A Mechanism Model Parameter Iterative Optimization Method Based on Data and Neural Networks

Abstract

This invention discloses an iterative optimization method for mechanistic model parameters based on data and neural networks. First, a mechanistic model is constructed based on existing experience. Key optimization parameters are analyzed and selected, and an initial parameter value model is built as the model to be optimized. Second, state data such as the aircraft's flight trajectory are collected and preprocessed. Third, an iterative optimization model for parameters is constructed using intelligent optimization algorithms such as neural networks. The model is trained using the preprocessed data, allowing the simulation results of the mechanistic model to gradually approximate the actual data, ultimately yielding an optimized aircraft mechanistic model. This invention integrates the advantages of mechanistic modeling and neural network modeling, achieving iterative optimization of the mechanistic model driven by a hybrid mechanism and data approach.

Description

Technical Field

[0001] This invention relates to an iterative optimization method for mechanistic model parameters based on data and neural networks, belonging to the field of simulation modeling technology. Background Technology

[0002] Currently, there is a significant practical need for multi-granularity, multi-level, high-precision modeling in fields such as aviation, aerospace, shipbuilding, weaponry, and military equipment. How to fully utilize data resources and promote the development of high-fidelity modeling technology is a key focus and challenge for researchers and engineers.

[0003] The iterative optimization method for mechanism model parameters based on data and neural networks is a specific implementation of data-mechanism hybrid simulation modeling. It is also a good combination of artificial intelligence and simulation modeling, which can effectively improve the applicability and intelligence of simulation and has important engineering value for simulation model construction.

[0004] A Chinese patent discloses a method for identifying aerodynamic parameters of controlled projectiles and rockets based on Elman recurrent neural networks. This method applies Elman recurrent neural networks to identify aerodynamic parameters of gliding guided projectiles during controlled flight. Based on a model and sample data, an Elman neural network model is constructed. The number of input layer nodes, hidden layer neurons, activation function, and output layer nodes of the Elman neural network model are determined, and the neural network structure is adjusted. Based on the actual situation of the gliding projectile, the error function is solved, and the network weights are updated. Its limitation is that the iterative optimization process of the mechanistic model parameters cannot consider special states such as the highest and farthest points of the aircraft.

[0005] A Chinese patent discloses a method for identifying aerodynamic parameters of an aircraft based on a physical information neural network. The method involves establishing a dynamic and aerodynamic model of the aircraft to be identified, designing control input signals, conducting simulated flight tests using the model from step one to acquire flight data, inputting the flight data, setting the loss function as the mean square error of the test data, and training a deep neural network between time and aircraft state variables. Based on the obtained deep neural network, the parameters to be identified are set, and an automatic differentiator is used to add differential equation residual terms to the loss function. The deep neural network is then trained again until the loss function converges or reaches a set threshold. Its limitation is that it cannot consider the influence of the model on long-period parameters, including the aircraft's maximum range and maximum flight distance.

[0006] A Chinese patent discloses a method and apparatus for aircraft dynamics modeling based on a NARX neural network. The method includes: obtaining input and output data of the aircraft dynamics model based on Simulink simulation, and preprocessing the data to generate training and testing data; training and testing the aircraft dynamics model using a NARX neural network; and establishing a longitudinal dynamics model of the aircraft based on the trained and tested NARX neural network structure. This patent enables the prediction of aircraft angle of attack and pitch velocity parameters under input conditions such as stochastic elevator and throttle inputs. Its limitation is that it only predicts the aircraft's angle of attack and pitch angle, without including parameters such as thrust.

[0007] Analysis of existing patented technologies reveals several key issues: the types of parameter iterations are limited, focusing primarily on aerodynamic parameters; the parameters optimized through iteration are mostly those of the aircraft model itself, neglecting to iteratively optimize performance parameters such as the aircraft's maximum distance from its farthest point and maximum flight altitude. This results in increased repetitive work for model developers and prolongs system development time. Summary of the Invention

[0008] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an iterative optimization method for mechanism model parameters based on data and neural networks. On the basis of mechanism modeling, the method combines data with the mechanism model to achieve iterative optimization of model parameters, thereby improving the accuracy and adaptability of the model.

[0009] The technical solution of this invention is:

[0010] An iterative optimization method for mechanistic model parameters based on data and neural networks, comprising:

[0011] S1: Analyze the existing mechanism model of the aircraft and select the key optimization parameters of the model;

[0012] S2: Collect historical data on the flight trajectory status of the aircraft, preprocess the historical data, and remove abnormal data;

[0013] S3: Construct a parameter iterative optimization model. The model input is the state variables of the aircraft at a certain moment, including but not limited to flight time, position state deviation, velocity state deviation, acceleration state deviation, and heading angle state deviation. The model output is the key optimization parameters of the aircraft mechanism model. Based on the aircraft mechanism model using the current key optimization parameters, calculate the estimated state value at the next moment, and perform subtraction with the actual state value at the next moment in the actual trajectory to construct a loss function.

