Aircraft sequential test design method based on expectation probability box overall improvement criterion

Abstract

The invention relates to the technical field of aircraft test design, in particular to an aircraft sequential test design method based on an expected probability box overall improvement criterion, and the method specifically comprises the following steps: S1, carrying out initial test design, and obtaining a sample set which influences an output result in an aircraft test; s2, establishing an agent model by using a Gaussian process regression model according to the information of the known sample set D; s3, on the basis of the established agent model, determining a next test sample point according to a point sampling criterion corresponding to the overall improvement of the expected probability box; s4, calculating the real response of the aircraft at the test sample point, and updating the sample set; s5, judging whether a test stop criterion is met or not, and if yes, outputting a final agent model; and if not, repeating the operations of S2-S5. According to the method, uncertainty in an aircraft test can be quantified, and the most valuable sample point is selected in combination with a probability box overall improved sampling point criterion, so that the overall precision of an agent model is improved, and a more reliable basis is provided 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 in particular to a test design method based on an overall improvement of an 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 an important part of ensuring its safety, stability and reliability. Aircraft equipment tests often face various uncertainties, which come from a wide range of sources, mainly including geometric uncertainty, load uncertainty, environmental uncertainty, cognitive uncertainty and material uncertainty. This affects the evaluation of aircraft performance and the accuracy of test results. In aircraft tests, common input variables include environmental parameters, aircraft status, control input, structure and mass parameters, power system parameters, flight missions and control strategies, external disturbances and system state parameters. All these input variables interact with each other and affect the flight performance, stability and mission completion of the aircraft.

[0003] In the design of aircraft tests, for some key issues, the accuracy requirements of the entire proxy model are very high. For example, in the evaluation of the aerodynamic performance of the aircraft, we may need to use the proxy model to predict parameters such as the lift coefficient and the drag coefficient under different flight conditions. The accurate prediction of these performance parameters directly affects the feasibility and safety of the aircraft design. If the proxy model cannot accurately fit the performance characteristics of the aircraft, there may be large errors in the test results, resulting in design decision errors and even affecting the actual flight performance of the aircraft. In addition, when performing multi-objective optimization of aircraft, such as finding the best compromise between fuel efficiency, maneuverability and flight stability, an accurate proxy model can help designers identify the optimal operating range and avoid blindness and inefficiency in the design process. Therefore, one of the key tasks of experimental design is to improve the overall accuracy of the proxy model by reasonably 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 is 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 (objective function minimum criterion (MP criterion), expected improvement criterion (EI criterion) and confidence interval lower bound criterion (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-focusing on local accuracy: Traditional methods often focus on the fitting accuracy of individual sample points and ignore the improvement of global accuracy. Although the proxy model can have a good fitting effect near some 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 proxy model is still low.

[0006] (2) Not considering the range of uncertainty: Traditional point selection criteria usually rely on the prediction of the response value by the proxy model without fully considering the overall range of model prediction uncertainty. This results in the model being unable to reflect all potential system uncertainties and unable to 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 process of aircraft test design, the establishment of surrogate models is usually the core of test optimization. The role of surrogate models is to approximate the complex behavior of aircraft systems through limited test data, so as to provide designers with prediction and optimization guidance for aircraft performance. Surrogate models can be constructed based on different mathematical methods, such as Gaussian process regression (GPR), support vector regression (SVR), etc., all of which have different advantages and disadvantages. However, in actual aircraft test design, especially in the optimization of complex aircraft systems, the accuracy requirements are often very high. In this case, the goal of test design is not only to obtain a rough prediction through the surrogate model, but also to accurately reflect the key characteristics of the aircraft such as dynamic behavior, aerodynamic performance, structural response, etc. through an accurate surrogate model. This is of vital significance for tasks such as aircraft performance evaluation, optimal design, and fault prediction. In order to achieve this goal, the test design must be able to identify and select the most valuable sample points to maximize the accuracy of the surrogate model under limited test resources.

[0009] The P-box model combines the traditional probability distribution model with the interval model. Its core idea is to characterize the uncertainty of system parameters through the cumulative distribution function (CDF) of the upper and lower boundaries. Compared with the traditional single probability distribution model, the P-box model can handle both random uncertainty and cognitive uncertainty, providing a more conservative and tolerant boundary, which enables P-box to provide more comprehensive analysis results in complex scenarios with multiple uncertain factors.

