Aircraft flutter boundary rapid prediction method based on sequence-to-sequence model

Abstract

The invention discloses an aircraft flutter boundary rapid prediction method based on a sequence-to-sequence model, and relates to the technical field of aircraft flutter boundary prediction. According to the method, the capturing capability of a GRU neural network on time sequence features, the focusing effect of an additive and dot product attention mechanism on key coupling features and the sequence mapping advantage of a sequence-to-sequence model are fused, and the dynamic time sequence data is effectively processed by a sliding window mechanism and the model training stability is guaranteed by a gradient truncation mechanism; compared with a traditional fluid-solid coupling simulation method, the fluid-solid coupling simulation method has the advantages that the structure motion law of pneumatic and structure coupling and the time sequence dependency relationship of unsteady aerodynamic force can be accurately learned, flutter boundary prediction results under different flow working conditions can be quickly generated, the prediction efficiency is greatly improved, meanwhile, the prediction precision and model robustness are ensured, and the method is suitable for large-scale popularization and application. The method can effectively adapt to the flutter boundary rapid evaluation requirement under the complex flow working condition of an aircraft.

Description

Technical Field

[0001] This invention relates to the field of aircraft flutter boundary prediction technology, and in particular to a fast prediction method for aircraft flutter boundaries based on a sequence-to-sequence model. Background Technology

[0002] In recent years, with the increasing complexity of flight missions and the extreme nature of flight conditions, the structures of modern aircraft have gradually become more elastic, making aeroelastic problems increasingly prominent in the design process. As the most common aeroelastic problem in aircraft, flutter has few limitations, a wide range of occurrences, and is extremely destructive. Therefore, flutter characteristics need to be considered in the design of many new types of aircraft, with a wide range of applications. Thus, in the engineering field, the accurate characterization of flutter boundaries plays a crucial guiding role in research on aircraft design, flight mechanics, and flight control.

[0003] In the current engineering context, solving flutter problems and flutter boundary conditions for aircraft still primarily relies on traditional experimental methods or CFD / CSD coupled calculations. While both methods can yield flutter boundaries with acceptable accuracy, they both have significant drawbacks. For example, experimental methods are costly, highly destructive, and difficult to implement under extreme conditions such as hypersonic and transonic speeds. CFD / CSD coupled calculations have long solution cycles and are difficult to provide results within the rapid iterative cycles of aircraft design. Therefore, improving the efficiency of solving flutter boundary problems while meeting engineering and research requirements remains a key demand in the aerospace and other engineering fields. Summary of the Invention

[0004] The purpose of this invention is to provide a fast prediction method for aircraft flutter boundaries based on sequence-to-sequence models, so as to improve the above-mentioned technical problems.

[0005] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0006] A fast prediction method for aircraft flutter boundaries based on a sequence-to-sequence model, comprising:

[0007] Different flow conditions are set up and the motion law of the aircraft structure is generated. Combined with the unsteady flow solution method, the unsteady aerodynamic force of the aircraft is calculated.

[0008] Construct a GRU neural network; based on the GRU neural network and the attention mechanism, construct a sequence-to-sequence model; the attention mechanism adopts either additive attention or dot product attention.

[0009] Based on the structural motion laws and unsteady aerodynamic forces of each aircraft, the network parameters of the GRU neural network are adjusted by combining the continuity truncation mechanism; the network parameters of the sequence-to-sequence model are adjusted by combining the continuity truncation mechanism, sliding window mechanism and gradient truncation mechanism to generate an unsteady aerodynamic force model.

[0010] The system collects the real-time structural motion of the aircraft at the current moment and the unsteady aerodynamic forces at the previous moment, and solves the structural dynamics equations and unsteady aerodynamic models to generate flutter boundary prediction results.

[0011] In the above scheme, the present invention integrates the ability of GRU neural network to capture temporal features, the focusing effect of additive and dot product attention mechanism on key coupling features, and the advantages of sequence mapping from sequence to sequence model. Combined with the sliding window mechanism for effective processing of dynamic temporal data and the gradient cutoff mechanism for ensuring model training stability, it can accurately learn the temporal dependencies in unsteady aerodynamic sequences and quickly generate flutter boundary prediction results under different flow conditions. Compared with traditional fluid-structure interaction simulation methods, it significantly improves prediction efficiency while ensuring prediction accuracy and model robustness, and can effectively meet the needs of rapid flutter boundary assessment under complex flow conditions of aircraft.

[0012] Furthermore, the generated aircraft structural motion laws and unsteady aerodynamic forces include:

[0013] The generated aircraft structure motion laws and unsteady aerodynamic forces include:

[0014] Different flow conditions are set; each flow condition includes corresponding environmental parameters, namely Mach number, Reynolds number, temperature, density and pressure, as well as the dynamic pressure parameter corresponding to the Mach number;

[0015] Based on the flow conditions, determine the amplitude and frequency of the corresponding aircraft structure response, and design the motion law of the aircraft structure under each flow condition.

