Nonlinear aerodynamic damping estimation method and system based on LSTM (Long Short Term Memory) and storage medium

Abstract

The invention discloses a nonlinear aerodynamic damping estimation method based on LSTM, and the method comprises the following steps: 1, building a nonlinear state space model of a structure based on structural response, including a state equation, an observation equation and a relation between nonlinear aerodynamic damping and structural vibration amplitude; 2, performing updating and covariance prediction on response data by using unscented Kalman filtering; 3, correcting the Kalman gain in real time by using a long short-term memory network; 4, performing state updating and covariance updating based on the corrected Kalman gain; 5, training the long-short-term memory network through an unsupervised learning mode, optimizing the filtering performance, and defining a mean square error of a posterior observation predicted value and a real observation value as a loss function; and 6, calculating the nonlinear aerodynamic damping according to the estimated nonlinear aerodynamic damping parameters. The invention further discloses a nonlinear aerodynamic damping estimation system based on the LSTM and a storage medium.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic analysis technology, specifically a nonlinear aerodynamic damping estimation method, system, and storage medium based on LSTM. Background Technology

[0002] In the field of vortex-induced vibration analysis of highly flexible structures such as large wind turbine towers, long-span bridges, high-rise buildings, transmission towers, and chimneys, aerodynamic damping is a key parameter characterizing energy dissipation during the interaction between the structure and airflow. Its generation mechanism is complex, involving not only fluid-structure interaction phenomena but also being closely related to unsteady vortex shedding processes, thus exhibiting highly significant amplitude-dependent nonlinear characteristics. Therefore, accurate estimation of aerodynamic damping has become a core challenge in assessing the safety and comfort of structures under wind-induced vibration.

[0003] Traditional methods for estimating aerodynamic damping primarily rely on wind tunnel testing and system identification techniques. Among these, the least squares method and stochastic decrement techniques are widely used due to their relative simplicity and broad applicability. However, these traditional methods fall short when dealing with strongly nonlinear systems, proving inadequate for effectively addressing related problems.

[0004] In recent years, nonlinear Kalman filters (such as unscented Kalman filters, or UKF) have gradually emerged in this field due to their unique advantage of not requiring linearization of the system. UKF approximates the state distribution through Sigma point propagation, which can handle nonlinear estimation problems relatively well to a certain extent. However, its performance is highly dependent on the accurate prior settings of the covariance matrices of process noise and observation noise (denoted as Q and R, respectively). But in practical engineering applications, the statistical characteristics of noise are often difficult to know accurately and change over time. Inaccurate noise model settings can lead to reduced filtering accuracy, slower convergence speed, and even serious problems such as estimation divergence. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a nonlinear aerodynamic damping estimation method, system and storage medium based on LSTM, which aims to efficiently and accurately identify the aerodynamic damping of structures with nonlinear characteristics without the need to pre-set noise parameters, and to solve the estimation error caused by UKF due to model mismatch and unknown noise.

[0006] To achieve the above objectives, the present invention provides the following technical solution: This invention first proposes a nonlinear aerodynamic damping estimation method based on LSTM, characterized by the following steps: Step 1: Construct a nonlinear state-space model of the structure based on the structural response, including the state equation, observation equation, and the relationship between nonlinear aerodynamic damping and structural vibration amplitude; Step 2: Use unscented Kalman filtering to update the response data and predict the covariance, and obtain the original Kalman gain; Step 3: Use a long short-term memory network to correct the Kalman gain in real time, including: obtaining the state prediction error and measurement prediction error, standardizing them and inputting them into the long short-term memory network, outputting the Kalman gain correction matrix, and adding it to the original Kalman gain calculated by the unscented Kalman filter to obtain the corrected Kalman gain. Step 4: Perform state update and covariance update based on the corrected Kalman gain; Step 5: Train the Long Short-Term Memory network using unsupervised learning to optimize filtering performance, and define the mean square error between the predicted and actual posterior observations as the loss function. Step 6: Calculate the nonlinear aerodynamic damping based on the estimated nonlinear aerodynamic damping parameters.

