CN113361000B - Coherent analysis method for vibration correlation characteristics of low-frequency structure - Google Patents

Coherent analysis method for vibration correlation characteristics of low-frequency structure Download PDF

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CN113361000B
CN113361000B CN202110411371.9A CN202110411371A CN113361000B CN 113361000 B CN113361000 B CN 113361000B CN 202110411371 A CN202110411371 A CN 202110411371A CN 113361000 B CN113361000 B CN 113361000B
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谢小平
陈永振
周长江
王续达
吕顺娣
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Qingdao International Academician Port Group Intelligent Construction Development Co ltd
Hunan University
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Abstract

The invention discloses a coherent analysis method for vibration correlation characteristics of a low-frequency structure, which comprises the following steps: (1) preparing a test coherence analysis; (2) collecting a plate structure vibration signal; (3) the input of the structural vibration signal and the judgment of the signal property automatically judge the type of the input signal according to the characteristics of the signal in a Matlab program; (4) and (3) realizing a method for combining coherent analysis and sheet metal contribution in a Matlab program. Performing corresponding analysis in a self-adaptive manner according to the type of the input signal to obtain a partial correlation coefficient graph and a wavelet time-frequency coherence graph; (5) and (4) drawing a correlation coefficient graph according to the analysis result of the step (4), and determining the plate with the largest contribution to the structural vibration and noise. According to the method, the coherent analysis and the metal plate contribution are combined, so that not only can stable and unstable noise signals be accurately and effectively identified, but also the corresponding method can be adopted to carry out sequencing analysis on the metal plate contribution in a self-adaptive manner, and the plate structure with the largest structural vibration and noise contribution is determined.

Description

Coherent analysis method for vibration correlation characteristics of low-frequency structure
The technical field is as follows:
the invention mainly relates to the technical field of automobile low-frequency structure noise identification and correlation analysis, in particular to a coherent analysis method for low-frequency structure vibration correlation characteristics suitable for steady-state and unsteady-state noises, which is mainly applied to test analysis of the contribution of vehicle plate structure vibration to noise under steady-state and unsteady-state working conditions.
Background art:
with the rapid development of the automobile industry and the increasing maturity of the automobile market, consumers are concerned about the riding comfort of vehicles. The in-vehicle noise level is one of the main factors affecting ride comfort. The low-frequency and medium-frequency noises of the vehicle are mainly caused by the fact that an external excitation source acts in the vehicle through a structure transmission path, and the high-frequency noises in the vehicle are mainly caused by the fact that the excitation source passes through an air transmission path. In-vehicle driving and riding personnel are sensitive to low frequency noise, which is primarily related to vibration and self-mode of the body panel structure. A great deal of research results show that the energy of the vibration signal of the vehicle panel structure is mainly concentrated in a low-frequency band, which is derived from the vibration of the panel structure under the action of various excitation sources, so that a panel structure with a large contribution to noise needs to be found by a relevant method for the low-frequency band.
In practical engineering applications, partial coherence analysis is often used to analyze the frequency and peak characteristics of noise signals, and may also be used to analyze the degree of correlation of one or more noise source signals, so that a partial coherence analysis method may be used to analyze the correlation of stationary noise. The method can also be used for identifying and positioning the noise sources except the mutual influence among the decoupling plate parts, and carrying out sequencing analysis on the contribution amounts of different noise sources and different plate part structures. For unsteady signals, wavelet transform can be used to process the unsteady signals. The correlation researchers also proposed a wavelet coherence method capable of performing correlation analysis on unsteady signals, which was originally applied to the aspects of meteorological hydrology and electroencephalogram research. With the continuous development of wavelet coherence algorithms, the method is also gradually applied to engineering field research. In addition, the influence of the plate structure vibration at different positions of the vehicle body on the noise in the vehicle is different, so that the plate with the largest contribution to the noise in the vehicle can be found out by a method for analyzing the contribution of the plate.
