LSTM-based nonlinear aerodynamic damping estimation method, system, and storage medium

Abstract

The application discloses a nonlinear aerodynamic damping estimation method based on an LSTM, and comprises the following steps: step one: constructing a nonlinear state space model of a structure based on a structural response, including a state equation, an observation equation and a relationship between nonlinear aerodynamic damping and a structural vibration amplitude; step two: updating and covariance prediction of response data by using an unscented Kalman filter; step three: real-time correction of Kalman gain by using a long short-term memory network; step four: state updating and covariance updating based on the corrected Kalman gain; step five: training the long short-term memory network in an unsupervised learning mode, optimizing filter performance, and defining a mean square error of a posterior observation prediction value and a true observation value as a loss function; and step six: calculating nonlinear aerodynamic damping according to the estimated nonlinear aerodynamic damping parameters. The application further discloses an LSTM-based nonlinear aerodynamic damping estimation system and a storage medium.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerodynamic analysis, and particularly relates to a nonlinear aerodynamic damping estimation method based on LSTM, a system and a storage medium. BACKGROUND

[0002] In the field of vortex-induced vibration analysis of high-flexible structures such as large wind turbine towers, large-span bridges, high-rise buildings, power transmission towers and chimneys, aerodynamic damping can be regarded as a key parameter for characterizing the energy dissipation of the interaction between the structure and the airflow. Its generation mechanism is complex, involving fluid-structure coupling phenomena and being closely related to the unsteady vortex shedding process, and thus showing a very significant amplitude-dependent nonlinear characteristic. Therefore, accurate estimation of aerodynamic damping has become a core problem for evaluating the safety and comfort of the structure under the action of wind vibration.

[0003] Traditional aerodynamic damping estimation methods mainly rely on wind tunnel tests and system identification techniques. Among them, the least squares method and random decrement technique have been widely used due to their relatively simple operation and wide application range. However, when facing strong nonlinear systems, these traditional methods are not effective enough to handle related problems.

[0004] In recent years, nonlinear Kalman filters such as unscented Kalman filter (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 better handle nonlinear estimation problems to some extent. However, its performance is highly dependent on the accurate prior setting of the process noise and observation noise covariance matrices (denoted as Q and R, respectively). In actual engineering applications, the statistical characteristics of noise are often difficult to accurately obtain and may change over time. If the noise model is not accurately set, the filtering accuracy will be reduced, the convergence speed will be slowed down, and even serious problems such as estimation divergence may occur. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a nonlinear aerodynamic damping estimation method based on LSTM, a system and a storage medium, which aims to efficiently and accurately identify the aerodynamic damping of structures with nonlinear characteristics without the need for accurate prior setting of noise parameters, and to solve the estimation error caused by model mismatch and unknown noise of UKF.

[0006] To achieve the above purpose, the present application provides the following technical solutions.

[0007] The present application first proposes a nonlinear aerodynamic damping estimation method based on LSTM, characterized by the following steps:

[0008] Step one: Construct the nonlinear state space model of the structure based on structural response, including state equation, observation equation and the relationship between nonlinear aerodynamic damping and structural vibration amplitude;

[0009] Step two: Update and covariance prediction of response data using unscented Kalman filter to obtain the original Kalman gain;

[0010] Step three: Real-time correction of Kalman gain using long short-term memory network, including: obtaining state prediction error and measurement prediction error, standardizing and inputting long short-term memory network, outputting Kalman gain correction matrix, and adding the original Kalman gain calculated by unscented Kalman filter to obtain the corrected Kalman gain;

[0011] Step four: State update and covariance update based on the corrected Kalman gain;

[0012] Step five: Train the long short-term memory network in an unsupervised learning manner to optimize the filtering performance, and define the mean square error of the posterior observation prediction value and the true observation value as the loss function

[0013] Step six: Calculate the nonlinear aerodynamic damping based on the estimated nonlinear aerodynamic damping parameters.