[0014] S4: The parameter iterative optimization model is trained using preprocessed historical data, so that the simulation results of the mechanism model gradually approach the actual data, and the optimized aircraft mechanism model is obtained.

[0015] Furthermore, in step S1, based on the existing mechanism model of the aircraft, the key optimization parameters of the model are analyzed and selected, specifically as follows:

[0016] S11: Classify the parameters in the existing mechanism model of the aircraft and extract the parameters with the greatest impact on the flight trajectory in each category;

[0017] S12: Select flight trajectory error as the objective function to measure the deviation between the simulated trajectory and the actual trajectory; record the changes in flight trajectory for each parameter extracted in the perturbation step S11, evaluate the degree of influence of each parameter on the objective function, and identify the multiple parameters that are most critical to the output of the mechanism model as key optimization parameters.

[0018] Furthermore, in step S11, the parameters in the existing mechanism model of the aircraft are classified, including but not limited to aerodynamic parameters, inertial parameters, control parameters, and guidance parameters.

[0019] Extract the parameters that have the greatest impact on the flight trajectory from each category:

[0020] Among the aerodynamic parameters, the parameters that have the greatest impact on flight trajectory include lift coefficient, drag coefficient, and side force coefficient.

[0021] Among the inertial parameters, the parameters that have the greatest impact on the flight trajectory include the total mass and moment of inertia of the aircraft;

[0022] Among the control parameters, the parameters that have the greatest impact on flight trajectory include rudder deflection and thrust;

[0023] Among the guidance parameters, the parameters that have the greatest impact on the flight trajectory include the aircraft's guidance mode and guidance rate; among them, the guidance mode is the method of controlling the aircraft to fly along a predetermined trajectory.

[0024] Furthermore, in step S12, the method for identifying the multiple parameters most critical to the output of the mechanistic model is as follows:

[0025] First, determine the baseline values ​​of all input parameters in the mechanistic model, and calculate and record the objective function values ​​when all parameters are at the baseline values. Then, using the OAT method, change only one input parameter at a time and calculate the change in the objective function after the parameter is changed.

[0026] By assessing the change in the objective function after each parameter is changed, the sensitivity of each parameter is evaluated. All parameters are then ranked according to the sensitivity index to identify the parameters that have a significant impact on the objective function.

[0027] Further, in step S2, historical data of the aircraft's flight trajectory status are collected, including parameters at different flight conditions and at different time points, including position, speed, acceleration, heading angle and attitude angle; the obtained historical data are preprocessed, and the preprocessing operations are as follows: first, outlier detection and filtering are performed to clean and correct outlier data; then, state variable difference and normalization processing are performed.

[0028] Further, in step S3, the loss function is obtained by subtracting the estimated state value at the next moment calculated based on the aircraft mechanism model from the actual state value at the next moment in the actual trajectory, as follows:

[0029] Let the current coordinates of the spacecraft's position be [p] x(k) ,p y(k) ,p z(k) The next position coordinates predicted by the mechanism model are [p] x(k+1) ,p y(k+1) ,p z(k+1) The actual coordinates at the next moment are [p] x(k+1) ,p y(k+1) ,p z(k+1) The difference between the estimated and actual positions is obtained by subtracting the values:

[0030] [p x(k+1) -p x(k+1) ,p y(k+1) -p y(k+1) ,p z(k+1) -p z(k+1) ]

[0031] Calculate the absolute distance as the loss function value:

[0032]

[0033] After making the loss function dimensionless, the updated loss function is:

[0034]

[0035] Where, As a dimensionless factor, all terms of the loss function are dimensionless, and 120% to 150% of the maximum distance between two adjacent time points is taken.

[0036] Furthermore, in step S3, a parameter iterative optimization model is constructed using a BP neural network.

[0037] Furthermore, the Adam adaptive learning rate neural network optimization method is adopted. By tracking the first and second moments of the gradient, the learning rate of each parameter is adjusted, so that the learning rate is adaptively adjusted in each training step. This achieves parameter iterative optimization driven by a mixture of mechanism and data, thereby improving training efficiency and convergence speed.

[0038] Furthermore, the accuracy of the optimized aircraft mechanism model is verified:

[0039] The preprocessed historical data is divided into training data and test data; the training data is used to train the parameter iterative optimization model.