[0010] Therefore, in order to more effectively handle 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 scientificity 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 expected probability box overall improvement criterion. The core of this method is to quantify the uncertainty in the aircraft test by introducing the expected probability box (P-box) model, and select the most "valuable" sample points in combination with the overall improved sampling point criterion of the probability box. The overall accuracy of the proxy model can be improved by reasonably selecting sampling points, 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, obtaining a sample set D that affects the output results of the aircraft test, D = (X, y);

[0015]

[0016] Among them, 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] The output results of the aircraft test include but are not limited to speed, acceleration, altitude, air pressure, temperature, thrust, fuel consumption, attitude, heading, 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 by the sample set with sample size n respectively; and They represent the minimum and maximum standard deviations of the predictions of the proxy model constructed by the sample set with a sample size of n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed by the sample set with a sample size of n+1; and They represent the minimum and maximum standard deviations of the proxy model predictions 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, calculating the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and updating 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 quality 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 route and mission execution.

[0032] Furthermore, the external disturbance includes but is not limited to the influence of airflow disturbance, turbulence and 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] Among them, 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 proxy 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 observed data, E represents the unit matrix, and y represents the observed 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 boundary cumulative distribution function (CDF) of the probability box, F and F Y (y) represents the lower boundary 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(μ 1 ,σ 1 2 ), N(μ 2 ,σ 2 2 ), the area of ​​the probability box is calculated in two cases:

[0047] When the prediction means are the same but the prediction variances are different, that is, μ 1 =μ 2 And σ 2 >σ 1 ,

[0048]

[0049] When the prediction variance is the same but the prediction means are different, that is, μ 1 <μ 2 And σ 1 =σ 2 ,

[0050] unc(·)=μ 2 -μ 1 .

[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 assessment.

[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 point criterion of the overall improvement of the expected probability box not only focuses on the predicted response value and uncertainty of each sample point, but also considers the range of the entire predicted response value 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 cognitive uncertainty (such as design assumptions, model errors, etc.) in aircraft tests, thereby providing comprehensive information for sampling point selection; thereby, 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. The present invention can optimize the accuracy of the proxy model. The sampling criteria of the present invention pay special attention to the improvement of the overall accuracy of the proxy model. In the aircraft test design, different sampling points have different effects on the fitting effect of the model, and some sampling points have greater value in improving the accuracy of the model; therefore, the present invention can select those sample points that are most valuable for improving the accuracy of the proxy model through the overall improvement of the expected probability box. These sample points can cover the key areas in the design space, ensure the global fitting ability of the proxy model, and thus make the model's prediction of aircraft performance more accurate.

[0055] 3. The present invention can flexibly handle multi-source uncertainties. Aircraft test design often faces various types of uncertainties, including physical uncertainty and cognitive uncertainty. Through the probability box model, the present invention can flexibly handle these multi-source uncertainties 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 a complex aircraft system, 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 make efficient use of limited resources. In aircraft test design, test resources are usually limited. Therefore, how to obtain as much effective information as possible with limited test resources is the key to optimizing the design. The sampling point criterion of the overall improvement of the expected probability box can effectively reduce redundant tests by optimizing the sampling strategy and focus 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 It is a flow chart of an aircraft sequential test design method 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 are two special probability boxes based on GPR provided by the embodiment of the present invention (a is the same for all prediction means of the proxy model but different standard deviations of the predictions, i.e., μ 1 =μ 2 And σ 2 >σ 1 , b is the same standard deviation of all predictions of the surrogate model but different means of the predictions, that is, μ 1 <μ 2 And σ 1 =σ 2 );

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

[0061] Figure 5 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 solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 in conjunction with 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, obtaining a sample set D that affects the output results of the aircraft test, 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 is necessary to explain here that aircraft testing is a very critical link in aerospace engineering. Through comprehensive evaluation of the performance, structure, power system and other aspects of the aircraft, the safety, stability and efficiency of the aircraft in actual operation are ensured. In the process of aircraft testing, output variables are a crucial part of the test data. They not only help engineers understand the working status of the aircraft, but also provide important references for aircraft design optimization and troubleshooting. The main output variables in aircraft testing include speed and acceleration, altitude and air pressure, temperature, thrust and fuel consumption, attitude and heading, vibration and structural stress, etc.

[0072] The speed and acceleration of an aircraft are one of the most basic and important output variables. Speed ​​includes the horizontal speed, vertical speed, and relative speed of the aircraft. The horizontal speed affects the heading stability of the aircraft, while the vertical speed is usually directly related to the lift system of the aircraft (such as wings or engine thrust). The acceleration of the aircraft is usually measured by acceleration sensors (such as gyroscopes and accelerometers).

