Turbulence excitation-oriented flutter wind tunnel test impulse response generation method and system

Abstract

The present application relates to the technical field of wind tunnel test, and discloses a kind of flutter wind tunnel test impulse response generation method and system for turbulent excitation, wherein the method comprises: model construction: combined convolution sampling method and deep feature extraction method are used to construct hybrid Transformer generative model, and the mathematical relationship between turbulent response signal and impulse response signal in structural dynamics system is established by hybrid Transformer generative model;Model training: according to the model training effect, different normalization methods are used to preprocess data;Adopt the loss function of time domain and frequency domain mean square error mixture, and the model is optimized by a plurality of training optimization methods;Signal generation: the measured turbulent response signal is used as input to generate corresponding impulse response signal.The present application can directly convert the turbulent response signal dynamically collected in the wind tunnel into impulse response signal.

Description

Technical Field

[0001] This invention relates to the field of wind tunnel testing technology, and in particular to a method and system for generating impulse responses in flutter wind tunnel tests oriented towards turbulent excitation. Background Technology

[0002] Flutter, or aircraft flutter, is a self-excited and divergent vibration of an elastic body under the influence of airflow, caused by the coupling of elastic, inertial, and aerodynamic forces. It can damage the system structure and even cause serious flight accidents within a short period. To avoid flutter, numerous flutter experiments are required during the development phase or major modifications of aircraft to determine their flutter boundaries. As a crucial method for studying flutter, flutter wind tunnel experiments offer significant advantages such as cost-effectiveness, short cycle time, and reliable data. By continuously measuring the vibration signals of a flutter model in an artificial wind field and extracting the modal information of the structure using signal processing techniques, flutter boundaries can be verified and flutter characteristics studied. In engineering, flutter wind tunnel experiments are highly correlated with signal processing methods. On the one hand, compared to numerical simulation, wind tunnel data is relatively sparse, and the accuracy of experimental results is highly dependent on the signal processing method. On the other hand, the design of the signal processing method determines the selection, placement, and excitation method of sensors. How to fully utilize the relatively sparse wind tunnel data to improve the accuracy of structural modal estimation has become a hot topic in the field of signal processing.

[0003] In flutter wind tunnel tests, limitations imposed by the size and structure of the flutter model make it difficult to install active excitation devices to obtain high signal-to-noise ratio response signals. Therefore, natural excitation is typically applied using wind tunnel turbulence. However, the signal acquisition process under natural excitation is susceptible to background noise interference from wind tunnel airflow and sensor noise, resulting in poor turbulent response signal quality and low signal-to-noise ratio. This necessitates a high degree of reliance on effective signal processing algorithms to extract modal information, and it is difficult to guarantee the accuracy of modal parameter identification. Therefore, if the structural vibration of the flutter model is considered as a nonlinear dynamic system, flutter wind tunnel experiments under turbulent natural excitation mean that the system input is unknown, only the system output is known, and the system model parameters need to be estimated based on the system output.

[0004] To address the natural excitation problem caused by air turbulence, some scholars have proposed combining an autoregressive (AR) model with a response term and a moving average (MA) model with Gaussian white noise excitation. This approach establishes the relationship between the Gaussian white noise sequence and the turbulent response by constructing difference equations. Sampling data is used to estimate the coefficient vector and modal order of the difference equations, and finally, the flutter boundary is calculated based on the stability criterion of the characteristic equation. To give the parameters to be estimated by the ARMA method physical meaning and further improve prediction accuracy, some scholars have introduced recursive maximum likelihood (RML) estimation to estimate the constructed stability parameters, effectively improving the solution efficiency.

[0005] However, when faced with parameter estimation tasks involving high-order modes, ARMA models still have excessively long execution times and struggle to eliminate spurious modes. Researchers have proposed the Random Decrement Technique (RDT), a widely used time-domain method in engineering. RDT uses the overall average value of turbulent environmental data to approximate the free vibration response of a structure excited by Gaussian white noise. The free vibration response is often referred to as the random decrement (RD) function or RD feature. To improve the noise resistance of the response signal and enhance the accuracy of RD feature extraction, researchers have continued to combine signal processing methods, including Empirical Mode Decomposition (EMD), Analytical Mode Decomposition (AMD), and bandpass filtering, with RDT, developing various hybrid algorithms. Generally, because the modal design of wind tunnel flutter models is relatively pure, and the experimental wind speed is close to the flutter velocity critical value, the damping of one or two key modes can be relatively small. In this case, the RDT method can achieve good results in calculating the free vibration response, and therefore it is widely used in wind tunnel flutter experiments.

[0006] However, the emergence of shock waves in the transonic stage causes the aerodynamic forces of the flutter model to exhibit nonlinear changes. Especially when conducting high-aspect-ratio flutter wind tunnel experiments, the multimodal coupling in the response signal becomes more complex, and the energy distribution of each mode is relatively low and dispersed, making its contribution to vibration less significant. In this case, the effect of using the RDT method to obtain modal information is no longer ideal, and the improvement of parameter estimation accuracy is also limited. In addition, the Stochastic Subspace Identification (SSI) method, based on the system's stochastic response data, estimates modal parameters by applying subspace techniques, thereby achieving stochastic system identification. Since the input stationarity assumption matches the wind field aerodynamic forces well, and the identified modes can be presented through frequency domain stability plots, SSI also has engineering application value. Based on different methods of constructing the feature matrix, SSI has gradually developed into two technical routes: data-driven SSI (SSI-DATA) and covariance-driven SSI (SSI-COV). However, the SSI method requires traversing multiple orders for modal parameter estimation, and the execution process in multimodal scenarios is time-consuming, which is not conducive to real-time analysis.

[0007] To overcome the performance limitations of traditional methods in complex multimodal scenarios, some researchers have proposed leveraging the powerful nonlinear reconstruction capabilities of deep learning and adopting a sequence-to-sequence approach. They utilize Long Short-Term Memory (LSTM) neural networks to construct generative models, transforming turbulent response signals into impulse response signals. This method, employing a Recurrent Neural Network (RNN) framework for time-series data prediction, provides a novel approach to solving modal analysis problems under turbulent excitation, opening a new paradigm for AI-enabled flutter wind tunnel experimental data processing. Theoretically, classic RNNs possess memory capabilities and can be used for time-series data prediction; however, they suffer from the vanishing gradient problem when processing long sequences, making it difficult to learn long-term dependencies.

