A method for sequential test design of aircraft based on the expected probability box boundary improvement criterion

Abstract

The present invention relates to the technical field of aircraft test design, and in particular to an aircraft sequential test design method based on an expected probability box boundary improvement criterion, which specifically includes the following steps: S1, initial test design, obtaining a sample set that affects the output results in the aircraft test; S2, establishing a proxy model using a Gaussian process regression model based on information of a known sample set D; S3, based on the established proxy model, determining the next test sample point according to a sampling point criterion corresponding to the expected probability box boundary improvement criterion; S4: calculating the true response of the aircraft at the test sample point and updating the sample set; S5: judging whether the test stop criterion is met, and if so, outputting the final proxy model; if not, repeating the operations of S2-S5. The present invention quickly and effectively finds the maximum or minimum value of the objective function by selecting appropriate sampling points in the test design. This new optimization criterion has significant advantages, especially in finding the maximum value problem.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft test design, in particular to a sequential test design method for aircraft equipment, and more particularly to a test design method based on an improved expected probability box (P-box) boundary, for processing and analyzing uncertainties in aircraft tests and optimizing test resources. Background Art

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

[0003] In aircraft test design, while traditional sequential testing methods can improve the accuracy of surrogate models to a certain extent, their optimization effects cannot meet all requirements under specific tasks, especially when the core objective is to find the maximum or minimum value of the objective function. The goal of aircraft test design is not simply to improve the predictive accuracy of the surrogate model. In certain application scenarios, our main concern is to find the maximum or minimum value of the objective function. For example, in optimizing 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 places very high demands on experimental design.

[0004] In actual aircraft testing, experimental resources are often limited, and the goal of experimental design is to maximize information acquisition within these limited resources. Sequential experimental design methods were proposed to address this issue. While traditional sequential experimental design methods, such as the sequential sampling method based on Bayesian optimization, have achieved some success in improving surrogate model accuracy, they are often limited by several factors when it comes to finding the optimal value of the objective function:

[0005] (1) Limitations of sampling point selection: Traditional Bayesian optimization methods focus on improving the accuracy of surrogate models, and usually optimize the model by selecting sampling points that 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, attempting 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 might be to find the optimal aerodynamic characteristics. Traditional methods often select points that minimize the surrogate model's error, but these points may not lie within the objective function's minimum region. Since the entire surrogate model doesn't necessarily require high accuracy in experimental design, we can directly guide the optimization process by selecting strategically important sample points, quickly narrowing the minimum region and improving the efficiency of finding the minimum.

[0007] (2) Low efficiency in the 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 experimental methods may conduct redundant experiments during the optimization process, or the design information of the experiment may not be fully transmitted, resulting in low experimental efficiency. For example, in the early stage of the experiment, 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] Furthermore, traditional methods are slow to optimize, especially in complex aircraft experiments. This process can require multiple sampling and testing cycles, with feedback from each sampling cycle used to update the surrogate model, gradually approaching the optimal solution. However, if the sampling strategy doesn't fully consider optimal resource utilization, experimental efficiency will be significantly reduced, making it impossible to accurately find the optimal value of the objective function within limited time and resources.

[0009] (3) Risk of local optimality: Traditional sequential testing 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 current model's predictive ability in local areas 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 thus cannot effectively find the optimal value globally.

[0010] (4) Inadequate handling of uncertainties: Aircraft tests typically 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. Traditional sequential experimental design methods usually focus on the accuracy of the surrogate model when dealing with uncertainties, ignoring 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 experimental design to avoid misleading the search path for the minimum value is a crucial issue.