[0007] Furthermore, in step one, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is expressed as follows: in: Nonlinear aerodynamic damping; air density; The width of the structure; This represents the effective structural mass per unit height; The amplitude of structural vibration; , , , and These are nonlinear aerodynamic damping parameters, and all are constants; The observation equation is expressed as: in: , and These represent displacement, velocity, and acceleration, respectively. The state-space equation is expressed as: in: The external load is defined as zero-mean Gaussian white noise; Indicates the modal angular frequency. For frequency; , , , and Let be the structural aerodynamic damping parameters, and: ; ; ; ; , This indicates the structural damping ratio.

[0008] Furthermore, in step two, the method for updating the response data and predicting covariance using unscented Kalman filtering comprises the following steps: 21) Initial state estimate and the initial state covariance matrix Defined as: in: Represent the initial state space equations; Indicates taking the expected value; Indicates taking the covariance; Obtain the state vector and measurement vector: in: and At time step The state vector and measurement vector at the location; and These represent the nonlinear state transition function and the nonlinear measurement function, respectively. It is the current time step; and These are the covariance matrices. and Uncorrelated zero-mean Gaussian white noise; For process noise covariance; To measure the noise covariance; 22) Calculate the sigma point at time step Using scaling and unscented transformation, generate 1 sample sigma point, State vector The dimension is represented as: in: For scaling parameters; Decide The distribution of sigma points in the surrounding area; It is the second scaling parameter, which is the square root of the matrix. The OK; 23) Time update, predicting the state vector Its covariance : in: and To assign weighting coefficients; 24) Measurement update, predict measurement vector Its covariance : 25) Obtain the original Kalman gain: in: This represents the cross-covariance matrix.

[0009] Furthermore, in step three, the method for real-time correction of the Kalman gain using a long short-term memory network comprises the following steps: 31) Obtain the state prediction error of the unscented Kalman filter. and measurement prediction error : in: and These are the predicted state vector and the measurement vector, respectively. For time step The state vector at that time; For time step Measurement vector at time; 32) Obtain the state prediction error and measurement prediction error The two standardized vectors are then concatenated into a single feature vector, which is used as the input to the Long Short-Term Memory network. 33) Input the eigenvectors into the Long Short-Term Memory network and output the Kalman gain correction matrix. ; 34) The original Kalman gain With Kalman gain correction matrix Adding them together yields the corrected Kalman gain. .

[0010] Furthermore, in step four, the method for updating the state and covariance based on the modified Kalman gain is as follows: in: and These are the state vector and the covariance matrix, respectively. and These are the predicted state vector and the measurement vector, respectively. The corrected Kalman gain; The predicted covariance.

[0011] Furthermore, in step five, the method for training the LSTM network using unsupervised learning includes: The updated state vector is used to compute the posterior observation predictions. The mean square error between the predicted posterior observation and the actual observation is defined as the loss function. Unsupervised training uses the Adam optimizer and sets up an early stopping mechanism to avoid overfitting.

[0012] This invention also proposes a system for implementing the LSTM-based nonlinear aerodynamic damping estimation method described above, characterized in that it includes: The state modeling module is used to construct a nonlinear state-space model of the structure. The UKF prediction module is configured to perform Sigma point sampling and covariance prediction to obtain the raw Kalman gain. The LSTM gain correction module dynamically corrects the Kalman gain through timing error analysis. The adaptive training module optimizes the LSTM network parameters based on the posterior observation error. The damping calculation module is used to output the estimated value of nonlinear aerodynamic damping.

[0013] The present invention also proposes a storage medium storing a computer program, which, when executed by a processor, implements the LSTM-based nonlinear aerodynamic damping estimation method described above.