[0008] As an improvement on RNNs, LSTM effectively addresses the gradient propagation problem in long sequence modeling by introducing a gating mechanism. It can continuously capture relatively persistent information features in long sequence prediction tasks and is widely used in time series prediction. However, in flutter wind tunnel experiments, the turbulent response signal sequences continuously acquired by the data acquisition system are extremely long, typically containing tens of thousands of data points in a single operating condition. The extremely long distance resulting from these tens of thousands of data points causes information attenuation in the LSTM network, making it difficult to capture long-term dependencies and leading to problems such as decreased accuracy of generated signals and low computational efficiency. Furthermore, LSTM-based generative models struggle to handle sequences of arbitrary length; they can only perform pruning operations on data shorter than the designed length, thus exhibiting limitations in model adaptability. Summary of the Invention

[0009] To address the aforementioned issues, this invention proposes a method and system for generating impulse responses in flutter wind tunnel tests oriented towards turbulent excitation. By employing convolution operations, a mathematical relationship is established between the turbulent response signal and the impulse response signal of the structural dynamics system. When turbulent excitation cannot be directly measured, the measured turbulent response signal is used as input to generate the corresponding impulse response signal using a hybrid Transformer generative model.

[0010] The technical solution adopted in this invention is as follows:

[0011] A method for generating impulse response in flutter wind tunnel tests oriented towards turbulent excitation, comprising:

[0012] Model Construction: A hybrid Transformer generative model is constructed by combining convolutional sampling and deep feature extraction methods, and the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system is established through the hybrid Transformer generative model;

[0013] Model training: Based on the differences in time-domain symmetry and zero-point distribution between turbulent and impulse responses, different normalization methods are used to preprocess the data according to the model training effect; a loss function that combines time-domain and frequency-domain mean square errors is adopted, and the hybrid Transformer generative model is optimized through various training optimization methods;

[0014] Signal generation: The measured turbulent response signal is used as input to generate the corresponding impulse response signal through a trained hybrid Transformer generative model.

[0015] Furthermore, in the model construction, the hybrid Transformer generative model constructed by combining the convolutional sampling method and the depth feature extraction method includes: an input projection module, a convolutional downsampling unit, a position encoder, a depth feature extraction module, an upsampling unit, and an output layer that sequentially execute signal processing procedures.

[0016] Furthermore, the signal processing procedures of the input projection module and the convolutional downsampling unit include:

[0017] During forward propagation, the input projection module transforms the input turbulent response signal to a higher dimension through linear projection;

[0018] The projected turbulent response signal is fed into a convolutional downsampler containing two layers of one-dimensional convolution. The length of the turbulent response signal is compressed by the first layer of convolution and then fed into the ReLU activation function. The same convolution and ReLU activation operation is performed again to further compress the length of the turbulent response signal. Finally, the initial feature extraction of the turbulent response signal is completed by dimensionality transformation and linear projection to adjust the features.

[0019] Furthermore, the signal processing procedures of the position encoder and depth feature extraction module include:

[0020] The position encoder generates a position encoding matrix with dimensions matching the input data of the current layer based on sine and cosine encoding. The position encoding matrix is ​​added to the input data of the current layer, enabling the model to have the ability to perceive the position of time series data in order to understand the order of all elements in the sequence.

[0021] The encoded data is fed into the deep feature extraction module. After being processed sequentially by several feature extraction sub-modules and stacked multiple times, the deep extraction and fusion of signal features are completed. The feature extraction sub-module includes a feedforward neural network unit, a multi-head self-attention unit, and a depthwise separable convolutional unit connected in sequence. The feedforward neural network unit is configured to preprocess the input data to enhance the nonlinear expressive ability of the model. The multi-head self-attention sub-unit is configured to capture long-range dependencies of the data. The depthwise separable convolutional unit is configured to extract local features of the data.

[0022] Furthermore, the signal processing procedures of the upsampler and output layer include:

[0023] The compressed signal sequence length is extended to the original sequence length using an upsampler;

[0024] The output layer concatenates the output of the upsampler with the original sequence through a skip connection. After being fused and dimensionality reduced by a convolutional kernel, the sequence is fed into an activation function to generate the final normalized impulse response signal.

[0025] Furthermore, in model training, the training optimization method includes:

[0026] Gradient clipping: Before the optimizer updates the model parameters, the norm of the gradient vector of all model parameters is limited to a preset threshold; if the norm of the gradient vector exceeds the preset threshold, scaling is performed.

[0027] Mixed-precision training: The forward propagation computation of the model is automatically converted into half-precision computation through the context manager, and the loss scaling factor is dynamically adjusted according to whether the gradient overflows through the gradient scaler.

[0028] Furthermore, in model training, the training optimization method includes:

[0029] Dynamic learning rate adjustment: Real-time monitoring of validation loss. When the validation loss fails to improve after multiple consecutive monitoring, the scheduler is triggered to dynamically adjust the learning rate. The counter is reset after training improves.

[0030] Gradient checkpointing: Gradient checkpointing is applied to optimize memory in the deep feature extraction module. When gradients need to be calculated in training mode, the intermediate activation values ​​are not saved during forward propagation, only the input and output are recorded; during back propagation, the intermediate activations are recalculated based on the recorded inputs, and gradients are calculated only for key nodes.

[0031] A flutter wind tunnel test impulse response generation system for turbulent excitation includes:

[0032] The model building module is configured to combine convolutional sampling methods and deep feature extraction methods to build a hybrid Transformer generative model, and to establish the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system through the hybrid Transformer generative model;

[0033] The model training module is configured to preprocess the data using different normalization methods based on the time-domain symmetry and zero-point distribution differences of turbulent and impulse responses, according to the model training effect. A loss function that combines time-domain and frequency-domain mean square errors is used, and the hybrid Transformer generative model is optimized through various training optimization methods.

