CN-122016277-A - Response kurtosis prediction method of single-degree-of-freedom system based on ultra-high-si excitation

CN122016277ACN 122016277 ACN122016277 ACN 122016277ACN-122016277-A

Abstract

The invention discloses a response kurtosis prediction method of a single-degree-of-freedom system based on super Gaussian excitation, which comprises the following steps of (1) setting a cutoff frequency of a super Gaussian excitation signal and setting a signal component exceeding the cutoff frequency to be 0; the method comprises the steps of (1) calculating a parameter x, (3) calculating a kurtosis transfer rule model, and (4) calculating to obtain response kurtosis. The invention introduces cut-off frequency to make the frequency characteristic of the super Gaussian exciting signal more consistent with the real working condition. And the parameters such as the resonance frequency, the resonance gain, the cut-off frequency and the like of the system are integrated through the parameter x, a kurtosis transfer rule model is established to replace the existing simple linear fitting model, the internal function relation between each parameter and kurtosis transfer is revealed, and the prediction error of response kurtosis is greatly reduced. By adjusting the input power spectral density PSD of the ultra-high-intensity excitation signal, the problem of kurtosis transmission failure caused by excitation spectral distortion is avoided, and the burst characteristic of the ultra-high-kurtosis excitation can be effectively transmitted to the system response.

Inventors

XU FEI
WANG WENJIA

Assignees

盐城工学院

Dates

Publication Date: 20260512
Application Date: 20260202

Claims (8)

1. A response kurtosis prediction method of a single degree of freedom system based on ultra-high excitation, ultra-high-si excitation signal as the input signal of the single degree of freedom system, the method is characterized in that: the method for predicting the response kurtosis generated by the single-degree-of-freedom system after being excited by the ultra-high-intensity excitation signal comprises the following steps: (1) Setting a cutoff frequency Ucut for the ultra-high excitation signal, and setting a signal component exceeding the cutoff frequency Ucut to 0; (2) Calculating a parameter x: ; Wherein the method comprises the steps of The Q value is resonance gain; (3) Calculating a kurtosis transfer rule model: ; a, b, c, d is a model parameter, and nonlinear least square identification is performed according to a response kurtosis fitting curve to obtain an optimal solution of the parameter a, b, c, d; (4) Calculating and obtaining response kurtosis kres: ; Where K is a reference value of the smooth vibration, Is the input kurtosis of a single degree of freedom system.
2. The method for predicting response kurtosis of a single degree of freedom system based on ultra-high-order excitation of claim 1, wherein the ultra-high-order excitation signal is Where G (t) is a stationary Gaussian signal and u (t) is a varying amplitude modulated signal.
3. The method for predicting the response kurtosis of the single-degree-of-freedom system based on the ultra-high excitation of claim 1, wherein the pseudo-velocity transfer function of the single-degree-of-freedom system is expressed as: ; ; Where S is the laplace variable, Is the damping coefficient.
4. The method for predicting the response kurtosis of a single degree of freedom system based on ultra-high excitation according to claim 1, wherein K=3, Greater than 3.
5. The method for predicting the response kurtosis of the single-degree-of-freedom system based on the ultra-high excitation of claim 1, wherein in the step (3), the method for obtaining the optimal solution of the parameter a, b, c, d by nonlinear least squares identification according to the response kurtosis fitting curve is as follows: (11) Generating a required ultra-high-order excitation signal according to a given input power spectral density PSD, loading the ultra-high-order excitation signal into a single-degree-of-freedom system arranged in a simulation system, solving response kurtosis through a digital filtering method, and storing the response kurtosis in an array; (12) Changing resonant frequency Kurtosis of input Cut-off frequency Ucut and resonance gain Q, obtaining a plurality of response kurtosis values and storing the response kurtosis values in an array; (13) Drawing according to the response kurtosis values in the array to obtain a response kurtosis fitting curve; (14) Using a four-parameter second-order model And (3) approximating a response kurtosis fitting curve, carrying out nonlinear least square identification on model parameters by adopting a Nelder-Mead simplex algorithm, and automatically iterating through a MATLAB function fminesearch to obtain an optimal parameter solution.
6. The method for predicting the response kurtosis of the single degree of freedom system based on ultra-high excitation of claim 1, wherein the optimal solution of the model parameters is a=1.4899, b=0.5955, c=1.3705, and d= 0.6008.
7. The method for predicting the response kurtosis of the single degree of freedom system based on ultra-high-order excitation according to claim 1 or 5, wherein the step (1) further comprises adjusting the input power spectral density PSD of the ultra-high-order excitation signal, and the adjusting method is as follows: (S1) setting an initial ultra-high-si excitation signal y (t); The initial ultra-high excitation signal y (t) acts on the single-degree-of-freedom system; (S2) acquiring an actual excitation signal actually applied to the single-degree-of-freedom system; (S3) carrying out power spectral density PSD analysis on the acquired actual excitation signal to obtain an actual excitation PSD curve of the single-degree-of-freedom system; if the actual excitation PSD curve has a peak in a section near the resonance frequency fn, reducing the energy value of the initial input power spectral density PSD near the resonance frequency fn to form an adjusted input power spectral density PSD; If the actual excitation PSD curve has a valley value in a section near the resonance frequency fn, the energy value of the initial input power spectral density PSD near the resonance frequency fn is increased to form an adjusted input power spectral density PSD.
8. The method for predicting the response kurtosis of the single-degree-of-freedom system based on the ultra-high excitation of claim 7, wherein the interval around the resonance frequency fn is a frequency interval set by fn.