[0016] Based on the structural motion laws of aircraft under various flow conditions, unsteady aerodynamic forces under different flow conditions are calculated using unsteady flow solution methods.

[0017] Furthermore, the sequence-to-sequence model is an improved seq2seq model; the improved seq2seq model includes a cascaded encoder, attention layer, and decoder; both the encoder and decoder employ a GRU neural network; and the attention layer employs an additive attention mechanism or a dot product attention mechanism.

[0018] Furthermore, the generation of the unsteady aerodynamic model includes:

[0019] Based on adjacent time points, the structural motion law and its corresponding unsteady aerodynamic forces are continuously truncated through a continuity truncation mechanism to obtain a short sequence of structural motion laws.

[0020] Short sequences of structural motion laws are input into a GRU neural network to generate initial unsteady aerodynamic forces.

[0021] The GRU loss function is calculated by combining the initial unsteady aerodynamic forces and labels; based on the GRU loss function, the network parameters of the GRU neural network are adjusted to obtain the trained GRU neural network; the labels are real unsteady aerodynamic forces.

[0022] Short sequences of structural motion laws are input into a sequence-to-sequence model, and unsteady aerodynamic forces are generated by combining sliding window and attention mechanisms.

[0023] A loss function is constructed based on unsteady aerodynamic forces and their labels.

[0024] Based on the loss function, the network parameters of the sequence-to-sequence model are adjusted through gradient cutoff mechanism and temporal backward gradient propagation mechanism until the number of iterations is reached or the error threshold condition is met, and the trained sequence-to-sequence model is obtained.

[0025] The trained GRU neural network and the trained sequence-to-sequence model are used as unsteady aerodynamic models.

[0026] In the above scheme, this invention clearly defines the architecture of the unsteady aerodynamic model. By generating short sequences through a continuity truncation mechanism, it avoids the loss of dynamic continuity features caused by time-series data truncation, ensuring the model can learn the complete dependencies between features. The introduction of additive attention or dot-product attention mechanisms addresses the problem of insufficient attention to key coupling features (such as the correlation between displacement abrupt changes and aerodynamic peaks under specific conditions) in traditional models, enhancing the model's ability to focus on core information. The gradient truncation mechanism suppresses gradient explosion or vanishing phenomena in time-series backpropagation, solving the problem of unstable model parameter updates during long-series training, improving training convergence efficiency, and laying the model foundation for rapid and reliable prediction of flutter boundaries.

[0027] Furthermore, the generation of unsteady aerodynamic forces includes:

[0028] The generation of unsteady aerodynamic forces includes:

[0029] Combine the sliding window mechanism to set encoder input constraints;

[0030] Based on encoder input constraints, the initial unsteady aerodynamic forces are processed by the encoder to generate coded feature vectors;

[0031] The encoded feature vector is input into the attention layer, and a feature vector with fused attention is generated through additive attention mechanism or dot product attention mechanism;

[0032] The unsteady aerodynamic sequence and the feature vector after attention fusion are input into the decoding layer. The decoder is trained through teaching and learning to generate unsteady aerodynamics.

[0033] In the above scheme, this invention introduces a sliding window mechanism. The core effect of this mechanism is to ensure the stability and temporal continuity of the input sequence while preserving the dynamic correlation between adjacent time steps. This invention also introduces two attention mechanisms (additive / dot product), which allow the model to focus on key coupled features. Additive attention generates a weight distribution by calculating the correlation between features at each time step and the decoding task; dot product attention uses this weight to weightedly fuse encoded features, highlighting the information most relevant to the current prediction. The introduction of attention mechanisms solves the problem of traditional models treating all temporal features "equally," enhancing the ability to capture the core coupling law of working conditions and dynamics, and improving feature representativeness.

[0034] Furthermore, the generated flutter boundary prediction result includes:

[0035] Select any flow condition and obtain the corresponding aircraft structural motion law at the initial moment; set the aerodynamic force value at the initial moment to 0;

[0036] The selected flow conditions, the current motion law of the aircraft structure, and the unsteady aerodynamic forces of the previous moment are input into the trained GRU neural network to generate the unsteady aerodynamic forces of the next moment.

[0037] Based on the unsteady aerodynamic forces at the next moment, the structural motion state at the next moment is generated by solving the structural dynamics equations.

[0038] Repeat the iterative solution process until the number of generated structural motion states meets the threshold.

[0039] The selected flow conditions, the current structural motion state, and the unsteady aerodynamic forces from the previous moment are input into the trained sequence-to-sequence model to generate the unsteady aerodynamic forces for the next moment.

[0040] Based on the unsteady aerodynamic forces at the next moment, the structural dynamics equations are solved to generate the new structural motion state at the next moment.

[0041] Determine whether the motion state of the new structure under the current working condition meets the response conditions; if so, take the parameter corresponding to the current flow condition as the critical dynamic pressure; traverse all flow conditions and iterate until the critical dynamic pressure under all flow conditions is obtained and integrated to generate flutter boundary prediction results.

