Sequential test design method for aircraft based on expected probability box overall improvement criterion

Abstract

The present invention relates to the technical field of aircraft test design, and in particular to an aircraft sequential test design method based on an overall improvement criterion of an expected probability box, specifically comprising the following steps: S1, initial test design, obtaining a sample set that affects the output results in the aircraft test; S2, establishing a proxy model using a Gaussian process regression model based on information from a known sample set D; S3, on the basis of the established proxy model, determining the next test sample point based on a sampling criterion corresponding to the overall improvement of the expected probability box; S4, calculating the true response of the aircraft at the test sample point and updating the sample set; S5, determining whether the test stopping criterion is met, and if so, outputting the final proxy model; if not, repeating the operations of S2-S5. The present invention can quantify the uncertainty in the aircraft test, select the most valuable sample points in combination with the sampling criterion of the overall improvement of the probability box, so as to improve the overall accuracy of the proxy model and provide a more reliable basis for aircraft design.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft test design, in particular to a sequential test design method for aircraft equipment, and more particularly to a test design method based on an overall improvement of the expected probability box (P-box), which is used to process and analyze uncertainties in aircraft tests and optimize test resources. Background Art

[0002] In flight test design, aircraft performance verification is a crucial step in ensuring its safety, stability, and reliability. Aircraft equipment testing often faces various uncertainties, originating from a wide range of sources, including geometric uncertainty, payload uncertainty, environmental uncertainty, cognitive uncertainty, and material uncertainty. This uncertainty impacts both the assessment of aircraft performance and the accuracy of test results. Furthermore, common input variables in aircraft testing include environmental parameters, aircraft state, control inputs, structural and mass parameters, powertrain parameters, flight mission and control strategy, external disturbances, and system state parameters. All of these input variables interact to influence the aircraft's flight performance, stability, and mission accomplishment.

[0003] In aircraft design experiments, critical issues require extremely high accuracy from the entire surrogate model. For example, in aircraft aerodynamic performance evaluation, a surrogate model may be needed to predict parameters such as the lift coefficient and drag coefficient under different flight conditions. The accurate prediction of these performance parameters directly impacts the feasibility and safety of the aircraft design. If the surrogate model fails to accurately fit the aircraft's performance characteristics, test results may contain significant errors, leading to incorrect design decisions and even compromising the aircraft's actual flight performance. Furthermore, when conducting multi-objective aircraft optimization, such as finding the optimal compromise between fuel efficiency, maneuverability, and flight stability, an accurate surrogate model can help designers identify the optimal operating range, avoiding blind and inefficient design. Therefore, a key task in design experiments is to improve the overall accuracy of the surrogate model by rationally selecting sampling points, thereby providing a more reliable basis for aircraft design.

[0004] In actual aircraft tests, test resources are usually limited, and the purpose of test design is to maximize the acquisition of information under limited test resources. The sequential test design method was proposed to solve this problem. When solving this problem, the existing sequential test design methods usually rely on the predicted value of the surrogate model and its uncertainty to guide the selection of sampling points. However, common sampling point criteria (the minimum value criterion of the objective function (MP criterion), the expected improvement criterion (EI criterion) and the lower bound criterion of the confidence interval (LCB criterion)) usually only focus on the response value and its uncertainty, while ignoring the need to improve the overall accuracy of the surrogate model. Specifically, the traditional sequential test method faces the following problems:

[0005] (1) Over-focus on local accuracy: Traditional methods often focus on the fitting accuracy of individual sample points, ignoring the improvement of global accuracy. Although the surrogate model can fit well near certain sample points, if the sample points are unevenly distributed or fail to cover the key areas of the design space, the accuracy of the entire surrogate model will still be low.

[0006] (2) Failure to consider the range of uncertainty: Traditional sampling criteria often rely on the proxy model’s prediction of the response value without fully considering the overall range of the model’s prediction uncertainty. This results in the model being unable to reflect all potential system uncertainties and accurately capture the randomness and cognitive errors in the aircraft system.

[0007] (3) Ignoring the mutual influence between sampling points: Traditional methods often rely solely on the posterior distribution of a single point to select sampling points, ignoring the possible interactions between sampling points, resulting in the neglect of certain key areas and affecting the global fitting ability of the surrogate model.