[0014] The beneficial effects of this invention are as follows: This invention presents an LSTM-based nonlinear aerodynamic damping estimation method that uses a Long Short-Term Memory (LSTM) network to intelligently correct the Kalman gain of the Unscented Kalman Filter (UKF) in real time. This effectively overcomes the problem of decreased estimation accuracy caused by model mismatch and unknown noise statistical characteristics in traditional UKF, significantly improving the estimation accuracy of aerodynamic damping parameters and system state. By employing an unsupervised training mechanism, using the posterior observation error of the output state as the loss function, the LSTM network can autonomously learn and compensate for the complex nonlinear dynamics of the system without the need for manually labeled data. This achieves self-optimization and self-adaptation of the algorithm, demonstrating strong robustness and versatility. At the same time, this invention significantly reduces the dependence on user expert experience and prior knowledge, allowing for more relaxed initial parameter settings and simplifying the application process. Furthermore, the design incorporates multiple mechanisms such as gain constraint, gradient clipping, and covariance regularization, which together ensure the long-term numerical stability and reliability of the algorithm.

[0015] In summary, this invention successfully integrates data-driven and model-driven methods, providing a high-precision and robust advanced solution for structural wind-induced vibration response analysis and state estimation of similar complex nonlinear systems, which has significant theoretical value and promising engineering applications. Attached Figure Description

[0016] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a schematic diagram of the bridge tower structure; Figure 2 This is a flowchart of the nonlinear aerodynamic damping estimation method based on LSTM of the present invention; Figure 3 For structural damping Contractual wind speed Random crosswind response data; Figure 4 A comparison chart showing the measured displacement and the displacement estimated by LSTM-UKF; Figure 5 This is a comparison chart of the measured speed and the speed estimated by LSTM-UKF. Figure 6 This is a comparison chart of the parameter values ​​of nonlinear aerodynamic damping estimated by LSTM-UKF and the target values; Figure 7 To compare the estimated aerodynamic damping values ​​obtained by UKF with the target values ​​under different given process noise conditions; Figure 8 To compare the aerodynamic damping estimates obtained by LSTM-UKF with the target values ​​under different given process noise conditions. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0018] This embodiment uses a bridge tower structure as an example. The nonlinear aerodynamic damping estimation method based on LSTM (LSTM-UKF method) of this invention is used to calculate the nonlinear aerodynamic damping of a bridge tower structure. The effectiveness and accuracy of the estimated nonlinear aerodynamic damping are evaluated by comparing it with the true value. The bridge tower structure is as follows: Figure 1 As shown.

[0019] like Figure 2 As shown, the nonlinear aerodynamic damping estimation method based on LSTM in this embodiment includes the following steps.

[0020] Step 1: Construct a nonlinear state-space model of the structure based on the structural response, including the state equation, observation equation, and the relationship between nonlinear aerodynamic damping and structural vibration amplitude.

[0021] Specifically, the intrinsic relationship between aerodynamic damping and structural vibration amplitude is derived using the structural crosswind response equation and harmonic balance technology. The relationship between nonlinear aerodynamic damping and structural vibration amplitude is as follows: in: Nonlinear aerodynamic damping; air density; The width of the structure; This represents the effective structural mass per unit height; The amplitude of structural vibration; , , , and These are nonlinear aerodynamic damping parameters, and all are constants.

[0022] The observation equation is expressed as: in: , and These represent displacement, velocity, and acceleration, respectively. The state-space equation is expressed as: in: The external load is defined as zero-mean Gaussian white noise; Indicates the modal angular frequency. For frequency; , , , and Let be the structural aerodynamic damping parameters, and: ; ; ; ; , This indicates the structural damping ratio.

[0023] In this embodiment, a third-order polynomial model is used to estimate the nonlinear aerodynamic damping of the bridge tower structure. The nonlinear aerodynamic damping is represented by a third-order polynomial model. for: in: The parameters are estimated using LSTM-UKF.

[0024] The measurement equation is defined as: in: , and Indicates displacement, velocity, and acceleration; The state-space equations are: in: The external load is defined as zero-mean Gaussian white noise; Indicates the modal angular frequency. For frequency; , and Let be the structural aerodynamic damping parameters, and: ; ; ; These are nonlinear aerodynamic damping parameters, and all are constants.

[0025] Specifically, in this embodiment, the nonlinear state-space equations solved using the fourth-order Runge-Kutta method are expressed as follows: Step 2: Use unscented Kalman filtering (UKF) to update the response data and predict the covariance to obtain the original Kalman gain.

