediate quantities of P Component standard uncertainty: ; This allows us to obtain the load components and attitude angles of the balance axis system. B Component standard uncertainty and P Component standard uncertainty; Step 4.4: Generate inter-layer transfer information. This involves identifying and estimating the variable labels and attitude angles of the balance axis loads and corrected attitude angles. B Component standard uncertainty P The component standard uncertainty, probability distribution type, and probability distribution parameters are encapsulated to form information transmitted between the preceding layers: ; The inter-layer information transfer from the preceding stage is performed as step 5 in the nonlinear uncertainty propagation region. B Components and P Input of component Monte Carlo propagation.

[0044] Furthermore, step 5 includes the following steps.

[0045] Step 5.1, based on the estimated values ​​of the balance shaft load and the corrected attitude angle, B The standard uncertainty of the components and their corresponding probability distributions are used to generate the first... r Group B Component random samples: ; in, Number of samplings M No less than one million times; Step 5.2, proceed B Component nonlinear propagation, in B During component propagation, P The component remains at the center value or is not introduced. P Random perturbation of components, B Component random sample input load coordinate transformation sub-model: ; go through MSecondary dissemination, obtaining B Component propagation output sample set: ; Step 5.3, based on the estimated values ​​of the balance shaft load and the corrected attitude angle, P The standard uncertainty of the components and their corresponding probability distributions are used to generate the first... r Group P Component random samples: ; Step 5.4, proceed P Component nonlinear propagation, in P During component propagation, B The component remains at the center value or is not introduced. B Random perturbation of components, P Component random sample input load coordinate transformation sub-model: ; go through M Secondary dissemination, obtaining P Component propagation output sample set: ; Step 5.5, will B Component propagation output sample set and P Component propagation output sample set The output is sent to step 6 for calculating the wind shaft loads. B Component propagation estimate P Component propagation estimates and corresponding standard uncertainties.

[0046] Furthermore, step 6 includes the following steps: Step 6.1, Statistics B Component propagation output sample set, for the first j Each wind shaft load component is assumed to be... B The component propagation output samples are: ; but B The component propagation estimate is: ; B The standard uncertainty of the component is: ; Step 6.2, Statistics P Component propagation output sample set, let the first... j individual wind shaft load components P The component propagation output samples are: ; but P The component propagation estimate is: ; P The standard uncertainty of the component is: ; Step 6.3, according to B Component propagation estimates and P The component propagation estimate determines the first j The section output estimates of the load components of the wind shaft system are preferably obtained by using the arithmetic mean: ; This yields the estimated output vector for the wind shaft load section: ; Step 6.4, forming the information transfer between subsequent layers. The estimated values ​​of each load component of the wind shaft system are output in sections. B Component standard uncertainty and P The component standard uncertainty is encapsulated to form information for inter-layer transmission in subsequent stages: ; The information transmitted between subsequent layers serves as the input for step 7, which involves calculating aerodynamic coefficients and synthesizing uncertainties in the uncertainty propagation section of the subsequent layer.

[0047] Furthermore, step 7 includes the following steps: Step 7.1, establish the input quantity for the next stage. B / P Two-component information. The inputs to the subsequent uncertainty propagation section include: ; Among them, the estimated values ​​of total pressure, static pressure, and model geometric parameters, B Component standard uncertainty and P The standard uncertainty of the components is obtained from step 3; the estimated value of the wind shaft load, B Component standard uncertainty and P The component standard uncertainty is obtained from step 6; Step 7.2, calculate the estimated aerodynamic coefficients. Calculate the dynamic pressure based on the total pressure and static pressure: ; Substitute the estimated values ​​of wind shaft load, dynamic pressure, and model geometric parameters into the aerodynamic coefficient measurement model: ; The estimated values ​​of drag coefficient, lift coefficient, lateral force coefficient, and various moment coefficients are obtained. Step 7.3, calculate the sensitivity coefficient of the input quantity, for the first... k aerodynamic coefficient Let the input quantity in the subsequent uncertainty propagation section be... Its sensitivity coefficient is: ; Step 7.4, propagate separately B Components and P Components, aerodynamic coefficient of B The standard uncertainty of the component is: ; P The standard uncertainty of the component is: ; Step 7.5, calculate the combined standard uncertainty. Based on aerodynamic coefficient B Component standard uncertainty and P Component standard uncertainty, calculate combined standard uncertainty: ; Expanded uncertainty is calculated according to a preset inclusion factor. calculate: ; Step 7.6: Output the estimated values ​​of each aerodynamic coefficient. B Component standard uncertainty P Use at least one of the component standard uncertainty, combined standard uncertainty, and expanded uncertainty to complete the uncertainty assessment of wind tunnel force measurement test results.