[0008] In the design of aircraft tests, the establishment of surrogate models is often the core of test optimization. Surrogate models approximate the complex behavior of aircraft systems using limited test data, thereby providing designers with guidance for predicting and optimizing aircraft performance. Surrogate models can be constructed based on various mathematical methods, such as Gaussian process regression (GPR) and support vector regression (SVR), each with its own advantages and disadvantages. However, in actual aircraft test design, especially in the optimization of complex aircraft systems, accuracy requirements are often extremely high. In such cases, the goal of test design is not simply to obtain a rough prediction using a surrogate model; rather, a precise surrogate model is required to accurately reflect key characteristics such as the aircraft's dynamic behavior, aerodynamic performance, and structural response. This is crucial for tasks such as aircraft performance evaluation, optimal design, and fault prediction. To achieve this goal, test design must be able to identify and select the most valuable sample points to maximize the accuracy of the surrogate model within limited test resources.

[0009] The P-box model combines traditional probability distribution models with interval models. Its core concept is to characterize the uncertainty of system parameters through the cumulative distribution function (CDF) with upper and lower bounds. Compared with traditional single probability distribution models, the P-box model can simultaneously handle both aleatory and epistemic uncertainty, providing a more conservative and tolerant bound. This enables P-box to provide more comprehensive analysis results in complex scenarios with multiple uncertainties.

[0010] Therefore, in order to more effectively deal with the uncertainty of input variables in aircraft tests, the present invention introduces a probability box (P-box) model and proposes an experimental design method based on the overall improvement of the expected probability box (P-box). In flight test design, the application of the P-box model can provide a new perspective to quantify and analyze uncertainty. By incorporating random uncertainty (such as material properties, geometric size variations) and cognitive uncertainty (such as the subjective lack of understanding of designers) into a unified framework, the P-box model helps to more comprehensively evaluate the uncertainty in equipment tests. This not only helps to optimize the design process and reduce costs, but also improves the efficiency of flight tests and the accuracy of results. Through this comprehensive uncertainty analysis method, the performance of equipment in actual use can be more accurately predicted, thereby improving the performance and reliability of the equipment and ensuring the scientific nature and practicality of flight test design. Summary of the Invention

[0011] The purpose of the present invention is to provide an aircraft sequential test design method based on the overall improvement criterion of the expected probability box. The core of this method is to quantify the uncertainty in the aircraft test by introducing the expected probability box (P-box) model, and to select the most "valuable" sample points in combination with the sampling point criterion of the overall improvement of the probability box. By reasonably selecting the sampling points, the overall accuracy of the proxy model is improved, thereby providing a more reliable basis for aircraft design.

[0012] To achieve the above object, the technical solution adopted by the present invention is:

[0013] The present invention provides an aircraft sequential test design method based on an expected probability box overall improvement criterion, comprising the following steps:

[0014] S1. Initial test design: obtain the sample set D that affects the output of the aircraft test, where D = (X, y);

[0015]

[0016] Where each row of X represents a sample point, x represents the input variable for evaluating the output results in the aircraft test, d represents the dimension of the spatial parameter, n represents the sample size, and y represents the output results of the aircraft test;

[0017] Outputs of the aircraft test include, but are not limited to, speed, acceleration, altitude, air pressure, temperature, thrust, fuel consumption, attitude, heading, and vibration and structural stress;

[0018] S2. Based on the information of the known sample set D, a Gaussian process regression model (GPR) is used to establish a proxy model f(X), y = f(X);

[0019] S3. Based on the established proxy model, the next test sample point is determined according to the sampling point criterion corresponding to the overall improvement criterion of the expected probability box;

[0020] The formula of the sampling point criterion is:

[0021]

[0022] in, and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with sample size n; and They represent the minimum standard deviation and maximum standard deviation of the prediction of the proxy model constructed by the sample set with sample size n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with a sample size of n+1; and They represent the minimum standard deviation and maximum standard deviation of the proxy model prediction constructed by the sample set with a sample size of n+1; k represents the variable that balances the prediction mean and prediction standard deviation,

[0023] S4. Calculate the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and update the sample set;

[0024] S5. Determine whether the test stopping criteria are met. If so, output the final proxy model; if not, repeat the operations of S2-S5.