[0011] In aircraft testing, maximizing the objective function is often a core task in experimental design. For example, when evaluating aircraft performance, we may need to determine parameters such as the maximum lift coefficient, minimum fuel consumption, optimal flight altitude, and optimal maneuvering speed under a specific flight regime. These objective values ​​are key decision-making factors in aircraft design and performance optimization. Therefore, the focus of experimental design is often not on building a highly accurate global surrogate model, but rather on accurately finding the objective function's maximum value or the extreme value of a key parameter through the appropriate selection of sampling points. For example, in some aircraft optimization tasks, we may not be concerned with accurately modeling the entire system, but rather with finding a local optimal solution within a complex design space using a limited number of experiments. In these cases, the accuracy of the surrogate model is not particularly demanding; the key lies in quickly and efficiently exploring the optimal point. Therefore, the goal of optimization methods has shifted from "fitting the most accurate model" to "effectively finding the objective function's maximum value." This shift requires new experimental design methods to be both efficient and flexible, enabling rapid convergence to the objective minimum within limited resources.

[0012] The P-box model combines traditional probability distribution models with interval models. Its core concept is to characterize the uncertainty of system parameters through upper and lower bounds of the cumulative distribution function (CDF). Compared with traditional single probability distribution models, the P-box model can simultaneously handle both aleatory and epistemic uncertainty, providing a more conservative and tolerant bound. This enables P-box to provide more comprehensive analysis results in complex scenarios with multiple uncertainties.

[0013] Therefore, in order to more effectively deal with the uncertainty of input variables in aircraft tests, the present invention introduces a probability box (P-box) model and proposes an experimental design method based on the 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 scientific nature 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 improvement of the expected probability box (P-box) boundary. By introducing the improvement of the expected probability box boundary, the experimental design no longer simply pursues the high-precision fitting of the overall surrogate model, but pays more attention to quickly and effectively finding the maximum or minimum value of the objective function through the selection of appropriate sampling points. 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: obtain a sample set D that affects the output results of the aircraft test, where 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 loads;

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

[0022] S3: Based on the established proxy model, the next experimental 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 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 for the sample set with sample size n; and They represent the minimum standard deviation and maximum standard deviation of the prediction of the proxy model constructed by the sample set with sample size n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with a sample size of n+1; and They represent the minimum standard deviation and maximum standard deviation of the proxy model prediction constructed by the sample set with a sample size of n+1; k represents the variable that balances the prediction mean and prediction standard deviation,

[0028] S4: Calculate the true 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 mass 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 path and mission execution.

[0037] Furthermore, the external disturbance includes but is not limited to airflow disturbance, turbulence and the influence of 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] Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x);

[0042] The predicted mean of the surrogate 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 observation data, E represents the unit matrix, and y represents the observation 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,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. This invention accurately finds the minimum value: The optimization criterion of the desired probability box boundary enables the aircraft's sampling points to be effectively focused on the region with the objective function's minimum value. By introducing the probability box model, the uncertainty range can be quantified, and sampling points that can quickly guide the target to the objective function's extreme value are preferentially selected. Compared with traditional Bayesian optimization methods, this method focuses more on finding local optimal solutions rather than accurately fitting the global model.

[0064] 2. The present invention can flexibly handle uncertainty: By improving the expected probability box bounds, the present invention can simultaneously handle both random uncertainty (such as manufacturing errors and environmental changes) and epistemic uncertainty (such as design assumptions and insufficient tester experience) in aircraft testing. This consideration of multiple sources of uncertainty enables the experimental design to not only accurately capture the extreme values ​​of the objective function but also fully address various uncertainties in complex environments, ensuring the optimal solution is found under varying conditions.

[0065] 3. This invention also effectively utilizes limited resources: Traditional methods, with limited experimental resources, often gradually optimize results by improving the accuracy of surrogate models. This process often leads to redundant sampling and wastes valuable experimental resources. However, the optimization criterion for improving the expected probability box boundary can reduce redundant experiments while ensuring the efficiency of the minimum value search. By focusing on key areas, it maximizes the effective information of the experimental data and fully utilizes limited resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Flowchart of a method for sequential test design of an aircraft based on an expected probability box overall improvement criterion provided by an embodiment of the present invention;

