A method for eliminating the influence region of continuous wavelet transform based on LSTM neural network

Abstract

This invention discloses a method for eliminating the influence region of continuous wavelet transform based on an LSTM neural network. Specifically, the method involves preprocessing the turbulent excitation response signal from a flutter flight test in the time domain to create a dataset for training a regression model, including a training set and a validation set. This dataset is then used to train the LSTM regression model. The trained regression model is used to extrapolate a segment of data points before and after the start of the data flow, ensuring that the length of the added data points is the same as the length of the influence region generated by the continuous wavelet transform. Based on the length of the added data points, the portion corresponding to the added data points in the time-frequency matrix is ​​truncated after the continuous wavelet transform, thereby eliminating the influence region of the continuous wavelet transform. This method aims to address the problem of poor dense mode separation and large damping identification errors caused by the presence of the influence region when using continuous wavelet transform to analyze the turbulent excitation response signal from a flutter flight test.

Description

Technical Field

[0001] This invention belongs to the field of aircraft flutter signal processing, specifically involving a method for eliminating the influence region in the continuous wavelet transform time-frequency plot using a long short-term memory neural network (LSMT), which is applied to the analysis of aircraft flutter data using continuous wavelet transform. Background Technology

[0002] In flutter flight tests, the acquired turbulent excitation response signals often exhibit low signal-to-noise ratios and dense modalities. Wavelet analysis's multi-resolution capabilities can be used to separate dense modes and suppress noise, and damping parameters can be identified relatively accurately using natural excitation techniques or random decrement methods. However, the presence of influence regions in the time-frequency diagram during continuous wavelet transforms can affect the separation of dense modes and the identification of damping parameters during modal parameter identification, thus reducing the accuracy of modal parameter identification.

[0003] Therefore, to better achieve dense mode separation and damping parameter identification, and thus improve the accuracy of flutter boundary prediction, it is necessary to eliminate the influence region. Boundary extension methods are commonly used to eliminate the influence region, such as zero-filling, periodic extension, symmetrical extension, and point-symmetric extension. However, these methods have poor fitting to the original signal, and the extended signal exhibits different trends than the original signal, thus failing to effectively eliminate the influence region. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by proposing a method for eliminating the influence region in continuous wavelet transforms using a Long Short-Term Memory (LSTM) neural network. By leveraging the LSTM's ability to process long-term sequences, the signal is fitted and regressed to obtain an extended signal that more closely resembles the original signal, thus achieving better influence region elimination.

[0005] This invention is implemented as follows:

[0006] The method of this invention preprocesses the turbulent excitation response signal of flutter flight test in the time domain, organizing it into a dataset for training a regression model, including a training set and a validation set. This dataset is then used to train an LSTM regression model, resulting in the regression model. The trained regression model is used to fit and extrapolate a segment of data points before the start of the data and after the end of the data, ensuring that the length of the added data points is the same as the length of the influence region generated by the continuous wavelet transform. Based on the length of the added data points, the portion corresponding to the added data points in the time-frequency matrix is ​​truncated after the continuous wavelet transform, thereby eliminating the influence region of the continuous wavelet transform. The method of using an LSTM neural network to fit the regression extension signal to eliminate the influence region of the continuous wavelet transform specifically includes the following steps:

[0007] (1) Signal preprocessing: The obtained structural response signal under turbulent excitation is subjected to bandpass filtering and detrending processing. Then, the free vibration response of the structure is obtained by random subtraction method or natural excitation technique.