[0026] In this embodiment, structural damping is utilized. Contractual wind speed The random crosswind response data was collected at a frequency of 25 Hz. ,like Figure 3As shown, this is used to verify the accuracy and convenience of the LSTM-UKF method in identifying nonlinear aerodynamic damping. The target value of the aerodynamic damping parameter under this condition is... , , .

[0027] Specifically, the steps of UKF in updating response data, predicting covariance, and obtaining the original Kalman gain are as follows.

[0028] 21) Define the initial state estimate and the initial state covariance matrix : in: Represent the initial state space equations; Indicates taking the expected value; This indicates the covariance.

[0029] This embodiment selects an initial value. ,Pick Additionally, the covariance of process noise is defined. and measurement noise covariance Process noise in nonlinear Kalman filtering The selection of and R is crucial for accurate estimation; however, the characteristics of process noise and measurement noise remain unknown, making accurate modeling difficult. Inappropriate noise settings not only significantly reduce computational accuracy but can also cause filter divergence, a problem particularly pronounced in high-dimensional systems, becoming a key factor affecting system performance. In this embodiment, LSTM can be used to correct the Kalman gain based on the error between the predicted and actual measured values, thereby reducing the impact of inaccurate noise presets. Therefore, the noise selection does not need to be too precise; a small value is acceptable. In this embodiment, initial process noise is selected. The noise measurement is set to... ).

[0030] In a nonlinear discrete system, the state-space vector and measurement vector are obtained: in: and At time step The state vector and measurement vector at the location; and Represents nonlinear state transition functions and nonlinear measurement functions; It is the current time step; and These are the covariance matrices. and Uncorrelated zero-mean Gaussian white noise; For process noise covariance; To measure the noise covariance.

[0031] 22) Calculate the sigma point.

[0032] At time step Using scaling and unscented transformation, generate 1 sample sigma point, State vector The dimensions are as follows: in: For scaling parameters; Decide The distribution of surrounding sigma points is selected in this embodiment as follows. ; This is the second scaling parameter, which is set to 0 in this embodiment, and is the square root of the matrix. The OK.

[0033] 23) Time update.

[0034] Sigma points through nonlinear state transition functions The propagation is performed, and then the prior predicted state vector is obtained by distributing and summing the values ​​according to their weights. Its covariance It can be predicted that: in: and The weighting coefficients are represented as follows: in: These are parameters that produce higher-order effects in covariance estimation, and It is the optimal value of the Gaussian distribution.

[0035] 24) Measurement update.

[0036] By analyzing the predicted covariance Then, using a scaling-unscented transformation, generate 2. +1 new sample sigma point, State vector The dimension. The new sigma point is obtained through a nonlinear measurement function. Propagation is performed to predict the measurement vector. Its covariance .

[0037] cross-covariance matrix Represented as: 25) Obtain the original Kalman gain.

[0038] The covariance of the obtained measurement vector and mutual covariance The original Kalman gain obtained from UKF is obtained.

[0039] Step 3: Use a Long Short-Term Memory (LSTM) network to correct the Kalman gain of the UKF in real time. This includes: obtaining the state prediction error and measurement prediction error, standardizing them, inputting them into the LSTM network, outputting the Kalman gain correction matrix, and adding it to the original Kalman gain calculated by the unscented Kalman filter to obtain the corrected Kalman gain.

[0040] 31) Obtain the state prediction error of the unscented Kalman filter from the prediction step of the UKF. and measurement prediction error ; First step The initial state vector is the preset state vector, and each subsequent step uses the state vector estimated in the previous step.

[0041] 32) Obtain the state prediction error and measurement prediction error The two standardized vectors are then concatenated into a single long feature vector, which is used as the input to the LSTM network. In this embodiment, It is a 6*1 vector. The vector is 3*1, and the input vector is 9*1.