[0040] Simulation experiments were conducted based on the optimized aircraft mechanism model. The simulation results were compared with the test data to evaluate the accuracy of the aircraft mechanism model and obtain the model deviation, which was then used to correct the aircraft mechanism model.

[0041] Furthermore, in step S4, the preprocessed historical data is used to train the parameter iterative optimization model, so that the simulation results of the mechanism model gradually approach the actual data. After completing the iterative optimization, the parameter iterative optimization model outputs the key optimization parameters of the aircraft corresponding to the current input. If the parameter is constant, the output of the parameter is a constant value. If the parameter is a time-varying quantity, the parameter will change with different inputs, and the parameter iterative optimization model parameters corresponding to different times are obtained.

[0042] The advantages of this invention compared to the prior art are:

[0043] (1) This invention solves the problems of low efficiency, low intelligence level and low accuracy of model parameters in the existing simulation modeling process by introducing a neural network algorithm to iteratively optimize the parameters of the mechanism model. It integrates the advantages of mechanism modeling and neural network modeling to realize the iterative optimization of the mechanism model driven by mechanism and data.

[0044] (2) This invention selects the parameters to be optimized in the mechanism model through sensitivity analysis, which solves the problem of lack of effective basis for selecting the parameters to be identified in the model. All parameters are sorted according to the sensitivity index to achieve the selection of the parameters to be optimized that have the greatest impact on the objective function.

[0045] (3) This invention solves the problem that direct fitting of neural networks is not easy to converge by constructing a loss function that combines the predicted value of the mechanism model with the actual historical data value, and realizes the iterative optimization of neural network parameters under the constraint of the mechanism model. Attached Figure Description

[0046] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0047] Figure 1 This is a flowchart of the mechanistic model parameter iterative optimization method based on data and neural networks according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the motion equations of an aircraft according to an embodiment of the present invention;

[0049] Figure 3 This is a flowchart of the aircraft trajectory data processing according to an embodiment of the present invention;

[0050] Figure 4 This is a schematic diagram of the BP neural network iterative optimization model according to an embodiment of the present invention. Detailed Implementation

[0051] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0052] This invention proposes an iterative optimization method for mechanistic model parameters based on data and neural networks. It consists of two main layers: a model layer and a data layer. The model layer is used to construct the iterative optimization model and the data layer is used to process the model data. Together, they complete the iterative optimization of the mechanistic model.

[0053] Taking an aircraft model as an example, the process of this method is as follows: Figure 1 As shown, the specific steps include the following:

[0054] S1: Based on existing experience, construct a mechanism model, analyze and select key optimization parameters of the model, and construct an initial parameter value model as the model to be optimized.

[0055] S10: Model Object Determination

[0056] The model object is a six-degree-of-freedom (DOF) aircraft model. A six-DOF aircraft model is a mathematical model that describes the motion state of an aircraft in three-dimensional space, such as... Figure 2 As shown, it covers the aircraft's three translational degrees of freedom (displacement along the X, Y, and Z axes) and three rotational degrees of freedom (rotation about the X, Y, and Z axes).

[0057] Based on Newtonian mechanics, the vector equation for the motion of the aircraft's center of mass in inertial space is:

[0058] ma i =F+mg

[0059] We are usually concerned with the motion of the aircraft relative to the Earth, specifically the velocity of the aircraft's center of mass relative to the Earth, i.e., the relative velocity, expressed in terms of V. k The relative acceleration is expressed as dV. k / dt. Because the Earth has an angular velocity of rotation, the Earth coordinate system S e It is not an inertial frame of reference, therefore the equations of relative motion contain variables related to angular velocity ω. e The resulting inertial force term.

[0060] The absolute acceleration a of the aircraft i Equal to relative acceleration dV k / dt, entrainment acceleration a e And the acceleration a c The sum is:

[0061] a i =dV k / dt+a e +a c

[0062] The entrainment acceleration is:

[0063] a e =ω E ×(ω E ×r)

[0064] The Gothic acceleration is:

[0065] a c =2ω E ×V k

[0066] The gravitational acceleration produced by a spherical Earth can be expressed as:

[0067] g = -(μ / r) 3 )r

[0068] The combined equations of motion of the aircraft relative to the ground can be obtained as follows:

[0069]

[0070] Its representation in the aircraft track coordinate system is as follows:

[0071]

[0072] The kinematic equations of the center of mass under the assumption of a spherical Earth are as follows:

[0073]

[0074] The dynamic equation for the rotational motion of the aircraft is:

[0075]

[0076] The absolute angular velocity ω of the aircraft should be equal to the sum of the following three parts: the angular velocity of Earth's rotation ω E S u Compared to S e angular velocity ω ue and S b Compared to S u angular velocity ω bu .

