Multi-trajectory correction method based on double-driven flight aerodynamic heat agent model

Abstract

The application provides a multiple trajectory correction method based on a double driving flight aerodynamic heat agent model, and relates to the technical field of aerocraft wind tunnel aerodynamic heat test. The method first constructs a double driving agent model containing an ICKF physical driving model and an MLP data driving model; secondly, a multi-time scale trajectory window is constructed by using an aerocraft mass center motion equation set, and a multiple candidate trajectory set is generated by injecting random disturbance into state parameters; then, trajectory weighted fusion under a single model is carried out based on a likelihood weight, and an independent heat flow estimated value is obtained; next, statistical confidence and physical confidence are introduced, and a two-dimensional comprehensive confidence weight is calculated; finally, the prediction results of the double driving model are weighted and fused, and an aerodynamic heat optimal estimated value is output. The application breaks the single model bottleneck, effectively suppresses the measurement noise and low frequency drift, and forcibly guarantees the physical legality of the prediction results, and significantly improves the precision and robustness of the aerodynamic heat estimation.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic and thermal testing technology for aircraft wind tunnels, and more specifically, to a multi-trajectory correction method based on a dual-drive flight aerodynamic and thermal proxy model. Background Technology

[0002] With the rapid development of aerospace technology, aircraft face harsh aerothermal environments during hypersonic flight. Accurate prediction and estimation of aerothermal data during flight are of paramount importance for the design of thermal protection systems, structural strength assessment, and flight safety control of aircraft.

[0003] Currently, the main methods for acquiring aerodynamic thermal data include wind tunnel experiments, numerical simulation (CFD), and calculations using empirical engineering formulas. However, these traditional methods have certain limitations in practical applications. On the one hand, the wind tunnel experimental environment often differs from actual flight conditions, requiring complex corrections when applying experimental data to actual flight missions. On the other hand, numerical simulation involves enormous computational demands, making it difficult to meet the real-time estimation requirements during flight. Furthermore, traditional engineering calculation methods have limited accuracy and are insufficient for describing complex nonlinear aerodynamic thermal processes.

[0004] To address the aforementioned issues, several modified aerodynamic models based on filtering algorithms have emerged in the prior art. For example, patent application CN202411082980.4, entitled "A Flight Aerodynamic Thermal Estimation Method Based on Iterated Cubic Kalman Filtering," discloses a modified aerodynamic thermal model that uses Iterated Cubic Kalman Filter (ICKF) for parameter identification. This model improves the accuracy of aerodynamic thermal estimation to a certain extent by treating airflow parameters and aircraft parameters as unknowns for identification, and solves the problem of traditional models performing poorly under the interference of uncertain parameters.

[0005] However, this single-model-based approach still exhibits shortcomings in generalization ability and robustness when facing complex flight environments and variable data noise. Particularly in flight experiment data processing, there is a lack of technical solutions that can effectively integrate physical mechanism models and data-driven models, and combine multiple trajectory information for real-time, high-precision correction. Therefore, how to propose a flight aerodynamic thermal estimation model that can comprehensively utilize the advantages of multiple surrogate models and possess stronger data denoising and trajectory correction capabilities has become an urgent technical problem to be solved in this field. Summary of the Invention

[0006] The present invention aims to solve at least one of the aforementioned technical problems existing in the prior art.

[0007] Therefore, this invention provides a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model.

[0008] This invention provides a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal surrogate model, comprising: S1. Construct a dual-drive aerodynamic heat proxy model, including a physical drive correction model obtained by parameter identification using iterative capacitive Kalman filtering, and a data drive model trained using a multilayer perceptron network; wherein, both the physical drive correction model and the data drive model take the flight state parameters of the aircraft as input and the predicted aerodynamic heat flux value as output. S2. Generate a set of multiple candidate trajectories, including using the equations of motion of the aircraft's center of mass to construct a multi-timescale trajectory window containing a short-scale high-frequency window and a long-scale trend window through the forward difference method, and injecting random perturbations into the flight state parameters to generate n independent candidate state trajectories, wherein each candidate state trajectory contains a sequence of flight state parameters that evolve over time. S3. Obtain independent model estimates and calculate the comprehensive confidence weight; First, input the flight state parameters in each candidate state trajectory into the physics-driven correction model and the data-driven model respectively to obtain the corresponding candidate aerodynamic heat value set. Calculate the likelihood weight corresponding to each candidate state trajectory, and perform trajectory-level weighted fusion of the candidate aerodynamic heat value set based on the likelihood weight to obtain independent heat flux estimates for the physics-driven correction model and the data-driven model respectively; Subsequently, calculate the comprehensive confidence weight for each independent heat flux estimate. The comprehensive confidence weight is formed by fusing statistical confidence based on Mahalanobis distance and physical confidence based on aerodynamic thermophysical prior constraints. The aerodynamic thermophysical prior constraints include at least heat flux nonnegativity constraints and dynamic consistency constraints. S4. The weighted fusion of multiple models is used to obtain the final correction result. The weighted fusion calculation at the model level is performed on the independent heat flow estimates of the physical-driven correction model and the data-driven model using the comprehensive confidence weight to obtain the final flight aerodynamic thermal correction estimate.