[0014] Further, in step one, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is represented as:

[0015]

[0016] wherein: is the nonlinear aerodynamic damping; is the air density; is the structural width; represents the effective structural mass per unit height; is the structural vibration amplitude; 、 、 、 and are nonlinear aerodynamic damping parameters, and are all constants;

[0017] The observation equation is represented as:

[0018]

[0019] wherein: , and represent displacement, velocity and acceleration, respectively;

[0020] The state space equation is represented as:

[0021]

[0022] where: is a defined zero-mean Gaussian white noise excitation; denotes the modal circular frequency, is the frequency; , , , and are the structural aerodynamic damping parameters, and: ; ; ; ; , denotes the structural damping ratio.

[0023] Further, in the step two, the method steps of updating and covariance prediction of the response data using unscented Kalman filter are:

[0024] 21) Initial state estimate and initial state covariance matrix are defined as:

[0025]

[0026]

[0027] where: denotes the initial state space equation; denotes taking the expectation; denotes taking the covariance;

[0028] The state vector and measurement vector are obtained as:

[0029]

[0030]

[0031] where: and are the state vector and measurement vector at time step , respectively; and denote the nonlinear state transition function and nonlinear measurement function, respectively; is the current time step; and are uncorrelated zero-mean Gaussian white noise of covariance matrices and , respectively; is the process noise covariance; To measure the noise covariance;

[0032] 22) Calculate sigma points, at time step , using scaled unscented transformation, generate samples sigma points, for state vector of dimension

[0033]

[0034]

[0035]

[0036]

[0037] where: is a scaling parameter; determines the sigma point distribution around; is a second scaling parameter, is the th row of the matrix square root ;

[0038] 23) Time update, predict state vector and its covariance :

[0039]

[0040]

[0041]

[0042] where: and are assigned weight coefficients;

[0043] 24) Measurement update, predict measurement vector and its covariance :

[0044]

[0045]

[0046]

[0047] 25) Obtain original Kalman gain:

[0048]

[0049]

[0050] wherein: represents the cross-covariance matrix.

[0051] Further, in the step three, the method steps for real-time correction of Kalman gain by using long short-term memory network are:

[0052] 31) obtaining state prediction error and measurement prediction error of the unscented Kalman filter:

[0053]

[0054]

[0055] wherein: and are the predicted state vector and the measurement vector, respectively; is the state vector at time step ; is the measurement vector at time step ;

[0056] 32) standardizing the obtained state prediction error and measurement prediction error , and splicing the two standardized vectors into a feature vector as the input of the long short-term memory network;

[0057] 33) inputting the feature vector into the long short-term memory network to output a Kalman gain correction matrix ;

[0058] 34) adding the original Kalman gain and the Kalman gain correction matrix to obtain the corrected Kalman gain .

[0059] Further, in the step four, the method for state updating and covariance updating based on the corrected Kalman gain is:

[0060]

[0061]

[0062] wherein: and are the state vector and the covariance matrix, respectively; and are the predicted state vector and the measurement vector, respectively; for the revised Kalman gain; the predicted covariance.

[0063] Further, in the step five, the method for training the LSTM network in an unsupervised learning manner comprises:

[0064] calculating the posterior observation prediction value using the updated state vector , defining the mean square error between the posterior observation prediction value and the true observation value as a loss function;

[0065] The unsupervised training adopts an Adam optimizer and sets an early stopping mechanism to avoid overfitting.

[0066] The application further provides a system for implementing the LSTM-based nonlinear aerodynamic damping estimation method, and the system comprises:

[0067] a state modeling module configured to construct a nonlinear state space model of the structure;

[0068] a UKF prediction module configured to perform Sigma point sampling and covariance prediction and obtain an original Kalman gain;

[0069] an LSTM gain revision module configured to dynamically revise the Kalman gain through time series error analysis;

[0070] an adaptive training module configured to optimize LSTM network parameters based on posterior observation errors;

[0071] a damping calculation module configured to output a nonlinear aerodynamic damping estimation value.

[0072] The application further provides a storage medium, wherein the storage medium stores a computer program, and the computer program is executed by a processor to implement the LSTM-based nonlinear aerodynamic damping estimation method.