[0008] (2) Transform the time series of free vibration signals into a dataset suitable for training the LSTM model. Given a time series x(1), x(2), ... x(N) of length N, generate a training set L = {(v1, y1) ... (v...} with l samples according to the rules. l ,y l Each sample (v) in the training set i ,y i ), by feature v i and target value y i Composition. Wherein, the feature v in the i-th sample... i It consists of the i-th value to the (N-1+i-1)-th value in the time series, i.e., v i = [x(i) x(i+1) x(i+2)…x(N-1+i-1)], containing a total of h feature values. The target value in the i-th sample is feature v. i The next value of the time series, i.e., y i = x(N-l+i). Where N is the length of the time series, l is the number of samples in the training set, and v is the feature in the sample. i The number of eigenvalues ​​h contained in the data satisfies the following relationship:

[0009] l=Nh (1)

[0010] (3) Construct an LSMT model, consisting of 30 LSTM layers, as well as some additional fully connected layers and activation functions. The input to the model is a feature v. i The time series values ​​within the given time frame are used as the output, which is the data after the next predicted time step, i.e., the target value y. i The time series of the signal to be extended is mirrored and inverted, transforming x(1), x(2), ... x(N) into x(N), x(N-1), ... x(1). Then, l samples are generated from the mirrored and inverted time series according to the training dataset generation rules given in step 2. The LSTM is trained using this training dataset, and the gradient descent optimization algorithm is used to minimize the model's loss function.

[0011] (4) Determine the signal extension length m: The signal extension length aims to completely eliminate the influence region within the time-frequency graph after wavelet transform. The general expression for the wavelet basis function is:

[0012]

[0013] Where 'a' is the scaling parameter, 'b' is the translation parameter, and 't' is the time. The time value T at which the wavelet function's single-sided envelope decays to 0.1% of its extreme value is considered the duration of the endpoint effect caused by distortion in the signal during wavelet transform. When performing continuous wavelet transforms on a signal, the larger the scale 'a' of the wavelet basis function, the larger the area of ​​influence in the time-frequency plot. The wavelet basis function scale corresponds to the signal frequency in the time-frequency plot. Therefore, the time value T at which the single-sided envelope of the wavelet basis function with the largest scale in a single wavelet transform decays to its extreme value of 0.1% is taken as the signal extension time. The signal sampling rate is f. s Therefore, the extension length of the signal is

[0014] m=T / fs (3)

[0015] (5) The extension is performed on the mirrored data, and the flipped time series is X'(N) = [x'(1), x'(2), ... x'(N)]. The last Nl points of the time series are used as feature points and input into the trained LSTM model to obtain the predicted value x'(N+1) of the first time series. The time series is updated to X'(N+1) = [x'(1), x'(2), ... x'(N), x'(N+1)] and so on. When extending the m-th predicted value, the last N+ml-1 points of the time series X'(N+m-1) = [x'(1), x'(2), ... x'(N), ..., x'(N+m-1)] are used as features and input into the trained LSTM model to obtain the m-th predicted value. Finally, the extended time series X'(N+m) is obtained. The extended time series is mirrored again to obtain X(N+m). The first m points are the predicted signal extension values, and the last N points are the original signal values.

[0016] (6) Perform a continuous wavelet transform on the predicted extended signal to obtain the time-frequency matrix M(n,N+m). The number of columns in the time-frequency matrix is ​​equal to the length of the time series, and the number of rows depends on the scaling function. The first m columns of the time-frequency matrix are the continuous wavelet transform coefficients of the predicted extended signal. Deleting the m columns of wavelet coefficients yields a new time-frequency matrix M(n,N). The new time-frequency matrix is ​​the result of the continuous wavelet transform of the original signal after the removal of the influence zone.

[0017] The advantages of this invention compared to the prior art are as follows:

[0018] This invention addresses the problem of the influence region in continuous wavelet transform (LLT) modal parameter identification affecting the separation of dense modes and the identification error of damping parameters. It proposes a method using a Long Short-Term Memory (LSTM) neural network to eliminate the influence region in LLT. This method uses an LSTM to fit and regress the original structural dynamic response signal in the time domain. After obtaining the regression model of the original signal, the signal is extrapolated, extending by the required length at both the beginning and end of the signal. After performing LLT, the influence region falls exactly within the corresponding part of the extended signal. Finally, the corresponding part of the extended signal is truncated from the LLT time-frequency matrix of the LLT, thus eliminating the LLT. This improves the accuracy of LLT modal parameter identification results and meets the needs of flutter boundary prediction.