[0009] The multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to the above-described technical solution of the present invention may also have the following additional technical features: In the above technical solution, the physical drive correction model is expressed as:

[0010] in, This indicates the heat flow on the outer surface of the aircraft. This indicates a correction for atmospheric air density; Indicates the equivalent Mach number of the aircraft; Indicates flight speed parameters; Represents the atmospheric gas constant; This indicates a correction for the static temperature of the atmosphere; Indicates airflow parameters; Indicates atmospheric static temperature; This indicates the flight speed of an aircraft, i.e., the Mach number; Indicates the temperature of the aircraft wall; Indicates the equivalent area of ​​the aircraft; Indicates the coordinates of the measuring points on the aircraft; The parameter identification process of the physics-driven correction model includes: By treating airflow parameters, aircraft parameters, and Mach number conversion values ​​as unknowns, parameter identification is performed, and a nonlinear state equation is constructed.

[0011] in, This represents the state vector of the system at time k+1; This represents the state vector of the system at time k; Indicates airflow parameters, Indicates aircraft parameters, This represents the Mach number conversion value, and the superscript k+1 indicates the time corresponding to the parameter; The nonlinear state transition equations of the system; This represents the process noise at time k; And the measurement equation:

[0012] in, Indicates the system's measured values; Define the symbol; This represents the heat flux value at time k, which is the actual measured value in the measurement equation; Represents the nonlinear measurement equation; Indicates measurement noise; Based on nonlinear state equations and measurement equations, the iterative capacitive Kalman filter algorithm is used to update and estimate the state vector.

[0013] In the above technical solution, in step S1, the multilayer perceptron network includes three hidden fully connected layers. Mach number, velocity, altitude, angle of attack, sideslip angle, and position coordinates on the busbar are used as network input features, and heat flux value is used as the output. Mean squared error is used as the loss function for training to obtain the data-driven model. The data-driven model is expressed as:

[0014] in, This represents the heat flux value at time k; This represents the state vector of the system at time k; This represents the data-driven surrogate model function; M represents the aircraft's flight speed, i.e., Mach number; V represents the aircraft's displacement velocity; h represents the aircraft's altitude; α represents the aircraft's angle of attack; β represents the aircraft's sideslip angle; X represents the aircraft's position coordinates on the generatrix; and the superscript k of each input variable represents the time corresponding to that input variable.

[0015] In the above technical solution, in step S2, the equations of motion of the aircraft's center of mass are defined in the vertical plane, and the expressions are as follows:

[0016]

[0017]

[0018] Where m represents the mass of the aircraft; V represents the flight displacement velocity; and t represents time. The variable g represents air resistance; g represents gravitational acceleration. Indicates the inclination angle of the flight path; y represents lift; y represents altitude.

[0019] In the above technical solution, in step S2, for the short-scale high-frequency window, the recursive equations for the estimated state quantities at the previous k-1 times are derived from the actual state quantities at time k based on the forward difference method as follows:

[0020]

[0021]

[0022] in, This represents the velocity estimate at time k-1; This represents the actual velocity value at time k; Indicates the drag coefficient; Indicates atmospheric air density; Indicates the reference area; This indicates the single-step time step size of the forward difference; This represents the tilt angle of the actual flight trajectory at time k; This represents the estimated inclination angle of the flight trajectory at time k-1; Indicates the lift coefficient; This represents the height estimate at time k-1; This represents the actual height value at time k; In the above technical solution, in step S2, for the long-scale trend window, by setting a time span greater than the single-step length, a single-step recursive operator is continuously compounded to derive the state estimate at time step from the actual state quantity at time k. The recursive equation is as follows:

[0023] in, Let represent the column vector of state estimates at time step 1 derived from time k; This represents the velocity estimate at time step derived from time k. This represents the estimated inclination angle of the flight trajectory at time step, derived from time k. This represents the height estimate at time step derived from time k; This represents the column vector of the true state quantities at time k; step represents the time index corresponding to the long-scale trend window. This represents the single-step recursive operator determined by the short-scale high-frequency window recursive equation; Indicates k-step consecutive times. Composite functions of operator operations.

[0024] In the above technical solution, in step S3, the likelihood weight corresponding to each candidate state trajectory is calculated, and the candidate aerodynamic calorific value set is weighted and fused at the trajectory level based on the likelihood weight, including:

[0025]

[0026] in, This represents the likelihood weight corresponding to the i-th trajectory generated at time step i; This represents the heat flux estimate calculated based on the i-th trajectory at time step i; This represents the actual measured value of heat flow at time step 1. This represents an exponential function with base e. This indicates finding the square of the norm; This represents the independent heat flux estimate of a single model at time step 1 after trajectory weighted fusion.

[0027] In the above technical solution, in step S3, for the m-th surrogate model, the formula for calculating its statistical confidence at time k is:

[0028] in, Let represent the statistical confidence level of the m-th surrogate model at time k; exp(·) is an exponential function; The Mahalanobis distance is calculated using the following formula:

[0029] in, This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; This represents the actual measurement state vector at time k; I represents the actual measured heat flux value at time k; I represents the identity matrix. The superscript T represents the measurement noise covariance matrix; the superscript T represents the transpose of the matrix; the superscript -1 represents the inversion of the matrix.