[0042] Conversely, the parameters corresponding to the flow condition are adjusted, the motion law of the aircraft structure corresponding to the adjusted flow condition is collected and iterated until the response conditions are met.

[0043] Furthermore, the response condition refers to the structural motion response exhibiting constant amplitude oscillations.

[0044] In the above scheme, a reduced-order model is constructed to approximate the flow, replacing the traditional fluid-structure interaction solution. This avoids the inefficiency of brute-force solutions and significantly improves the efficiency of solving the critical dynamic pressure under a single operating condition. By traversing all flow conditions and integrating the results, it can be ensured that the flutter boundary covers all aerodynamic conditions that the aircraft may encounter (such as different Mach numbers), rather than being limited to local conditions, thus making the prediction results comprehensive and engineering-applicable.

[0045] Furthermore, the loss function can be any one of mean squared error (MSEloss), mean absolute error (MAEloss), relative error (Reloss), and exponential mean squared error (expMSEloss).

[0046] In the above scheme, the selection of a loss function can guide the model training in a targeted manner according to the flutter prediction requirements (such as suppressing large errors and adapting to noise), ensuring convergence stability and improving the accuracy of prediction and its fit with the physical scene. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0049] Figure 2 This is a schematic diagram of the grid in Embodiment 2 of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and illustrated in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0051] Example 1:

[0052] Please see Figure 1 This embodiment provides a fast prediction method for aircraft flutter boundaries based on a sequence-to-sequence model, including:

[0053] S1. Set different flow conditions and generate the motion law of the aircraft structure. Combine the unsteady flow solution method to calculate the unsteady aerodynamic force of the aircraft.

[0054] S1 includes:

[0055] S1-1. Set different flow conditions; each flow condition includes corresponding environmental parameters, namely Mach number, Reynolds number, temperature, density and pressure, as well as the dynamic pressure parameter corresponding to the Mach number;

[0056] S1-2. Based on the flow conditions, determine the amplitude and frequency of the corresponding aircraft structure response, and design the motion law of the aircraft structure under each flow condition.

[0057] Specifically, the simulation process is the same for each flow condition. Therefore, taking any flow condition as an example, first determine the rigid body parameters of the aircraft under the selected flow condition, such as the physical properties of the rigid body (inertial characteristics that affect the motion response of the aircraft), such as geometric shape, mass, moment of inertia, and center of mass position. Based on experience, determine the amplitude and frequency of the aircraft structure response under the selected flow condition, and design the aircraft structure motion law under the selected flow condition. The aircraft structure motion law is a Gaussian white noise signal with a certain amplitude and frequency range, and ensures that it can cover the estimated amplitude and frequency range.

[0058] S1-3. Based on the structural motion law of the aircraft under various flow conditions, calculate the unsteady aerodynamic forces under different flow conditions using unsteady flow solution methods; the unsteady aerodynamic forces include lift, drag, torque, other generalized forces and their corresponding coefficients (such as lift coefficient, drag coefficient, etc.).

[0059] Specifically, a virtual flow field model is built using unsteady flow solving tools. A three-dimensional space containing the aircraft is constructed and divided into countless tiny meshes, with a denser mesh on and around the aircraft surface to ensure computational accuracy. At the same time, a dynamic mesh mechanism is set up so that when the aircraft moves according to its structural motion laws, the mesh can deform synchronously, with the lower mesh being stretched and the upper mesh being compressed, always keeping a close fit to the real-time position of the aircraft and ensuring that the flow field calculation can be dynamically updated to follow the motion.

[0060] Subsequently, the flow field is solved step-by-step along the time axis: starting from t=0, the initial motion state and parameters of the set flow conditions are input, and the pressure and aerodynamic velocity distribution of each grid in the flow field at this time are calculated using unsteady flow solvers. At t=0.1 seconds, the aircraft position and angle of attack are updated according to the aircraft's structural motion law, the grid shape is dynamically adjusted, and the flow field pressure and velocity at the current moment are recalculated. This process is repeated until all time points covered by the aircraft's structural motion law are covered, finally obtaining a complete sequence of aerodynamic distributions (flow field distribution) around the aircraft at each moment.

[0061] Based on the flow field distribution, unsteady aerodynamic forces are extracted. First, the aerodynamic pressure and viscous friction of each grid on the aircraft surface are integrated to obtain the total force at each moment. Then, the total force is converted into dimensionless coefficients. Taking lift as an example, it is standardized using the dynamic pressure and the aircraft reference area at that moment to obtain the lift coefficient. Similarly, the drag coefficient, moment coefficient, etc., are calculated. These coefficients eliminate the influence of incoming flow velocity and aircraft size, reflecting only the correlation between the motion state and aerodynamic characteristics. Finally, they are projected onto a generalized coordinate system to obtain the generalized aerodynamic forces.