[0019] The LSTM neural network-based continuous wavelet transform influence region elimination method of the present invention can solve the problem of influence region on dense mode separation and damping parameter identification when using continuous wavelet transform to analyze signals, improve the accuracy of mode parameter identification using continuous wavelet transform, and achieve better flutter boundary prediction. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the process of using LSTM to eliminate the influence region of the continuous wavelet transform time-frequency diagram in this invention.

[0021] Figure 2 This is the random response of the structure of the present invention under turbulent excitation;

[0022] Figure 3 This invention extracts the structural free vibration response from the random response of the structure.

[0023] Figure 4 This is the loss function curve during the training of the LSTM model in this invention;

[0024] Figure 5 This is the result of signal extension in an embodiment of the present invention;

[0025] Figure 6 This is the result of continuous wavelet transform before signal extension in the embodiments of the present invention;

[0026] Figure 7 This is the result of continuous wavelet transform after signal extension in the embodiments of the present invention;

[0027] Figure 8 This is a comparison of the logarithmic magnitude curves of the wavelet transform coefficients at the wavelet ridge before and after the elimination of the influence region in this embodiment of the invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the following examples provide a more detailed description of the invention. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0029] like Figure 1 As shown, Figure 1 The flowchart of this invention describes a method for eliminating the influence region of continuous wavelet transform by fitting a regression extension signal using an LSTM neural network.

[0030] The method of this invention preprocesses the signal to be extended into a dataset for training the regression model according to the following steps: a time series of length N x(1), x(2), ... x(N), and a training set L = {(v1, y1) ... (v... y1)} with l samples is generated according to the rules. l ,y l Each sample (v) in the training set i ,y i ), by feature v i and target value y i Composition. Wherein, the feature v in the i-th sample... i It consists of the i-th value to the (N-l+i-1)-th value in the time series, and contains a total of h feature values.

[0031] The regression model was trained using this dataset in conjunction with an LSTM network, and its predictive power was validated using a validation set.

[0032] The latter part of the signal to be extended is input into the regression model to obtain the predicted value. Then, the original signal and the predicted value are concatenated to form a new signal. The latter part of the new signal is then input into the regression model for further prediction, thus achieving multi-point extension of the signal. The extended signal is then subjected to continuous wavelet transform to obtain the time-frequency matrix of the extended signal, and the extended portion of this time-frequency matrix is ​​truncated.

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0034] To generate a turbulent excitation response signal for a two-degree-of-freedom vibration system using the Newmark-β method, such as... Figure 2 As shown. The signal sampling rate is 1024Hz, and the duration is 2.5 seconds. The signal is processed using a random subtraction method. The resulting free vibration signal of the structure is shown below. Figure 3As shown. For the free vibration signal of a structure, all its effective information is concentrated in the initial stage of the signal, and the presence of damping causes the signal to decay rapidly to zero. Therefore, for the free vibration signal of a structure, it is necessary to extend the signal forward. The latter part of the signal only needs to be padded with zeros at the position where the signal decays to zero. The following descriptions all start from eliminating the influence zone of the continuous wavelet transform at the starting position of the free vibration signal of the structure.

[0035] The duration of the free vibration signal obtained using the random decrement method remains 2.5 seconds, and the sampling rate remains unchanged. Therefore, this signal is a time series with 2560 points, which is used to construct the LSTM training set. First, the number of feature values ​​in each sample in the training set is determined, and here the number of feature values ​​is selected as 30. According to equation (1), the number of samples is 995.

[0036] Build an LSTM model. Create an input layer with 30 nodes, equal to the number of features in the sample. Construct a 30-node LSTM layer, one ReLU activation layer, one fully connected layer, and one regression layer. Set the initial learning rate to 5e-3 and the number of training iterations to 1000. After 800 iterations, reduce the learning rate to 0.005×0.1, and shuffle the dataset after each training iteration. The RMSE curve and loss function curve during training are shown below. Figure 4 As shown. Data extension is performed after training.

[0037] First, determine the data extension length. Then, select complex Morlet wavelet basis functions for continuous wavelet transform. Choose the center frequency f. c The bandwidth parameter f is 1. b The value is 2. According to equation (1), the duration of the signal extension is determined to be 0.5s. According to equation (2), the number of points that need to be extended in the signal time series is m = 512.

