Aircraft sequential test design method based on expected probability box boundary 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 boundary 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, according to a sampling point criterion corresponding to a boundary improvement criterion of an expected probability box, determining a next test sample point; 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, the maximum value or the minimum value of the target function is quickly and effectively found through proper sampling point selection in the test design, and the brand new optimization criterion has remarkable advantages especially in the problem of finding the maximum value and the minimum value.

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 improved expected probability box (P-box) boundary, 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 aircraft test design, although traditional sequential test methods can improve the accuracy of surrogate models to a certain extent, the optimization effects of these methods cannot meet all requirements under specific tasks, especially when the core goal of the task is to find the maximum or minimum value of the objective function. The goal of aircraft test design is not just to improve the prediction accuracy of the surrogate model. Especially in some application scenarios, we are mainly concerned with finding the maximum value of the objective function - whether it is the maximum or minimum value. For example, in the optimization of the aerodynamic performance of an aircraft, we may need to find the optimal flight attitude, the optimal lift and drag coefficients, or minimize fuel consumption and structural loads. Such problems are often highly nonlinear, complex, and uncertain, so their optimization process has very high requirements for experimental design.

[0004] In actual aircraft tests, test resources are usually limited, and the purpose of test design is to maximize information acquisition under limited test resources. The sequential test design method is proposed to solve this problem. Although traditional sequential test design methods, such as the sequential sampling method based on Bayesian optimization, have achieved certain results in improving the accuracy of surrogate models, they are often limited by several factors in finding the maximum value of the objective function:

[0005] (1) Limitations of sampling point selection: Traditional Bayesian optimization methods mainly focus on improving the accuracy of surrogate models, and usually optimize the model by selecting sampling points that can maximize the accuracy of the surrogate model. This method usually focuses on the contribution of each sampling point to the predicted value and uncertainty of the surrogate model, trying to reduce the prediction error. However, this method does not fully consider the strategic role of sampling points in global optimization. In many cases, the goal of experimental design is not to improve the accuracy of the model, but to find the minimum value of the objective function as quickly as possible through the reasonable selection of sampling points.

[0006] For example, in aircraft performance evaluation, the goal may be to find the best aerodynamic characteristics of the aircraft. Traditional methods tend to select points that minimize the error of the proxy model, but these points may not be in the minimum region of the objective function. Since the accuracy of the entire proxy model is not necessarily required in the experimental design, we can directly guide the optimization process by selecting sample points with higher strategic significance, quickly narrow the area where the maximum value is located, and thus improve the efficiency of finding the maximum value.

[0007] (2) Inefficient use of experimental resources: Aircraft tests are often accompanied by high costs and limited resources. In this case, how to achieve the optimal design or find the maximum value with limited experimental resources becomes an important challenge in experimental design. Traditional sequential test methods may conduct redundant tests during the optimization process, or the design information of the test may not be fully transmitted, resulting in low test efficiency. For example, in the early stage of the test, if the accuracy of the surrogate model is low, the traditional method may select a large number of sampling points to improve the accuracy of the model, but these sampling points do not directly point to the maximum value area of ​​the objective function, resulting in a waste of experimental resources.

[0008] In addition, the optimization process of traditional methods is relatively slow, especially in complex aircraft tests. The optimization process may require multiple sampling and testing, and the feedback of each sampling is used to update the proxy model, thereby gradually approaching the optimal solution. However, if the strategy of each sampling does not fully consider the optimal use of resources, the test efficiency will be greatly reduced, resulting in the inability to accurately find the maximum value of the objective function within limited time and resources.

[0009] (3) Risk of local optimum: Traditional sequential test methods may fall into local optimal solutions during the optimization process. Since Bayesian optimization methods usually rely on the predictions and uncertainties of the surrogate model to guide the selection of sampling points, this may cause the optimization process to over-rely on the prediction ability of the current model in the local area and ignore the need for global optimization. Especially in complex aircraft systems, the maximum or minimum value of the objective function often appears in a very narrow or complex design space area. Traditional methods may miss these key areas and fail to effectively find the optimal value globally.

