Geometric nonlinear flutter boundary prediction method based on chaos phase space principal component

Abstract

The invention belongs to the technical field of aerodynamic performance characteristic analysis of aircrafts, and particularly relates to a geometric nonlinear flutter boundary prediction method based on a chaos phase space principal component. According to the method, nonlinear flutter characteristics are analyzed and flutter boundaries are predicted by analyzing attractor characteristics of system response signals, and planarity of attractors is represented by analyzing variance contribution rates EVR of first two dimensions of a phase space matrix by utilizing characteristics of pie-shaped attractors of the response signals in a phase space when flutter occurs in a geometric nonlinear structure. The flutter characteristics of a wing with geometric nonlinear characteristics are quantitatively analyzed and described, a brand-new extrapolation prediction method of the flutter critical speed is provided based on the rule that the index changes along with the wind speed, and accurate prediction of the nonlinear flutter boundary can be achieved.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic performance characteristic analysis technology of aircraft, specifically involving a geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space. Background Technology

[0002] With the development of high-altitude long-endurance aircraft and new unmanned aerial vehicles (UAVs), high-aspect-ratio wings are widely used due to their advantages of lightweight design and high lift-to-drag ratio. These wing structures are lightweight and highly flexible, making them prone to significant bending and torsional deformation under flight loads. This results in a significant geometric deviation between the structure's equilibrium state and its theoretical shape, thus greatly affecting the aircraft's aeroelastic properties. Flutter, a typical aeroelastic instability phenomenon, manifests as the rapid accumulation of vibrational energy under airflow excitation, leading to self-excited vibrations with a sharp increase in amplitude. Under the influence of geometric nonlinear effects, the wing may exhibit complex nonlinear vibration responses. If flutter is not identified and effectively suppressed in a timely manner during design or operation, it will accelerate structural fatigue, weaken strength margins, and even cause catastrophic structural damage, seriously threatening flight safety and mission reliability.

[0003] Current mainstream flutter signal processing methods are all based on the assumptions of system linearity and stationarity. They establish appropriate data models for subcritical test signals, extract fixed modal parameters (frequency and damping ratio) or system stability parameters, and finally extrapolate the flutter critical velocity by curve fitting of these parameters.

[0004] Existing nonlinear flutter analysis methods are all based on the assumptions of system linearity and stationarity. These methods are not suitable for quantitatively describing the nonlinear characteristics of structures. At the same time, existing flutter boundary prediction methods all rely on the concept of intrinsic modes. However, large aspect ratio wings undergo large deformations during flight. At this time, the structural response no longer follows the principle of linear superposition, and the linear mode parameters no longer have clear physical meanings, making the prediction results inaccurate and the factors considered insufficient. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting geometric nonlinear flutter boundaries based on principal components of chaotic phase space. This method analyzes the nonlinear flutter characteristics and predicts the flutter boundaries by analyzing the attractor features of the system response signal. Alternatively, traditional quantitative indicators of chaotic phase space can be used to characterize the attractor features, thus enabling accurate prediction of nonlinear flutter boundaries.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: the geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space includes the following steps: Step 1: Signal preprocessing The discrete vibration signals acquired during flight tests were preprocessed to remove outliers and DC components. Specifically, if the absolute value of the difference between a point in the signal and the signal mean is greater than three times the signal standard deviation, that point is considered an outlier to be removed. After removing all outliers, the mean is subtracted from all points in the signal to remove the DC component, as expressed by the following formula:

[0007]

[0008] in, The original signal, N For signal length, for The mean, The standard deviation of the signal; Step 2: Determine the embedding dimension *m* and time delay *τ* for the preprocessed signal to perform phase space reconstruction. The determination of the embedding dimension *m* quantifies the dynamic unfolding degree under different embedding dimensions by varying the distance between nearest neighbors, thereby determining the optimal embedding dimension. The determination of the time delay *τ* selects a suitable embedding dimension by quantifying the information correlation under different delays in the time series. τ ;get m After τ, the phase space is reconstructed, and its matrix form is as follows: , in, τ For time delay, m For the embedding dimension; Furthermore, the determination of the embedding dimension m is performed using the Cao method, and the specific process includes: (1) Construction m peacekeeping m +1-dimensional phase space:

[0009] (2) For each point Find its nearest neighbor. ; (3) Calculate the nearest neighbor distance ratio:

[0010] (4) Define indicators:

[0011] when When the curve approaches 1, the corresponding m This is the optimal embedding dimension; Furthermore, the determination of the time delay τ employs the mutual information method, and the specific process includes: (1) Divide the time series into several adjacent intervals; (2) Calculate mutual information :

[0012] in, for Falling in i The probability of each interval. for Falling in j The probability of each interval. For joint probability; choose The first minimum value is used as the optimal delay time. τ ; Step 3: Calculate the proportion of the first two dimensions of the principal components in the entire phase space. For the phase space matrix obtained in step two Y Calculate its covariance matrix using the following formula. C :

[0013] Further singular value decomposition of the covariance matrix is ​​performed:

[0014] in, U and V These are the left and right singular vector matrices, respectively. It is a singular value matrix. It is a singular value. r Let be the rank of the matrix; Calculate the proportion of the first two dimensions of the principal components in the entire phase space, i.e., the variance contribution rate. EVR : ; Step 4, Fit and Extrapolate. By plotting the variance contribution rate EVR The graph showing the variation of wind speed steps is fitted and extrapolated. EVR The critical flutter velocity is the wind speed at which the flutter reaches approximately 90%. V f That is, to obtain the prediction of the geometric nonlinear flutter boundary.

[0015] The beneficial effects of this invention are as follows: This invention provides a geometric nonlinear chatter boundary identification method based on principal components of chaotic phase space. It analyzes the nonlinear chatter characteristics and predicts chatter boundaries by analyzing the attractor features of the system response signal. It utilizes the disc-shaped attractor feature of the response signal when a geometric nonlinear structure chatters, and analyzes the variance contribution of the first two dimensions of the phase space matrix. EVRBy characterizing the planarity of the attractor, the flutter characteristics of an airfoil with geometrically nonlinear features are quantitatively analyzed and described. Based on the law of variation of this index with wind speed, a novel extrapolation prediction method for flutter critical velocity is proposed, which can achieve accurate prediction of nonlinear flutter boundary. Attached Figure Description

[0016] Figure 1 This is a flowchart of the technical solution of the present invention; Figure 2 This is a schematic diagram of the attractor structure of the present invention in flutter phase space; Figure 3 This is a graph showing the variation of the variance contribution rate with wind speed step during the implementation of this invention. Detailed Implementation

[0017] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0018] To achieve the above objectives, the present invention provides the following specific embodiments: Figure 1 As shown, the geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space includes the following steps: Step 1: Signal preprocessing The discrete vibration signals acquired during flight tests were preprocessed to remove outliers and DC components. Specifically, if the absolute value of the difference between a point in the signal and the signal mean is greater than three times the signal standard deviation, that point is considered an outlier to be removed. After removing all outliers, the mean is subtracted from all points in the signal to remove the DC component, as expressed by the following formula:

[0019]

[0020] in, The original signal, N For signal length, for The mean, The standard deviation of the signal; Step 2: Determine the embedding dimension *m* and time delay *τ* for the preprocessed signal to perform phase space reconstruction. The determination of the embedding dimension *m* quantifies the dynamic unfolding degree under different embedding dimensions by varying the distance between nearest neighbors, thereby determining the optimal embedding dimension. The determination of the time delay *τ* selects a suitable embedding dimension by quantifying the information correlation under different delays in the time series. τ ;get m After τ, the phase space is reconstructed, and its matrix form is as follows: , Furthermore, the determination of the embedding dimension m is performed using the Cao method, and the specific process includes: (1) Construction m peacekeeping m +1-dimensional phase space:

[0021] (2) For each point Find its nearest neighbor. ; (3) Calculate the nearest neighbor distance ratio:

[0022] (4) Define indicators:

[0023] when When the curve approaches 1, the corresponding m This is the optimal embedding dimension.

[0024] Furthermore, the determination of the time delay τ employs the mutual information method, and the specific process includes: (1) Divide the time series into several adjacent intervals; (2) Calculate mutual information :

[0025] in, for Falling in i The probability of each interval. for Falling in j The probability of each interval. For joint probability; choose The first minimum value is used as the optimal delay time. τ .