[0042] 33) Input the concatenated feature vectors into the LSTM network. LSTM, through its gating mechanism (forget gate, input gate, output gate), learns the complex dynamic relationship between the current error signal and historical error patterns, obtaining the final Kalman gain correction matrix. The neural network model in this embodiment employs a two-layer LSTM structure to process the input temporal data (a 9-dimensional vector in this embodiment), with a hidden state dimension of 24, to capture long-term dependencies in the sequence. The model ultimately passes through a fully connected layer with a Tanh activation function, mapping the output of the last time step of the LSTM to an 18-dimensional vector. This activation function first restricts the original output to the range [-1, 1]; subsequently, the output is scaled by multiplying by 0.001, generating a small correction in the range [-0.001, 0.001]. Finally, this vector is reshaped into a tensor of shape (batch_size, 6, 3) as an incremental adjustment term to the Kalman gain matrix. .

[0043] 34) Add the standard Kalman gain calculated by UKF to the correction amount of the LSTM output to obtain the fused, corrected, and better Kalman gain. In this embodiment, the output Kalman gain matrix is ​​in 6*3 format.

[0044] Step 4: Perform state update and covariance update based on the corrected Kalman gain, as follows.

[0045] in: and These are the state vector and the covariance matrix, respectively. and These are the predicted state vector and the measurement vector, respectively. The corrected Kalman gain; The predicted covariance.

[0046] The state vector and covariance are updated using the new Kalman gain obtained from the update.

[0047] Step 5: Train the LSTM network using unsupervised learning to optimize filtering performance, including: calculating posterior observation predictions using the updated state vector. The mean squared error between the predicted and actual posterior observations is defined as the loss function; unsupervised training uses the Adam optimizer and sets an early stopping mechanism to avoid overfitting.

[0048] Specifically, in this embodiment, the steps for training an LSTM network using unsupervised learning are as follows.

[0049] 51) Define the loss function: Calculate the posterior observation prediction using the updated state vector. The mean square error between the predicted posterior observation and the actual observation is defined as the loss function.

[0050] 52) Backpropagation and Optimization: Maintaining the computational graph: During the training phase, the computational graph of the entire process (UKF prediction - LSTM correction - state update - loss calculation) must be kept intact. Before each backpropagation, the optimizer's gradient is set to zero. During backpropagation, the gradient propagates backward from the loss function, through the observation model and the state update equation, eventually reaching all the parameters of the LSTM network. Parameter update: The optimizer Adam updates the LSTM parameters based on the gradients, enabling the network to produce better corrections in the next iteration.

[0051] 53) Training and Evaluation Modes: During the training phase, the complete forward and backward propagation process described above is executed to update the LSTM weights. An early stopping mechanism is implemented during training to prevent overfitting. In this embodiment, when the error changes by less than 0.000001 within 500 consecutive steps, the parameter updates are considered stable, training is stopped, and the currently trained parameters are saved as parameters for the testing / application phase. During the testing / application phase, gradient calculation is disabled, and only forward propagation is performed to obtain the corrected Kalman gain to improve efficiency and prevent accidental parameter modification. In this embodiment, the training data is the first 30% of the response data, and the testing data is the last 70% of the response data.

[0052] Step 6: Calculate the nonlinear aerodynamic damping based on the estimated nonlinear aerodynamic damping parameters.

[0053] The iterative update is repeated for each sample point until all sample points have been processed, yielding the estimated state vector. The 3rd, 4th, and 5th rows of the state vector represent the nonlinear aerodynamic damping parameters at each time step. To ensure the stability of the aerodynamic damping parameters used, the mean of a relatively stable time-history data segment is taken as the estimated nonlinear aerodynamic damping parameters. , and And then substitute the parameters into the relationship between nonlinear aerodynamic damping and structural vibration amplitude: The estimated nonlinear aerodynamic damping can then be obtained.