[0010] (4) Inadequate handling of uncertainties: Aircraft tests usually involve multiple sources of uncertainty, including flight environment, material properties, manufacturing errors, design assumptions, etc. These uncertainties have a significant impact on the optimization results. When dealing with uncertainties, traditional sequential test design methods usually focus on the accuracy of the surrogate model and ignore the role of uncertainty in the global optimization process. Especially when searching for the minimum value of the objective function, how to quantify and manage these uncertainties through reasonable test design to avoid misleading the search path for the maximum value is a crucial issue.

[0011] In aircraft tests, the maximum value of the objective function is usually one of the core tasks of experimental design. For example, when evaluating the performance of an aircraft, we may need to find the maximum lift coefficient, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed and other parameters of the aircraft under a certain flight state. These target values ​​are the key decision basis for aircraft design and performance optimization. Therefore, the focus of experimental design is often not on establishing a high-precision global proxy model, but on accurately finding the maximum value of the objective function or the extreme value of an important parameter by reasonably selecting sampling points. For example, in some aircraft optimization tasks, we may not care about the accurate modeling process of the entire system, but are more concerned about how to find a local optimal solution through a limited number of experiments in a complex design space. At this time, the accuracy requirement of the proxy model is not particularly high, and the key is how to quickly and effectively explore the optimal point. Therefore, the goal of the optimization method changes from "fitting the most accurate model" to "effectively finding the maximum value of the objective function". This change requires the new experimental design method to be not only efficient, but also flexible, and able to quickly converge to the target maximum value under the condition of limited resources.

[0012] 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) with upper and lower bounds. 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.

[0013] 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 improvement of the expected probability box (P-box) boundary. 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

[0014] In order to solve the above technical problems, the purpose of the present invention is to provide a sequential experiment design method based on the expected probability box (P-box) boundary improvement. By introducing the expected probability box boundary improvement, the experimental design no longer simply pursues the high-precision fitting of the overall proxy model, but pays more attention to quickly and effectively finding the maximum or minimum value of the objective function through appropriate sampling point selection. This new optimization criterion has significant advantages, especially in finding the maximum value problem.

[0015] To achieve the above object, the technical solution adopted by the present invention is:

[0016] The invention provides an aircraft sequential test design method based on an expected probability box boundary improvement criterion, comprising the following steps:

[0017] S1. Initial test design, obtaining a sample set D that affects the output results in the aircraft test, D = (X, y);

[0018]

[0019] 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;

[0020] The output of the aircraft test is aircraft design and performance optimization, including but not limited to optimal lift and drag coefficients, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed, optimal flight attitude, and minimization of fuel consumption and structural load;

[0021] S2: Based on the information of the known sample set D, the Gaussian process model is used to establish the proxy model f(X), y = f(X);

[0022] S3: Based on the established proxy model, the next test sample point is determined according to the acquisition function corresponding to the boundary improvement criterion of the expected probability box;

[0023] The acquisition function of the minimum optimal problem based on the probability box mortal boundary change is expressed as:

[0024]

[0025] The acquisition function of the maximum optimization problem based on the boundary change of the probability box is expressed as:

[0026]

[0027] 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.

[0028] S4: Calculate the real response of the aircraft at the test point and update the sample set;

[0029] S5: Determine whether the test stopping criteria are met. If so, output the optimal value of the final proxy model; if not, repeat the operations of S2-S5.

[0030] 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.

[0031] Furthermore, the environmental parameters include but are not limited to temperature, humidity, air pressure, wind speed and wind direction.

[0032] 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.

[0033] Furthermore, the control input parameters include but are not limited to control surface angles, engine thrust, and pilot control inputs.

[0034] 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.

[0035] Furthermore, the power system parameters include but are not limited to the engine thrust output, fuel consumption rate and multi-engine power distribution.

[0036] 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.

[0037] Furthermore, the external disturbance includes but is not limited to the influence of airflow disturbance, turbulence and ground obstacles.

[0038] Furthermore, the system status parameters include but are not limited to sensor input and fault detection signals.

[0039] Furthermore, the proxy model is

[0040] f(x)~GP(μ(x),K(x,x')),

[0041] 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);

[0042] The predicted mean of the proxy model is:

[0043]

[0044] 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;

[0045] The prediction variance of the surrogate model is

[0046]

[0047] 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 .