[0025] Furthermore, the input variables include but are not limited to environmental parameters, aircraft state parameters, control input parameters, structure and mass parameters, power system parameters, flight mission and control strategy, external disturbances and system state parameters.

[0026] Furthermore, the environmental parameters include but are not limited to temperature, humidity, air pressure, wind speed and wind direction.

[0027] Furthermore, the state parameters of the aircraft include but are not limited to speed (airspeed and ground speed), flight altitude, angle of attack, yaw angle, pitch angle and roll angle.

[0028] Furthermore, the control input parameters include but are not limited to control surface angles, engine thrust, and pilot control inputs.

[0029] Furthermore, the structure and mass parameters of the aircraft include but are not limited to mass distribution, center of gravity position and moment of inertia.

[0030] Furthermore, the power system parameters include but are not limited to the engine thrust output, fuel consumption rate and multi-engine power distribution.

[0031] Furthermore, the flight mission and control strategy include but are not limited to trajectory planning, input to the autopilot system, and guidance of the aircraft's flight path and mission execution.

[0032] Furthermore, the external disturbance includes but is not limited to airflow disturbance, turbulence and the influence of ground obstacles.

[0033] Furthermore, the system status parameters include but are not limited to sensor input and fault detection signals.

[0034] Furthermore, the proxy model is

[0035] f(x)~GP(μ(x),K(x,x')),

[0036] Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x);

[0037] The predicted mean of the surrogate model is:

[0038]

[0039] in, Represents the new point x * The predicted mean at μ(x * ) represents the new point x * The prior mean at K(x * ,X) represents the new point x * and the covariance vector between all known points X; K(X,X) represents the covariance matrix between all known points X, is the variance of the noise, representing the random error in the observation data, E represents the unit matrix, and y represents the observation value vector corresponding to the known point X;

[0040] The prediction variance of the surrogate model is

[0041]

[0042] in, Represents the new point x *The prediction variance at K(x * ,x * ) represents the new point x * Its own covariance vector; K(X,x * ) represents all known points X and new points x * The covariance vector between .

[0043] Furthermore, the area of ​​the probability box is used as the uncertainty measure unc(·) of the output of the proxy model, then

[0044]

[0045] in, and Both represent the upper bound cumulative distribution function (CDF) of the probability box, F and F Y (y) represents the lower bound cumulative distribution function (CDF) of the probability box, The upper and lower bounds of the probability box represent the distance between the cumulative distribution functions and are often used to measure uncertainty;

[0046] The probability density distributions corresponding to the upper and lower boundaries of the probability box are N(μ1,σ1 2 ), N(μ2,σ2 2 ), the area of ​​the probability box is calculated in two cases:

[0047] When the predicted means are the same but the predicted variances are different, that is, μ1=μ2 and σ2>σ1,

[0048]

[0049] When the prediction variances are the same but the prediction means are different, that is, μ1<μ2 and σ1=σ2,

[0050] unc(·)=μ2-μ1.

[0051] The present invention also provides an application of an aircraft sequential test design method based on an expected probability box overall improvement criterion in the prediction and multi-objective optimization of aircraft performance, aircraft stability, and mission completion evaluation.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention can consider the overall uncertainty range. The sampling criteria for the overall improvement of the expected probability box not only focus on the predicted response value and uncertainty of each sample point, but also consider the entire range of predicted response values ​​and the corresponding uncertainty range. Through the probability box model, the present invention can describe the random uncertainty (such as material properties, geometric changes, etc.) and epistemic uncertainty (such as design assumptions, model errors, etc.) in aircraft tests, thereby providing comprehensive information for sampling point selection. As a result, the sampling points can not only improve the accuracy of a certain local area, but also improve the accuracy of the proxy model as a whole.

[0054] 2. This invention optimizes the accuracy of the proxy model. The sampling criteria of this invention specifically focus on improving the overall accuracy of the proxy model. In aircraft test design, different sampling points have varying impacts on the model's fit, with some being more valuable for improving model accuracy. Therefore, by improving the overall expected probability box, this invention selects the sample points that are most valuable for improving the accuracy of the proxy model. These sample points cover key areas in the design space, ensuring the global fit of the proxy model and, in turn, making the model's predictions of aircraft performance more accurate.