[0030] In the above technical solution, in step S3, for the m-th proxy model, the physical confidence level is calculated based on the physical constraint violation degree:

[0031]

[0032] in, Indicates the degree of physical constraint violation; l is the constraint rule index. The dynamic consistency constraint includes the requirement that the flight state parameters of the trajectory must satisfy the momentum and energy conservation of the equations of motion of the aircraft's center of mass, that is, the trajectory state residual does not exceed the maximum residual allowed by dynamics. The penalty weight for violating the first prior constraint; An indicator function that indicates whether the corresponding constraint is violated; it takes a value of 1 when the constraint is violated and a value of 0 when the constraint is satisfied. This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; Let represent the physical confidence of the m-th surrogate model at time k; exp(·) is an exponential function.

[0033] In the above technical solution, step S4 involves weighted fusion of multiple models to obtain the final corrected result, including:

[0034] in, This represents the final aerodynamic thermal correction estimate at time k, i.e., the final heat flux estimate. This represents the statistical confidence level of the m-th surrogate model at time k; This represents the physical confidence level of the m-th proxy model at time k; This represents the heat flux value estimated by the m-th model at time k.

[0035] In summary, due to the adoption of the above-mentioned technical features, the beneficial effects of the present invention are: This invention constructs a dual-driven architecture of physics and data, breaking through the performance bottleneck of a single model. Given that existing technologies typically rely on only a single physical mechanism model or a purely data-driven model, this invention creatively combines a physical mechanism model represented by Iterative Volumetric Kalman Filter (ICKF) with a data-driven model represented by Multilayer Perceptron (MLP) in parallel. The physical model provides a solid foundation for interpretability and generalization, while the data-driven model compensates for the lack of complex nonlinear mapping capabilities. The complementary advantages of both significantly improve the prediction accuracy and generalization ability of the aerodynamic thermal proxy model under various complex flight conditions.

[0036] This invention proposes a multi-timescale trajectory window that balances transient response and steady-state anti-drift capability. Addressing the issue of drastic state changes and high-frequency noise during hypersonic flight, this invention constructs a short-scale high-frequency window and a long-scale trend window. The short-scale window can quickly capture and respond to highly dynamic abrupt changes in flight states such as angle of attack and Mach number; the long-scale window can effectively constrain the overall dynamic trend of the trajectory and suppress low-frequency drift errors accumulated over long-term flight, thereby significantly enhancing the robustness of trajectory extrapolation at the time domain level.

[0037] This invention introduces a multiple candidate trajectory evolution mechanism to effectively suppress measurement noise and uncertainty interference. Instead of being limited to traditional single deterministic trajectory derivation, this invention generates multiple candidate trajectories by injecting random perturbations into flight state parameters and then uses likelihood weights for trajectory fusion. This processing method based on set theory and probability allows the model to more fully extract measurement information when facing noisy flight experimental data. Through cross-verification and averaging between trajectories, random perturbations are effectively smoothed, resulting in more stable aerodynamic thermal estimation data.

[0038] This invention also designs a comprehensive confidence score based on both physical and statistical dimensions, completely eliminating abnormal predictions that violate physical principles. Traditional neural networks (such as MLPs) are prone to outputting absurd results when encountering unseen extreme conditions (i.e., they become "black boxes" and uncontrollable). This invention not only uses Mahalanobis distance to measure the "statistical confidence score" of data tracking in the fusion weights, but also forcibly introduces non-negativity constraints on heat flow and dynamic consistency constraints as penalty terms for "physical confidence score." This means that any prediction results that violate the laws of conservation of energy, momentum, or fundamental thermodynamics will be given extremely low weights or even directly rejected by prior physical knowledge during the model fusion stage, thereby ensuring the absolute physical legitimacy and high engineering reliability of the final aerodynamic thermal estimation results.

[0039] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0040] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to an embodiment of the present invention; Figure 2 This is a schematic diagram showing the error comparison results of a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to an embodiment of the present invention and a traditional method for laminar flow data. Detailed Implementation

[0041] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0042] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0043] The following reference Figure 1 and Figure 2 This describes a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model, provided by some embodiments of the present invention.

[0044] Some embodiments of this application provide a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model.

[0045] like Figure 1 As shown, the first embodiment of the present invention proposes a multi-trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model, including the following steps S1 to S4.

[0046] S1. Construct a dual-drive aero-thermal proxy model, including a physical drive correction model obtained by parameter identification using iterative capillary Kalman filtering, and a data drive model trained using a multilayer perceptron network; wherein, both the physical drive correction model and the data drive model take the flight state parameters of the aircraft as input and the predicted aero-thermal flux value as output.

[0047] To overcome the errors caused by the uncertainty of parameters in a single physical mechanism model, and the weak generalization ability of a single pure data-driven model under complex flight conditions, this disclosure constructs a dual-driven aerodynamic thermal proxy model at the underlying level, combining both physical and data-driven approaches. The dual-driven aerodynamic thermal proxy model includes: a physical-driven correction model obtained through parameter identification using iterative capillary Kalman filtering, and a data-driven model trained using a multilayer perceptron network. Both the physical-driven correction model and the data-driven model take the aircraft's flight state parameters as input and predict aerodynamic thermal values ​​as output.