[0077] Establish the rotational kinematics differential equations, i.e., the rates of change of relative attitude angles dφ / dt, dθ / dt, and dψ / dt, and the relative angular velocity component ω. rxb ω ryb and ω rzb The relationship.

[0078]

[0079] S11: Determination of Key Optimization Parameters for the Model

[0080] 1) Parameter classification

[0081] First, the model parameters are divided into the following categories, and the parameters that have the greatest impact on the flight trajectory are selected, including aerodynamic parameters (lift coefficient, drag coefficient, side force coefficient, etc.), inertial parameters (mass distribution, moment of inertia, etc.), control parameters (control surface deflection angle, thrust, etc.), and guidance parameters (guidance method, guidance rate, etc.).

[0082] Aerodynamic parameters: Aerodynamic parameters are key factors describing the behavior of an aircraft in airflow, including lift coefficient, drag coefficient, and side force coefficient. The lift coefficient represents the lift generated by the aircraft in the vertical direction and depends on the angle of attack and airfoil design; the drag coefficient describes the air resistance encountered by the aircraft in its forward direction and is affected by surface smoothness and angle of attack; the side force coefficient reflects the lateral air forces experienced by the aircraft in the transverse direction, affecting its lateral stability. These parameters are crucial in aircraft modeling and simulation, as they influence flight trajectory, fuel efficiency, and flight stability.

[0083] Inertial parameters describe the mass distribution and rotational characteristics of an aircraft, including its total mass and moment of inertia. Total mass affects the aircraft's gravitational and acceleration responses, while the moment of inertia measures the aircraft's resistance to rotation along its axes. Mass distribution determines the aircraft's center of gravity, while the moment of inertia affects its attitude stability and control response. Accurate understanding of these inertial parameters helps optimize the aircraft's handling and stability, ensuring good performance under various flight conditions.

[0084] Control parameters: Control parameters are key factors determining an aircraft's attitude and motion, including rudder deflection and thrust. Rudder deflection refers to the angle of deflection of various control surfaces (such as elevators, rudders, and ailerons), which controls the aircraft's pitch, yaw, and roll attitude by changing the direction of airflow. Thrust refers to the intensity of thrust generated by the engine, directly affecting the aircraft's acceleration and speed. By precisely adjusting these control parameters, stable aircraft control and the target flight trajectory can be achieved.

[0085] Guidance parameters are core elements of an aircraft's navigation and control system, involving two key aspects: guidance mode and guidance rate. Guidance mode refers to the method used to control the aircraft to fly along a predetermined trajectory, which can be achieved through various technologies, such as guidance (PN) and pure tracking. Different guidance modes are suitable for different mission requirements and can affect the aircraft's path planning and ultimate target attainment capabilities. Guidance rate refers to the speed at which the aircraft follows the target or adjusts its course, affecting its responsiveness and the accuracy of path adjustment. A high guidance rate can improve the aircraft's response speed, enabling it to respond more quickly to changes in the external environment and target position, thereby improving the aircraft's stability and flexibility. A balance must be found between response speed and stability when designing and adjusting guidance parameters. By optimizing these guidance parameters, the aircraft's tracking capability and navigation accuracy can be significantly improved, ensuring that it flies along the expected route and accurately reaches the designated target.

[0086] 2) Sensitivity analysis

[0087] Flight trajectory error is chosen as the objective function to measure the deviation between the simulated and actual trajectories. Each parameter is perturbed within a reasonable range, and the changes in the flight trajectory are recorded. These changes are then evaluated, and key parameters for optimization are selected.

[0088] In aircraft trajectory analysis, flight trajectory error is chosen as the objective function to measure the deviation between the simulated and actual trajectories. Each parameter is perturbed within a reasonable range, and the changes in the flight trajectory are recorded to assess the impact of each parameter on the objective function. This method effectively identifies the parameters most critical to the model output, allowing resources to be focused on optimizing these parameters.

[0089] For detailed analysis, the OAT (One-at-a-Time) method was employed, which involves changing only one parameter at a time and observing its impact on the objective function. First, baseline values ​​for all input parameters in the model were established. These baseline values ​​are typically based on real-world data, literature data, or expert experience. For each input parameter, keeping other parameters constant, only the current parameter was changed, and the changes in the objective function were recorded.

[0090] Calculate and record the objective function value F0 when all parameters are at baseline. Perturb each input parameter in turn and calculate the change ΔF of the objective function after the perturbation. The perturbation method can be to increase or decrease the parameter value. Specific methods include: linear perturbation, increasing or decreasing the parameter value by 10%; range perturbation, performing multiple perturbations within the allowable range of the parameter, such as increasing or decreasing the parameter value by 5%, 10%, 15%, etc.