[0034] The signal generation module is configured to take the measured turbulent response signal as input and generate the corresponding impulse response signal using a trained hybrid Transformer generative model.

[0035] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method for generating the flutter wind tunnel test impulse response oriented to turbulent excitation.

[0036] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for generating the flutter wind tunnel test impulse response oriented to turbulent excitation.

[0037] The beneficial effects of this invention are as follows:

[0038] a) To enhance the Transformer's ability to capture local features, this invention adds a Convolutional Neural Network (CNN) and a Feedforward Network (FFN) to the core layer of the model, and combines them with Multi-Head Self-Attention (MHSA) to construct a hybrid model with richer feature transformation and non-linear expression capabilities. Continuous functions are used for dynamic encoding, enabling the model to more efficiently handle longer sequences not seen during training, thus enhancing generalization ability.

[0039] b) Due to the differences in time-domain symmetry and zero-point distribution between turbulent and impulse responses, this invention employs different normalization methods to preprocess the data based on the model training effect. To ensure the accuracy of the generated signal, a loss function combining time and frequency domain mean square error is used, along with optimization techniques including gradient clipping, mixed-precision training, learning rate adjustment, and sample skip connections, thus balancing model training efficiency and computational accuracy.

[0040] c) Both simulation data and actual flutter wind tunnel experimental data were tested, verifying the effectiveness of the invention. Furthermore, regarding modal parameter estimation and flutter boundary prediction of the structural system, comparisons were made with the most commonly used engineering methods, including RDT and SSI methods, as well as two LSTM-based generative modeling methods, demonstrating the high engineering application value of the invention. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for generating the impulse response of a flutter wind tunnel test oriented to turbulent excitation in Embodiment 1 of the present invention.

[0042] Figure 2 This is a schematic diagram of the time-frequency relationship between turbulent excitation and response signals.

[0043] Figure 3 This is a schematic diagram of the Transformer network structure.

[0044] Figure 4 The figure shows the time-domain plot of a first-order signal in the training set (damped 0.018; frequency 15Hz). In the figure: (a) first-order turbulent response signal; (b) first-order impulse response signal.

[0045] Figure 5The figure shows the time-domain plot of a second-order signal in the training set (damping 0.122, 0.157; frequency 6Hz, 37Hz). In the figure: (a) second-order turbulent response signal; (b) second-order impulse response signal.

[0046] Figure 6 The figure shows the time-domain plot of a third-order signal in the training set (damping 0.054, 0.002, 0.088; frequency 7Hz, 33Hz, 65Hz). In the figure: (a) third-order turbulent response signal; (b) fourth-order impulse response signal.

[0047] Figure 7 This is a training loss curve.

[0048] Figure 8 The figure shows a first-order turbulent response signal from a test set. In the figure: (a) time domain signal; (b) frequency domain signal.

[0049] Figure 9 The figure shows the prediction results of a first-order impulse response signal in the test set. In the figure: (a) Time domain comparison results; (b) Frequency domain comparison results.

[0050] Figure 10 The figure shows a second-order turbulent response signal from a test set. In the figure: (a) time domain signal; (b) frequency domain signal.

[0051] Figure 11 The figure shows the prediction results of a second-order impulse response signal in the test set. In the figure: (a) Time domain comparison results; (b) Frequency domain comparison results.

[0052] Figure 12 The figure shows a third-order turbulent response signal from a test set. In the figure: (a) time domain signal; (b) frequency domain signal.

[0053] Figure 13 The figure shows the prediction results of a third-order impulse response signal in the test set. In the figure: (a) Time domain comparison results; (b) Frequency domain comparison results. Detailed Implementation

[0054] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. 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.

[0055] Example 1

[0056] Flutter wind tunnel testing is an essential step in aircraft development. In engineering, wind tunnel turbulence is widely used to apply natural excitation, and time-domain analysis is employed to perform modal analysis on the turbulent response of flutter models, thereby determining the flutter boundaries of the aircraft. Compared to turbulent response signals, impulse response signals have significant advantages in modal characteristic characterization and anti-interference capabilities. Directly extracting modal parameters from impulse response signals can simplify the system identification process and effectively improve data processing efficiency.

[0057] Furthermore, due to its self-attention mechanism and parallel architecture, the Transformer has a natural advantage over LSTM in handling ultra-long-term sequence tasks. By encoding the positions of all elements in the sequence and calculating correlation weights, the Transformer can capture ultra-long-range dependencies, paying attention to all data in the input sequence at each prediction. This contributes to producing more consistent and accurate time series when performing generative time series tasks. In addition, when using the Transformer generative model, it is not limited by sequence length when computational resources are sufficient, and can support changes in sampling rate and sampling time, avoiding systematic errors introduced by manually pruning the sequence. Therefore, compared to LSTM, the Transformer model is more suitable for performing impulse response generation tasks in flutter wind tunnel experiments.

[0058] Based on this, in order to accurately and efficiently identify the key dynamic parameters of a structure, this embodiment proposes a method for generating the impulse response of a flutter wind tunnel test oriented towards turbulent excitation. This method can be used to directly convert the turbulent response signal dynamically acquired in the wind tunnel into an impulse response signal. This method establishes a mathematical relationship between the turbulent response signal and the impulse response signal of the structural dynamic system through convolution operations. When the turbulent excitation cannot be directly measured, the measured turbulent response signal is used as input to generate the corresponding impulse response signal using a hybrid Transformer generative model. Simulation results show that this method can predict the time-frequency characteristics of multi-order signals well and exhibits a certain degree of generalization.

[0059] The method for generating the impulse response of a flutter wind tunnel test oriented towards turbulent excitation in this embodiment is as follows: Figure 1 ,include:

[0060] Model Construction: A hybrid Transformer generative model is constructed by combining convolutional sampling and deep feature extraction methods, and the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system is established through the hybrid Transformer generative model;

[0061] Model training: Based on the differences in time-domain symmetry and zero-point distribution between turbulent and impulse responses, different normalization methods are used to preprocess the data according to the model training effect; a loss function that combines time-domain and frequency-domain mean square errors is adopted, and the hybrid Transformer generative model is optimized through various training optimization methods;

[0062] Signal generation: The measured turbulent response signal is used as input to generate the corresponding impulse response signal through a trained hybrid Transformer generative model.