[0055] 3. The present invention can flexibly handle multiple sources of uncertainty. Aircraft test design often faces multiple types of uncertainty, including physical uncertainty and cognitive uncertainty. Through the probability box model, the present invention can flexibly handle these multiple sources of uncertainty and incorporate them into the sampling criteria. This not only improves the reliability of the proxy model but also makes the selection of sampling points more in line with actual conditions. For example, when faced with complex aircraft systems, the model may have large uncertainties. It is expected that the overall improved sampling criteria of the probability box can help designers better identify key areas and conduct effective sampling.

[0056] 4. The present invention can efficiently utilize limited resources. In aircraft test design, test resources are usually limited. Therefore, how to obtain as much effective information as possible within limited test resources is the key to optimizing the design. The sampling point criterion for the overall improvement of the expected probability box can effectively reduce redundant tests by optimizing the sampling strategy, focusing on key points that can maximize the accuracy of the proxy model. Through this method, the present invention can not only reduce the number of tests, but also ensure the efficient use of test data, thereby reducing test costs and improving test efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Flowchart of a method for sequential test design of an aircraft based on an expected probability box overall improvement criterion provided by an embodiment of the present invention;

[0058] Figure 2 is a probability box based on GPR provided by an embodiment of the present invention;

[0059] Figure 3 These are two special probability boxes based on GPR provided by the embodiments of the present invention (a is the case where all predictions of the proxy model have the same mean but different standard deviations, i.e., μ1=μ2 and σ2>σ1; b is the case where all predictions of the proxy model have the same standard deviation but different means, i.e., μ1<μ2 and σ1=σ2);

[0060] Figure 4 The HEG cylindrical half model and computational grid provided by the embodiment of the present invention;

[0061] Figure 5 It is the shock wave position comparison provided by the embodiment of the present invention;

[0062] Figure 6 is the wall pressure distribution provided by the embodiment of the present invention;

[0063] Figure 7 is the wall heat flux distribution provided by the embodiment of the present invention;

[0064] Figure 8 This is a comparison of the results of various criteria for 20 sequential samplings with different initial sample points provided by an embodiment of the present invention (a is the test result with the initial sample point being 120 and the root mean square error (RMSE) being the measurement indicator; b is the test result with the initial sample point being 120 and the minimum absolute difference being the measurement indicator; c is the test result with the initial sample point being 100 and the root mean square error (RMSE) being the measurement indicator; d is the test result with the initial sample point being 100 and the minimum absolute difference being the measurement indicator). DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0066] The implementation of the present invention is described in detail below with reference to specific embodiments.

[0067] like Figure 1 As shown, the present invention provides an aircraft sequential test design method based on the expected probability box overall improvement criterion, comprising the following steps:

[0068] S1. Initial test design: obtain the sample set D that affects the output of the aircraft test, where D = (X, y);

[0069]

[0070] Where each row of X represents a sample point, x represents the input variable for evaluating the output results in the aircraft test, d represents the dimension of the spatial parameter, and n represents the sample size;

[0071] It's important to note that aircraft testing is a critical component of aerospace engineering. It comprehensively evaluates the aircraft's performance, structure, and powertrain to ensure its safety, stability, and efficiency in actual operation. During aircraft testing, output variables are a crucial component of test data. They not only help engineers understand the aircraft's operating status but also provide important insights for design optimization and troubleshooting. Key output variables in aircraft testing include velocity and acceleration, altitude and pressure, temperature, thrust and fuel consumption, attitude and heading, vibration, and structural stress.

[0072] Aircraft velocity and acceleration are among the most fundamental and important output variables. Velocity includes horizontal velocity, vertical velocity, and relative velocity. Horizontal velocity influences the aircraft's directional stability, while vertical velocity is often directly related to the aircraft's lift system (such as wings or engine thrust). Aircraft acceleration is typically measured using acceleration sensors (such as gyroscopes and accelerometers).