[0048] In some embodiments, the physics-driven correction model is represented as:

[0049] in, This indicates the heat flow on the outer surface of the aircraft. This indicates a correction for atmospheric air density; Indicates the equivalent Mach number of the aircraft; Indicates flight speed parameters; Represents the atmospheric gas constant; This indicates a correction for the static temperature of the atmosphere; Indicates airflow parameters; Indicates atmospheric static temperature; This indicates the flight speed of an aircraft, i.e., the Mach number; Indicates the temperature of the aircraft wall; Indicates the equivalent area of ​​the aircraft; This indicates the coordinates of the measurement points on the aircraft.

[0050] Due to the airflow parameters included in the aerodynamic thermal model derived from aerodynamics during specific flight tests... Aircraft parameters The Mach number transformation value *trans* often contains uncertainties, causing the basic model to fail to achieve good prediction results. Therefore, this embodiment treats these three parameters as unknowns for parameter identification and uses the ICKF algorithm to construct a physics-driven correction model.

[0051] The parameter identification process of the physics-driven correction model includes: By treating airflow parameters, aircraft parameters, and Mach number conversion values ​​as unknowns, parameter identification is performed, and a nonlinear state equation is constructed.

[0052] in, This represents the state vector of the system at time k+1; This represents the state vector of the system at time k; Indicates airflow parameters, Indicates aircraft parameters, This represents the Mach number conversion value, and the superscript k+1 indicates the time corresponding to the parameter; The nonlinear state transition equations of the system; This represents the process noise at time k; And the measurement equation:

[0053] in, Indicates the system's measured values; Define the symbol; This represents the heat flux value at time k, which is the actual measured value in the measurement equation; Represents the nonlinear measurement equation; Indicates measurement noise; and All are independent Gaussian white noise sequences, and satisfy the following: , and They are respectively and The covariance matrix.

[0054] Based on nonlinear state equations and measurement equations, the iterative capacitive Kalman filter algorithm is used to update and estimate the state vector.

[0055] The prediction steps of this physics-driven correction model include: first, setting the mean and covariance of the probability distribution of the initial system; second, performing a prediction step, calculating the values ​​of each volume point and the corresponding weights, and performing volume point state prediction, target state prediction, and prediction covariance calculation; next, performing an update step, calculating the measurement prediction value, measurement covariance, state measurement covariance, and Kalman gain; and finally, performing a final estimation, introducing the confidence iteration parameter under Kalman gain to complete the update and estimation of the state vector and covariance.

[0056] It should be noted that the modified aerodynamic thermal model based on iterative capacitive Kalman filtering described above is an existing model in this field. For details on the specific volume point generation rules, the derivation of the Choleski decomposition, and the more detailed prediction and update operation steps of this model, please refer to the aforementioned published patent (patent application number: CN202411082980.4, titled: A method for estimating flight aerodynamic thermal based on iterative capacitive Kalman filtering), which will not be elaborated here.

[0057] To compensate for the limitations of physical models in describing extremely nonlinear aerodynamic thermal processes, this embodiment constructs an aerodynamic thermal proxy model based on an MLP network in parallel.

[0058] In some embodiments, a multilayer perceptron network is used to train aerodynamic thermal flight data offline. Incoming flow flight state parameters are set as network inputs, specifically including Mach number, velocity, altitude, angle of attack, sideslip angle, and position coordinates on the generatrix, with heat flux values ​​as output. During data preprocessing, the input and output data are normalized to improve the convergence speed of network training. In terms of network structure, three hidden fully connected layers are used, each with 16, 64, and 16 neurons respectively.

[0059] During the network training phase, 800 sets of laminar flow data were selected as the dataset, with the test set accounting for 20%. Mean squared error (MSE) was chosen as the loss function, and the network was trained for 450 epochs. After training, a heat flow prediction proxy model with strong nonlinear mapping capabilities was obtained, and its mathematical expression can be written as:

[0060] in, This represents the heat flux value at time k; This represents the state vector of the system at time k; This represents the data-driven surrogate model function; M represents the aircraft's flight speed, i.e., Mach number; V represents the aircraft's displacement velocity; h represents the aircraft's altitude; α represents the aircraft's angle of attack; β represents the aircraft's sideslip angle; X represents the aircraft's position coordinates on the generatrix; and the superscript k of each input variable represents the time corresponding to that input variable.

[0061] Finally, the trained data-driven agent model is stored in an offline file and used as a known inference model for subsequent trajectory weighted fusion algorithms.

[0062] S2. Generate a set of multiple candidate trajectories, including using the equations of motion of the aircraft's center of mass to construct a multi-timescale trajectory window containing a short-scale high-frequency window and a long-scale trend window through the forward difference method, and injecting random perturbations into the flight state parameters to generate n independent candidate state trajectories, wherein each candidate state trajectory contains a sequence of flight state parameters that evolve over time.