[0038] Signal extension is performed by inputting the last 30 data points from the time series of the mirrored original signal into a trained LSTM model as features to obtain a predicted value. This predicted value is then appended to the end of the mirrored signal, and the last 30 data points of the updated signal are selected again as feature values ​​and input into the LSTM model to predict data points. This process is repeated 512 times to obtain the result of extending the mirrored signal by 512 data points. Finally, the extended signal is mirrored again to obtain the result of extending the original signal by 512 data points, as shown below. Figure 5 As shown.

[0039] A continuous wavelet transform is performed on the unextended signal, and wavelet ridges are extracted. The results are as follows. Figure 6 . Figure 6 (a) is the time-frequency diagram of the continuous wavelet transform of the free vibration signal of the structure. Figure 6(b) shows the logarithmic magnitude curve of the continuous wavelet transform coefficients corresponding to the wavelet ridge. It can be seen that the influence of the affected region on the signal is mainly concentrated in the initial stage of the signal, causing energy leakage. The damping parameters and their errors obtained by fitting the ridge extracted from the continuous wavelet transform of the unextended signal and identifying the modal parameters are shown in Table 1. Then, a continuous wavelet transform is performed on the extended signal to obtain the time-frequency matrix. Deleting the wavelet coefficients in the time range corresponding to the extended signal from the time-frequency matrix yields the time-frequency matrix of the original signal after the affected region has been eliminated. Visualizing this matrix yields the time-frequency plot, as shown in Table 1. Figure 7 As shown.

[0040] The effectiveness of the influence zone elimination is verified by examining the amplitude curves of the wavelet transform coefficients containing the signal components in the time-frequency plot. Wavelet ridges are extracted from the time-frequency plot, and the wavelet coefficients in each ridge line correspond to the wavelet transform coefficients of one signal component. Because the analysis focuses on the free vibration response signal of the structure, the amplitude curve of the wavelet transform coefficients of each signal component is a logarithmic curve. Theoretically, after taking the logarithm, the logarithmic amplitude curve of a signal component's wavelet transform coefficient should be a straight line. However, due to the presence of the influence zone, signal energy leakage occurs in the initial stage of the signal; therefore, the extracted logarithmic amplitude curve is a convex curve for a period of time at the beginning of the signal. Figure 8 As shown in (a), the logarithmic amplitude curve extracted within the initial 0.1s of the signal is severely distorted. After eliminating the affected area using the method described above, the logarithmic amplitude curve at that location is essentially restored to a straight line, as shown in (a). Figure 8 As shown in (b). Therefore, the proposed method using LSTM to eliminate the influence region of the continuous wavelet transform has a good effect. The modal parameter identification results using the continuous wavelet transform with the eliminated influence region are compared with the identification results without the eliminated influence region, as shown in Table 1:

[0041] Table 1.

[0042]

[0043] As can be seen from the comparison of the charts, the proposed continuous wavelet transform influence region elimination method can significantly reduce the influence of the influence region and improve the accuracy of modal parameter identification results.