[0073] An aircraft's flight altitude and air pressure are output variables closely related to flight performance. Altitude not only affects the aircraft's flight path and range, but also directly impacts engine performance and aerodynamics. The external air pressure of an aircraft is typically inversely proportional to its flight altitude.

[0074] Temperature is an important output variable in aircraft testing, particularly related to engine performance, aerodynamic characteristics, and the durability of the aircraft structure. Aircraft temperature monitoring typically includes: external temperature, engine temperature, and fuselage temperature.

[0075] Thrust is a key output variable of an aircraft's propulsion system, directly affecting its liftoff capability, flight speed, and range. Thrust data is typically monitored by the engine control system and fed back to ground control via sensors. Fuel consumption is a crucial metric for evaluating aircraft economy and range. During aircraft testing, fuel consumption is often correlated with factors such as altitude, speed, and engine type. By monitoring fuel consumption, aircraft operating strategies can be optimized to reduce fuel consumption.

[0076] An aircraft's attitude and heading are important indicators of its flight stability and directly impact its control and navigation systems. An aircraft's attitude, including pitch, roll, and yaw angles, is typically measured by an inertial measurement unit (IMU) or gyroscope. Attitude data helps assess an aircraft's stability, maneuverability, and responsiveness during flight. Heading, the direction of flight, is typically measured by a magnetometer or GPS. Heading stability directly impacts the aircraft's navigation system, ensuring it remains on course.

[0077] Aircraft encounter various external forces during flight, causing vibration or stress in their structures. Aircraft vibrations primarily originate from the engine, aerodynamic forces, and the aircraft's own structural inhomogeneities. Vibration sensors (such as accelerometers) can detect the vibration amplitude and frequency of various parts of the aircraft, helping engineers understand the aircraft's stability. The stress of an aircraft's structure is a key factor in assessing its durability and safety. Stress sensors can monitor stress changes in structural components such as the aircraft's fuselage, wings, and tail in real time to prevent structural damage caused by excessive stress.

[0078] Common input variables in aircraft testing include environmental parameters, aircraft state, control inputs, structural and mass parameters, powertrain parameters, flight mission and control strategy, external disturbances, and system state parameters. Environmental parameters typically include temperature, humidity, air pressure, wind speed, and direction, which affect the aircraft's aerodynamic characteristics. Aircraft state parameters include speed (airspeed and ground speed), altitude, angle of attack, yaw, pitch, and roll angles, which directly affect the aircraft's controllability and stability. Control inputs primarily include control surface angles, engine thrust, and pilot inputs, which determine the aircraft's attitude and maneuverability. Aircraft structural and mass parameters, such as mass distribution, center of gravity, and moment of inertia, also have a significant impact on flight stability. Powertrain parameters include engine thrust output, fuel consumption, and multi-engine power distribution, which determine the aircraft's acceleration performance and endurance. Flight mission and control strategy involve trajectory planning, autopilot system input, and other factors, guiding the aircraft's flight path and mission execution. External disturbances, including airflow disturbances, turbulence, and the effects of ground obstacles, are particularly significant during low-altitude flight. Finally, system state parameters, such as sensor inputs and fault detection signals, are used to monitor the aircraft's status in real time and ensure safe and stable flight. All of these input variables interact to influence the aircraft's flight performance, stability, and mission accomplishment.

[0079] S2. Based on the information of the known sample set D, a proxy model f(X) is established using the Gaussian process model, where y = f(X);

[0080] f(x)~GP(μ(x),K(x,x')),

[0081] Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x);

[0082] The predicted mean of the surrogate model is:

[0083]

[0084] in, Represents the new point x * The predicted mean at μ(x * ) represents the new point x * The prior mean at K(x * ,X) represents the new point x * and the covariance vector between all known points X; K(X,X) represents the covariance matrix between all known points X, is the variance of the noise, representing the random error in the observation data, E represents the unit matrix, and y represents the observation value vector corresponding to the known point X;

[0085] The proxy model prediction variance is

[0086]

[0087] in, Represents the new point x * The prediction variance at K(x * ,x * ) represents the new point x * Its own covariance vector; K(X,x * ) represents all known points X and new points x * The covariance vector between ;

[0088] S3. Based on the established proxy model, the next test sample point is determined according to the acquisition function corresponding to the overall improvement criterion of the expected probability box;