[0048] With drag coefficient Lift coefficient Pitch moment coefficient Taking the three results as an example, in the typical angle of attack The uncertainty assessment results of the lower aerodynamic coefficients are shown in Table 2, including the estimated values, B Corresponding standard uncertainty P The corresponding standard uncertainty and combined standard uncertainty. The combined standard uncertainty at different angles of attack is represented by a line graph, such as... Figure 2 .

[0049] Table 2: ; As shown in Table 2, this invention can retain the commonly used methods in wind tunnel testing while completing the nonlinear propagation of load coordinate transformation.B / P Two-component representation. Lift coefficient. The combined standard uncertainty is 0.00126, which is relatively large among the three aerodynamic coefficients. This indicates that the uncertainty level of the lift coefficient is relatively high under this operating condition, possibly related to the rapid change of lift load with angle of attack and the influence of attitude angle correction. (Drag coefficient) The combined standard uncertainty is 0.00063, and the pitching moment coefficient is... The combined standard uncertainty is 0.00082, which is on the small order of magnitude.

[0050] Depend on Figure 2 It can be seen that the standard uncertainty of each aerodynamic coefficient changes to varying degrees with the angle of attack. Among them, and The standard uncertainty varies significantly with the angle of attack, indicating that the lift coefficient and pitching moment coefficient are quite sensitive to changes in angle of attack, load distribution, and coordinate transformation. The relatively smooth change in standard uncertainty indicates that the drag coefficient uncertainty has good stability within the selected angle of attack range. Therefore, this invention can practically obtain evaluation outputs that conform to industry standards and relatively objectively reflect the impact of actual angle of attack variations on the evaluation results.

[0051] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for evaluating the fusion uncertainty of complex measurement systems, characterized in that, Includes the following steps: Step 1: Obtain raw measurement data to characterize the physical quantities of the object being measured and establish a multi-stage measurement model; Step 2: Divide the multi-stage measurement model into at least one pre-stage uncertainty propagation segment, at least one nonlinear uncertainty propagation segment, and at least one post-stage uncertainty propagation segment, wherein the pre-stage uncertainty propagation segment is located upstream of the nonlinear uncertainty propagation segment, the post-stage uncertainty propagation segment is located downstream of the nonlinear uncertainty propagation segment, and the nonlinear uncertainty propagation segment contains at least one nonlinear propagation sub-model. Step 3: Identify the input quantities and their uncertainty sources in the preceding uncertainty propagation segment, the nonlinear uncertainty propagation segment, and the subsequent uncertainty propagation segment, and divide the uncertainty of each input quantity into deviation limits. B Component and precision limits P Components, and respectively determine the estimated value of the input quantity, B Component standard uncertainty P Component standard uncertainty and corresponding probability distribution; Step 4: In the preceding uncertainty propagation section, a preceding analytical propagation method based on the Guide to Measurement Uncertainty (GUM) is used to obtain intermediate quantity estimates as inputs to the nonlinear uncertainty propagation section. B Component standard uncertainty P The standard uncertainty of the components and their corresponding probability distributions form the information transmitted between the preceding layers. Step 5: Based on the inter-layer transfer information from the preceding layers, perform [further steps] in the nonlinear uncertainty propagation section. B Components and P Each component generates a random sample, and these random samples are then input into the nonlinear propagation sub-model for Monte Carlo propagation to obtain the results. B Component propagation output sample set and P Component propagation outputs the sample set; Step 6, respectively for the... B Component propagation output sample set and the P Statistical analysis is performed on the component propagation output sample set to obtain the output quantity of the nonlinear uncertainty propagation segment. B Component propagation estimate P Component propagation estimate B Component standard uncertainty and P Component standard uncertainty, and according to the above B Component propagation estimate and the P The component propagation estimate determines the segment output estimate of the output of the nonlinear uncertainty propagation segment, forming the subsequent inter-layer transmission information; Step 7: Input the inter-level transfer information and the uncertainty information of other input quantities in the subsequent uncertainty propagation section into the subsequent uncertainty propagation section, and propagate and synthesize them separately using the subsequent analytical propagation method based on the GUM concept. B Components and P Components, to obtain an estimate of the target output quantity, B Component standard uncertainty P Component standard uncertainty and combined standard uncertainty; The pre-stage analytical propagation based on the GUM concept, the Monte Carlo propagation in the nonlinear uncertainty propagation section, and the post-stage analytical propagation based on the GUM concept are interconnected through the inter-layer information transfer between the pre-stage and post-stage stages, forming a fused uncertainty propagation chain.