In the above four methods, most of the signals collected in the engineering test are non-steady signals, and the signal characteristics of the non-steady signals change with time, so the original partial coherence analysis method capable of analyzing the steady signals is not suitable for the non-steady signals, and the correlation relationship between the non-steady signals cannot be solved. Although the wavelet transform method can process unsteady signals, it can process only a single unsteady signal in turn, and cannot explore the correlation between two or more unsteady signals. A correlation researcher identifies a noise source in the unsteady driving process of an automobile by using a wavelet coherence method, obtains the coherence function size and the phase relationship between unsteady noise signals from a time domain and a frequency domain, but cannot further explain the phase relationship between the unsteady noise signals and the time domain and does not give out a detailed coherence coefficient diagram and a detailed phase diagram. The method for analyzing the contribution of the plate generally adopts a modeling simulation means, can obtain the contribution of the vibration of different plates of the vehicle body to the noise in the vehicle under a certain frequency, and is not suitable for the condition that continuous peak values appear on signals. The research on the unsteady signals by the method solves the problem of excessive noise in the vehicle from the perspective of noise sources or sheet metal contribution, and less combines coherent analysis and sheet metal contribution to adaptively identify noise and find a main noise source in a specific continuous frequency range.
The noun explains:
LMS SCADAS data acquisition system: LMS SCADAS the data collection system is a portable, multi-purpose data collection system manufactured by LMS corporation. Lab software can be seamlessly integrated with the hardware, all test settings can be quickly completed, and the test task can be efficiently completed while the best data quality and precision are ensured. And the hardware supports various sensors, has various signal conditioning functions and can be used for carrying out test tasks such as noise and vibration signal acquisition. The embodiment of the invention adopts an LMS SCADAS Mobile 5-slot portable case, and 2 rotating speeds and 2 signal sources are integrated on the case. The SCM-V8-E has 8-channel voltage and has the functions of fixed sampling, order tracking and octave filtering.
Multiple input single output model: the multi-input single-output model is a linear mathematical model considering a single output signal to a response signal to a plurality of inputs, and is established on the basis of the single-input single-output model. For a single input single output system with noise n (t) at the output, the system will often have some noise n (t) that is not related to the input signal x (t) added to the output of the system as part of the measured system output signal y (t). Where the noise n (t) is uncorrelated with the input signal x (t) and the signal y (t) is the actual output but cannot be measured. For the single-input single-output system, if the input signals have the same time and only one output is generated, the system becomes a multi-input single-output system, and the model is a multi-input single-output model. Song crystal defines a single-input single-output model in document [1], and describes a process of deriving a multiple-input single-output model from a single-input single-output model.
Alternative data methods: the concept of substitute data was originally proposed by Theiler et al in document [2 ]. One particular method of generating so-called "replacement data" is set forth in document [2 ]. The substitute data generated by this method is smooth while preserving the second order statistical properties of the original data. Specifically, the substitute data keeps the amplitude value of the power spectrum of the original data unchanged.
[1] Song Jing, research on identifying the noise source of the whole automobile by using a partial coherence function method, is described in [ Master graduation thesis of Siwa university ], Sichuan, Siwa university, 2006:31.
[2]Theiler J,Eubank S,Longtin A,et al.Testing for Nonlinearity in Time Series:The Method of Surrogate Data[J].Physica D,1992:58-77.
The invention content is as follows:
the invention aims to provide a coherent analysis method for low-frequency structure vibration correlation characteristics aiming at the problems in the prior art, and the coherent analysis method introduces coherent analysis into plate contribution analysis, not only can accurately and effectively identify steady-state and unsteady-state noise signals, but also can adaptively adopt a corresponding method to carry out sequencing analysis on the sheet metal contribution aiming at a low-frequency section in which the energy of a plurality of plate structure vibration signals is concentrated together, and determine a plate structure with the maximum structural vibration and noise contribution. .