[0089] In this embodiment, the probability box is the envelope of all possible cumulative distribution functions (CDFs) of the parameter. The probability box can be obtained by integrating along the upper and lower boundaries of the probability box. In combination with the characteristics of the probability box, the area of ​​the probability box is used as the uncertainty measure unc(·) of the output, as shown in Figure 2 As shown,

[0090]

[0091] in, and Both represent the upper bound cumulative distribution function of the probability box,F and F Y (y) represents the lower boundary cumulative distribution function of the probability box, The upper and lower bounds of the probability box represent the distance between the cumulative distribution functions, which are usually used to measure uncertainty; Φ represents the cumulative distribution function of the standard normal distribution, μ L and μ U are expressed as the minimum mean and maximum mean, i.e., the minimum and maximum expected values ​​predicted by the surrogate model; and They are expressed as the minimum variance and maximum variance, i.e., the minimum variance and maximum variance predicted by the surrogate model, u(·) represents the unit step function. When the value in the brackets is positive, the function value is 1, otherwise it is 0.

[0092] Assume that the probability density distributions corresponding to the upper and lower boundaries of the probability box are N(μ1,σ1 2 ) and N(μ2,σ2 2 ), and its corresponding cumulative distribution function is Figure 3 As shown, the area of ​​the probability box is calculated in the above two cases; the two cases are that all the prediction means of the proxy model are the same but the standard deviations of the predictions are different, that is, μ1=μ2 and σ2>σ1 (see Figure 3 a) All prediction standard deviations of the surrogate model are the same but the prediction means are different, i.e. μ1<μ2 and σ1=σ2 (see Figure 3 b).

[0093] for Figure 3 The area of ​​the probability box in a is:

[0094]

[0095] Since the above formula is very complicated to calculate according to conventional integration, the characteristic function I is used in the calculation process, that is,

[0096]

[0097] get

[0098]

[0099] Similarly for Figure 3 The area of ​​the probability box in b is;

[0100]

[0101] So we get:

[0102] unc(·)=μ2-μ1

[0103] It is expected that the probability box sizes of the two proxy models before and after adding the sample point will change significantly, which to some extent reflects that the added sample point is valuable; for the known proxy model, the maximum and minimum values ​​of its posterior distribution are Taking another sample, we get a new posterior distribution with the maximum and minimum values ​​being Therefore, the sampling criterion based on the change in the probability box size of the surrogate model before and after adding the alternative sample points is expressed as:

[0104]

[0105] Available through Ensure the balance between the predicted mean and the predicted standard deviation; therefore, the sampling criterion formula (collection function) can be expressed as:

[0106]

[0107] in, and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with sample size n; and They represent the minimum standard deviation and maximum standard deviation of the prediction of the proxy model constructed by the sample set with sample size n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with a sample size of n+1; and They represent the minimum standard deviation and maximum standard deviation of the proxy model prediction constructed by the sample set with a sample size of n+1; k represents the variable that balances the prediction mean and prediction standard deviation,

[0108] S4. Calculate the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and update the sample set;

[0109] S5. Determine whether the test stopping criteria are met. If so, output the final proxy model; if not, repeat the operations of S2-S5.

[0110] The core principle of this invention is to use Bayesian optimization (Gaussian process regression is one of the commonly used proxy models in Bayesian optimization) to find the complex global optimal solution through an iterative process. First, based on the probability box overall improvement criterion, the sample set D that affects the output of the aircraft is 1:i-1 Build the proxy model; then select the next most valuable sample point x according to the maximum acquisition function (i) ; Then according to the selected sample point x (i) Evaluate the objective function value y (i) =f(x (i))+ε (i) If the stopping criterion is met, the optimal value of the final proxy model is directly output; if the stopping criterion is not met, the newly obtained sample point pair {x (i) ,y (i)}Add to historical sample set D 1:i-1 and updates the proxy model in preparation for the next iteration.