[0062] Finally, the structural motion patterns at each moment are paired with the corresponding unsteady aerodynamic forces to form a complete set of samples. By changing the flow conditions, the above process is repeated to generate more samples, ultimately constructing a "motion pattern-unsteady aerodynamic force" database covering multiple operating conditions. These samples will then serve as training data for subsequent GRU networks and improved Seq2seq models. That is, using the aircraft structural motion patterns as input and unsteady aerodynamic force coefficients as output, accurate prediction from motion to aerodynamic forces is achieved, forming a complete data closed loop.

[0063] In this embodiment, the aircraft can be the entire aircraft or aircraft components (airfoil, wing, fuselage).

[0064] S2. Construct a GRU neural network; based on the GRU neural network and the attention mechanism, construct a sequence-to-sequence model; the attention mechanism adopts either additive attention or dot product attention.

[0065] Specifically, the sequence-to-sequence model is an improved seq2seq model; the improved seq2seq model includes a cascaded encoder, attention layer, and decoder; both the encoder and decoder use GRU neural networks; the attention layer uses an additive attention mechanism or a dot product attention mechanism.

[0066] S3. Based on the structural motion laws of each aircraft and its unsteady aerodynamic forces, the network parameters of the GRU neural network are adjusted by combining the continuity truncation mechanism, the network parameters of the sequence-to-sequence model are adjusted by combining the continuity truncation mechanism, the sliding window mechanism and the gradient truncation mechanism, and the unsteady aerodynamic force model is generated.

[0067] The generation of the unsteady aerodynamic model includes:

[0068] S3-1. By using a continuity truncation mechanism, the structural motion law and its corresponding unsteady aerodynamic forces are continuously truncated to obtain a short sequence of structural motion laws.

[0069] Specifically, based on adjacent time points, the motion laws and unsteady aerodynamic forces of each structure are truncated to form several short sequences, generating corresponding generalized displacement sequences and unsteady aerodynamic force sequences. Simultaneously, to further improve the network's training effect, a pre-term is constructed for the unsteady aerodynamic force sequences, storing the generalized aerodynamic forces at the previous time point at each breakpoint (i.e., the pre-term aerodynamic force). This pre-term aerodynamic force is then paired one-to-one with the data pairs consisting of the generalized displacement sequence and the generalized aerodynamic force data, forming a generalized displacement-pre-term aerodynamic force-generalized aerodynamic force sequence (short sequences of structural motion laws), which serves as backup sequence pairs. By processing the structural motion laws and unsteady aerodynamic forces of each aircraft through a continuity truncation mechanism, the loss of input data information can be minimized, maintaining the continuity of the sequences.

[0070] S3-2. Input the short sequence of structural motion laws into the GRU neural network to generate initial unsteady aerodynamic forces;

[0071] It should be noted that GRU neural networks excel at capturing dynamic dependencies in time-series data, and their simplified structure and high computational efficiency enable them to quickly process time-series sequences of aircraft structural motion patterns, coupling them with structural equations to generate reliable initial values ​​for structural responses. Furthermore, the gating mechanism of GRU neural networks can alleviate the gradient problem in long sequences, ensuring the accuracy of initial values. Therefore, this embodiment selects GRU neural networks to lay a high-quality input foundation for the subsequent Seq2seq model, thereby improving the prediction accuracy of the flutter prediction architecture.

[0072] The GRU neural network processes the generalized displacement sequence of this time series data through its own gating mechanism (reset gate, update gate), and then continuously iterates and updates the hidden state at each time step, so that the hidden state always carries the correlation between historical time series information and current features.

[0073] Finally, the GRU neural network transforms the hidden state of this final time step into the initial unsteady aerodynamic force through a simple linear mapping (fully connected layer).

[0074] S3-3. Combine the initial unsteady aerodynamic forces and labels to calculate the GRU loss function; based on the GRU loss function, adjust the network parameters of the GRU neural network to obtain the trained GRU neural network; wherein, the GRU loss function can be the MSE loss function; the labels are real unsteady aerodynamic forces.

[0075] S3-4. Input the short sequence of structural motion laws into the sequence-to-sequence model, and combine the sliding window mechanism and attention mechanism to generate unsteady aerodynamic forces;

[0076] S3-4 includes:

[0077] S3-4-1. Set encoder input constraints according to the continuity truncation mechanism and sliding window mechanism;

[0078] Specifically, the continuity truncation mechanism refers to setting the encoder's input constraints by using a sliding window mechanism to truncate short sequences at adjacent time points from a continuous long-time generalized displacement sequence according to the short sequence length (hyperparameter) set during the training phase (e.g., if the length is 5 during training, t0-t4, t1-t5, etc. are truncated sequentially). This fixes the length of the input sequence while ensuring temporal continuity. It helps ensure that the encoder's input form is completely matched with that during training, avoiding feature extraction errors caused by length mismatch, while ensuring data continuity, thereby stably and accurately extracting the dynamic features in the generalized displacement.