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

[0068] Figure 3 These are four types of probability boxes based on GPR provided by an embodiment of the present invention (a indicates 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, i.e., μ1 < μ2 and σ2 > σ1; b indicates that the predicted mean of the proxy model is the same and the predicted standard deviation is different, i.e., μ1 = μ2 and σ1 < σ2; c indicates 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 upper half, i.e., μ1 < μ2 and σ1 > σ2; d indicates that the predicted mean of the proxy model is different and the predicted standard deviation is the same, i.e., 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 by the embodiment of the present invention;

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

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

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

[0076] Figure 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 solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0078] The implementation of the present invention is described in detail below with reference to 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 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's important to note that aircraft testing is a critical component of aerospace engineering. It comprehensively evaluates the aircraft's performance, structure, and powertrain to ensure its safety, stability, and efficiency in actual operation. During aircraft testing, output variables are a crucial component of test data. They not only help engineers understand the aircraft's operating status but also provide important insights for design optimization and troubleshooting. Key output variables in aircraft testing include velocity and acceleration, altitude and pressure, temperature, thrust and fuel consumption, attitude and heading, vibration, and structural stress.

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

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

[0087] f(x)~GP(μ(x),K(x,x')),

[0088] Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x);

[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 observation data, E represents the unit matrix, and y represents the observation 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 points are 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 shown in the following example: 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 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 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.

[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 There are four cases as shown, namely, there are two cases where the two CDF curves have an intersection and there is 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, above and on the CDF = 0.5; therefore, the area of ​​the above probability box is divided into four cases for calculation; these four cases are: the predicted mean and the predicted standard deviation of the surrogate model are different and the intersection of the upper and lower boundaries of the probability box is 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 surrogate 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, i.e. 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, calculate S1(·);

[0103]

[0104] in,

[0105] Since the above formula is very complicated to calculate according to conventional integration, the indicator function I is 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 adding the sample point 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, and lower right, which are marked as S1, S2, S3, and S4 respectively;

[0120] like Figure 5 As shown, the P-box is divided into two parts by CDF=0.5, denoted as S and 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 but 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 bounds are expected to change the most, and when considering the maximum optimization problem, the two lower bounds 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 sampling 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 sampling criterion (collection function) for 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 are expressed as the maximum mean and minimum mean respectively; 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 true response of the aircraft at the test point and update the sample set;

[0144] The core principle of this invention is to use Bayesian optimization (Gaussian process regression is one of the commonly used proxy models in Bayesian optimization) to find the complex global optimal solution through an iterative process. First, 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 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 numbers Ma ≥ 5), thermochemical nonequilibrium effects (such as the excitation and relaxation of high-temperature gas internal energy modes and complex chemical reactions between components) occur in the flow field around the vehicle. These effects have a significant impact on the aerodynamic characteristics, aero-thermal environment, flow field structure, optical radiation characteristics, plasma environment, electromagnetic scattering characteristics, and electromagnetic communications of the hypersonic vehicle. Due to operating costs and technical limitations, the thermochemical nonequilibrium flow field information available from ground-based high-enthalpy test equipment is relatively limited, making it difficult to systematically study the high-temperature gas effects on vehicles under real-world flight conditions. Therefore, numerical simulation methods are often used to predict and evaluate the high-temperature gas effects on hypersonic vehicles. NNW-HYFLOW, supported by the National Numerical Wind Tunnel (NNW) project and powered by the Fenglei open source software framework, will be developed as a domestically developed industrial CFD software based on a structured / unstructured hybrid grid for hypersonic applications. It features key features such as simulation of high-temperature gas thermochemical nonequilibrium effects and computational analysis of related aerodynamic, aero-thermal, and aerophysical properties. Numerical simulations were conducted using typical examples such as the HEG wind tunnel test. Research has shown that NNW-HYFLOW offers advantages such as underlying code reuse, good functional compatibility, strong expansion capabilities, and flexible interfaces. Its current test version already possesses excellent numerical simulation capabilities for hypersonic non-equilibrium flows. It demonstrates high numerical calculation accuracy in the prediction and evaluation of thermochemical non-equilibrium effects and their impacted aerodynamic characteristics, aerodynamic thermal environment, and plasma distribution characteristics, preliminarily meeting the requirements for numerical simulation of high-temperature non-equilibrium flows in complex hypersonic vehicles. Regarding thermochemical non-equilibrium effects, the following verification and confirmation of the completed solver functions of the NNW-HYFLOW software are conducted in terms of the calculation accuracy of non-equilibrium flow field characteristics such as shock wave position, electron number density, non-equilibrium aerodynamics and aerodynamic thermal environment, as well as its applicability to complex engineering shapes.