[0063] In actual flight tests, the aircraft's state changes drastically and is accompanied by complex measurement noise. To effectively suppress high-frequency noise and low-frequency drift, this embodiment uses the ensemble Kalman algorithm to construct a multi-timescale trajectory window using the aircraft's center-of-mass motion equations, and generates multiple candidate trajectories through state perturbations.

[0064] First, we construct the fundamental dynamic equations of the aircraft. Assuming the Ax axis of the ground coordinate system lies within the flight plane (vertical plane), the coordinate z of the aircraft's center of mass and the trajectory deflection angle are always zero. Assuming the longitudinal plane of symmetry of the aircraft always coincides with the flight plane, the velocity tilt angle and sideslip angle are also zero. Under this assumption, the equations of motion for the aircraft's center of mass, defined in the vertical plane, are as follows:

[0065]

[0066]

[0067] Where m represents the mass of the aircraft; V represents the flight displacement velocity; and t represents time. The variable g represents air resistance; g represents gravitational acceleration. Indicates the inclination angle of the flight path; y represents lift; y represents altitude.

[0068] Lift and drag can be calculated using the following formulas:

[0069]

[0070] in, The lift coefficient; The drag coefficient is related to both the Mach number, angle of attack, and deflection angle (all of which are known).

[0071] Secondly, a multi-timescale trajectory window is designed. Considering the time-domain characteristics of the flight trajectory, this embodiment designs two complementary time-scale windows to cover the dynamic characteristics of the entire flight path: One is a short-scale high-frequency window. This window adopts a single-step design, and its core function is to capture highly dynamic changes in flight state, quickly respond to sudden changes in angle of attack or Mach number, and suppress high-frequency measurement noise. The process noise characteristic corresponding to this window is designed as low-variance Gaussian noise to ensure the sensitivity of the state response.

[0072] Another is the long-scale trend window. This window uses a multi-step design (e.g., 2-10 steps), and its core function is to constrain the overall dynamic trend of the trajectory and suppress low-frequency cumulative drift caused by long-endurance flight. The process noise characteristic corresponding to this window is designed as large-variance Gaussian noise to ensure the robustness of the trend constraint.

[0073] First, we derive the recursive equations for a short-scale, high-frequency window (i.e., a single step size). Assuming the true state quantity at time k is known, from the above equations of motion of the centroid, we can derive the recursive equations for the state estimates at the previous k-1 times using the forward difference method, as follows:

[0074]

[0075]

[0076] in, This represents the velocity estimate at time k-1; This represents the actual velocity value at time k; Indicates the drag coefficient; Indicates atmospheric air density; Indicates the reference area; This indicates the single-step time step size of the forward difference; This represents the tilt angle of the actual flight trajectory at time k; This represents the estimated inclination angle of the flight trajectory at time k-1; Indicates the lift coefficient; This represents the height estimate at time k-1; This represents the actual height value at time k.

[0077] For ease of subsequent explanation, the above single-step state transition process can be abstracted and recorded as a recursive operator. ,Right now:

[0078] Thus through the first The true state quantity at any given moment Received Estimated state quantities at time 1 :

[0079] in, Represents the state quantity obtained based on time k. The velocity estimate at time; Represents the state quantity obtained based on time k. The estimated inclination angle of the flight trajectory at any given time; Represents the state quantity obtained based on time k. Estimated altitude at any given time.

[0080] Then, the multi-step recursive equation for the long-scale trend window is derived. A single-step recursive operator is constructed based on the short-scale high-frequency window. The state estimate for any number of steps (let's say step) can be derived through continuous composite operations. Induction reveals that the state estimate at time k is derived from the true state quantity. Derivation of the state estimate at time step 1 The recurrence relation is as follows:

[0081] in, Let represent the column vector of state estimates at time step 1 derived from time k; This represents the velocity estimate at time step derived from time k. This represents the estimated inclination angle of the flight trajectory at time step, derived from time k. This represents the height estimate at time step derived from time k; This represents the column vector of the true state quantities at time k; step represents the time index corresponding to the long-scale trend window. This represents the single-step recursive operator determined by the short-scale high-frequency window recursive equation; Indicates k-step consecutive times. Composite functions of operator operations.

[0082] Therefore, we can obtain all estimated and actual values ​​of the state at each step, as shown below:

[0083] in, This is the sequence of flight state parameters.

[0084] Finally, multiple independent candidate state trajectories are generated. After constructing the multi-timescale trajectory windows, in order to maximize the use of existing real measurement information, this embodiment introduces the Kalman ensemble approach into trajectory extrapolation. Specifically, for the step, based on the flight center-of-mass motion equations and forward difference equations, small random perturbations (i.e., small-variance or large-variance Gaussian noise) are added to the flight state parameters (velocity, altitude, trajectory inclination) to generate n mutually independent random state trajectories. This method replaces the traditional fixed single-trajectory generation method. Each generated candidate state trajectory contains a dynamic flight state parameter sequence that evolves over time, providing rich data set support for subsequent multiple aerodynamic and thermal predictions by the surrogate model.