Description

Response kurtosis prediction method of single-degree-of-freedom system based on ultra-high-si excitation Technical Field The invention belongs to the technical field of mechanical vibration and signal processing, and particularly relates to a single-degree-of-freedom system response kurtosis prediction method based on ultra-high-si excitation. Background During product transportation, service and complex environment testing, the mechanical structure is often subjected to random vibration load. Conventional random vibration tests typically generate gaussian random signals based on Power Spectral Density (PSD) control to simulate actual conditions, with the implicit assumption that the vibration excitation follows a gaussian distribution. However, in actual scenes such as when a vehicle runs on complex terrain, when aerospace equipment encounters airflow disturbance, when a ship sails in severe sea conditions or when a building bears earthquake action, the measured vibration signal often shows remarkable non-Gaussian characteristics, and is expressed as a large number of burst peaks and asymmetric waveforms, namely ultra-Gaussian characteristics. Such a super-gaussian vibration excitation can cause greater peak stress to the mechanical structure, significantly increasing the risk of fatigue damage to the structure. If the vibration table test is still carried out by using Gaussian distribution, the occurrence probability of a high-amplitude event is seriously underestimated, so that the prediction of the fatigue life of the structure is deviated, and further the early failure of the structure and even serious safety accidents are caused. For example, when a vehicle runs on a complex terrain, the super-Gaussian vibration excitation transmitted by the ground is amplified by the suspension, and serious potential safety hazards such as suspension fracture can be caused. The prior art scheme generates a non-gaussian excitation signal by an amplitude modulation method, the signal is input into a single degree of freedom System (SDOF), and the signal is responded by a numerical simulation computing system. In order to analyze the kurtosis transfer rule, the existing method decomposes the excitation signal by a frequency decomposition method, and researches the kurtosis of the decomposed signalKurtosis with system responseRelation between them, an empirical linear fitting model is established。 The prior art has the obvious defects that the cutoff frequency parameter is not introduced, the cutoff frequency directly determines the time correlation and the burstiness of excitation and has obvious influence on kurtosis transmission, meanwhile, the prior model does not reveal the internal function relation between the kurtosis transmission and the cutoff frequency, the system resonance gain Q and other key parameters, so that the response kurtosis prediction error is overlarge, and the requirements of high-precision fatigue life assessment and reliability analysis in engineering practice cannot be met. Disclosure of Invention The invention aims to solve the technical problem of providing a response kurtosis prediction method of a single-degree-of-freedom system based on ultra-Gaussian excitation, which is used for predicting the response kurtosis of the single-degree-of-freedom system excited by an ultra-Gaussian excitation signal. The technical proposal adopted by the invention for solving the technical problems is that the response kurtosis prediction method of the single-degree-of-freedom system based on the ultra-high-degree-of-freedom excitation is adopted, the ultra-high-degree-of-freedom excitation signal is used as the input signal of the single-degree-of-freedom system, The method for predicting the response kurtosis generated by the single-degree-of-freedom system after being excited by the ultra-high-intensity excitation signal comprises the following steps: (1) Setting a cutoff frequency Ucut for the ultra-high excitation signal, and setting a signal component exceeding the cutoff frequency Ucut to 0; (2) Calculating a parameter x: ; Wherein the method comprises the steps of The Q value is resonance gain; (3) Calculating a kurtosis transfer rule model: ; a, b, c, d is a model parameter, and nonlinear least square identification is performed according to a response kurtosis fitting curve to obtain an optimal solution of the parameter a, b, c, d; (4) Calculating and obtaining response kurtosis kres: ; Where K is a reference value of the smooth vibration, Is the input kurtosis of a single degree of freedom system. Preferably, the ultra-high-si excitation signalWhere G (t) is a stationary Gaussian signal and u (t) is a varying amplitude modulated signal. Preferably, the pseudo velocity transfer function of the single degree of freedom system is expressed as: ; ; Where S is the laplace variable, Is the damping coefficient. Preferably, the composition, k=3,Greater than 3. Preferably, in the step (3), the method for