[0079] S3-4-2. Based on encoder input constraints, the encoder processes short sequences of structural motion patterns to generate encoded feature vectors.

[0080] Specifically, the short sequence is processed step-by-step using a GRU neural network. The encoder's processing is the same as that of the GRU neural network, ultimately generating an encoded feature vector. When the short sequence of structural motion patterns exceeds the fixed length of the input sequence limited by the encoder's input constraints, a new short sequence of structural motion patterns is generated. The encoder's input constraints ensure that the input shape is perfectly aligned with the training phase, allowing the encoder to directly reuse the structural motion-aerodynamic coupling temporal dependencies learned during training. This ultimately generates an encoded feature vector that accurately condenses key information, laying a reliable foundation for subsequent processing by the attention layer and decoder.

[0081] S3-4-3. Input the encoded feature vector into the attention layer, and generate the feature vector after fusion attention through additive attention mechanism or dot product attention mechanism;

[0082] This section uses additive attention as an example; dot-product attention is processed similarly. Specifically, the encoder's output feature vector (containing compressed features from multiple time steps) is used as the key and value vectors, while the decoder's initial hidden state (or the query signal of the current decoding step) is introduced as the query vector. Two independent linear transformation layers map the key and value vectors to the same dimension, resulting in mapped key and query vectors. The mapped key and query vectors are added together, and a non-linearity is introduced through the tanh activation function. This is then passed through a linear layer with an output dimension of 1 to obtain the raw attention score for each time step. Finally, the raw scores for all time steps are normalized using the softmax function to obtain the additive attention weight distribution. Then, the original encoded feature vector undergoes feature transformation and is concatenated with the obtained attention weight distribution to form the context variable (the feature vector after attention fusion).

[0083] In this embodiment, an attention mechanism is introduced to assist in reorganizing the empirical information from the encoder, thereby improving the predictive performance of the decoder. Compared to directly inputting the encoder's output into the decoder, introducing a dot product attention mechanism or an additive attention mechanism to process the encoder's output can provide stronger representativeness and guidance, thus helping to improve the predictive accuracy of the decoder.

[0084] S3-4-4: Input the unsteady aerodynamic force sequence and the feature vector after attention fusion into the decoding layer, and train the decoder through teacher forcing to generate unsteady aerodynamic forces.

[0085] Specifically, unsteady aerodynamic sequences are input into the decoder in batches, and a teacherforcing strategy is adopted, that is, the real preceding unsteady aerodynamic data are directly used as the decoder input, rather than relying on the decoder's previous prediction results, thus avoiding the accumulation of early prediction errors.

[0086] After being input into the decoder, the unsteady aerodynamic force sequence first undergoes feature transformation (standardization or linear mapping) to adapt its feature dimensions to those of subsequent modules. Then, the context information is concatenated with the transformed unsteady aerodynamic force pre-terms and input into a GRU neural network. Through a gating mechanism, the temporal dependencies of the sequence are learned, gradually capturing the mapping logic between previous unsteady aerodynamic forces and displacement-related features and the current unsteady aerodynamic forces. Finally, an unbiased linear layer adjusts the feature dimensions to 1, yielding the unsteady aerodynamic forces of the current step.

[0087] In the practical application of GRU neural networks and improved seq2seq models, the output data obtained by solving GRU neural networks and structural dynamics equations simultaneously is used as one of the input data for the improved seq2seq model.

[0088] S3-5. Based on unsteady aerodynamic forces and their labels, construct a loss function; the loss function adopts any one of mean square error (MSEloss), mean absolute error (MAEloss), relative error (Reloss), and exponential mean square error (expMSEloss).

[0089] S3-6. Based on the loss function, the network parameters of the sequence-to-sequence model are adjusted through gradient truncation mechanism and temporal backward gradient propagation mechanism until the number of iterations is reached or the error threshold condition is met, thus obtaining the trained sequence-to-sequence model; wherein, the error threshold condition is that the error calculated by the evaluation error function is less than a preset error threshold.

[0090] Specifically, a loss function is used to calculate the error between the unsteady aerodynamic forces and the unsteady aerodynamic forces (labels). This error value is compared with a preset error threshold. If the error is less than the threshold, training can be terminated early; if the error is greater than or equal to the threshold, the subsequent training process continues.

[0091] When the error is greater than or equal to the threshold, based on the error, the backward gradient propagation (BPTT) mechanism is used to propagate the error backward from the decoder output layer to each layer of the network (including GRU layers, fully connected layers, etc.) step by step. The gradients of network parameters (such as the gating weights of GRU, the output layer weights, etc.) are calculated layer by layer, accumulating the impact of each time step on the parameters. When adjusting network parameters, if the error decreases too slowly, the learning rate can be increased; if the gradient fluctuates greatly, the batch size can be decreased.