[0044] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for eliminating the influence region of continuous wavelet transform based on LSTM neural network, characterized in that, The method is as follows: Step 1: Preprocess the turbulent excitation response signal of the flutter flight test in the time domain and organize it into a dataset for training the regression model; Step 2: Use the dataset to train the LSTM regression model to obtain the regression model; Step 3: Using the regression model obtained from the training, fit and extrapolate a segment of data points to the time-domain signal before the start of the data and after the end of the data, so that the length of the added data points is the same as the length of the influence area generated by the continuous wavelet transform. Step three specifically refers to: Determine the signal extension length *m*: The signal extension length aims to completely eliminate the influence region within the time-frequency graph after wavelet transform; the general expression for the wavelet basis function is: Where a is the scale parameter, b is the translation parameter, and t is the time; The time value T at which the single-sided envelope of the wavelet function decays to 0.1% of its extreme value is considered to be the time length during which the end-point effect of distortion occurs in the signal when performing wavelet transform. When performing continuous wavelet transform on a signal, the larger the scale 'a' of the wavelet basis function, the larger the range of the influence region in the time-frequency plot; the scale of the wavelet basis function corresponds to the signal frequency in the time-frequency plot. The time value T at which the single-sided envelope of the wavelet basis function at the largest scale in a wavelet transform decays to its extreme value of 0.1% is taken as the signal extension time length; the signal sampling rate is f. s Therefore, the extension length of the signal is: m = Tfs (3); Step 4: Based on the length of the added data points, truncate the portion of the time-frequency matrix corresponding to the added data points after the continuous wavelet transform to eliminate the influence region of the continuous wavelet transform. A continuous wavelet transform is performed on the predicted extended signal, resulting in a time-frequency matrix M(n,N+m). The number of columns in the time-frequency matrix is ​​equal to the length of the time series, and the number of rows depends on the scaling function. The first m columns of the time-frequency matrix are the continuous wavelet transform coefficients of the predicted extended signal. Deleting the m columns of wavelet coefficients yields a new time-frequency matrix M(n,N). The new time-frequency matrix is ​​the result of the continuous wavelet transform of the original signal after the removal of the influence zone.

2. The method for eliminating the influence region of continuous wavelet transform based on LSTM neural network according to claim 1, characterized in that, The dataset in step one includes a training set and a validation set; specifically: signal preprocessing: the obtained structural response signal under turbulent excitation is subjected to bandpass filtering and detrending processing; then the free vibration response of the structure is obtained through random decrement method or natural excitation technique; The time series of free vibration signals is transformed into a dataset suitable for training the LSTM model; a time series of length N x(1), x(2), ... x(N) is used to generate a training set L = {(v1, y1) ... (v...} with l samples according to the rules. l ,y l )}; Each sample (v) in the training set i ,y i ), by feature v i and target value y i Composition; where the feature v in the i-th sample i It consists of the i-th value to the (N-1+i-1)-th value in the time series, i.e., v i = [x(i)x(i+1)x(i+2)…x(N-1+i-1)], containing a total of h feature values; the target value in the i-th sample is feature v. i The next value of the time series, i.e., y i = x(N-l+i); where N is the length of the time series, l is the number of samples in the training set, and v is the feature in the sample. i The number of eigenvalues ​​h contained in the data satisfies the following relationship: l=Nh (1).

3. The method for eliminating the influence region of continuous wavelet transform based on LSTM neural network according to claim 1, characterized in that, The second step is specifically as follows: Build an LSMT model, which includes 30 LSTM layers, as well as additional fully connected layers and activation functions; The input to the model is a feature v i The time series values ​​within the given time frame are used as the output, which is the data after the next predicted time step, i.e., the target value y. i The time series of the signal to be extended is mirrored and inverted to transform x(1), x(2), ... x(N) into x(N), x(N-1), ... x(1). Then, l samples are generated from the mirrored and inverted time series according to the training dataset generation rules given in the above steps. The LSTM is trained using the training dataset, and the gradient descent optimization algorithm is used to minimize the loss function of the model.

4. The method for eliminating the influence region of continuous wavelet transform based on LSTM neural network according to claim 1, characterized in that, The extension is still performed on the mirrored and flipped data. The flipped time series is X'(N)=[x'(1),x'(2),…x'(N)]; the last Nl points of the time series are used as feature points and input into the trained LSTM model to obtain the predicted value x'(N+1) of the first time series; the time series is updated to X'(N+1)=[x'(1),x'(2),…x'(N),x'(N+1)] and so on. When extending the m-th predicted value, the last N+ml-1 points of the time series X'(N+m-1)=[x'(1),x'(2),…x'(N),…,x'(N+m-1)] are used as features and input into the trained LSTM model to obtain the m-th predicted value. Finally, the extended time series X'(N+m) is obtained; the extended time series is mirrored again to obtain X(N+m); where the first m points are the predicted signal extension values ​​and the last N points are the original signal values.

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