[0148] Numerical simulations were conducted for the HEG shock tunnel cylindrical model test. The calculations used a single-temperature, five-component Dunn-Kang chemical model with a wall temperature of Tw = 300K. The computational grid is as follows: Figure 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 Figure 9 and Figure 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 detachment shock wave position 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 RMSE value and the absolute difference between the minimum value; the former mainly indicates the overall accuracy of the constructed proxy model, the smaller the RMSE value, the higher the accuracy of the constructed proxy model, and vice versa; the latter mainly indicates the effect of the constructed proxy model in finding the minimum value, the smaller the absolute difference, the closer the found minimum value is to the true minimum value, and vice versa.

[0151] Figure 11 The comparison between the two sampling criteria and the proposed criteria is given to verify the advantages of the proposed method. The overall accuracy of the constructed proxy model is measured by the size of the RMSE value (see Figure 11 a and Figure 11 c) The optimization effect is measured by the size of the minimum absolute difference (see Figure 11 b and Figure 11 d); and the effectiveness of the proposed algorithm in finding the model minimum 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 scope of protection of the present invention.

Claims

1. A method for sequential test design of aircraft based on the expected probability box boundary improvement criterion, characterized by: The following steps are involved: S1. Initial test design: obtain the sample set D that affects the output results in the aircraft test, where D = (X, y); Where, each row of X represents a sample point, x represents the input variable used to evaluate the output results in the aircraft test, d represents the dimension of the spatial parameter, n represents the sample size, and y represents the output results of the aircraft test; 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 loads; S2: Based on the information of the known sample set D, a surrogate model f(X) is established using the Gaussian process regression model; S3: Based on the established proxy model, the next test sample points are determined according to the sampling criteria corresponding to the boundary improvement criteria of the expected probability box; The point selection criterion for the minimum optimization 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 the probability box is expressed as: in, and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with sample size n; and They represent the minimum standard deviation and maximum standard deviation of the prediction of the proxy model constructed by the sample set with sample size n; and They represent the minimum mean and maximum mean predicted by the proxy model constructed for the sample set with a sample size of n+1; and They represent the minimum standard deviation and maximum standard deviation of the proxy model prediction constructed by the sample set with a sample size of n+1; k represents the variable that balances the prediction mean and prediction standard deviation, S4: Calculate the true response of the aircraft at the test sample points 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 mass parameters, power system parameters, flight mission and control strategy, external disturbances and system state parameters.

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

8. The aircraft sequential test design method based on the expected probability box 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, guiding the aircraft's flight path and mission execution.

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 effects 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, characterized in that: The proxy model is f(x)~GP(μ(x),K(x,x')), Where GP(μ(x),K(x,x')) represents a Gaussian process, μ(x) is the prior mean function of function f(x), and K(x,x') is the prior covariance function of function f(x); The predicted mean of the surrogate model is: in, Represents the new point x * The predicted mean at μ(x * ) represents the new point x * The prior mean at K(x * ,X) represents the new point x * and the covariance vector between all known points X; K(X,X) represents the covariance matrix between all known points X, is the variance of the noise, representing the random error in the observation data, E represents the unit matrix, and y represents the observation value vector corresponding to the known point X; The prediction variance of the surrogate model is in, Represents the new point x * The prediction variance at K(x * ,x * ) represents the new point x * Its own covariance vector; K(X,x * ) represents all known points X and new points x * The covariance vector between .

12. The aircraft sequential test design method based on the expected probability box boundary improvement criterion according to claim 1, 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, Represents the distance between the upper and lower bounds of the probability box cumulative distribution function, which is 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,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 loads of an aircraft.

Images