[0085] S3. Obtain independent model estimates and calculate the comprehensive confidence weight; First, input the flight state parameters in each candidate state trajectory into the physical-driven correction model and the data-driven model respectively to obtain the corresponding candidate aerodynamic calorimetric value set. Calculate the likelihood weight corresponding to each candidate state trajectory, and perform trajectory-level weighted fusion of the candidate aerodynamic calorimetric value set based on the likelihood weight to obtain independent heat flux estimates for the physical-driven correction model and the data-driven model respectively; Subsequently, calculate the comprehensive confidence weight for each independent heat flux estimate. The comprehensive confidence weight is formed by fusing statistical confidence based on Mahalanobis distance and physical confidence based on aerodynamic thermophysical prior constraints. The aerodynamic thermophysical prior constraints include at least heat flux nonnegativity constraints and dynamic consistency constraints.

[0086] Specifically, after generating multiple candidate state trajectories, this embodiment first performs fusion at the trajectory level of a single model to obtain independent heat flow estimates for each surrogate model, thereby obtaining heat flow estimates for different trajectories at each time step. Subsequently, a comprehensive confidence weight is calculated for these independent estimates to support the final fusion between models. This comprehensive confidence weight covers both statistical and physical dimensions.

[0087] In some embodiments, the flight state parameters of each candidate state trajectory generated in step S2 are independently input into the physics-driven correction model and the data-driven model constructed in step S1, thereby obtaining a set of candidate aerodynamic heat values ​​for each model under different perturbation trajectories. Since different random perturbation trajectories vary in their closeness to reality, this embodiment uses a likelihood function to calculate the likelihood weight corresponding to each trajectory, and then performs a weighted summation of the candidate heat flux values ​​under the same surrogate model based on this weight. The specific calculation formula is as follows:

[0088]

[0089] in, This represents the likelihood weight corresponding to the i-th trajectory generated at time step i; This represents the heat flux estimate calculated based on the i-th trajectory at time step i; This represents the actual measured value of heat flow at time step 1. This represents an exponential function with base e. This indicates finding the square of the norm; This represents the independent heat flux estimate of a single model at time step 1 after trajectory weighted fusion. Through the above calculation, the system eliminates random errors from a single trajectory and obtains smoother and more independent estimation results for each model.

[0090] In some embodiments, to quantify the consistency between the independent estimation results output by each model and the actual measurement data, this embodiment introduces Mahalanobis distance for evaluation. Specifically, in step S3, for the m-th surrogate model, the formula for calculating its statistical confidence at time k is:

[0091] in, Let represent the statistical confidence level of the m-th surrogate model at time k; exp(·) is an exponential function; The Mahalanobis distance is calculated using the following formula:

[0092] in, This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; This represents the actual measurement state vector at time k; I represents the actual measured heat flux value at time k; I represents the identity matrix. The superscript T represents the measurement noise covariance matrix; the superscript T represents the transpose of the matrix; the superscript -1 represents the inversion of the matrix.

[0093] The higher the calculated statistical confidence value, the higher the consistency between the model's predicted trajectory and the measurement data.

[0094] Purely data-driven models are prone to producing anomalous results that violate physical principles under unseen operating conditions. To completely eliminate such anomalous trajectories that are not based on physical understanding, this embodiment embeds hard constraints of aerodynamic thermophysics into the confidence quantification. In some embodiments, at least two insurmountable a priori physical constraints are defined: the first is a non-negativity constraint on heat flux, meaning that the heat flux on the outer surface of the aircraft cannot be negative, requiring... The second constraint is the dynamic consistency constraint, which requires that the norm of the residual parameters of the predicted trajectory must be less than or equal to the maximum allowable residual threshold in dynamics, i.e. This ensures that the model output satisfies the momentum and energy conservation laws of the center-of-mass motion equations. This represents the maximum residual allowed by dynamics, which is related to the specific dynamic constraints of the aircraft.

[0095] Based on the aforementioned physical prior constraints, this embodiment defines the physical constraint violation degree, and thereby calculates the physical confidence degree of the m-th model at time k, using the following formula:

[0096]

[0097] in, Indicates the degree of physical constraint violation; l is the constraint rule index, for example, l=1 corresponds to the non-negative thermal flow constraint, and l=2 corresponds to the dynamic consistency constraint; The penalty weight for violating the first prior constraint needs to be set according to the specific situation, and is generally 1; An indicator function that indicates whether the corresponding constraint is violated; it takes a value of 1 when the constraint is violated and a value of 0 when the constraint is satisfied. This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; Let represent the physical confidence of the m-th surrogate model at time k; exp(·) is an exponential function. The larger the value, the higher the physical legitimacy of the trajectory and the stronger the physical confidence.

[0098] When the comprehensive confidence weight is obtained by fusing the statistical confidence based on Mahalanobis distance and the physical confidence based on aerodynamic thermophysical prior constraints, it can be calculated based on the product of the two.

[0099] S4. The weighted fusion of multiple models is used to obtain the final correction result. The weighted fusion calculation at the model level is performed on the independent heat flow estimates of the physical-driven correction model and the data-driven model using the comprehensive confidence weight to obtain the final flight aerodynamic thermal correction estimate.

[0100] The core objective of step S4 is to use the dual-dimensional comprehensive confidence score composed of "statistical confidence score + physical confidence score" to dynamically adjust the decision weight of the two proxy models in the final output, so as to achieve complementary advantages.