[0048] Furthermore, the area S(·) of the probability box is used as the uncertainty measure unc(·) of the output of the proxy model, then

[0049]

[0050] in, and Both represent the upper bound cumulative distribution function of the probability box, F and F Y (y) represents 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 often used to measure uncertainty;

[0051] 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 four cases:

[0052] When μ1<μ2, and σ1<σ2

[0053]

[0054] When μ1=μ2, and σ1<σ2

[0055]

[0056] When μ1<μ2, and σ1>σ2

[0057]

[0058] When μ1<μ2, and σ1=σ2

[0059] S(·)=μ2-μ1,

[0060] Where Φ represents the cumulative distribution function of the standard normal distribution,

[0061] The present invention also provides an aircraft sequential test design method based on the expected probability box boundary improvement criterion for use in evaluating and determining the aircraft's optimal lift and drag coefficients, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed, optimal flight attitude, and minimizing fuel consumption and structural load.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. The present invention can accurately find the maximum value: The optimization criteria of the expected probability box boundary of the present invention enables the sampling points of the aircraft to effectively focus on the area with the maximum value of the objective function. By introducing the probability box model, the uncertainty range can be quantified, and sampling points that can be quickly guided to the vicinity of the extreme value of the objective function can be preferentially selected. Compared with the traditional Bayesian optimization method, this method pays more attention to finding the local optimal solution rather than the precise fitting of the global model.

[0064] 2. The present invention can flexibly handle uncertainty: The present invention can simultaneously handle random uncertainty (such as manufacturing errors, environmental changes, etc.) and cognitive uncertainty (such as design assumptions, lack of experience of test personnel, etc.) in aircraft tests by improving the expected probability box boundary. This consideration of multi-source uncertainty enables the test design to not only accurately capture the extreme value of the objective function, but also fully cope with various uncertainties in complex environments, ensuring that the optimal solution is found under variable conditions.

[0065] 3. The present invention can also effectively utilize limited resources: Traditional methods often gradually optimize results by improving the accuracy of proxy models under limited experimental resources. This process usually leads to redundant sampling and wastes precious experimental resources. The optimization criteria for improving the expected probability box boundary can reduce redundant experiments while ensuring the efficiency of the maximum value search, maximize the effective information of the experimental data by focusing on the key areas, and make full use of limited resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] 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;

[0067] Figure 2 is a probability box based on GPR provided by an embodiment of the present invention;

[0068] Figure 3 are four types of probability boxes based on GPR provided by an embodiment of the present invention (a means that the predicted mean and the predicted standard deviation of the proxy model are different and the intersection of the upper and lower boundaries of the probability box is located in the lower half, that is, μ1<μ2 and σ2>σ1; b means that the predicted mean of the proxy model is the same and the predicted standard deviation is different, that is, μ1=μ2 and σ1<σ2; c means that the predicted mean and the predicted standard deviation of the proxy model are different and the intersection of the upper and lower boundaries of the probability box is located in the upper half, that is, μ1<μ2 and σ1>σ2; d means that the predicted mean of the proxy model is different and the predicted standard deviation is the same, that is, μ1<μ2 and σ1=σ2);

[0069] Figure 4 Schematic diagram of the offset of the probability box position and shape provided by an embodiment of the present invention;

[0070] Figure 5 The probability box S provided by the embodiment of the present invention i (i=1,2,3,4) schematic diagram;

[0071] Figure 6 A schematic diagram of an acquisition function based on probability box boundary changes provided by an embodiment of the present invention;

[0072] Figure 7 HEG cylindrical half model and computational grid provided for the embodiment of the present invention;

[0073] Figure 8 is the shock wave position comparison provided by the embodiment of the present invention;

[0074] Fig. 9 is the wall pressure distribution provided by the embodiment of the present invention;

[0075] Fig.10 is the wall heat flux distribution provided by the embodiment of the present invention;

[0076] Fig.11 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 60 and the root mean square error (RMSE) being the measurement indicator; b is the test result with the initial sample point being 60 and the minimum absolute difference being the measurement indicator; c is the test result with the initial sample point being 80 and the root mean square error (RMSE) being the measurement indicator; d is the test result with the initial sample point being 80 and the minimum absolute difference being the measurement indicator). DETAILED DESCRIPTION

[0077] 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.