[0111] Specific examples:

[0112] Under hypersonic flight conditions (Mach numbers Ma ≥ 5), thermochemical nonequilibrium effects (such as the excitation and relaxation of high-temperature gas internal energy modes and complex chemical reactions between components) occur in the flow field around the vehicle. These effects have a significant impact on the aerodynamic characteristics, aero-thermal environment, flow field structure, optical radiation characteristics, plasma environment, electromagnetic scattering characteristics, and electromagnetic communications of the hypersonic vehicle. Due to operating costs and technical limitations, the thermochemical nonequilibrium flow field information available from ground-based high-enthalpy test equipment is relatively limited, making it difficult to systematically study the high-temperature gas effects on vehicles under real-world flight conditions. Therefore, numerical simulation methods are often used to predict and evaluate the high-temperature gas effects on hypersonic vehicles. NNW-HYFLOW, supported by the National Numerical Wind Tunnel (NNW) project and powered by the Fenglei open source software framework, will be developed as a domestically developed industrial CFD software based on a structured / unstructured hybrid grid for hypersonic applications. It features key features such as simulation of high-temperature gas thermochemical nonequilibrium effects and computational analysis of related aerodynamic, aero-thermal, and aerophysical properties. Numerical simulations were conducted using typical examples such as the HEG wind tunnel test. Research has shown that NNW-HYFLOW offers advantages such as underlying code reuse, good functional compatibility, strong expansion capabilities, and flexible interfaces. Its current test version already possesses excellent numerical simulation capabilities for hypersonic non-equilibrium flows. It demonstrates high numerical calculation accuracy in the prediction and evaluation of thermochemical non-equilibrium effects and their impacted aerodynamic characteristics, aerodynamic thermal environment, and plasma distribution characteristics, preliminarily meeting the requirements for numerical simulation of high-temperature non-equilibrium flows in complex hypersonic vehicles. Regarding thermochemical non-equilibrium effects, the following verification and confirmation of the completed solver functions of the NNW-HYFLOW software are conducted in terms of the calculation accuracy of non-equilibrium flow field characteristics such as shock wave position, electron number density, non-equilibrium aerodynamics and aerodynamic thermal environment, as well as its applicability to complex engineering shapes.

[0113] Numerical simulations were conducted for the HEG shock tunnel cylindrical model test. The calculations used a single-temperature, five-component Dunn-Kang chemical model with a wall temperature of Tw = 300K. The computational grid is as follows: Figure 4 As shown, the mesh volume of the symmetry surface is 129×91, and the height of the first layer is △h=1.0×10-6m. Figure 5The pressure contour distribution of the cross section (z = 0.01m) is given, and Figure 6 and Figure 7 The calculated wall pressure and heat flux distributions for both fully catalytic wall (FCW) and non-catalytic wall (NCW) conditions are presented. The calculated shock wave positions are in good agreement with both experimental and actual responses, while the wall pressure distributions are consistent with the experimental results. Furthermore, the calculated heat flux distribution trends for both wall conditions are consistent with the actual physical mechanisms and theoretical analysis, demonstrating the NNW-HYFLOW software's reliable capabilities for non-equilibrium flow simulation and shock wave capture, as well as its high computational accuracy in predicting non-equilibrium aerodynamic forces and aerodynamic heat in high-temperature gases.

[0114] Based on the 400 groups of samples obtained from the above experiments, 17-dimensional input and output are the heat flow coefficients on the grid points; a sequential experimental design based on the overall improvement of the expected probability box is carried out, and the results are compared with the most commonly used acquisition functions (EI and LCB); the measurement indicators are the RMSE value and the absolute difference between the minimum value; the former mainly indicates the overall accuracy of the constructed proxy model, the smaller the RMSE value, the higher the accuracy of the constructed proxy model, and vice versa; the latter mainly indicates the effect of the constructed proxy model in finding the minimum value, the smaller the absolute difference, the closer the found minimum value is to the true minimum value, and vice versa.

[0115] Figure 8 The comparison between the two sampling criteria and the proposed criteria is given to verify the advantages of the proposed method. The overall accuracy of the constructed proxy model is measured by the size of the RMSE value (see Figure 8 a and Figure 8 c) The optimization effect is measured by the size of the minimum absolute difference (see Figure 8 b and Figure 8 d); and the effectiveness of the proposed algorithm as a method for establishing a high-precision proxy model in aircraft test design was verified through multiple independent repeated experiments.