[0091] By calculating the change ΔF of the objective function i To evaluate the sensitivity of each parameter, the sensitivity index can be represented by the change in the objective function, as shown in the following formula:

[0092]

[0093] All parameters are sorted according to sensitivity indicators to identify the parameters that have the greatest impact on the objective function. At the same time, the parameters are further screened based on traditional experience, and the resulting parameters are the key optimization targets.

[0094] S2: Collect state data such as the flight trajectory of the aircraft and preprocess it to become training data.

[0095] S20: Aircraft trajectory data collection

[0096] The trajectory data includes the aircraft's position, velocity, acceleration, and heading angle at different points in time. It collects trajectory data under various initial conditions (including launch point, target point, and initial flight direction) to obtain multiple trajectory data sets, which are then further processed to obtain training data. This information can be acquired using various high-precision measurement devices, including airborne sensors, the Global Positioning System (GPS), and the Inertial Navigation System (INS). Airborne sensors typically include accelerometers, gyroscopes, and magnetometers, used to monitor the aircraft's dynamic changes in real time; GPS provides precise position and velocity data; and the INS supplements the data from other sensors by measuring angular velocity and acceleration, ensuring accurate positioning and navigation even when GPS signals are insufficient.

[0097] S21: Aircraft trajectory data processing

[0098] Because aircraft trajectory data can be affected by various factors, such as sensor errors, communication failures, or environmental interference, these factors may lead to outliers or noise in the data. For example, the data may exhibit abrupt changes in velocity, unreasonable displacement, or discontinuous trajectory paths. If these outliers are not handled properly, they can negatively impact subsequent data analysis and model optimization. Therefore, it is essential to first perform outlier detection on the trajectory data to identify potential discontinuous regions or erroneous data, such as… Figure 3 As shown.

[0099] To further improve data quality, filtering techniques are often used to smooth trajectory data. Filtering is a method to improve data quality by removing noise or interference signals. Commonly used filtering techniques include moving average filtering and Kalman filtering. Moving average filtering smooths short-term fluctuations by calculating local averages of data points and is suitable for handling uniform noise; while Kalman filtering is a recursive filter that can effectively estimate the state in dynamic systems and is suitable for handling noise with dynamic characteristics.

[0100] Once outlier data is identified, data cleaning and correction are essential. This includes removing erroneous data and filling in missing values ​​using interpolation. Interpolation is a mathematical method for estimating missing data points, effectively smoothing the data and maintaining its continuity. In addition to interpolation, trends and patterns in historical data can be used to correct the data, ensuring its rationality and consistency. After processing, further data validation is performed to confirm that the processed data accurately reflects the aircraft's motion status.

[0101] At this point, continuous and smooth aircraft trajectory data is obtained, which is further processed into training and testing data that can be used by the neural network. For any trajectory data, the trajectory data is sliced ​​according to a fixed time step Δt to obtain state information at different times.

[0102] [x0,x1,x2,...,x k ,...,x f ]

[0103] In the formula, x represents the aircraft state at a certain moment, including position, velocity, acceleration, and heading angle information, forming a high-dimensional vector. The subscripts indicate the time series, where t0 indicates the start of flight, and the time interval between any two moments is Δt, i.e., t k+1 -t k =Δt,t f This represents the last moment of the current flight trajectory. For simplicity, the t-th moment will be... k The state variable at time x is represented as x k Therefore, this high-dimensional vector matrix can be used to describe the state variables in a certain spacecraft trajectory.

[0104] The state variables are differentially processed, that is, all state variables at the next time step are subtracted from the state variables at the previous time step to obtain new state difference data, which is represented as follows:

[0105] [Δx1,Δx2,...,Δx k ,...,Δx f ] = [x1-x0,x2-x1,...,x k -x k-1 ,...,x f -x f-1 ]

[0106] Finally, the data is normalized. The main purpose of normalization is to adjust data of different scales to a relatively consistent range, typically by scaling feature values ​​to the range [-1, 1]. This prevents certain features from dominating model updates during training due to their excessive magnitude, ensuring that the model has the same sensitivity when processing various features. Using Min-MaxScaling normalization, for a given feature value Δx, the scaled value Δx' is calculated using the following formula:

[0107]

[0108] Furthermore, the anti-normalization method is as follows:

[0109] Δx=Δx′·(max(Δx)-min(Δx))+min(Δx)

[0110] S22: Classification of Aircraft Training Data and Test Data

[0111] Training data is the dataset used to build and train the neural network model. Through the training data, the model can learn the dynamic characteristics and behavioral patterns of the aircraft. The training data should have broad coverage, encompassing various possible flight conditions and scenarios, so that the model can learn to handle diverse situations. In this method, the training data is the aircraft state difference data after the normalization process described above, i.e., the [Δx1', Δx2', ..., Δx] values ​​for each trajectory. f ').