[0063] Specifically, this paper details the method for generating flutter wind tunnel test impulse response for turbulent excitation in this embodiment through several aspects, including system modeling, a modal parameter estimation framework based on hybrid Transformer, test verification and result analysis, and supplementary explanation of activation functions.

[0064] I. System Modeling

[0065] (1) Signal Model

[0066] According to the theory of linear time-invariant (LTI) systems, when an LTI physical system is continuously input with a series of pulse signals... At that time, regardless of the pulse signal The system response result, from the moment of input, can be derived from the corresponding impulse response result. The signal is obtained by direct superposition, where N is the number of pulse signals. Therefore, for any input signal... The system response result can be expressed as:

[0067] (1)

[0068] Among them, the symbol " " indicates that a convolution operation is performed; The system impulse response signal is used to characterize the dynamic characteristics of a physical system in response to a unit impulse.

[0069] From the frequency domain perspective, after Fourier transform, the convolution operation in equation (1) can be transformed into the following product operation:

[0070] (2)

[0071] in, for The frequency domain form; for The frequency domain form; Known as the frequency response function (FRF), it contains rich modal parameter information and energy transfer characteristics in structural dynamic systems.

[0072] In flutter wind tunnel tests, due to limitations in the excitation method, the input to the structural dynamic system is a turbulent signal, exhibiting wide bandwidth and random characteristics, and is typically modeled as Gaussian white noise in engineering. Therefore, under steady-state small perturbation conditions, the turbulent response signal and the impulse response signal satisfy the following:

[0073] (3)

[0074] in, This represents the turbulent response signal, which can be acquired in real time using sensors such as accelerometers and strain gauges; The turbulent excitation signal represents a Gaussian distribution and satisfies... ,variance It can characterize the degree of instability of airflow in a wind field; As an impulse response signal, it can be represented as follows in a multi-modal scenario:

[0075] (4)

[0076] in ，M The modal order of the system; Indicates the first m First-order modal amplitude; Indicates the first m First modal frequency; Indicates the first m First-order modal damping.

[0077] Figure 2 A schematic diagram illustrating the time / frequency domain correlation between the turbulent excitation signal, the impulse response signal, and the turbulent response signal is provided. Based on... Figure 2 It is known that in flutter wind tunnel tests, the turbulent excitation signal is assumed to be composed of a Gaussian white noise sequence, the impulse response signal is an unknown signal containing rich modal information, and the turbulent response signal obtained through convolution is a known signal. Therefore, theoretically, if any two of the above three signals can be obtained, the third signal can be uniquely determined.

[0078] In fact, when conducting flutter wind tunnel tests, turbulent response signals can be obtained by collecting sensor voltage signals and then converting them into time-domain vibration signals. However, turbulent excitation in wind tunnel tests It is difficult to measure accurately, therefore the impulse response signal cannot be directly calculated according to equation (3). The emergence and widespread application of generative models have provided new methods and pathways for capturing detailed features of time-series signals, including vibration signals, and for performing nonlinear transformations. When the turbulent excitation is unknown, a generative neural network model can be constructed through pre-training, and the impulse response signal can be predicted based on simulation data, thereby establishing a complex nonlinear mapping relationship between the turbulent response signal and the impulse response signal.

[0079] (2) Basic structure of Transformer

[0080] Unlike RNNs, including LSTM, the Transformer model uses an attention mechanism to capture dependencies in time series data, directly establishing a relationship between any two elements in the sequence, regardless of distance. For example... Figure 3 As shown, the classic Transformer network consists of multiple encoder and decoder modules: the encoder includes multi-head self-attention layers and feedforward neural network layers; the decoder adds a cross-attention layer in the middle of the encoder. The core of the Transformer is the self-attention mechanism, which can effectively improve the feature capture ability of long-term sequences and the robustness of the learning process. Figure 3 In this context, h represents the number of layers, and N is a constant. For an input sequence X, three learnable weight matrices are defined. Self-attention can be calculated as:

[0081] (5)

[0082] in, Used to define the query vector matrix; Represents the key vector matrix; Represents a value vector matrix; The dimension of the key vector, i.e., the matrix. The number of columns; The function is used to normalize the probabilities of the scaled attention intensity matrix row by row. The function is defined as follows:

[0083] (6)

[0084] in, For the first in the vector j One element; J Represents the vector dimension.

[0085] like Figure 3As shown on the left, when multiple self-attention modules are used in parallel, different heads can focus on different information, thus forming a multi-head attention mechanism. This mechanism significantly improves the decoupling ability of the essential features of the data by automatically filtering non-critical information and strengthening the extraction of core features. Specifically, the input sequence X is divided into channels along its channel dimension. H The system employs multiple self-attention modules in parallel for feature transformation to capture diverse data features. Subspace features are fused along the feature dimension using a tensor concatenation operation. After processing by a learnable projection transformation layer, the concatenated result is mapped back to the original dimension. The calculation process can be described as follows:

[0086] (7)

[0087] in, This indicates that tensor splicing is being performed; Indicates the output projection matrix. Let R represent the dimension of the value vector, and let R represent the set of real numbers. In equation (7), the th... h The size can be calculated as:

[0088] (8)

[0089] in, , and To learn weight matrices for subspaces of different matrices, satisfying , and .

[0090] Since self-attention modules cannot capture the order of input data, when processing time-series prediction tasks, it is necessary to encode the positions of the input sequence and then add the positional information to the input sequence as input to the encoder module. In practice, sine and cosine coding is most commonly used, which can be specifically described as:

[0091] (9)

[0092] in, Indicates the position of the target data in the sequence; , is used to define the index of target data on a certain dimension.