[0101] Specifically, in step S4, the weighted fusion of multiple models yields the final corrected result, including:

[0102] in, This represents the final aerodynamic thermal correction estimate at time k, i.e., the final heat flux estimate. This represents the statistical confidence level of the m-th surrogate model at time k; This represents the physical confidence level of the m-th proxy model at time k; This represents the heat flux value estimated by the m-th model at time k.

[0103] In actual operation, the aforementioned weighted fusion mechanism possesses adaptive adjustment capabilities. For example, when encountering highly dynamic or extremely abrupt flight conditions, if the data-driven model outputs abnormal results that violate physical principles such as energy conservation, its physical constraint violation will increase sharply, leading to a decrease in the model's physical confidence. Approaching zero, the fusion formula automatically suppresses the weight of the data-driven model, smoothly transferring the "dominance" of the final prediction to the more robust physics-driven correction model, thus avoiding system crashes or outputting absurd aerodynamic and thermal correction values. Conversely, in the stable flight range with smaller parameter fluctuations, the data-driven model can fit the nonlinear mapping more delicately, its statistical confidence weight increases, and the system will adopt more of its predictions to improve overall accuracy.

[0104] Furthermore, to verify the advancement of the method in this embodiment, a comparison was made with simulation experimental data. For example... Figure 2 As shown, the predicted aerodynamic thermal curve (red curve) obtained using the multi-trajectory weighted fusion method (including a dual-drive fusion model) of this invention, compared with the curves output by simply using traditional engineering calculation methods (purple curve) and numerical simulation methods (green curve), shows the highest degree of fit between the final prediction result and the actual flight aerodynamic thermal measurement data (blue curve, i.e., the Q experimental value). Especially when processing long-term time series and operating condition data with abrupt changes, the relative error between the predicted value and the actual value obtained by this method is at an extremely low level, fully demonstrating that the dual-drive multi-trajectory correction method has excellent data denoising ability, model generalization, and extremely high reliability in engineering applications.

[0105] In this specification, the illustrative expressions of the terms used do not necessarily refer to the same embodiments or examples. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0106] Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention shall be included within the scope of protection of this invention.

Claims

1. A multi-trajectory correction method based on a dual-drive flight aerodynamic-thermal surrogate model, characterized in that, include: S1. Construct a dual-drive aerodynamic heat proxy model, including a physical drive correction model obtained by parameter identification using iterative capacitive Kalman filtering, and a data drive model trained using a multilayer perceptron network; wherein, both the physical drive correction model and the data drive model take the flight state parameters of the aircraft as input and the predicted aerodynamic heat flux value as output. S2. Generate a set of multiple candidate trajectories, including using the equations of motion of the aircraft's center of mass to construct a multi-timescale trajectory window containing a short-scale high-frequency window and a long-scale trend window through the forward difference method, and injecting random perturbations into the flight state parameters to generate n independent candidate state trajectories, wherein each candidate state trajectory contains a sequence of flight state parameters that evolve over time. S3. Obtain independent model estimates and calculate the comprehensive confidence weight; First, input the flight state parameters in each candidate state trajectory into the physical-driven correction model and the data-driven model respectively to obtain the corresponding candidate aerodynamic heat value set. Calculate the likelihood weight corresponding to each candidate state trajectory, and perform trajectory-level weighted fusion of the candidate aerodynamic heat value set based on the likelihood weight to obtain independent heat flux estimates for the physical-driven correction model and the data-driven model respectively; Subsequently, calculate the comprehensive confidence weight for each independent heat flux estimate. The comprehensive confidence weight is formed by fusing statistical confidence based on Mahalanobis distance and physical confidence based on aerodynamic thermophysical prior constraints, which include at least heat flux nonnegativity constraints and dynamic consistency constraints; S4. The weighted fusion of multiple models is used to obtain the final correction result. The weighted fusion calculation at the model level is performed on the independent heat flow estimates of the physical driving correction model and the data driving model using the comprehensive confidence weight to obtain the final flight aerodynamic thermal correction estimate. The physical-driven correction model is expressed as follows: in, This indicates the heat flow on the outer surface of the aircraft. This indicates a correction for atmospheric air density; Indicates the equivalent Mach number of the aircraft; Indicates flight speed parameters; Represents the atmospheric gas constant; This indicates a correction for the static temperature of the atmosphere; Indicates airflow parameters; Indicates atmospheric static temperature; This indicates the flight speed of an aircraft, i.e., the Mach number; Indicates the temperature of the aircraft wall; Indicates the equivalent area of ​​the aircraft; Indicates the coordinates of the measuring points on the aircraft; The parameter identification process of the physics-driven correction model includes: By treating airflow parameters, aircraft parameters, and Mach number conversion values ​​as unknowns, parameter identification is performed, and a nonlinear state equation is constructed. in, This represents the state vector of the system at time k+1; This represents the state vector of the system at time k; Indicates airflow parameters, Indicates aircraft parameters, This represents the Mach number conversion value, and the superscript k+1 indicates the time corresponding to the parameter; The nonlinear state transition equations of the system; This represents the process noise at time k; And the measurement equation: in, Indicates the system's measured values; Define the symbol; This represents the heat flux value at time k, which is the actual measured value in the measurement equation; Represents the nonlinear measurement equation; Indicates measurement noise; Based on nonlinear state equations and measurement equations, the iterative capacitive Kalman filter algorithm is used to update and estimate the state vector; In step S1, the multilayer perceptron network comprises three hidden fully connected layers, using Mach number, velocity, altitude, angle of attack, sideslip angle, and position coordinates on the bus as network input features, and heat flux value as output. The mean squared error is used as the loss function for training to obtain the data-driven model; the data-driven model is expressed as: in, This represents the heat flux value at time k; This represents the state vector of the system at time k; This represents the data-driven surrogate model function; M represents the aircraft's flight speed, i.e., Mach number; V represents the aircraft's displacement velocity; h represents the aircraft's altitude; α represents the aircraft's angle of attack; β represents the aircraft's sideslip angle; X represents the aircraft's position coordinates on the generatrix; the superscript k of each input variable indicates the time corresponding to the input variable. In step S3, for the m-th surrogate model, the formula for calculating its statistical confidence at time k is: in, Let represent the statistical confidence level of the m-th surrogate model at time k; exp(·) is an exponential function; The Mahalanobis distance is calculated using the following formula: in, This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; This represents the actual measurement state vector at time k; I represents the actual measured heat flux value at time k; I represents the identity matrix. This represents the measurement noise covariance matrix; the superscript T indicates the transpose of the matrix; the superscript -1 indicates the matrix inversion; In step S3, for the m-th proxy model, the physical confidence score is calculated based on the physical constraint violation score: in, Indicates the degree of physical constraint violation; l is the constraint rule index. The dynamic consistency constraint includes the requirement that the flight state parameters of the trajectory must satisfy the momentum and energy conservation of the equations of motion of the aircraft's center of mass, that is, the trajectory state residual does not exceed the maximum residual allowed by dynamics. The penalty weight for violating the first prior constraint; An indicator function that indicates whether the corresponding constraint is violated; it takes a value of 1 when the constraint is violated and a value of 0 when the constraint is satisfied. This represents the state variables estimated by the m-th model at time k; This represents the heat flux value estimated by the m-th model at time k; Let represent the physical confidence of the m-th surrogate model at time k; exp(·) is an exponential function.