[0078] The implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0079] like Figure 1 As shown, the present invention provides an aircraft sequential test design method based on the expected probability box boundary improvement criterion, comprising the following steps:

[0080] S1: Initial test design, obtaining the sample set D that affects the output results of the aircraft test, D = (X, y);

[0081]

[0082] 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;

[0083] 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.

[0084] The output results of the aircraft in this embodiment include optimal lift and drag coefficients, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed, optimal flight attitude, and minimized fuel consumption and structural load.

[0085] 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.

[0086] S2: Based on the information of the known sample set D, the Gaussian process model is used to establish the proxy model f(X), y = f(X);

[0087] f(x)~GP(μ(x),K(x,x')),

[0088] 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);

[0089] The predicted mean of the surrogate model is:

[0090]

[0091] 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;

[0092] The prediction variance of the surrogate model is

[0093]

[0094] 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 ;

[0095] S3: Based on the proxy model established in step S2, the next test sample point is determined according to the sampling point criterion corresponding to the expected probability box boundary improvement criterion;

[0096] In this embodiment, the probability box is the envelope of all possible cumulative distribution functions of the parameter. The probability box can be obtained by integrating along the upper and lower bounds of the probability box. Combined with the characteristics of the probability box, the area S(·) of the probability box is used as the uncertainty measure unc(·) of the output, as follows: Figure 2 As shown,

[0097]

[0098] in, and Both represent the upper bound cumulative distribution function of the probability box, Fand F Y (y) represents 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, 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 and maximum variance predicted by the proxy model. u(·) represents the unit step function. When the value in the brackets is positive, the function value is 1, otherwise it is 0.

[0099] 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, there are four cases, namely, the two CDF curves have an intersection and no intersection; when there is an intersection, it can be divided into three cases according to the location of the intersection, namely, the intersection is below CDF = 0.5, above and on the straight line; therefore, the area of ​​the above probability box is divided into four cases for calculation; these four cases are that the predicted mean and predicted standard deviation of the proxy model are different and the intersection of the upper and lower boundaries of the probability box is located in the lower half, that is, μ1 < μ2 and σ2 > σ1 (see Figure 3 a) The proxy models have the same prediction mean and different prediction standard deviations, i.e. μ1 = μ2 and σ1 < σ2 (see Figure 3 b) The predicted mean and predicted standard deviation of the proxy model are different and the intersection of the upper and lower boundaries of the probability box is located in the upper half, that is, μ1<μ2 and σ1>σ2 (see Figure 3 c) The proxy models have different prediction means and the same prediction standard deviation, that is, μ1<μ2 and σ1=σ2 (see Figure 3 d).

[0100] for Figure 3 The area of ​​the probability box in a is:

[0101]

[0102] First, S1(·) is calculated;

[0103]

[0104] in,

[0105] 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,

[0106]

[0107] Then you can get

[0108]

[0109] Similarly:

[0110]

[0111] In summary

[0112]

[0113] for Figure 3 The area of ​​the probability box in b is:

[0114]

[0115] for Figure 3 The area of ​​the probability box in c is:

[0116]

[0117] for Figure 3 The area of ​​the probability box in d is:

[0118]

[0119] It is expected that the probability boxes of the two proxy models before and after the sample point is added will not only change in size, but also have a certain offset in shape and position, which can more accurately reflect the impact of the sample point on the proxy model, such as Figure 4 As shown; CDF = 0.5 divides the shadow into 4 parts, upper left, lower left, upper right, lower right, respectively denoted as S1, S2, S3, S4;

[0120] like Figure 5 As shown, the P-box is divided into two parts by CDF = 0.5, denoted as S upper , S lower ; When there is no intersection, calculate S upper ; It can be regarded as half of the sum of the probability box enclosed by the CDF curve of the normal distribution with different means and the same variance and the probability box enclosed by the CDF curve of the normal distribution with the same mean and different variance. When there is an intersection, S is calculated. lower , you can subtract the corresponding S upper get;

[0121] The specific calculations for S1, S2, S3, and S4 are as follows:

[0122] (1) For S1:

[0123] when

[0124] when

[0125]

[0126] (2) For S2:

[0127] when

[0128] when

[0129]

[0130] (3) For S3

[0131] when

[0132] when

[0133]

[0134] (4) For S4

[0135]

[0136]

[0137]