[0093] II. Modal parameter estimation framework based on hybrid Transformer

[0094] (1) Hybrid Transformer Model

[0095] In reality, unlike typical signal generation tasks, wind tunnel turbulence data is characterized by high sampling rates and large data scales, posing significant challenges to generative models, such as gradient vanishing and poor real-time performance. Furthermore, the computational explosion, loss of local information, and difficulty in capturing high-frequency signal features brought about by ultra-long sequences place high demands on generative neural network models. From an engineering perspective, an ideal task model needs to maintain strong global feature modeling capabilities while ensuring accurate capture of local features to prevent modal distortion, and also maintain computational efficiency to achieve dynamic extraction of modal information. Compared to the gating mechanism used in LSTM models, the self-attention mechanism of Transformer models is very good at capturing global dependencies in time series, making it more suitable for ultra-long time series generation tasks. However, simple self-attention modules are less efficient at capturing local signal features, such as difficulty in effectively describing the relationships between adjacent frames and sharp peaks in the response signal, and they incur high computational costs.

[0096] Therefore, this embodiment proposes a hybrid Transformer generative model that combines convolutional sampling and deep feature extraction, aiming to improve the network architecture of the classic Transformer model and enhance computational efficiency. The overall network model mainly consists of six parts: Input Projection Module, Convolution Subsampler, Position Encoder, Deep Feature Extraction Module, Upsampler, and Output Layer.

[0097] During the forward propagation process, first, the length is... Batch size is The input turbulent response signal is linearly projected to a higher dimension. This prepares for subsequent complex feature extraction. The projected signal is fed into a downsampler containing two layers of one-dimensional convolutions. After the first convolutional layer, the signal length is compressed to [value missing]. ,in This is the downsampling stride; after feeding the signal into the ReLU activation function, the same convolution and activation operations are performed again to further compress the signal length. After dimensional transformation and linear projection to adjust the features, the initial feature extraction of the turbulent response signal is completed. A feature is generated using formula (9). The position encoding matrix is ​​added to the input data of this layer, enabling the model to understand the order of all elements in the sequence, thus possessing the ability to perceive the position of time series data. The deep feature extraction module consists of... The system consists of several feature extraction sub-modules stacked sequentially. Each feature extraction sub-module contains units such as a feedforward neural network, multi-head self-attention, and depthwise separable convolution. The number of stacking layers for the modules is specified. The encoded data is fed into the deep feature extraction module. After sequential processing by the feature extraction sub-modules and multiple stacking steps, deep feature extraction and fusion are completed. Subsequently, an upsampler is used to extend the length of the compressed sequence. Doubled to the length of the original sequence And adjust the number of channels to This prepares the product for entering the output layer; among which, This represents the upsampling factor. Finally, a skip connection is used to concatenate the output of the upsampler with the original sequence, resulting in an output with dimension [missing value]. The data, after being fused and dimensionality-reduced by a convolutional kernel of size 1, is then fed into the activation function. The final normalized impulse response signal is generated.

[0098] It's important to note that the skip connections used in the output layer allow the input signal to bypass all the complex processing steps, such as the intermediate convolutional modules and feature extraction modules, and be concatenated with the upsampled features. The core idea is to use the most original output information to guide and correct the final output. The skip connection setup prevents the loss of important information during multiple transformations, ensuring the fidelity and accuracy of the output, and also provides stability support for backpropagation, helping to mitigate the potential gradient vanishing problem.

[0099] The following section will focus on the core module of deep feature extraction.

[0100] Feedforward neural networks are a fundamental component of modern deep learning architectures, playing a crucial role in nonlinear transformation and feature enhancement. The feedforward neural network unit is responsible for preprocessing the data input to the deep feature extraction module to enhance the model's nonlinear expressive power. Dimensional input tensor The output after processing by the feedforward neural network unit can be mathematically represented as:

[0101] (10)

[0102] Among them, the symbol " " indicates that the operations of the composite function are performed sequentially; The function is used to randomly discard some input values, thereby preventing overfitting; Represents the ReLU activation function; The layer normalization function is used to independently normalize the feature vector at each time step:

[0103] (11)

[0104] Among them, the symbol " " indicates that the Hadamard product operation is performed; Indicates time step t eigenvectors; For dimension A vector of all 1s; Used to maintain numerical stability; These are learnable parameters; and They represent the eigenvectors respectively. The mean and variance of.

[0105] and Both represent linear layers, the first linear layer. Used to expand the feature dimensions, while the second linear layer This compresses the feature dimension back to its original size before input; the corresponding scaling operation can be expressed as:

[0106] (12)

[0107] in, ; ; The output of the first linear layer has a dimension of ; The output of the second linear layer has dimensions equal to the input tensor. Consistent; ; ; ; .

[0108] Therefore, in order to further improve the stability of training, The calculation results are fused with the original input through scaling residual connections to obtain the output of the feedforward neural network unit:

[0109] (13)

[0110] Wherein, scaling factor It is used to balance training speed and the stability of the training process.

[0111] Preprocessed data for the output of feedforward neural network units The multi-head attention unit calculates the relational weights of all positions in the sequence and uses relative position encoding to inject the sequence's order information. This enables the model to handle sequences of different lengths (capable of handling scenarios with sequence lengths different from the training set) while capturing global dependencies and long-range interactions. The relevant calculation process has been described above and will not be repeated here. Assume the multi-head self-attention calculation result obtained through equation (7) is... ,Will After calculating according to the layer normalization described in equation (17), it is compared with the input data of this layer. The output result obtained by performing residual connection is as follows:

[0112] (14)

[0113] Subsequently, depthwise separable convolutional units are used to extract... The local features and short-range dependencies are further refined to compensate for the shortcomings of the self-attention mechanism in local feature extraction. Unlike standard convolution operations that perform joint computation in both channel and spatial dimensions, depthwise separable convolutional units decompose the computation of spatial features and the fusion of channels into two independent steps, significantly reducing the computational complexity and number of parameters of the model, thus making it more suitable for the ultra-long time sequence generation context of this embodiment. In the depthwise convolution stage, a set of convolutional kernels is used. By processing the spatial features of each input channel independently, the following can be calculated:

[0114] (15)

[0115] Among them, the operation Indicates to Rounding down is performed to ensure that the center of the convolution kernel is aligned with the current position of the input sequence. t Alignment. In the channel fusion stage, a set of convolutional kernels is also used. Pointwise convolution is performed to fuse the features from multiple channels. The calculation process is as follows:

[0116] (16)

[0117] Will Transform into After residual connections, the final output of the depthwise separable convolutional unit is obtained. Finally, after layer normalization, the final output of the depth feature extraction module is obtained as follows:

[0118] (17)

[0119] In subsequent calculations, by using the output of the previous deep feature extraction module as the input of the next module, features can be sequentially passed between different modules, thereby progressively deepening the learning and representation of complex data features. In summary, this architecture captures long-range dependencies through a multi-head self-attention mechanism, extracts local features through depthwise separable convolutions, and provides nonlinear transformations through a feedforward network. This design balances feature extraction depth with computational efficiency, ensures gradient propagation through residual connections, and preserves original signal details through final feature concatenation, making it more suitable for modeling tasks involving extremely long sequences. Furthermore, it is worth noting that using depthwise separable convolutions reduces computational complexity from that of standard convolutions. Reduced to ,when , In this way, the theoretical computational load can be reduced by approximately 8.9 times. Furthermore, common deep learning-related functions involved in this embodiment are detailed below.

[0120] (2) Construction of simulation dataset

[0121] Generally, since low-frequency modes are more easily excited in flutter wind tunnel tests, the main focus of flutter models in engineering is on the lower-order modes. Therefore, this embodiment constructs a signal dataset of orders below 3 for method verification. Based on the structural response characteristics of an actual wind tunnel flutter model, the damping and frequency of each mode of the impulse response signal are set as shown in Table 1. The impulse response signals generated according to Table 1 total... The group was continuously sampled at a sampling rate of 2000Hz and a sampling time of 10s, with a data length of [missing information]. .

[0122] Table 1 - Parameter Configuration of Simulation Data Impulse Response Signal

[0123]

[0124] Assuming the generation length is also the same After obtaining the Gaussian white noise sequence, the turbulent response signal of the same length is calculated by convolution using equation (3). To more intuitively represent the turbulent response signal input to the model during model training and the impulse response signal used as the output label, Figure 4 , Figure 5 and Figure 6 The calculation results of a certain first-order, second-order, and third-order turbulent response signal and its corresponding impulse response signal in the training set are given respectively.

[0125] (3) Model training

[0126] Without loss of generality, the previously generated simulation data of each order are divided in an 8:1:1 ratio: after equal-interval extraction and complementation, the training set consists of 9432 groups (2880 groups of first-order signals, 3276 groups each of second-order and third-order signals), the validation set consists of 1180 groups (360 groups of first-order signals, 410 groups each of second-order and third-order signals), and the test set consists of 1180 groups (the number of signals of each order is the same as the validation set). It should be noted that, to ensure that each dataset covers a sufficiently diverse range of signals, signals of each order are extracted and combined according to a fixed interval principle to guarantee the generalization ability of the training model and the reliability of the test set.

[0127] To reduce the systematic error introduced by amplitude setting and satisfy the output layer activation function The requirement is to process arbitrary turbulence signals from the input model. and impulse response signal Normalization is performed. Considering the noise characteristics of the turbulent response data, to fully preserve the distribution pattern of the original data, arbitrary turbulent response data input to the model are normalized. Using min-max normalization:

[0128] (18)

[0129] in, ; ; Represents the data number, satisfying .

[0130] Because impulse response signals exhibit good positive and negative symmetry and contain multiple zeros, applying min-max normalization will introduce outlier interference, thereby disrupting data symmetry and ultimately affecting model training performance. Based on simulation comparison results, this embodiment uses the real impulse response signal as the model output label. Perform linear scaling:

[0131] (19)

[0132] To balance the time-domain and frequency-domain errors of the generated signal, a linear combination method is used to construct the loss function:

[0133] (20)

[0134] in, and These are preset constants used to characterize the degree of attention paid to time-domain and frequency-domain errors; This indicates the calculation of the mean square error between sequences A and B; This indicates that a short-time Fourier transform calculation is being performed. This represents the preprocessed true impulse response signal; This indicates that the result obtained through a generative neural network model is related to... The corresponding predicted impulse response signal.

[0135] Specifically, model training was performed on a workstation equipped with an NVIDIA GeForce RTX 4090 graphics card (48GB VRAM), an Intel Xeon Platinum 8347C processor (36 cores, 72 threads), and 384 GB of RAM. The software environment included Windows 10, PyTorch 2.7.1, and CUDA 12.9.

[0136] Preferably, in order to improve the training efficiency, stability and scalability of the model, this embodiment adopts the following four training optimization techniques based on the above simulation platform:

[0137] ① Gradient clipping. Before the optimizer updates the parameters, the norm of the gradient vectors of all model parameters is limited to a threshold (e.g., max_norm=0.5). If the gradient norm becomes too large, it will be scaled down to ensure that the gradients are always within a reasonable range. By limiting the gradients, the step size of each parameter update is ensured to be not too large, which greatly enhances the stability of the training process and effectively avoids the gradient explosion problem that may be encountered when training deep networks.

[0138] ② Mixed-precision training. Faced with a training set containing over 9000 samples and long sequence samples of 20,000 data points, mixed-precision training is employed to intelligently combine half-precision and single-precision floating-point numbers. Specifically, the Autocast context manager is used to automatically convert the model's forward propagation computation to half-precision, significantly reducing memory usage and improving computation speed. To prevent gradient underflow issues that may occur with half-precision computation, a gradient scaler is used to dynamically adjust the loss scaling factor based on whether gradient overflow is detected.

[0139] ③ Dynamic Learning Rate Adjustment. To ensure rapid convergence in the early stages of training and fine-grained optimization in the later stages, the ReduceLROnPlateau learning rate scheduler is used to dynamically adjust the learning rate. By monitoring the validation loss in real time, the scheduler is triggered to adjust the learning rate when the validation loss shows no improvement for five consecutive times. The counter is reset when training improves. Furthermore, this data-driven learning rate adjustment strategy synergizes with gradient clipping and mixed-precision training. Gradient clipping prevents gradient explosion during learning rate adjustment and provides a stable learning rate for mixed-precision training.