[0116] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for sequential test design of aircraft based on the expected probability box overall improvement criterion, characterized by: The specific steps include: S1. Initial test design: obtain the sample set D that affects the output results in the aircraft test, where D = (X, y); Where, each row of X represents a sample point, x represents the input variable used to evaluate the output results in the aircraft test, d represents the dimension of the spatial parameter, n represents the sample size, and y represents the output results of the aircraft test; Outputs of the aircraft test include, but are not limited to, speed, acceleration, altitude, air pressure, temperature, thrust, fuel consumption, attitude, heading, and vibration and structural stress; S2. Based on the information of the known sample set D, a surrogate model f(X) is established using the Gaussian process regression model; S3. Based on the established proxy model, the next test sample point is determined according to the sampling point criterion corresponding to the overall improvement criterion of the expected probability box; The formula of the sampling point criterion is: in, and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with sample size n; and They represent the minimum standard deviation and maximum standard deviation of the prediction of the proxy model constructed by the sample set with sample size n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with a sample size of n+1; and They represent the minimum standard deviation and maximum standard deviation of the proxy model prediction constructed by the sample set with a sample size of n+1; k represents the variable that balances the prediction mean and prediction standard deviation, S4. Calculate the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and update the sample set; S5. Determine whether the test stopping criteria are met. If so, output the final proxy model; if not, repeat the operations of S2-S5.

2. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 1 is characterized in that: The input variables include but are not limited to environmental parameters, aircraft state parameters, control input parameters, structure and mass parameters, power system parameters, flight mission and control strategy, external disturbances and system state parameters.

3. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The environmental parameters include but are not limited to temperature, humidity, air pressure, wind speed and wind direction.

4. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The state parameters of the aircraft include but are not limited to speed, flight altitude, angle of attack, yaw angle, pitch angle and roll angle, and the speed includes airspeed and ground speed.

5. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The control input parameters include but are not limited to control surface angles, engine thrust, and pilot control inputs.

6. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The structural and mass parameters of the aircraft include but are not limited to mass distribution, center of gravity position and moment of inertia.

7. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The power system parameters include but are not limited to engine thrust output, fuel consumption rate and multi-engine power distribution.

8. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The flight mission and control strategy include but are not limited to trajectory planning, input to the autopilot system, guiding the aircraft's flight path and mission execution.

9. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is characterized in that: The external disturbances include but are not limited to air flow disturbances, turbulence and the effects of ground obstacles.

10. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2, characterized in that: The system status parameters include but are not limited to sensor inputs and fault detection signals.

11. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 1 is characterized in that: The proxy model is f(x)~GP(μ(x),K(x,x')), Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x); The predicted mean of the surrogate model is: in, Represents the new point x * The predicted mean at μ(x * ) represents the new point x * The prior mean at K(x * ,X) represents the new point x * and the covariance vector between all known points X; K(X,X) represents the covariance matrix between all known points X, is the variance of the noise, representing the random error in the observation data, E represents the unit matrix, and y represents the observation value vector corresponding to the known point X; The prediction variance of the surrogate model is in, Represents the new point x * The prediction variance at K(x * ,x * ) represents the new point x * Its own covariance vector; K(X,x * ) represents all known points X and new points x * The covariance vector of .

12. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 1, characterized in that: The area of ​​the probability box is used as the uncertainty measure unc(·) of the output of the proxy model, then in, and Both represent the upper bound cumulative distribution function of the probability box, F and Both represent the lower bound cumulative distribution function of the probability box, The upper and lower bounds of the probability box represent the distance between the cumulative distribution functions and are used to measure uncertainty; The probability density distributions corresponding to the upper and lower boundaries of the probability box are N(μ1,σ1 2 ), N(μ2,σ2 2 ), the area of ​​the probability box is calculated in two cases: When the predicted means are the same but the predicted variances are different, that is, μ1=μ2 and σ2>σ1, When the prediction variances are the same but the prediction means are different, that is, μ1<μ2 and σ1=σ2, unc(·)=μ2-μ1.

13. Application of the aircraft sequential test design method based on the expected probability box overall improvement criterion according to any one of claims 1 to 12 in the prediction and multi-objective optimization of aircraft performance, aircraft stability, and mission completion evaluation.

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