[0073] The application has the following beneficial effects:

[0074] The LSTM-based nonlinear aerodynamic damping estimation method of the application, through real-time intelligent correction of Kalman gain of unscented Kalman filter (UKF) by long short-term memory network (LSTM), effectively overcomes the estimation precision decline problem caused by model mismatch and unknown noise statistical characteristics of traditional UKF, and significantly improves the estimation precision of aerodynamic damping parameters and system state; by adopting an unsupervised training mechanism, taking the posterior observation error of the output state as the loss function, without manual labeling data, the LSTM network can autonomously learn and compensate the complex nonlinear dynamics of the system, realize self-optimization and self-adaptation of the algorithm, and show strong robustness and universality; at the same time, the method greatly reduces the dependence on user expert experience and prior knowledge, and the initial parameter setting is more relaxed, simplifying the application process; in addition, multiple mechanisms such as gain limitation, gradient clipping and covariance regularization are included in the design, which jointly guarantee the long-term numerical stability and reliability of the algorithm.

[0075] In summary, the application successfully deepens the fusion of data-driven and model-driven methods, providing an advanced solution with high precision and high robustness for structural wind-induced vibration response analysis and state estimation of similar complex nonlinear systems, and has important theoretical value and engineering application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0076] In order to make the purpose, technical scheme and beneficial effects of the application more clear, the application provides the following drawings for illustration:

[0077] Figure 1 It is a schematic diagram of a bridge tower structure;

[0078] Figure 2 It is a flowchart of the LSTM-based nonlinear aerodynamic damping estimation method of the application;

[0079] Figure 3 It is random crosswind response data of structural damping and reduced wind speed ;

[0080] Figure 4 It is a comparison chart of measured displacement and LSTM-UKF estimated displacement;

[0081] Figure 5 It is a comparison chart of measured velocity and LSTM-UKF estimated velocity;

[0082] Figure 6 It is a comparison chart of the parameter value of nonlinear aerodynamic damping estimated by LSTM-UKF and the target value;

[0083] Figure 7 It is a comparison of aerodynamic damping estimation values estimated by UKF and target values under different given process noises;

[0084] Figure 8 Comparison of the estimated aerodynamic damping values by LSTM-UKF with the target values under different given process noise. DETAILED DESCRIPTION

[0085] The present application will be further described below in conjunction with the drawings and specific embodiments so that those skilled in the art can better understand the present application and implement it. The embodiments are not intended to limit the present application.

[0086] This embodiment takes a bridge tower structure as an example to calculate the nonlinear aerodynamic damping of a bridge tower structure by using the LSTM-based nonlinear aerodynamic damping estimation method (LSTM-UKF method) of the present application, and to evaluate the effectiveness and accuracy of the estimated nonlinear aerodynamic damping by comparing with the true value. The bridge tower structure is shown in Figure 1 .

[0087] As shown in Figure 2 , the LSTM-based nonlinear aerodynamic damping estimation method of this embodiment includes the following steps.

[0088] Step 1: Construct a nonlinear state space model of the structure based on the structural response, including the state equation, the observation equation, and the relationship between the nonlinear aerodynamic damping and the structural vibration amplitude.

[0089] Specifically, the internal relationship between the aerodynamic damping and the structural vibration amplitude is derived by means of the structural cross-wind response equation and the harmonic balance technique, and the relationship between the nonlinear aerodynamic damping and the structural vibration amplitude is:

[0090]

[0091] wherein: is the nonlinear aerodynamic damping; is the air density; is the structural width; represents the effective structural mass per unit height; is the structural vibration amplitude; 、 、 、 and are nonlinear aerodynamic damping parameters, and are all constants.

[0092] The observation equation is expressed as:

[0093]

[0094] wherein: , and represent displacement, velocity and acceleration, respectively.

[0095] The state-space equations are given by:

[0096]

[0097] where: is a defined zero-mean Gaussian white noise excitation; denotes the modal circular frequency, is the frequency; , , , and are the structural aerodynamic damping parameters, and: ; ; ; ; , denotes the structural damping ratio.

[0098] In this example, a 3rd order polynomial model is used to estimate the nonlinear aerodynamic damping of the bridge tower structure, and the nonlinear aerodynamic damping represented by a 3rd order polynomial model is is:

[0099]

[0100] where: are the parameters fitted by the LSTM-UKF estimation.