[0112] Test data is a dataset independent of the training data, used to evaluate the model's performance and validate its behavior on new data. Test data typically consists of data never seen by the model before, effectively testing its generalization ability and prediction accuracy. Test data should originate from the same source as the training data but should not be included in the training process to ensure that the model's evaluation results are not affected by the training process. Analyzing the test data allows us to understand the model's performance in real-world applications and assess its robustness and accuracy under different flight conditions.

[0113] The data is divided into training and testing data. The training data is used to evaluate the fit of the optimized model, while the testing data is used to evaluate its generalization ability. The split ratio is 80% for training and 20% for testing. This division ensures that the training data is sufficiently rich to allow the model to learn fully, while the testing data is sufficiently independent to effectively validate the model's performance. To further verify the model's reliability, cross-validation can be used. This involves dividing the dataset into multiple subsets and alternating between different subsets as training and testing data to comprehensively evaluate the model's performance on different datasets.

[0114] S3: Constructing a parameter iterative optimization model using intelligent optimization algorithms such as neural network algorithms.

[0115] 1) Construction of BP neural network model

[0116] Backpropagation (BP) neural networks are a widely used feedforward artificial neural network model with a multi-layered structure, such as... Figure 4 As shown, it includes an input layer, hidden layers, and an output layer. By learning from a training dataset, the BP neural network can adjust the weights and biases in the network, thereby modeling the complex nonlinear relationship between the input and output.

[0117] The training process of a BP neural network consists of two stages: forward propagation and backward propagation. In the forward propagation stage, input data is passed from the input layer through the hidden layers to the output layer, and a loss function is calculated to measure the difference between the model's output and the actual target. In the backward propagation stage, the error is propagated from the output layer back to the input layer through the hidden layers, the gradient is calculated, and the neuron weights are updated using gradient descent to reduce the loss function. Through multiple iterations of training, the network performance gradually converges to a satisfactory level.

[0118] The input to the neural network is the state difference component Δx' of the aircraft at a certain moment, specifically represented as...

[0119] x input =[t,Δp,ΔV,Δa,Δχ]

[0120] In the formula, t is time, Δp is the position state deviation between two adjacent moments, ΔV is the velocity state deviation between two adjacent moments, Δa is the acceleration state deviation between two adjacent moments, and Δχ is the heading angle state deviation between two adjacent moments.

[0121] The output consists of the key optimization parameters of the aircraft [B1,B2,...,B] n The parameter values ​​[b1, b2, ..., b] correspond to the current state variables. n ], representing

[0122] y output=[b1,b2,...,b n ]

[0123] After outputting the key optimization parameters, these parameters are substituted into the mechanistic model, and a single-step integration is performed to obtain the state prediction for the next time step. The difference between this prediction and the actual state value at the next time step is then calculated to obtain the loss function (the specific loss function will be described in detail later). After completing the iterative optimization, the output of the neural network will be the key parameters of the aircraft corresponding to the current state. If the parameter is a constant, the output of this parameter will be a constant value; if the parameter is a time-varying quantity, it will change with different inputs to obtain the model parameters corresponding to different time steps.

[0124] The activation function used is the ReLU activation function, and its equation is as follows:

[0125]

[0126] The calculation process of the aircraft dynamics model is still completed by the mechanism model, and the calculated results are transmitted to the output layer of the neural network. The parameters to be optimized will be included as features in the neural network model, and iterative optimization will be achieved through the loss function constructed subsequently.

[0127] 2) Construction of loss function

[0128] The loss function is obtained by subtracting the estimated state value of the next moment from the state value of the next moment in the actual trajectory.

[0129] Let the current coordinates of the spacecraft's position be [p] x(k) ,p y(k) ,p z(k) The next position coordinates predicted by the mechanism model are [p] x(k+1) ,p y(k+1) ,p z(k+1) The actual coordinates at the next moment are [p] x(k+1) ,p y(k+1) ,p z(k+1) The difference between the estimated and actual positions is obtained by subtracting the values.

[0130] [p x(k+1) -p x(k+1) ,p y(k+1) -p y(k+1) ,p z(k+1) -p z(k+1) ]

[0131] And calculate the absolute distance as the loss function.

[0132]

[0133] To better balance the loss function, it is made dimensionless, and the updated loss function is:

[0134]

[0135] In the formula, As a dimensionless factor, all terms of the loss function are dimensionless, and 120% to 150% of the maximum distance between two adjacent time points is taken.