[0138] When considering the minimum optimization problem, the two upper boundaries are expected to change the most, and when considering the maximum optimization problem, the two lower boundaries are expected to change the most; for the minimum optimization problem, when considering the change in standard deviation before and after sampling, that is, When the upper boundary changes, the absolute value is Considering the change of the predicted minimum mean before and after sampling, that is, When the upper boundary changes, the absolute value is For the minimum optimization problem, it is expected that the minimum mean and minimum standard deviation of the prediction will decrease after adding the candidate sample points. Similarly, considering the parameter The schematic diagram of the acquisition function based on the change of probability box boundary is as follows Figure 6 As shown, the point selection criterion (collection function) of the minimum optimization problem based on the boundary change of the probability box can be expressed as:

[0139]

[0140] Similarly, the point selection criterion (collection function) of the maximum optimization problem based on the boundary change of the probability box can be expressed as:

[0141]

[0142] Among them, μ L and μ U Respectively expressed as the maximum mean and minimum mean; σ L and σ U They are represented by the maximum standard deviation and the minimum standard deviation, n represents the sample size, and k represents the variable that balances the predicted mean and the predicted standard deviation.

[0143] S4: Calculate the real response of the aircraft at the test point and update the sample set;

[0144] 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, for the sample set D 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.

[0145] S5: Determine whether the test stopping criteria are met. If so, output the final proxy model; if not, repeat the operations of S2-S5.

[0146] Specific examples:

[0147] 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 is a verification and confirmation of 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.

[0148] 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 7 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 8 The pressure contour distribution of the cross section (z = 0.01m) is given, and Fig. 9 and Fig.10 The wall pressure distribution and heat flux distribution calculated under fully catalytic wall (FCW) and non-catalytic wall (NCW) conditions are given respectively.

[0149] It can be seen that the calculated position of the detached shock wave is very consistent with the experimental and actual response, the wall pressure value distribution is consistent with the experimental results, and 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 high-temperature gas non-equilibrium aerodynamics and aerodynamic heat.

[0150] 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.

[0151] Fig.11 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 Fig.11 a and Fig.11 c) The optimization effect is measured by the size of the minimum absolute difference (see Fig.11 b and Fig.11 d); and the effectiveness of the proposed algorithm in finding the minimum value of the model in aircraft test design was verified through multiple independent repeated experiments.

[0152] 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 boundary improvement criterion, characterized in that: The following steps are involved: 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 of the aircraft test is aircraft design and performance optimization, including but not limited to optimal lift and drag coefficients, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed, optimal flight attitude, and minimization of fuel consumption and structural load; S2: Based on the information of the known sample set D, the Gaussian process regression model is used to establish the proxy model f(X); S3: Based on the established proxy model, the next test sample point is determined according to the sampling point criterion corresponding to the boundary improvement criterion of the expected probability box; The point selection criterion for the minimum optimal problem based on the boundary change of the probability box is expressed as: The point selection criterion for the maximum optimization problem of boundary change based on probability box is expressed as: 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: Calculate the real response of the aircraft at the test sample points and update the sample set; S5: Determine whether the test stop sampling criteria are met. If so, output the optimal value of 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 boundary 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 boundary 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 boundary 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 boundary 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 method for sequential test design of aircraft based on the expected probability box boundary improvement criterion according to claim 2, 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 boundary 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 boundary 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 boundary 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 boundary 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 boundary 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 between .

12. The aircraft sequential test design method based on the expected probability box boundary improvement criterion according to claim 1 is characterized in that: The area S(·) 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 F Y (y) represents 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 often 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 four cases: When μ1<μ2, and σ1<σ2 When μ1=μ2, and σ1<σ2 When μ1<μ2, and σ1>σ2 When μ1<μ2, and σ1=σ2 S(·)=μ2-μ1, Where Φ represents the cumulative distribution function of the standard normal distribution, 13. Application of the aircraft sequential test design method based on the expected probability box boundary improvement criterion according to any one of claims 1 to 12 in aircraft design and performance optimization evaluation, characterized in that: The applications include, but are not limited to, evaluating and determining the optimal lift and drag coefficients, minimum fuel consumption, optimal flight altitude, optimal maneuvering speed, optimal flight attitude, and minimizing fuel consumption and structural load of an aircraft.

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