[0092] During the process of adjusting network parameters (learning rate, batch size, short sequence length) using the temporal backward gradient propagation mechanism, the gradient truncation module (grad_clipping) is enabled when calculating gradients to monitor the absolute value of the gradient (or L2 norm) of each parameter in real time. If the gradient exceeds the preset safety threshold, the gradient is scaled proportionally to the threshold range to avoid gradient explosion caused by abnormal gradient increase.

[0093] By combining the truncated gradients with the preset learning rate, all network parameters are updated using gradient descent (or other optimizers) to adjust the parameters in the direction of reducing error until the number of iterations is reached or the error threshold condition is met.

[0094] S3-7. The trained GRU neural network and the trained seq2seq model are combined into an unsteady aerodynamic model. The unsteady aerodynamic model is combined with the structural dynamics equations to perform flutter boundary prediction and generate flutter boundary prediction results.

[0095] In addition, when training the GRU neural network and seq2seq model, besides the training set (the motion laws of the aircraft structure and its unsteady aerodynamic forces), there are also validation and test sets, with a corresponding ratio of 7:2:1 or 8:1:1. After training the GRU neural network and seq2seq model using the training set, when validating them using the validation or test set, if the obtained error value does not meet the error threshold condition, training is repeated.

[0096] S4. Collect the real-time structural motion law of the aircraft at the current moment and the unsteady aerodynamic force at the previous moment, and solve the structural dynamics equation and the unsteady aerodynamic force model to generate flutter boundary prediction results.

[0097] S4 includes:

[0098] S4-1. Select any flow condition and obtain the corresponding aircraft structural motion law at the initial moment; at this time, set the initial aerodynamic force value to 0.

[0099] S4-2. Input the selected flow conditions, the current motion law of the aircraft structure, and the unsteady aerodynamic forces of the previous moment into the trained GRU neural network to generate the unsteady aerodynamic forces of the next moment.

[0100] S4-3. Based on the unsteady aerodynamic forces at the next moment, the structural dynamics equations are solved to generate the structural motion state at the next moment.

[0101] Specifically, unsteady aerodynamic forces are essentially generalized aerodynamic loads exerted on an aircraft structure, representing the driving force that causes the structure to move. Structural dynamics equations describe the physical laws governing how these driving forces cause structural motion.

[0102] When constructing structural dynamics equations, the degrees of freedom of motion of the aircraft components are first determined (e.g., heave and pitch). The inherent structural parameters (mass / mass moment, stiffness coefficient, damping coefficient) are obtained through structural design parameters or engineering calculations. These inherent structural parameters are the basic physical inputs for the structural dynamics equations. Then, based on the basic equilibrium principle of structural dynamics, mathematical expressions for inertial forces (related to acceleration), damping forces (related to velocity), and elastic forces (related to displacement) under each degree of freedom are constructed to ensure that the dimensions of the forces match the physical laws. Then, the unsteady aerodynamic forces (such as lift, torque, and other generalized forces) calculated by unsteady flow solution methods (such as CFD simulation) are used as external force terms and substituted into the equilibrium relationship (e.g., inertial force + damping force + elastic force = external force) to form a preliminary dynamic equation. Finally, the structural motion under different flow conditions is simulated through fluid dynamics simulation to verify the consistency between the calculated equation results and the simulation response, and to calibrate key parameters such as stiffness and damping. Finally, a structural dynamic equation that can accurately reflect the aerodynamic-structural coupling characteristics and can be solved in conjunction with a time-series neural network (GRU, Seq2seq) is obtained.

[0103] By substituting unsteady aerodynamic forces into this equation, we can obtain the structure's motion state (displacement, velocity, vibration amplitude, etc.) through solving. Essentially, it uses physical laws to transform external force input into motion output. Thus, unsteady aerodynamic forces are the external forces driving the structure's motion, and the structure's motion state is the result of motion under the action of these external forces.

[0104] S4-4. Repeat the iterative solution process until the number of generated structural motion states meets the quantity threshold; the quantity threshold can be set according to the actual situation.

[0105] S4-5. Input the selected flow condition, the current structural motion state, and the unsteady aerodynamic force of the previous moment into the trained sequence-to-sequence model to generate the unsteady aerodynamic force of the next moment. The selected flow condition corresponds to the flow condition selected in S4-1, and the corresponding initial value of the structural motion state is obtained. At this time, the initial aerodynamic force value is set to 0.

[0106] S4-6. Based on the unsteady aerodynamic forces at the next moment, solve the structural dynamics equations to generate the new structural motion state at the next moment.

[0107] S4-7. Determine whether the new structural motion state meets the response conditions; if so, use the parameter corresponding to the current flow condition as the critical dynamic pressure; otherwise, adjust the parameter corresponding to the flow condition and return to S4-1 until the response conditions are met. The response conditions refer to the structural motion state exhibiting constant amplitude oscillations.