[0101] The measurement equation is defined as:

[0102]

[0103] where: , and denote displacement, velocity, and acceleration;

[0104] The state-space equations are given by:

[0105]

[0106] where: is a defined zero-mean Gaussian white noise excitation; denotes the modal circular frequency, is the frequency; , and are the structural aerodynamic damping parameters, and: ; ; ; are the nonlinear aerodynamic damping parameters, and are all constants.

[0107] Specifically, the nonlinear state space equation solved by the fourth-order Runge-Kutta method is used in the embodiment, which is expressed as:

[0108]

[0109] Step two: update and covariance prediction of the response data using the unscented Kalman filter (UKF) to obtain the original Kalman gain.

[0110] In the embodiment, the random crosswind response data of the structural damping and the reduced wind speed are used, and the sampling frequency is 25 Hz, that is, , as shown in Figure 3 . The accuracy and convenience of the LSTM-UKF method in identifying nonlinear aerodynamic damping are verified. The target value of the aerodynamic damping parameter under this condition is , , .

[0111] Specifically, the method steps of the UKF for updating and covariance prediction of the response data and obtaining the original Kalman gain are as follows.

[0112] 21) Define the initial state estimation value and the initial state covariance matrix :

[0113]

[0114]

[0115] Wherein: represents the initial state space equation; represents taking expectation; represents taking covariance.

[0116] The initial value is selected in the embodiment, and ) is taken. In addition, the covariance of the process noise and the measurement noise covariance are defined. The process noise The selection of R and R is important for accurate estimation, however, the characteristics of process noise and measurement noise are always unknown and difficult to accurately model. Improper noise setting will not only significantly weaken the calculation accuracy, but also more likely to cause the divergence of the filter, and this problem is particularly prominent in high-dimensional systems, which is a key factor affecting system performance. In this embodiment, the Kalman gain can be corrected according to the error between the predicted value and the true measurement value by using LSTM, so as to reduce the influence caused by inaccurate noise preset. Therefore, the selection of noise can not be too accurate, and a smaller value is also feasible. In this embodiment, the initial process noise ) is set to ).

[0117] In a nonlinear discrete system, the state space vector and the measurement vector are obtained as follows:

[0118]

[0119]

[0120] wherein: and are the state vector and the measurement vector at the time step ; and represent the nonlinear state transition function and the nonlinear measurement function; is the current time step; and are uncorrelated zero-mean Gaussian white noise of the covariance matrices and ; is the process noise covariance; is the measurement noise covariance.

[0121] 22) Calculate the sigma points.

[0122] At the time step , the scaled unscented transformation is used to generate sigma points, is the dimension of the state vector , as follows:

[0123]

[0124]

[0125]

[0126]

[0127] wherein: is a scaling parameter; is determined by the surrounding sigma points, which in this embodiment are chosen to be ; is a second scaling parameter, which in this embodiment is set to 0, and is the first row of the matrix square root .

[0128] 23) Time update.

[0129] The sigma points are propagated through the nonlinear state transition function , and then assigned with weights and summed to obtain the predicted state vector , whose covariance can be predicted as:

[0130]

[0131]

[0132]

[0133] wherein: and are the assignment weight coefficients, which are expressed as:

[0134]

[0135]

[0136]

[0137] wherein: is a parameter that produces high-order effects in covariance estimation, and is the optimal value of the Gaussian distribution.

[0138] 24) Measurement update.

[0139] The predicted covariance is then subjected to a scaled unscented transformation to generate 2 +1 new sample sigma points, is the dimension of the state vector . The new sigma points are propagated through the nonlinear measurement function , thereby predicting the measurement vector and its covariance .

[0140]

[0141]

[0142]

[0143] Cross-covariance matrix is denoted as:

[0144]

[0145] 25) Obtain the original Kalman gain of UKF.

[0146] Through the covariance of the obtained measurement vector and the cross-covariance Obtain the original Kalman gain obtained by UKF.