2. The method according to claim 1, characterized in that, In step 1, a multi-stage measurement model is established based on the original measurement data and the data processing relationships of the complex measurement system. The complex measurement system comprises multiple series, parallel, or coupled measurement processing steps, and at least one measurement processing step includes nonlinear function operations, variable coupling, matrix transformation, coordinate transformation, iterative calculation, inversion calculation, or piecewise calculation.

3. The method according to claim 1, characterized in that, In step 2, the nonlinear propagation sub-model is determined according to at least one of the following conditions: Includes trigonometric functions, exponential functions, logarithmic functions, or non-integer power functions; Multiplication, division, or coupling operations involving two or more uncertain inputs that have a non-negligible nonlinear effect on the output distribution; Includes operations on coordinate transformation matrices, rotation matrices, or multi-component matrices; It includes iterative, inversion, optimization, or implicit solution processes; or it is designated as a measurement processing step that uses probability distribution propagation according to preset rules.

4. The method according to claim 1, characterized in that, In step 3, the deviation limit B component is determined by at least one of the following: instrument indication error, calibration error, installation error, environmental correction error, model correction error, and geometric dimension error; the accuracy limit P The component is determined by at least one of repeated measurement discreteness, short-term random fluctuations, and data acquisition noise.

5. The method according to claim 4, characterized in that, When the i The deviation limit of each input quantity is And the conversion factor corresponding to its probability distribution is At that time, its B The standard uncertainty of the component is: ； When the i The repeated measures sample standard deviation of the input quantities is: s i The number of repeated measurements is n i At that time, its P The standard uncertainty of the component is: 。 6. The method according to claim 1, characterized in that, In step 5, within the nonlinear uncertainty propagation region, for B Components and P Each component was sampled at least one million Monte Carlo samples. every time B During component propagation, P The component remains at its center value or is not introduced. P Component random perturbation; every time P During component propagation, B The component remains at its center value or is not introduced. B The components are subject to random perturbation.

7. The method according to claim 1, characterized in that, In step 6, let the... B The component propagation output sample set is The above P The component propagation output sample set is , Then calculate separately B Component propagation estimate , P Component propagation estimate and the corresponding sample standard deviation , , and according to Determine the output estimate for the section.

8. The method according to claim 1, characterized in that, In step 7, the post-stage analytical propagation method based on the GUM concept, according to the sensitivity coefficient of the target output to each input, applies the following to each input: B Component standard uncertainty and P The component standard uncertainties are summed and combined to obtain the target output quantity. B Component standard uncertainty and P Component standard uncertainty ,according to Obtain the composite standard uncertainty based on the preset coverage factor. according to Obtain the expanded uncertainty of the target output and output the estimated value of the target output. B Component standard uncertainty P At least one of component standard uncertainty, combined standard uncertainty, and expanded uncertainty.

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