[0108] Specifically, flutter is essentially a self-excited vibration resulting from the coupling of aerodynamics and structure. Critical dynamic pressure is the dividing point between structural stability and instability. Adjusting the flow conditions (primarily dynamic pressure) essentially involves finding this dividing point, determining the critical dynamic pressure through the structural motion state. By continuously adjusting the selected flow conditions (density, temperature, etc., changing the flow field dynamic pressure), and repeating the simultaneous solution process of the neural network and structural dynamic equations, until the predicted structural motion response exhibits constant-amplitude oscillations, the corresponding dynamic pressure parameter is taken as the critical dynamic pressure.

[0109] S4-8: Traverse all flow conditions, repeat S4-1 and S4-8 until the critical dynamic pressure under all flow conditions is obtained and integrated to generate flutter boundary prediction results.

[0110] In summary, this invention integrates the ability of GRU neural networks to capture temporal features, the focusing effect of additive and dot product attention mechanisms on key coupling features, and the advantages of sequence mapping from sequence to sequence models. Combined with the sliding window mechanism for effective processing of dynamic temporal data and the gradient truncation mechanism for ensuring model training stability, it can accurately learn the temporal dependencies in unsteady aerodynamic sequences and quickly generate flutter boundary prediction results under different flow conditions. Compared with traditional fluid-structure interaction simulation methods, it significantly improves prediction efficiency while ensuring prediction accuracy and model robustness, effectively meeting the needs for rapid flutter boundary assessment under complex flow conditions of aircraft.

[0111] It should be noted that, Figure 1 The execution entity of the method corresponding to the illustrated device can be a software and / or hardware device. The execution entity of this application can include, but is not limited to, at least one of the following: user equipment, network equipment, etc. User equipment can include, but is not limited to, computers, smartphones, personal digital assistants (PDAs), and the aforementioned electronic devices. Network equipment can include, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Cloud computing is a type of distributed computing, consisting of a super virtual computer composed of a group of loosely coupled computers. This embodiment does not impose any limitations on this.

[0112] Example 2:

[0113] The experimental environment was set up, and the NACA64A010 airfoil was selected as the experimental object. The corresponding airfoil parameters were: airfoil chord length 1, two degrees of freedom (heave and pitch), initial angle of attack of 0°, and initial heave attitude in static equilibrium. The flow conditions were set with the following parameters: uniform inflow Mach number 0.875 and pressure 101325 Pa. Under the current experimental environment, the temperature of the flow conditions was adjusted to change the dynamic pressure, and flutter boundary was predicted.

[0114] The mesh in this embodiment is as follows: Figure 2 As shown, Figure 2 The left image shows a structured mesh covering a large computational domain, while the right image shows a locally refined structured mesh near the airfoil. By refining the mesh in different regions, both computational efficiency and accuracy are considered, providing a foundation for high-precision calculation of aerodynamic loads and structural responses in fluid-structure interaction flutter analysis.

[0115] Three operating conditions are set, as shown in Table 1.

[0116] Table 1

[0117] Operating condition number Mach number Ma Dimensionless flutter velocity 1 0.825 0.66 2 0.875 0.6 3 0.875 1.95

[0118] Prediction was performed under three operating conditions using a single GRU neural network (Method 1) and our proposed method (a fast prediction method for aircraft flutter boundaries based on a sequence-to-sequence model). RMSE was used as the loss function, and the errors between Method 1 and our proposed method were calculated using the loss function, as shown in Table 2.

[0119] Table 2

[0120] Operating conditions Method 1 (RMSE) This method RMSE) 1 <![CDATA[1.1×10 -5 ]]> <![CDATA[6.12×10 -6 ]]> 2 <![CDATA[5.94×10 -7 ]]> <![CDATA[4.85×10 -7 ]]> 3 <![CDATA[1.95×10 -5 ]]> <![CDATA[1.44×10 -5 ]]>

[0121] As shown in Table 2, under the three different operating conditions, the error of this method is smaller than that of Method 1. This indicates that the combination of GRU neural network, seq2seq network and attention mechanism is beneficial for the prediction of flutter boundary.

[0122] Table 3

[0123] Operating conditions Theoretical value (clock speed / Hz) Method 1 (Frequency / Hz) This method (clock frequency / Hz) 1 14.306 13.708 14.286 2 12.925 12.851 12.896 3 27.322 25.371 25.798

[0124] As shown in Table 3, the natural frequencies of the structural response under different operating conditions are 14.306, 12.925, and 27.322, respectively. Overall, the proposed method's estimation of the dominant frequency of the structural response is closer to the theoretical value, thus demonstrating that the proposed method has higher dominant frequency estimation accuracy than GRU and showcasing its advantage in predicting the dominant frequency of the structural response under flutter conditions.