[0026] Step 3: Calculate the proportion of the first two dimensions of the principal components in the entire phase space. For the phase space matrix obtained in step two Y Calculate its covariance matrix using the following formula. C :

[0027] Further singular value decomposition of the covariance matrix is ​​performed:

[0028] in, U and V These are the left and right singular vector matrices, respectively. It is a singular value matrix. It is a singular value. r Let be the rank of the matrix; Calculate the proportion of the first two dimensions of the principal components in the entire phase space, i.e., the variance contribution rate. EVR : ; Step 4, Fit and Extrapolate. By plotting the variance contribution rate EVR The graph showing the variation of wind speed steps is fitted and extrapolated. EVR The critical flutter velocity is the wind speed at which the flutter reaches approximately 90%. V f That is, to obtain the prediction of the geometrically nonlinear flutter boundary, such as Figure 3 As shown.

[0029] When the embedding dimension and time delay are chosen appropriately and the system enters a fluttering state, the attractors in phase space exhibit a disc-like geometric structure and are approximately distributed on a two-dimensional plane, such as... Figure 2 As shown, the variance contribution rate of the first two principal components is calculated. EVR The Explained Variance Ratio (EVR) is used to quantitatively characterize the planarity of the attractor structure in phase space, thereby reflecting the stability of the system.

[0030] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting geometrically nonlinear flutter boundaries based on principal components of chaotic phase space, characterized in that, Includes the following steps: Step 1: Signal preprocessing The discrete vibration signals acquired during flight tests were preprocessed to remove outliers and DC components. Specifically, if the absolute value of the difference between a point in the signal and the signal mean is greater than three times the signal standard deviation, that point is considered an outlier to be removed. After removing all outliers, the mean is subtracted from all points in the signal to remove the DC component, as expressed by the following formula: ， ， in, The original signal, N For signal length, for The mean, The standard deviation of the signal; Step 2: Determine the embedding dimension *m* and time delay *τ* for the preprocessed signal to perform phase space reconstruction. The determination of the embedding dimension *m* quantifies the dynamic unfolding degree under different embedding dimensions by varying the distance between nearest neighbors, thereby determining the optimal embedding dimension. The determination of the time delay *τ* selects a suitable embedding dimension by quantifying the information correlation under different delays in the time series. τ ;get m After τ, phase space reconstruction is performed; Step 3: Calculate the proportion of the first two dimensions of the principal components in the entire phase space. For the phase space matrix obtained in step two Y Calculate its covariance matrix using the following formula. C : ， Further singular value decomposition of the covariance matrix is ​​performed: ， in, U and V These are the left and right singular vector matrices, respectively. It is a singular value matrix. It is a singular value. r Let be the rank of the matrix; Calculate the proportion of the first two dimensions of the principal components in the entire phase space, i.e., the variance contribution rate. EVR : ； Step 4, Fit and Extrapolate. By plotting the variance contribution rate EVR The graph showing the variation of wind speed steps is fitted and extrapolated. EVR The critical flutter velocity is the wind speed at which the flutter reaches approximately 90%. V f That is, to obtain the prediction of the geometric nonlinear flutter boundary.

2. The geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space as described in claim 1, characterized in that, The determination of the embedding dimension m is performed using the Cao method, and the specific process includes: (1) Construction m peacekeeping m +1-dimensional phase space: ， (2) For each point Find its nearest neighbor. ; (3) Calculate the nearest neighbor distance ratio: ， (4) Define indicators: ， when When the curve approaches 1, the corresponding m This is the optimal embedding dimension.

3. The geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space as described in claim 1, characterized in that, The determination of the time delay τ employs the mutual information method, and the specific process includes: (1) Divide the time series into several adjacent intervals; (2) Calculate mutual information : ， in, for Falling in i The probability of each interval. for Falling in j The probability of each interval. For joint probability; choose The first minimum value is used as the optimal delay time. τ .

4. A geometric nonlinear flutter boundary prediction method based on principal components of chaotic phase space as described in any one of claims 1-3, characterized in that: The matrix form of the phase space reconstruction is as follows: ， in, τ For time delay, m The embedding dimension.

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