[0147]

[0148] Step three: real-time correction of Kalman gain of UKF by using long short-term memory network (LSTM), including: obtaining state prediction error and measurement prediction error, inputting long short-term memory network after standardization processing, outputting Kalman gain correction matrix, and adding the original Kalman gain calculated by unscented Kalman filter to obtain the corrected Kalman gain.

[0149] 31) From the prediction step of UKF, obtain the state prediction error and the measurement prediction error of unscented Kalman filter.

[0150]

[0151]

[0152] The first step is the initial preset state vector, and the state vector estimated in the last step is obtained in each step.

[0153] 32) Standardize the obtained state prediction error and the measurement prediction error , splice the two vectors after standardization into a long feature vector as the input of the LSTM network. In this embodiment, is a 6*1 vector, is a 3*1 vector, and the input vector is a 9*1 vector.

[0154] 33) Concatenate the feature vectors and input them into the LSTM network. The LSTM learns the complex dynamic relationship between the current error signal and the historical error pattern by virtue of its gating mechanism (forget gate, input gate, output gate), and obtains the final Kalman gain correction matrix The neural network model in this embodiment. It adopts a double-layer LSTM structure to process the input time series data (9-dimensional vector in this embodiment), with a hidden state dimension of 24 to capture long-term dependencies in the sequence. The model finally maps the output of the last time step of the LSTM to an 18-dimensional vector through a fully connected layer with a Tanh activation function, which first limits the original output to the range [-1, 1]; then, the output is scaled by 0.001 to generate a small correction amount in the range [-0.001, 0.001]. Finally, this vector is reshaped into a tensor with shape (batch_size, 6, 3) as an incremental adjustment item for the Kalman gain matrix .

[0155] 34) Add the standard Kalman gain calculated by the UKF and the correction amount output by the LSTM to obtain the fused, corrected, and better Kalman gain In this embodiment, the output Kalman gain matrix is a 6*3 matrix.

[0156]

[0157] Step four: Perform state update and covariance update based on the corrected Kalman gain, as follows.

[0158]

[0159]

[0160] Where: and are the state vector and the covariance matrix, respectively; and are the predicted state vector and the measurement vector, respectively; is the corrected Kalman gain; is the predicted covariance.

[0161] Update the state vector and the covariance using the new Kalman gain obtained by the update.

[0162] Step five: Train the LSTM network through unsupervised learning to optimize the filtering performance, including: calculate the posterior observation prediction value using the updated state vector , define the mean square error between the posterior observation prediction value and the true observation value as the loss function; the unsupervised training uses the Adam optimizer, and the early stopping mechanism is set to avoid overfitting.

[0163] Specifically, in the present embodiment, the method steps of training the LSTM network in an unsupervised learning manner are as follows.

[0164] 51) Define the loss function: calculate the posterior observation prediction value using the updated state vector , define the mean square error between the posterior observation prediction value and the true observation value as the loss function.

[0165]

[0166]

[0167] 52) Back propagation and optimization: keep the computation graph, during the training phase, the computation graph of the entire process (UKF prediction-LSTM correction-state update-loss calculation) must be kept complete. Before each back propagation, set the gradient of the optimizer to zero. Back propagation call, the gradient will be propagated backward from the loss function, through the observation model, the state update equation, and finally to all parameters of the LSTM network. Parameter update, the optimizer Adam updates the parameters of the LSTM to make the network produce better correction in the next time.

[0168] 53) Training mode and evaluation mode: during the training phase, the above complete forward and backward propagation process is executed to update the LSTM weights, during training, the early stopping mechanism is set to avoid overfitting, in the present embodiment, when the error changes by less than 0.000001 in continuous 500 steps, it is considered that the parameter update is stable, the training is stopped, and the current trained parameters are saved as the parameters for the test / application phase. During the test / application phase, the gradient calculation is turned off, and only the forward propagation is performed to obtain the corrected Kalman gain, in order to improve the efficiency and prevent the parameters from being modified accidentally. In the present embodiment, the data used for training is the first 30% of the response data, and the data used for testing is the last 70% of the response data.

[0169] Step six: calculate the nonlinear aerodynamic damping according to the estimated nonlinear aerodynamic damping parameters.