[0073] The flight altitude and air pressure of an aircraft are output variables that are closely related to flight performance. Altitude not only affects the flight path and range of an aircraft, but also directly affects engine performance and aerodynamic performance. The external air pressure of an aircraft is usually inversely proportional to the flight altitude.

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

[0075] Thrust is the key output variable of the aircraft power system, which directly affects the aircraft's lift-off capability, flight speed and range. Thrust data is usually monitored by the engine control system and fed back to the ground control center through sensors. Fuel consumption is an important indicator for evaluating the economy and range of aircraft. In aircraft tests, fuel consumption rate is usually related to factors such as flight altitude, speed, and engine type. By monitoring fuel consumption, the aircraft's operating strategy can be optimized to reduce fuel consumption.

[0076] The attitude and heading of an aircraft are important indicators of its flight stability, and they directly affect the aircraft's control and navigation systems. The attitude of an aircraft includes pitch, roll, and yaw angles, which are usually measured by an inertial measurement unit (IMU) or a gyroscope. Attitude data helps evaluate the stability, controllability, and responsiveness of an aircraft in flight. Heading refers to the direction in which an aircraft is flying, and is usually measured by a magnetometer or GPS. The stability of the heading directly affects the aircraft's navigation system, ensuring that the aircraft flies along the intended route.

[0077] Aircraft will encounter various external forces during flight, causing vibration or stress in its structure. The vibration of the aircraft mainly comes from the engine, aerodynamic force and the structural unevenness of the aircraft itself. Vibration sensors (such as accelerometers) can detect the vibration amplitude and frequency of various parts of the aircraft to help engineers understand the stability of the aircraft. The stress of the aircraft structure is a key factor in evaluating its durability and safety. Through stress sensors, the stress changes of structural components such as the aircraft fuselage, wings, and tail can be monitored in real time to prevent structural damage caused by excessive stress.

[0078] In aircraft testing, common input variables include environmental parameters, aircraft state, control input, structure and mass parameters, power system parameters, flight mission and control strategy, external disturbances and system state parameters. Environmental parameters usually include temperature, humidity, air pressure, wind speed and direction, which affect the aerodynamic characteristics of the aircraft. The state parameters of the aircraft include speed (airspeed and ground speed), flight altitude, angle of attack, yaw angle, pitch angle and roll angle, which directly affect the control and stability of the aircraft. Control input mainly includes control surface angle, engine thrust and pilot control input, which determine the attitude and maneuverability of the aircraft. The structure and mass parameters of the aircraft, such as mass distribution, center of gravity position and moment of inertia, also have an important impact on flight stability. Power system parameters include engine thrust output, fuel consumption rate and multi-engine power distribution, which determine the acceleration performance and endurance of the aircraft. Flight mission and control strategy involve trajectory planning, input of autopilot system, etc., which guide the flight route and mission execution of the aircraft. External disturbances include airflow disturbances, turbulence, and the effects of ground obstacles, which are particularly important when flying at low altitudes. Finally, system state parameters such as sensor inputs and fault detection signals are used to monitor the aircraft state in real time and ensure the safety and stability of flight. All these input variables interact with each other and affect the flight performance, stability, and mission completion of the aircraft.

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

[0080] f(x)~GP(μ(x),K(x,x')),

[0081] Among them, 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 proxy 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 observed data, E represents the unit matrix, and y represents the observed 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. Combined with the characteristics of the probability box, the area of ​​the probability box is used as the uncertainty measure unc(·) of the output, as follows: Figure 2 As shown,

[0090]

[0091] in, and Both represent the upper boundary 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 They 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 represented 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(μ 1 ,σ 1 2 ) and N(μ 2 ,σ 2 2 ), and its corresponding cumulative distribution function is Figure 3 As shown, therefore, the area of ​​the probability box is calculated for 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, μ 1 =μ 2 And σ 2 >σ 1 (See Figure 3 a) All predictions of the surrogate model have the same standard deviation but different means, i.e. μ 1 <μ 2 And σ 1 =σ 2 (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 indicative function I is now used in the calculation process, that is,

[0096]

[0097] get

[0098]

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

[0100]

[0101] So we get:

[0102] unc(·)=μ 2 -μ 1

[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 maximum and minimum values ​​of Therefore, the point selection criterion based on the change in the size of the surrogate model probability box 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 point 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 by the sample set with sample size n respectively; and They represent the minimum and maximum standard deviations of the predictions of the proxy model constructed by the sample set with a sample size of n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed by the sample set with a sample size of n+1; and They represent the minimum and maximum standard deviations of the proxy model predictions 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, calculating the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and updating 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 the present 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 results 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 the 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 number Ma≥5), thermochemical non-equilibrium effects (excitation and relaxation of high-temperature gas internal energy modes, and complex chemical reaction processes between components, etc.) will appear in the flow field around the aircraft, which will have an important impact on the aerodynamic characteristics, aerodynamic thermal environment, flow field structure, light radiation characteristics, plasma environment, electromagnetic scattering characteristics and electromagnetic communication of hypersonic aircraft. Due to the constraints of operating costs and technical conditions, the thermochemical non-equilibrium flow field information that can be obtained by ground high-enthalpy test equipment is relatively limited, and it is difficult to achieve a systematic study of the high-temperature gas effect of the aircraft under real flight conditions. Therefore, numerical simulation methods are often used to predict and evaluate the high-temperature gas effect of hypersonic aircraft. Supported by the National Numerical Wind Tunnel (NNW) project and supported by the basic framework of Fenglei open source software, NNW-HYFLOW will be built into a domestically-produced industrial CFD software based on structured / unstructured hybrid grids and oriented to the field of hypersonic applications. It has the main features of simulating the thermochemical non-equilibrium effect of high-temperature gas and calculating and analyzing its related aerodynamic, aerodynamic heat and aerophysical characteristics. Numerical simulations were carried out in combination with typical examples such as the HEG wind tunnel test. The study shows that NNW-HYFLOW has the advantages of underlying code reuse, good functional compatibility, strong expansion capabilities and flexible interfaces. Its current test version already has good numerical simulation capabilities for hypersonic non-equilibrium flows. It has high numerical calculation accuracy in the prediction and evaluation of thermochemical non-equilibrium effects and their affected aerodynamic characteristics, aerodynamic thermal environment and plasma distribution characteristics, and preliminarily meets the needs of high-temperature non-equilibrium flow numerical simulations for hypersonic complex aircraft. In view of the thermochemical non-equilibrium effect, the following verifies and confirms the completed solver functions of the NNW-HYFLOW software from aspects such as the calculation accuracy of non-equilibrium flow field characteristics such as shock wave position, electron number density, non-equilibrium aerodynamic force and aerodynamic thermal environment, and the applicability to complex engineering shapes.

[0113] Numerical simulation tests were carried out for the HEG shock tunnel cylindrical model test. The calculation used a single temperature, five-component Dunn-Kang chemical model, and the wall temperature was 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 5 The pressure contour distribution of the cross section (z = 0.01m) is given, and Figure 6 and Figure 7The wall pressure distribution and heat flux distribution calculated under the conditions of fully catalytic wall (FCW) and non-catalytic wall (NCW) are given respectively. It can be seen that the calculated detached shock wave position is very consistent with the experimental and real response, and the wall pressure value distribution is consistent with the experimental results. At the same time, the heat flux distribution trend calculated under the two wall conditions is consistent with the actual physical mechanism and theoretical analysis, which proves that the NNW-HYFLOW software has reliable non-equilibrium flow field simulation and shock wave capture capabilities, and has high calculation accuracy in the prediction of non-equilibrium aerodynamics and aerodynamic heat of 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 absolute difference between the RMSE value and 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 A comparison between two sampling criteria and the criterion of the present invention is given to verify the advantages of the present invention; 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 protection scope of the present invention.

Claims

1. A method for sequential test design of aircraft based on the expected probability box overall improvement criterion, characterized in that: The specific steps include: S1. Initial test design, obtaining a sample set D that affects the output results in the aircraft test, 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; The output results of the aircraft test include but are not limited to speed, acceleration, altitude, air pressure, temperature, thrust, fuel consumption, attitude, heading, vibration and structural stress; S2. Based on the information of the known sample set D, a proxy 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 by the sample set with sample size n respectively; and They represent the minimum and maximum standard deviations of the predictions of the proxy model constructed by the sample set with a sample size of n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed by the sample set with a sample size of n+1; and They represent the minimum and maximum standard deviations of the proxy model predictions 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, calculating the true response of the aircraft at the test sample points obtained according to the above sampling criteria, and updating 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 quality 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 the engine's 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, and guiding the flight route and mission execution of the aircraft.

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 impact of ground obstacles.

10. The aircraft sequential test design method based on the expected probability box overall improvement criterion according to claim 2 is 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')), Among them, 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 proxy 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 observed data, E represents the unit matrix, and y represents the observed 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 is 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 boundary 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 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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