[0054] In this embodiment, the parameter values ​​of nonlinear aerodynamic damping are estimated based on 1000s of displacement data. Time step A total of 25,000 data points were used. The first 20% of the data was used as training data to update the weight parameters of the LSTM. The remaining 80% was used as test data to calculate the nonlinear aerodynamic damping. After training, the saved weight parameters were used to sequentially update the UKF and correct the Kalman gain of the LSTM for each data point, ultimately outputting estimated nonlinear aerodynamic damping parameters. The nonlinear aerodynamic damping was then calculated based on these parameters. Figure 4 This demonstrates a comparison between the measured displacement and the displacement estimated using the LSTM-UKF algorithm. Figure 5 The comparison between the measured velocity and the velocity estimated by the LSTM-UKF algorithm is shown. A comprehensive analysis of these two figures reveals a high degree of consistency between the measured displacement and velocity data and the estimates from the LSTM-UKF algorithm; the differences between the two are almost imperceptible. Figure 6 The figure shown is the result estimated by LSTM-UKF. , and The comparison charts of these three aerodynamic damping parameter values ​​with their actual values ​​clearly show that, in the subsequent stages when the parameter values ​​converge to a stationary state, the parameter values ​​estimated by LSTM-UKF closely match the actual target values ​​of the aerodynamic damping. Furthermore, the nonlinear aerodynamic damping estimated using the LSTM-UKF algorithm is also extremely close to the target value of the nonlinear aerodynamic damping in the simulation data. These comparison charts strongly demonstrate the superior accuracy of the LSTM-UKF algorithm in response estimation.

[0055] At the same time, in order to demonstrate the convenience of this method compared to the traditional UKF method, Figure 7 and Figure 8 The results show the aerodynamic damping results when the same displacement data is processed using the UKF and LSTM-UKF methods with different given process noise levels. The results indicate that when applying the unscented Kalman filter (UKF) method, when the process noise covariance matrix takes values ​​within... When the noise level is near the target value, the estimated aerodynamic damping value shows a high degree of agreement with the target value; however, when the process noise covariance matrix value changes, a significant deviation appears between the estimated aerodynamic damping and the target value. In contrast, the LSTM-UKF method, which combines a long short-term memory network with an unscented Kalman filter, achieves better results even when the given noise parameter is near the target value. Despite fluctuations in the vicinity of the target noise level, the aerodynamic damping value estimated by this method remains highly close to the target value. This phenomenon clearly demonstrates that the LSTM-UKF method has stronger robustness to noise parameter settings; even if the noise setpoint is not very precise, it can still accurately estimate the aerodynamic damping of the structure. This method effectively reduces the accuracy requirements for noise parameter tuning when using UKF for calculations, significantly reducing the tuning difficulty and saving time costs, and providing a more convenient and effective approach for accurate estimation of aerodynamic damping.

[0056] This embodiment also proposes a system for implementing the LSTM-based nonlinear aerodynamic damping estimation method described above, characterized by comprising: The state modeling module is used to construct a nonlinear state-space model of the structure. The UKF prediction module is configured to perform Sigma point sampling and covariance prediction to obtain the raw Kalman gain. The LSTM gain correction module dynamically corrects the Kalman gain through timing error analysis. The adaptive training module optimizes the LSTM network parameters based on the posterior observation error. The damping calculation module is used to output the estimated value of nonlinear aerodynamic damping.

[0057] This embodiment also proposes a storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the nonlinear aerodynamic damping estimation method based on LSTM as described above.

[0058] The embodiments described above are merely preferred embodiments for fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A nonlinear aerodynamic damping estimation method based on LSTM, characterized in that: Includes the following steps: Step 1: Construct a nonlinear state-space model of the structure based on the structural response, including the state equation, observation equation, and the relationship between nonlinear aerodynamic damping and structural vibration amplitude; Step 2: Use unscented Kalman filtering to update the response data and predict the covariance, and obtain the original Kalman gain; Step 3: Use a long short-term memory network to correct the Kalman gain in real time, including: obtaining the state prediction error and measurement prediction error, standardizing them and inputting them into the long short-term memory network, outputting the Kalman gain correction matrix, and adding it to the original Kalman gain calculated by the unscented Kalman filter to obtain the corrected Kalman gain. Step 4: Perform state update and covariance update based on the corrected Kalman gain; Step 5: Train the Long Short-Term Memory network using unsupervised learning to optimize filtering performance, and define the mean square error between the predicted and actual posterior observations as the loss function; Step 6: Calculate the nonlinear aerodynamic damping based on the estimated nonlinear aerodynamic damping parameters; In step three, the method for real-time correction of the Kalman gain using a long short-term memory network is as follows: 31) Obtain the state prediction error of the unscented Kalman filter. and measurement prediction error : in: and These are the predicted state vector and the measurement vector, respectively. For time step The state vector at that time; For time step Measurement vector at time; 32) Obtain the state prediction error and measurement prediction error The two standardized vectors are then concatenated into a single feature vector, which is used as the input to the Long Short-Term Memory network. 33) Input the eigenvectors into the Long Short-Term Memory network and output the Kalman gain correction matrix. ; 34) The original Kalman gain With Kalman gain correction matrix Adding them together yields the corrected Kalman gain. .