[0170] Repeat the iterative update for each sample point until all sample points are processed to obtain the estimated state vector. The 3rd, 4th and 5th rows in the state vector are the nonlinear aerodynamic damping parameters at each time, in order to stabilize the used aerodynamic damping parameters, the mean value of the data in the later stable time period is taken as the estimated nonlinear aerodynamic damping parameter 、 and . And the parameters are brought into the relationship between nonlinear aerodynamic damping and structural vibration amplitude:

[0171]

[0172] The estimated nonlinear aerodynamic damping can be obtained.

[0173] In this embodiment, the parameter value of nonlinear aerodynamic damping is estimated for 1000s displacement data. The time step , a total of 25000 data points, the first 20% of the data is used as training data to update the weight parameters of LSTM. The last 80% is used as test to calculate the nonlinear aerodynamic damping. After training, the saved weight parameters are used to update and correct the Kalman gain of each data point in turn, and finally the estimated nonlinear aerodynamic damping parameters are output, and then the nonlinear aerodynamic damping is calculated based on the parameters. As Figure 4 shows the comparison between the measured displacement and the displacement estimated by the LSTM-UKF algorithm, Figure 5 shows the comparison between the measured velocity and the velocity estimated by the LSTM-UKF algorithm. Comprehensive analysis of the two figures shows that the measured displacement and velocity data and the estimated values of the LSTM-UKF algorithm show a high degree of consistency, and it is almost impossible to detect differences between them. Figure 6 The estimated , and The three aerodynamic damping parameter values estimated by LSTM-UKF are compared with the actual values. From the figure, it can be clearly observed that when the parameter values converge to a stable state in the subsequent stage, the parameter values estimated by LSTM-UKF are highly consistent with the actual target values of aerodynamic damping; and the nonlinear aerodynamic damping estimated by LSTM-UKF is also very close to the nonlinear aerodynamic damping target value in the simulation data. The above series of comparison charts have strongly proved that the LSTM-UKF algorithm has excellent accuracy in response estimation.

[0174] At the same time, in order to reflect the convenience of this method relative to the traditional UKF method, Figure 7 and Figure 8 are the results of aerodynamic damping processed by UKF and LSTM-UKF methods respectively for the same displacement data with different given process noise. The results show that when the UKF method is used, when the process noise covariance matrix is ) nearby; while when the process noise covariance matrix value changes, the estimated aerodynamic damping and the target value will have a more obvious deviation. In contrast, when the LSTM-UKF method combining the long short-term memory network and the unscented Kalman filter is used, even if the given noise parameter fluctuates around ), the estimated aerodynamic damping value can still remain highly close to the target value. This phenomenon fully shows that the LSTM-UKF method has stronger robustness for the setting of the noise parameter, that is, even if the given noise value is not very accurate, the aerodynamic damping of the structure can still be accurately estimated. This method effectively reduces the accuracy requirement of the user on the noise parameter debugging when using the UKF for calculation, significantly reduces the debugging difficulty and saves the time cost, and provides a more convenient and effective way for the accurate estimation of the aerodynamic damping.

[0175] The embodiment also provides a system for implementing the LSTM-based nonlinear aerodynamic damping estimation method as described above, and the system has the following characteristics:

[0176] a state modeling module, configured to construct a nonlinear state space model of the structure;

[0177] a UKF prediction module, configured to perform Sigma point sampling and covariance prediction to obtain an original Kalman gain;

[0178] an LSTM gain correction module, configured to dynamically correct the Kalman gain through time series error analysis;

[0179] an adaptive training module, configured to optimize the LSTM network parameters based on the posterior observation error;

[0180] a damping calculation module, configured to output a nonlinear aerodynamic damping estimation value.

[0181] The embodiment also provides a storage medium, and the storage medium has a computer program stored thereon, and the computer program is executed by a processor to implement the LSTM-based nonlinear aerodynamic damping estimation method as described above.

[0182] The above-described embodiments are only preferred embodiments of the present application, and the protection scope of the present application is not limited thereto. Any equivalent replacement or transformation made by those skilled in the art on the basis of the present application is within the protection scope of the present application. The protection scope of the present application is subject to 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 steps The state vector at that time; For time steps 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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