In order to solve the problems, the technical scheme of the invention is as follows:
a coherent analysis method for vibration correlation characteristics of a low-frequency structure comprises the following steps:
step one, a preparation process of test coherence analysis: dividing regions and measuring points according to the plate structure; arranging a three-way acceleration sensor at each measuring point, and installing a data acquisition system;
step two, collecting a vibration signal of the plate structure: firstly, obtaining a frequency response function curve of each plate structure at each measuring point of the divided plate structure through a data acquisition system, and selecting a plurality of measuring points with obvious peak values in the frequency response function curve of the plate structure as final plate measuring points; finally, collecting a final structural vibration signal of a plate measuring point under a driving working condition;
inputting the final structural vibration signals of the plate measuring points under the driving working condition into a multi-input single-output model, and sorting the final structural vibration signals of the plate measuring points under the driving working condition; when the sequenced input signals are used as the input signals of the multi-input single-output system, the multi-input single-output system is changed into a multi-input single-output system under the condition input;
the expression of the multi-input single-output system at the time of conditional input is as follows:
Figure BDA0003024227230000031
wherein Y represents the total output signal; x represents the fourier transform of the respective signal; q represents the number of input signals; i represents the ith input signal; y is represented as output signal y (t); n denotes the ambient interference, Xi·(i-1)！Representing an input signal XiHas removed X1，X2，...，Xi-1To XiThe correlation effect of (1), i.e. when the input signals in the system are independent of each other; l isiyThe optimal frequency response function of the ith system is obtained;
according to the characteristics of the input structural vibration signal, the multi-input single-output system under the condition of input automatically judges the type of the signal by adopting a substitute data method; the method comprises the following specific steps:
suppose there is a Gaussian process { xl(t) } (- ∞ < t < + ∞), in which xl(t) is the first sample function having a Gaussian process, t represents time, [ alpha ], [ beta ], [ alpha ], [ beta ], [ alpha ] is a]To find the sign of the average, then μx(t)＝E[xl(t)]The global average at time t is determined arbitrarily; while r (t)1,t2)＝E[xl(t1)xl(t2)]，r(t1,t2) Representing the sample function at t1And t2Value of autocorrelation function of time, where t1And t2Each represents an arbitrary fixed time, and (∞ < t)2＜t1＜+∞)；
The structural vibration signal is stationary for a steady state process, i.e. the final plate measurement point, of which μx(t) and r (t)1,t2) Are all time independent, and therefore have μx(t)＝const，r(t1,t2)＝E[xl(t+τ)xl(t)]R (τ); where τ is t1-t2Is time delay;
wherein const represents a constant;
for steady state Gaussian process { xl(t)}(-∞＜t＜+∞)xl(t)，xlThe power spectral density function of (t) is:
Figure BDA0003024227230000041
wherein Sxx(ω) represents the power spectral density; ω represents frequency; x represents a sample function xl(t) or the structural vibration signal x (t) of the final plate measurement point; r isxxRepresenting a sample function xl(t) an autocorrelation function value; e represents a natural constant, i.e., e ≈ 2.71828183; j represents an imaginary number; d τ represents the derivation of τ; thus determining the nature of the structural vibration signal of the final plate measuring point, namely the nature is stationarity or non-stationarity;
if { xl(t) } is unsteady, i.e. the structural vibration signal at the final plate measurement point is non-stationary, the mu of the structural vibration signal at the final plate measurement pointx(t) and r (t)1,t2) The time is correlated, so that the power spectral density function of the structural vibration signal of the final plate measuring point is analyzed in a time-frequency domain to obtain the property of the structural vibration signal of the final plate measuring point;
the time-frequency distribution is used for analyzing the power spectrum of the unsteady random signal, and the power spectrum of the unsteady random signal is time-varying, so that the power spectrum of the unsteady random signal is in the original power spectrumIntroducing a time axis to form time-frequency distribution, and displaying the change condition of the power spectrum of the signal along with time through the time-frequency distribution; time-frequency distribution S of signal x (t)x,K(t, f) is expressed as:
Figure BDA0003024227230000051
wherein x represents x (t), namely a structural vibration signal of a final plate measuring point; k represents the order; f represents a frequency; s represents the time of substitution data s (t); x(s) represents substitution data s (t); t represents a time; i represents an imaginary unit; ds2Representing the derivation of the secondary derivative for the substitution data s (t); pi represents a circumferential ratio; h isk(t) is a Hermite function of order k, wherein
Figure BDA0003024227230000052
In the formula Hk(t) is a Hermite polynomial of order k; k! Represents a factorial of k;
setting the final structural vibration signal of the plate measuring point as x (t), and then Fourier transform of the structural vibration signal
X(f)＝∫e-i2πtfx(t)dt；