[0140] ④ Gradient Checkpointing. Gradient checkpointing, as a memory optimization strategy, effectively alleviates memory pressure by dynamically reconstructing the computation graph during backpropagation, balancing computational and storage resources. This technique is applied to the deep feature extraction module for memory optimization. When gradients need to be calculated in training mode, complete intermediate activation values ​​are not saved during forward propagation; only inputs and outputs are recorded. During backpropagation, intermediate activations are recalculated based on the recorded inputs, and gradients are calculated only for key nodes. This strategy reduces memory complexity from... Reduce to ,in n Indicates the number of network layers.

[0141] At this point, the generated training set data is fed into the hybrid Transformer model for training, with validation set data used for supervision. During training, the model parameters are dynamically updated, and the model parameters with the lowest validation error are saved. During training, the total number of epochs is set to 1000, and training is stopped. The model parameters with the lowest validation error are saved and used as the optimal model. Figure 7 The curves showing the changes in training error and validation error with the number of training epochs are presented. It can be seen that the loss function exhibits a significant decreasing trend and tends to converge with the increase in the number of training epochs, indicating that the model can effectively learn the data features and reflecting the correctness of the training process. Furthermore, the low validation loss error also demonstrates the model's good generalization ability.

[0142] III. Testing, Verification, and Result Analysis

[0143] First, the generative model constructed in this embodiment is validated using 1180 sets of simulation data from a test set not seen during the model training process. This set includes 360 sets of first-order signals, 410 sets of second-order signals, and 410 sets of third-order signals. To provide an intuitive understanding, Figure 8 and Figure 9 The first-order signal used as the model input in the test set and the corresponding labeled output signal (frequency 14, damping 0.01) are given respectively. Figure 8 In the figure, subfigure (a) shows the time-domain signal of the first-order turbulent response input to the model, and subfigure (b) shows the corresponding spectral curve. Figure 9 The actual impulse response signal and the predicted impulse response signal obtained through a generative model are presented. Subfigure (a) shows the complete 10-second time-domain signal, and subfigure (b) shows the corresponding frequency-domain signal. Combined with... Figure 8 and Figure 9 It can be seen that the proposed method has ideal prediction results for first-order signals that have not been seen in the simulation set. It performs well in both the time and frequency domains and demonstrates a certain generalization ability.

[0144] Figure 10The complete 10-second calculation results of a certain second-order turbulent response signal in the test set are given. The corresponding real modal parameters include first-order frequency of 22Hz, second-order frequency of 53Hz, first-order damping of 0.042, and second-order damping of 0.217. Figure 11 The actual second-order impulse response signal and the predicted impulse response signal obtained through a generative model are presented. Since the second-order signal decays to near zero in less than one second, for ease of description... Figure 11 Subgraph (a) in the image only shows the trend for the first 3 seconds. According to... Figure 11 Based on the described time / frequency domain characteristics, the impulse response signal predicted by the generative model is highly consistent with the labeled signal, and the trend of change is consistent.

[0145] Figure 12 The complete time-domain and frequency-domain calculation results (total 10 seconds) of the turbulent response signal of a certain third-order simulated signal in the test set are presented, with corresponding first-order frequencies of 13Hz, second-order frequencies of 45Hz, and third-order frequencies of 59Hz; first-order damping of 0.154, second-order damping of 0.122, and third-order damping of 0.228. Due to the rapid attenuation of this signal, for ease of comparison... Figure 13 The actual impulse response signal for the first 3 seconds and the predicted impulse response signal generated by the generative model are given (the signal for the last 7 seconds is at zero level). Combined with... Figure 12 and Figure 13 It can be seen that even for third-order signals with high nonlinearity, the proposed method can still accurately depict the time-domain and frequency-domain variation characteristics of the signal and achieve a relatively ideal generation effect.

[0146] IV. Supplementary Explanation of Activation Functions

[0147] In deep neural networks, activation functions are key components that introduce nonlinear transformations, determining how neurons are activated and transmit information. The hybrid Transformer model constructed in this embodiment primarily uses three activation functions: GELU, ReLU, and Tanh. These are deployed in different parts of the model, leveraging their respective characteristics.

[0148] The GELU activation function scales the input probabilistically, providing a smooth non-linear transformation and mitigating gradient vanishing. It is deployed in the feedforward network of the deep feature extraction module in the model, and its mathematical expression is as follows:

[0149] (twenty one)

[0150] in, Represents the original input value of the neuron; The cumulative distribution function represents the standard normal distribution. The value is less than or equal to The probability, therefore It can be seen that... The function determines the degree to which an input value passes probabilistically based on its magnitude, and is differentiable and smooth everywhere, making it suitable for time series modeling tasks.

[0151] ReLU is one of the simplest and most commonly used activation functions in deep learning. Its function is to set negative input values ​​to zero, thus introducing sparsity into the network, while simultaneously ensuring the gradient is always 1 in the positive region, mitigating the vanishing gradient problem. The ReLU function is defined as follows:

[0152] (twenty two)

[0153] In the above formula, when the input When, the output is ;when When the input to a neuron is always negative, its gradient will always be 0, which may prevent the neuron from updating its parameters. The ReLU function is simple to calculate and very fast during training, but if the input to a neuron is always negative, its gradient will always be 0, which may prevent the neuron from updating its parameters.

[0154] The Tanh function smoothly maps the input to The interval, achieving zero-centered output, enables more stable training of subsequent layers, and its mathematical definition is:

[0155] (twenty three)

[0156] From equation (23), it can be seen that the Tanh function is an S-shaped curve function symmetric about the origin, when When the gradient is large, it will approach zero. In the model proposed in this embodiment, the Tanh function is used as the activation function of the final output layer, which can limit the generated impulse response signal to a defined, bounded range. This conforms to the amplitude characteristics of the vibration response signal and helps to maintain the stability of the training process.