[0136] S4: Through parameter iterative optimization driven by a combination of mechanism and data, the simulation results of the mechanism model gradually approach the actual data, and finally the optimized aircraft mechanism model is obtained.

[0137] S40: Intelligent Iterative Optimization of Model Parameters

[0138] An Adam adaptive learning rate neural network optimization method is employed, which adjusts the learning rate for each parameter by tracking the first moment (mean) and second moment (variance) of the gradient. This method allows for adaptive adjustment of the learning rate in each training step, thereby improving training efficiency and convergence speed.

[0139] Adam incorporates the concept of momentum, which uses an exponentially weighted average of historical gradient values ​​to help optimization algorithms update gradients more stably. Momentum smooths gradient changes, reduces oscillations, and thus accelerates convergence. Adam also integrates the adaptive learning rate feature of RMSprop. RMSprop adjusts the learning rate by using an exponentially weighted average of the squared gradients of each parameter. This allows for different learning rates for different parameter updates, facilitating updates at different speeds in different directions, thereby improving training efficiency and effectiveness.

[0140] S41: Model Accuracy Verification

[0141] 1) Model Testing

[0142] After iterative optimization of the aircraft model, conducting simulation experiments is a crucial step in verifying the model's accuracy and performance. By running the aircraft model in a simulation environment, key flight state data, such as flight altitude, flight distance, time to reach maximum altitude, and time to reach the farthest point, are recorded. This simulation data is compared with actual flight records, and the deviation is calculated. The deviation is used to assess the model's accuracy by comparing the differences between simulation results and actual values, ensuring that the model accurately reflects the aircraft's performance in real-world environments. Through this comparative analysis, potential errors in the model can be identified and corrected, thereby improving the reliability and performance of the aircraft in practical applications.

[0143] 2) Qualitative error analysis

[0144] The deviation between simulation results and actual data is calculated. Quantitative statistics are achieved using mean squared error (MSE).

[0145] Based on 20% of the test data, the actual values ​​of flight altitude, flight distance, time to reach maximum altitude, and time to reach the farthest point are compared with the model simulation values ​​to obtain the model deviation.

[0146] This invention addresses the challenges of traditional mechanistic modeling, including nonlinearity, strong coupling leading to complex mechanisms, high learning costs, low development efficiency, low intelligence levels, and inaccurate model parameters. It proposes an iterative optimization method for mechanistic model parameters based on data and neural networks. First, key optimization parameters are analyzed and selected, and an initial parameter value model is constructed based on existing research experience as the model to be optimized. Then, an iterative optimization model is built using intelligent optimization algorithms such as neural networks. State data, such as the aircraft's flight trajectory, is collected and preprocessed to become training data. Through iterative parameter optimization driven by a hybrid mechanism and data approach, the simulation results of the mechanistic model gradually approximate the actual data, ultimately yielding an optimized aircraft mechanistic model. Simultaneously, the actual data is divided into training and testing data. The training data is used to evaluate the fit of the optimized model, while the testing data is used to evaluate its generalization ability. This evaluation and analysis improves the model's accuracy and reliability.

[0147] The application of this invention will effectively improve modeling efficiency and accuracy, providing a feasible solution for accurate and rapid modeling of mechanistic models. Firstly, a general hybrid modeling method combining mechanistic and data approaches is proposed, addressing the inaccuracies of purely mechanistic modeling and the difficulty in convergence of purely neural network fitting. This method integrates the advantages of both approaches, achieving optimization of the mechanistic model through parameter iterative optimization driven by the hybrid approach of mechanistic and data. Secondly, taking typical aircraft modeling as an example, this invention solves the challenge of accurately modeling aircraft when parameters are unknown. This method can be extended to various aircraft, maneuvering platforms, radar, and other modeling and simulation fields.