[0125] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0126] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A fast prediction method for aircraft flutter boundaries based on sequence-to-sequence models, characterized in that, include: Different flow conditions are set up and the motion law of the aircraft structure is generated. Combined with the unsteady flow solution method, the unsteady aerodynamic force of the aircraft is calculated. Construct a GRU neural network; A sequence-to-sequence model is constructed based on a GRU neural network and an attention mechanism; the attention mechanism adopts either an additive attention mechanism or a dot product attention mechanism. Based on the structural motion laws and unsteady aerodynamic forces of each aircraft, the network parameters of the GRU neural network are adjusted by combining the continuity truncation mechanism; the network parameters of the sequence-to-sequence model are adjusted by combining the continuity truncation mechanism, sliding window mechanism and gradient truncation mechanism to generate an unsteady aerodynamic force model. The system collects the real-time structural motion of the aircraft at the current moment and the unsteady aerodynamic forces at the previous moment, and solves the structural dynamics equations and unsteady aerodynamic models to generate flutter boundary prediction results.

2. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 1, characterized in that, The generated aircraft structure motion laws and unsteady aerodynamic forces include: Different flow conditions are set; each flow condition includes corresponding environmental parameters, namely Mach number, Reynolds number, temperature, density and pressure, as well as the dynamic pressure parameter corresponding to the Mach number; Based on the flow conditions, determine the amplitude and frequency of the corresponding aircraft structure response, and design the motion law of the aircraft structure under each flow condition. Based on the structural motion laws of aircraft under various flow conditions, unsteady aerodynamic forces under different flow conditions are calculated using unsteady flow solution methods.

3. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 1, characterized in that, The sequence-to-sequence model is an improved seq2seq model; the improved seq2seq model includes a cascaded encoder, attention layer and decoder; the encoder and decoder both use GRU neural networks; the attention layer uses an additive attention mechanism or a dot product attention mechanism.

4. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 1, characterized in that, The generation of the unsteady aerodynamic model includes: Based on adjacent time points, the structural motion law and its corresponding unsteady aerodynamic forces are continuously truncated through a continuity truncation mechanism to obtain a short sequence of structural motion laws. Short sequences of structural motion laws are input into a GRU neural network to generate initial unsteady aerodynamic forces. The GRU loss function is calculated by combining the initial unsteady aerodynamic forces and labels; based on the GRU loss function, the network parameters of the GRU neural network are adjusted to obtain the trained GRU neural network; the labels are real unsteady aerodynamic forces. Short sequences of structural motion laws are input into a sequence-to-sequence model, and unsteady aerodynamic forces are generated by combining sliding window and attention mechanisms. A loss function is constructed based on unsteady aerodynamic forces and their labels. Based on the loss function, the network parameters of the sequence-to-sequence model are adjusted through gradient cutoff mechanism and temporal backward gradient propagation mechanism until the number of iterations is reached or the error threshold condition is met, and the trained sequence-to-sequence model is obtained. The trained GRU neural network and the trained sequence-to-sequence model are used as unsteady aerodynamic models.

5. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 4, characterized in that, The generation of unsteady aerodynamic forces includes: Set encoder input constraints using a sliding window mechanism; Based on encoder input constraints, the initial unsteady aerodynamic forces are processed by the encoder to generate coded feature vectors; The encoded feature vector is input into the attention layer, and a feature vector with fused attention is generated through additive attention mechanism or dot product attention mechanism; The unsteady aerodynamic sequence and the feature vector after attention fusion are input into the decoding layer. The decoder is trained through teaching and learning to generate unsteady aerodynamics.

6. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 1, characterized in that, The generated flutter boundary prediction results include: Select any flow condition and obtain the corresponding aircraft structural motion law at the initial moment; set the aerodynamic force value at the initial moment to 0; The selected flow conditions, the current motion law of the aircraft structure, and the unsteady aerodynamic forces of the previous moment are input into the trained GRU neural network to generate the unsteady aerodynamic forces of the next moment. Based on the unsteady aerodynamic forces at the next moment, the structural motion state at the next moment is generated by solving the structural dynamics equations. Repeat the iterative solution process until the number of generated structural motion states meets the threshold. The selected flow conditions, the current structural motion state, and the unsteady aerodynamic forces from the previous moment are input into the trained sequence-to-sequence model to generate the unsteady aerodynamic forces for the next moment. Based on the unsteady aerodynamic forces at the next moment, the structural dynamics equations are solved to generate the new structural motion state at the next moment. Determine whether the motion state of the new structure under the current working condition meets the response conditions; if so, take the parameter corresponding to the current flow condition as the critical dynamic pressure; traverse all flow conditions and iterate until the critical dynamic pressure under all flow conditions is obtained and integrated to generate flutter boundary prediction results. Conversely, the parameters corresponding to the flow condition are adjusted, the motion law of the aircraft structure corresponding to the adjusted flow condition is collected and iterated until the response conditions are met.

7. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 6, characterized in that, The response condition refers to the structural response exhibiting constant amplitude oscillations.

8. The method for fast prediction of aircraft flutter boundaries based on a sequence-to-sequence model according to claim 4, characterized in that, The loss function can be any one of mean squared error (MSEloss), mean absolute error (MAEloss), relative error (Reloss), and exponential mean squared error (expMSEloss).

Images