[0157] Example 2

[0158] This embodiment provides a flutter wind tunnel test impulse response generation system for turbulent excitation, including:

[0159] The model building module is configured to combine convolutional sampling methods and deep feature extraction methods to build a hybrid Transformer generative model, and to establish the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system through the hybrid Transformer generative model;

[0160] The model training module is configured to preprocess the data using different normalization methods based on the time-domain symmetry and zero-point distribution differences of turbulent and impulse responses, according to the model training effect. A loss function that combines time-domain and frequency-domain mean square errors is used, and the hybrid Transformer generative model is optimized through various training optimization methods.

[0161] The signal generation module is configured to take the measured turbulent response signal as input and generate the corresponding impulse response signal using a trained hybrid Transformer generative model.

[0162] Example 3

[0163] This embodiment is based on embodiment 1:

[0164] This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the flutter wind tunnel test impulse response generation method of Embodiment 1 for turbulent excitation. The computer program can be in the form of source code, object code, executable file, or some intermediate form.

[0165] Example 4

[0166] This embodiment is based on embodiment 1:

[0167] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the flutter wind tunnel test impulse response generation method of Embodiment 1 for turbulent excitation. The computer program can be in the form of source code, object code, executable file, or some intermediate form. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0168] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed in this embodiment and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be modified within the scope of the concept described in this embodiment through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

[0169] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

Claims

1. A method for generating impulse response in flutter wind tunnel tests oriented towards turbulent excitation, characterized in that, include: Model Construction: A hybrid Transformer generative model is constructed by combining convolutional sampling and deep feature extraction methods, and the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system is established through the hybrid Transformer generative model; Model training: Based on the differences in time-domain symmetry and zero-point distribution between turbulent and impulse responses, different normalization methods are used to preprocess the data according to the model training effect; a loss function that combines time-domain and frequency-domain mean square errors is adopted, and the hybrid Transformer generative model is optimized through various training optimization methods; Signal generation: The measured turbulent response signal is used as input to generate the corresponding impulse response signal through a trained hybrid Transformer generative model; In the model construction, the hybrid Transformer generative model constructed by combining convolutional sampling method and deep feature extraction method includes: an input projection module, a convolutional downsampling unit, a position encoder, a deep feature extraction module, an upsampling unit, and an output layer that execute signal processing procedures in sequence. The signal processing procedures of the input projection module and the convolutional downsampler include: During forward propagation, the input projection module transforms the input turbulent response signal to a higher dimension through linear projection; The projected turbulent response signal is fed into a convolutional downsampler containing two layers of one-dimensional convolution. The length of the turbulent response signal is compressed by the first layer of convolution and then fed into the ReLU activation function. The same convolution and ReLU activation operation is performed again to further compress the length of the turbulent response signal. Finally, the features are adjusted by dimensionality transformation and linear projection to complete the initial feature extraction of the turbulent response signal. The signal processing procedures of the position encoder and depth feature extraction module include: The position encoder generates a position encoding matrix with dimensions matching the input data of the current layer based on sine and cosine encoding. The position encoding matrix is ​​added to the input data of the current layer, enabling the model to have the ability to perceive the position of time series data in order to understand the order of all elements in the sequence. The encoded data is fed into the deep feature extraction module. After being processed sequentially by several feature extraction sub-modules and stacked multiple times, the deep extraction and fusion of signal features are completed. The feature extraction sub-module includes a feedforward neural network unit, a multi-head self-attention unit, and a depthwise separable convolutional unit connected in sequence. The feedforward neural network unit is configured to preprocess the input data to enhance the nonlinear expressive ability of the model. The multi-head self-attention sub-unit is configured to capture long-range dependencies of the data. The depthwise separable convolutional unit is configured to extract local features of the data. The signal processing procedures of the upsampler and output layer include: The compressed signal sequence length is extended to the original sequence length using an upsampler; The output layer concatenates the output of the upsampler with the original sequence through a skip connection. After being fused and dimensionality reduced by a convolutional kernel, the sequence is fed into an activation function to generate the final normalized impulse response signal.

2. The method for generating impulse response in flutter wind tunnel tests oriented towards turbulent excitation according to claim 1, characterized in that, In model training, the training optimization method includes: Gradient clipping: Before the optimizer updates the model parameters, the norm of the gradient vector of all model parameters is limited to a preset threshold; if the norm of the gradient vector exceeds the preset threshold, scaling is performed. Mixed-precision training: The forward propagation computation of the model is automatically converted into half-precision computation through the context manager, and the loss scaling factor is dynamically adjusted according to whether the gradient overflows through the gradient scaler.

3. The method for generating impulse response in flutter wind tunnel tests oriented towards turbulent excitation according to claim 1, characterized in that, In model training, the training optimization method includes: Dynamic learning rate adjustment: Real-time monitoring of validation loss. When the validation loss fails to improve after multiple consecutive monitoring, the scheduler is triggered to dynamically adjust the learning rate. The counter is reset after training improves. Gradient checkpointing: Gradient checkpointing is applied to optimize memory in the deep feature extraction module. When gradients need to be calculated in training mode, the intermediate activation values ​​are not saved during forward propagation, only the input and output are recorded; during back propagation, the intermediate activations are recalculated based on the recorded inputs, and gradients are calculated only for key nodes.

4. A flutter wind tunnel test impulse response generation system for turbulent excitation, employing the flutter wind tunnel test impulse response generation method for turbulent excitation as described in claim 1, characterized in that, The flutter wind tunnel test impulse response generation system includes: The model building module is configured to combine convolutional sampling methods and deep feature extraction methods to build a hybrid Transformer generative model, and to establish the mathematical relationship between turbulent response signals and impulse response signals in the structural dynamics system through the hybrid Transformer generative model; The model training module is configured to preprocess the data using different normalization methods based on the time-domain symmetry and zero-point distribution differences of turbulent and impulse responses, according to the model training effect. A loss function that combines time-domain and frequency-domain mean square errors is used, and the hybrid Transformer generative model is optimized through various training optimization methods. The signal generation module is configured to take the measured turbulent response signal as input and generate the corresponding impulse response signal using a trained hybrid Transformer generative model.

5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method for generating the flutter wind tunnel test impulse response oriented to turbulent excitation as described in any one of claims 1-3.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for generating the flutter wind tunnel test impulse response oriented to turbulent excitation as described in any one of claims 1-3.

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