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CN-122020143-A - Geometric nonlinear flutter boundary prediction method based on chaotic phase space principal component

CN122020143ACN 122020143 ACN122020143 ACN 122020143ACN-122020143-A

Abstract

The invention belongs to the technical field of aircraft pneumatic performance characteristic analysis, and particularly relates to a geometric nonlinear flutter boundary prediction method based on a chaotic phase space main component. According to the method, nonlinear flutter characteristics and predicted flutter boundaries are analyzed through analyzing the characteristics of attractors of response signals of a system, characteristics of pie attractors of the response signals in a phase space when flutter occurs in a geometric nonlinear structure are utilized, the planeness of the attractors is represented through analyzing the variance contribution ratio EVR of the front two dimensions of a phase space matrix, the flutter characteristics of wings with geometric nonlinear characteristics are described through quantitative analysis, and a brand-new extrapolation prediction method of flutter critical speed is provided based on the rule of the index along with the change of wind speed, so that the nonlinear flutter boundaries can be accurately predicted.

Inventors

  • ZHENG HUA
  • MA XIAOTIAN
  • WANG JUNZHE

Assignees

  • 西北工业大学

Dates

Publication Date
20260512
Application Date
20260106

Claims (4)

  1. 1. A geometric nonlinear flutter boundary prediction method based on a chaotic phase space main component is characterized by comprising the following steps: Step one, the signal is preprocessed, The method comprises the steps of preprocessing a discrete vibration signal acquired by a flight test, removing wild points and removing direct current components, wherein when the absolute value of the difference between a certain point in the signal and the signal mean value is 3 times greater than the standard deviation of the signal, the point is the wild point to be removed, and after all the wild points are removed, subtracting the mean value from all the points of the signal to remove the direct current components, wherein the method is expressed as follows: , , Wherein, the For the original signal, N is the signal length, Is that Is used for the average value of (a), Is the standard deviation of the signal; Determining an embedding dimension m and a time delay tau for the preprocessed signals to reconstruct a phase space, wherein the determined embedding dimension m quantifies dynamic expansion degrees under different embedding dimensions through the distance change of nearest neighbors so as to judge the optimal embedding dimension; step three, calculating the main component duty ratio of the first two dimensions in the phase space in the whole phase space, For the phase space matrix Y obtained in the second step, calculating a covariance matrix C thereof according to the following formula: , singular value decomposition is further performed on the covariance matrix: , Wherein U and V are respectively left and right singular vector matrixes, As a matrix of singular values, R is the rank of the matrix, which is the singular value; The principal component duty ratio of the first two dimensions in the phase space in the whole phase space is calculated, namely the variance contribution ratio EVR: ; Fitting and extrapolation are carried out, And (3) fitting and extrapolating the EVR by drawing a change graph of the variance contribution ratio EVR along with the wind speed steps until the corresponding wind speed is close to 90%, namely the flutter critical speed V f , so as to obtain the prediction of the geometric nonlinear flutter boundary.
  2. 2. The method for predicting the geometric nonlinear flutter boundary based on the principal component of the chaotic phase space as claimed in claim 1, wherein the determining the embedding dimension m is a Cao method, and the specific process comprises: (1) Building m and m+1 dimensional phase spaces: , (2) For each point Find its nearest neighbor ; (3) Calculating the nearest neighbor distance ratio: , (4) Defining an index: , When (when) When the curve approaches 1, the corresponding m is the optimal embedding dimension.
  3. 3. The method for predicting the geometric nonlinear flutter boundary based on the principal component of the chaotic phase space as claimed in claim 1, wherein the determining time delay τ adopts a mutual information method, and the specific flow comprises the following steps: (1) Dividing the time sequence into a plurality of adjacent intervals; (2) Calculating mutual information : , Wherein, the Is that The probability of falling within the i-th interval, Is that The probability of falling within the j-th interval, For joint probability selection As the optimal delay time tau.
  4. 4. The method for predicting the geometric nonlinear flutter boundary based on the principal component of the chaotic phase space according to any one of claims 1 to 3, wherein the matrix form of the phase space reconstruction is as follows: , Where τ is the time delay and m is the embedding dimension.