2. The nonlinear aerodynamic damping estimation method based on LSTM according to claim 1, characterized in that: In step one, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is expressed as follows: in: Nonlinear aerodynamic damping; air density; The width of the structure; This represents the effective structural mass per unit height; The amplitude of structural vibration; , , , and These are nonlinear aerodynamic damping parameters, and all are constants; The observation equation is expressed as: in: , and These represent displacement, velocity, and acceleration, respectively. The state-space equation is expressed as: in: The external load is defined as zero-mean Gaussian white noise; Indicates the modal angular frequency. For frequency; , , , and Let be the structural aerodynamic damping parameters, and: ; ; ; ; , This indicates the structural damping ratio.

3. The nonlinear aerodynamic damping estimation method based on LSTM according to claim 1, characterized in that: In step two, the method for updating the response data and predicting covariance using unscented Kalman filtering is as follows: 21) Initial state estimate and the initial state covariance matrix Defined as: in: Represent the initial state space equations; Indicates taking the expected value; Indicates taking the covariance; Obtain the state vector and measurement vector: in: and At time step The state vector and measurement vector at the location; and These represent the nonlinear state transition function and the nonlinear measurement function, respectively. It is the current time step; and These are the covariance matrices. and Uncorrelated zero-mean Gaussian white noise; For process noise covariance; To measure the noise covariance; 22) Calculate the sigma point at time step Using scaling and unscented transformation, generate 1 sample sigma point, State vector The dimension is represented as: in: For scaling parameters; Decide The distribution of sigma points in the surrounding area; It is the second scaling parameter, which is the square root of the matrix. The OK; 23) Time update, predicting the state vector Its covariance : in: and To assign weighting coefficients; 24) Measurement update, predict measurement vector Its covariance : 25) Obtain the original Kalman gain: in: This represents the cross-covariance matrix.

4. The nonlinear aerodynamic damping estimation method based on LSTM according to claim 1, characterized in that: In step four, the method for updating the state and covariance based on the corrected Kalman gain is as follows: in: and These are the state vector and the covariance matrix, respectively. and These are the predicted state vector and the measurement vector, respectively. The corrected Kalman gain; The predicted covariance.

5. The nonlinear aerodynamic damping estimation method based on LSTM according to claim 1, characterized in that: In step five, the method for training the LSTM network using unsupervised learning includes: The updated state vector is used to compute the posterior observation predictions. The mean square error between the predicted posterior observation and the actual observation is defined as the loss function. Unsupervised training uses the Adam optimizer and sets up an early stopping mechanism to avoid overfitting.

6. A system for implementing the LSTM-based nonlinear aerodynamic damping estimation method as described in any one of claims 1-5, characterized in that: include: The state modeling module is used to construct a nonlinear state-space model of the structure. The UKF prediction module is configured to perform Sigma point sampling and covariance prediction to obtain the raw Kalman gain. The LSTM gain correction module dynamically corrects the Kalman gain through timing error analysis. The adaptive training module optimizes the LSTM network parameters based on the posterior observation error. The damping calculation module is used to output the estimated value of nonlinear aerodynamic damping.

7. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by a processor, implements the LSTM-based nonlinear aerodynamic damping estimation method as described in any one of claims 1-5.

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