2. The multiple trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to claim 1, characterized in that, In step S2, the equations of motion for the center of mass of the aircraft are defined in the vertical plane, and are expressed as follows: Where m represents the mass of the aircraft; V represents the flight displacement velocity; and t represents time. g represents air resistance; g represents gravitational acceleration. Indicates the inclination angle of the flight path; y represents lift during flight; y represents altitude during flight.

3. The multiple trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to claim 2, characterized in that, In step S2, for the short-scale high-frequency window, the recursive equations for the estimated state quantities at the previous k-1 times are derived from the actual state quantities at time k using the forward difference method as follows: in, This represents the velocity estimate at time k-1; This represents the actual velocity value at time k; Indicates the drag coefficient; Indicates atmospheric air density; Indicates the reference area; This indicates the single-step time step size of the forward difference; This represents the tilt angle of the actual flight trajectory at time k; This represents the estimated inclination angle of the flight trajectory at time k-1; Indicates the lift coefficient; This represents the height estimate at time k-1; This represents the actual height value at time k.

4. The multiple trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to claim 3, characterized in that, In step S2, for the long-scale trend window, by setting a time span greater than the single-step length, the single-step recursive operator is continuously compounded to derive the state estimate at time step from the actual state quantity at time k. The recursive equation is as follows: in, Let represent the column vector of state estimates at time step 1 derived from time k; This represents the velocity estimate at time step derived from time k. This represents the estimated inclination angle of the flight trajectory at time step, derived from time k. This represents the height estimate at time step derived from time k; This represents the column vector of the true state quantities at time k; step represents the time index corresponding to the long-scale trend window. This represents a single-step recursive operator determined by the recursive equation of a short-scale high-frequency window. Indicates k-step consecutive times. Composite functions of operator operations.

5. The multiple trajectory correction method based on a dual-drive flight aerodynamic thermal surrogate model according to claim 1, characterized in that, In step S3, the likelihood weight corresponding to each candidate state trajectory is calculated, and the candidate aerodynamic calorimetric set is weighted and fused at the trajectory level based on the likelihood weight, including: in, This represents the likelihood weight corresponding to the i-th trajectory generated at time step i; This represents the heat flux estimate calculated based on the i-th trajectory at time step i; This represents the actual measured value of heat flow at time step 1. This represents an exponential function with base e. This indicates finding the square of the norm; This represents the independent heat flux estimate of a single model at time step 1 after trajectory weighted fusion.

6. The multiple trajectory correction method based on a dual-drive flight aerodynamic thermal proxy model according to claim 1, characterized in that, In step S4, the weighted fusion of multiple models yields the final corrected result, including: in, This represents the final aerodynamic thermal correction estimate at time k, i.e., the final heat flux estimate. This represents the statistical confidence level of the m-th surrogate model at time k; This represents the physical confidence level of the m-th proxy model at time k; This represents the heat flux value estimated by the m-th model at time k.

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