Description

Geometric nonlinear flutter boundary prediction method based on chaotic phase space principal component Technical Field The invention belongs to the technical field of aircraft pneumatic performance characteristic analysis, and particularly relates to a geometric nonlinear flutter boundary prediction method based on a chaotic phase space main component. Background With the development of high-altitude long-endurance aircrafts and novel unmanned aerial vehicles, high-aspect-ratio wings are widely adopted because of the advantages of light weight and high lift-drag ratio. The wing structure is light and flexible, and is easy to generate remarkable bending and torsion deformation under the action of flight load, so that the balance state of the structure and the theoretical appearance are obviously geometrically offset, and the aeroelastic characteristic of the aircraft is greatly influenced. Flutter is a typical aeroelastic instability phenomenon, which is represented by rapid accumulation of vibration energy of a structure under airflow excitation, and self-excited vibration with sharply increased amplitude is induced. Under the influence of geometrical nonlinear effects, the wing may exhibit complex nonlinear vibration responses. If the flutter can not be identified and effectively restrained in time in the design or operation, the structural fatigue is accelerated, the strength margin is weakened, even the catastrophic structural damage is caused, and the flight safety and the task reliability are seriously threatened. The main stream flutter signal processing method at present is based on the system linearity and stability assumption, a proper data model is established for subcritical test signals, fixed modal parameters (frequency and damping ratio) or system stability parameters are extracted, and finally the parameters are fitted through curves and the flutter critical speed is extrapolated. The traditional nonlinear flutter analysis methods are based on the system linearity and stability assumption, and are not suitable for quantitatively describing nonlinear characteristics of a structure, and meanwhile, the traditional flutter boundary prediction methods are all dependent on the concept of an inherent mode, but large deformation can occur in the flight of a wing with a large aspect ratio, at the moment, the structure response does not follow the linear superposition principle any more, and linear mode parameters do not have definite physical significance any more, so that the prediction result is not accurate enough, and consideration factors are not comprehensive enough. Disclosure of Invention The invention aims to provide a geometrical nonlinear flutter boundary prediction method based on a main component of a chaotic phase space, which is used for analyzing nonlinear flutter characteristics and predicting flutter boundaries by analyzing attractor characteristics of a system response signal, and can also utilize a traditional quantization index of the chaotic phase space to characterize the attractor characteristics so as to realize accurate prediction of the nonlinear flutter boundaries. In order to achieve the above purpose, the technical scheme adopted by the invention is that the geometric nonlinear flutter boundary prediction method based on the main component of the chaotic phase space comprises the following steps: Step one, the signal is preprocessed, The method comprises the steps of preprocessing a discrete vibration signal acquired by a flight test, removing wild points and removing direct current components, wherein when the absolute value of the difference between a certain point in the signal and the signal mean value is 3 times greater than the standard deviation of the signal, the point is the wild point to be removed, and after all the wild points are removed, subtracting the mean value from all the points of the signal to remove the direct current components, wherein the method is expressed as follows: Wherein, the For the original signal, N is the signal length,Is thatIs used for the average value of (a),Is the standard deviation of the signal; Step two, determining an embedding dimension m and a time delay tau for the preprocessed signals to reconstruct a phase space, wherein the determined embedding dimension m quantifies dynamic expansion degrees under different embedding dimensions through the distance change of nearest neighbors so as to judge the optimal embedding dimension, the determined time delay tau is formed by selecting proper tau through quantifying information relativity under different delays of a time sequence, and after m and tau are obtained, the phase space reconstruction is performed, and the matrix form is as follows: , where τ is the time delay and m is the embedding dimension; further, the determining the embedding dimension m adopts a Cao method, and the specific flow comprises the following steps: (1) Building m and m+1 dimensional phase spaces: (2) F