[0148] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for iterative optimization of mechanistic model parameters based on data and neural networks, characterized in that, include: S1: Classify the parameters in the existing mechanics models of the aircraft, including but not limited to aerodynamic parameters, inertial parameters, control parameters, and guidance parameters; extract the parameters with the greatest impact on the flight trajectory from each category, analyze and select the key parameters for model optimization; specifically, the parameters with the greatest impact on the flight trajectory extracted from each category are as follows: Among the aerodynamic parameters, the parameters that have the greatest impact on flight trajectory include lift coefficient, drag coefficient, and side force coefficient. Among the inertial parameters, the parameters that have the greatest impact on the flight trajectory include the total mass and moment of inertia of the aircraft; Among the control parameters, the parameters that have the greatest impact on flight trajectory include rudder deflection and thrust; Among the guidance parameters, the parameters that have the greatest impact on the flight trajectory include the aircraft's guidance mode and guidance rate; among them, the guidance mode is the method of controlling the aircraft to fly along a predetermined trajectory. S2: Collect historical data on the flight trajectory status of the aircraft, preprocess the historical data, and remove abnormal data; S3: Construct a parameter iterative optimization model. The model input is the state variables of the aircraft at a certain moment, including but not limited to flight time, position state deviation, velocity state deviation, acceleration state deviation, and heading angle state deviation. The model output is the key optimization parameters of the aircraft mechanism model. Based on the aircraft mechanism model using the current key optimization parameters, calculate the estimated state value at the next moment, and perform subtraction with the actual state value at the next moment in the actual trajectory to construct a loss function. S4: The parameter iterative optimization model is trained using preprocessed historical data, so that the simulation results of the mechanism model gradually approach the actual data, and the optimized aircraft mechanism model is obtained.

2. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, In step S1, based on the existing mechanism model of the aircraft, the key optimization parameters of the model are analyzed and selected, specifically as follows: S11: Classify the parameters in the existing mechanism model of the aircraft and extract the parameters with the greatest impact on the flight trajectory in each category; S12: Select flight trajectory error as the objective function to measure the deviation between the simulated trajectory and the actual trajectory; record the changes in flight trajectory for each parameter extracted in the perturbation step S11, evaluate the degree of influence of each parameter on the objective function, and identify the multiple parameters that are most critical to the output of the mechanism model as key optimization parameters.

3. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 2, characterized in that, In step S12, the method for identifying the multiple parameters most critical to the output of the mechanistic model is as follows: First, determine the baseline values ​​of all input parameters in the mechanistic model, and calculate and record the objective function values ​​when all parameters are at the baseline values. Then, using the OAT method, change only one input parameter at a time and calculate the change in the objective function after the parameter is changed. By assessing the change in the objective function after each parameter is changed, the sensitivity of each parameter is evaluated. All parameters are then ranked according to the sensitivity index to identify the parameters that have a significant impact on the objective function.

4. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, In step S2, historical data of the aircraft's flight trajectory status are collected, including parameters at different flight conditions and at different time points, including position, speed, acceleration, heading angle and attitude angle. The obtained historical data is preprocessed. The preprocessing operation is as follows: first, outlier detection and filtering are performed to clean and correct outlier data; then, state variable difference and normalization processing are performed.

5. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, In step S3, the loss function is obtained by subtracting the estimated state value for the next moment from the estimated state value calculated based on the aircraft mechanism model and the actual state value for the next moment in the actual trajectory. Specifically: Let the current coordinates of the spacecraft's position be [p] x(k) ,p y(k) ,p z(k) The next position coordinates predicted by the mechanism model are [p] x(k+1) ,p y(k+1) ,p z(k+1) The actual coordinates at the next moment are [p] x(k+1) ,p y(k+1) ,p z(k+1) The difference between the estimated and actual positions is obtained by subtracting the values: Calculate the absolute distance as the loss function value: After making the loss function dimensionless, the updated loss function is: In the formula, As a dimensionless factor, all terms of the loss function are dimensionless, and 120% to 150% of the maximum distance between two adjacent time points is taken.

6. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, In step S3, a parameter iterative optimization model is constructed using a BP neural network.

7. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, The Adam adaptive learning rate neural network optimization method is adopted. By tracking the first and second moments of the gradient, the learning rate of each parameter is adjusted, enabling adaptive adjustment of the learning rate in each training step. This achieves parameter iterative optimization driven by a mixture of mechanism and data, thereby improving training efficiency and convergence speed.

8. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, The accuracy of the optimized aircraft mechanism model was verified: The preprocessed historical data is divided into training data and test data; the training data is used to train the parameter iterative optimization model. Simulation experiments were conducted based on the optimized aircraft mechanism model. The simulation results were compared with the test data to evaluate the accuracy of the aircraft mechanism model and obtain the model deviation, which was then used to correct the aircraft mechanism model.

9. The method for iterative optimization of mechanistic model parameters based on data and neural networks according to claim 1, characterized in that, In step S4, the parameter iterative optimization model is trained using preprocessed historical data, so that the simulation results of the mechanism model gradually approach the actual data. After completing the iterative optimization, the parameter iterative optimization model outputs the key optimization parameters of the aircraft corresponding to the current input. If the parameter is constant, the output of the parameter will be a constant value; If the parameter is a time-varying quantity, then the parameter will change with different inputs, resulting in the parameter iteration optimization model parameters corresponding to different times.

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