Wherein dt represents the derivation of t; f represents a frequency;
the substitute data s (t) is composed of
Figure BDA0003024227230000053
Generating; wherein the content of the first and second substances,
Figure BDA0003024227230000054
is in the range of [ - π, π]Uniformly distributed random phases for ensuring that s (t) and x (t) have the same fourier transform magnitude;
the stationarity of the signal is judged by comparing the similarity degree of the frequency spectrums at different time points; the distance of the spectrum from the average of the spectrum at different points in time is defined as:
Figure BDA0003024227230000055
Figure BDA0003024227230000056
in the formula: symbol'<>"means averaging; k represents the distance of the spectrum from the average value of the spectrum at different time points; sx,KRepresenting a power spectral density function; k represents the order; (t)nMeans time points, °); t is tnRepresents the nth time, wherein (N ═ 1,2, ·, N "); by degree representing the phase of signal x (t)
Figure BDA0003024227230000057
N "represents the length of signal x (t);
distance of frequency spectrum from average value of frequency spectrum at different time points
Figure BDA0003024227230000058
Is defined as:
Figure BDA0003024227230000061
wherein the symbols "" represent the normalization functions of the corresponding functions; g (f) represents a power spectral density function; h (f) represents a Hermite polynomial;
Figure BDA0003024227230000062
a normalization function representing a power spectral density function, namely:
Figure BDA0003024227230000063
Figure BDA0003024227230000064
a normalization function representing a Hermite polynomial, namely:
Figure BDA0003024227230000065
f represents a frequency;
Figure BDA0003024227230000066
fluctuation with time theta1Is defined as
Figure BDA0003024227230000067
The variance of (a), namely:
Figure BDA0003024227230000068
of substitution data s (t) determined above
Figure BDA0003024227230000069
The fluctuation with time is denoted as Θ0By comparison of theta1And Θ0Determining the stability of the structural vibration signal of the final plate measuring point; i.e. theta0The probability density function of (c) is denoted as f (Θ)0) Setting a threshold gamma, if f (theta)0) If the gamma is less than gamma, judging the signal to be an unsteady random signal; if f (theta)0) If the signal is more than gamma, judging the signal to be an unsteady random signal; if a certain section f (theta) of the input vibration signal data0) < gamma, another segment f (theta)0) If the signal is more than gamma, judging that the signal contains both steady-state and unsteady-state random signals;
step four, determining an analysis method of the input signal according to the property of the vibration input signal and analyzing the input signal:
4.1 if the final structural vibration signal of the plate measuring point is a steady-state signal, analyzing by adopting a method combining partial coherence analysis and metal plate contribution:
the self-power spectral density function of all vibration input signals is: gjj·r！＝Gjj·(r-1)！-|Lrj|2Grr·(r-1)！；
Wherein G isjj·(r-1)！Structure vibration input signal x independent of each other in terms of representing condition inputj(t) removal of x(r-1)(t) to xj(t) the self-power spectral density after correlation; l isrjRepresenting an optimal frequency response function of the multi-input single-output system when the condition is input; grr·(r-1)！Structure vibration input signal x independent of each other in terms of representing condition inputr(t) removal of x(r-1)(t) to xr(t) the correlated contribution self-power spectral density; r represents the total number of vibration input signals; j represents the j-th structure vibration inputAn incoming signal, wherein (j ═ 1, 2.., r);
then, the self spectrum of the vibration input signals and the cross spectrum between each input signal and the vibration input signals are solved one by one, and the obtained partial coherence function expression is as follows:
Figure BDA0003024227230000071
wherein the content of the first and second substances,
Figure BDA0003024227230000072
representing structural vibration input signal xi(t) and output signal y (t) removing x(r-1)(t) magnitude of partial coherence function after correlation with y (t); gamma ray2(f) Representing the magnitude of the partial coherence function; i denotes the ith structural vibration input signal, where (i ═ 1, 2.., r); y represents the output signal y (t);
the partial coherence function for accurately calculating the contribution of each vibration input signal to the sound pressure output signal through an iterative algorithm is as follows:
Figure BDA0003024227230000073
wherein: gii·(i-1)！(f) Is xi(t) removal of x(i-1)(t) to xi(t) conditioned self-spectra; gyy·(i-1)！(f) Is y (t) by removing x(i-1)(t) a conditional self-spectrum after influence on y (t), y (t) representing the output signal; giy·(i-1)！(f) Inputting a signal x for structural vibrationi(t) and output signal y (t) removing x(r-1)After the relevant influence of (t) on y (t), xi(t) and y (t) are conditional cross spectra; l isijExpressing the optimal frequency response function of the multi-input single-output system;
4.2 if the final structural vibration signal of the plate measuring point is an unsteady state signal, adopting a method combining wavelet coherence analysis and metal plate contribution:
selecting non-orthogonal Morlet wavelet basis functions, the definition of the non-orthogonal Morlet wavelet basis functions in time domain and frequency domain being:
Figure BDA0003024227230000074
wherein the center frequency omega0Taking 6; t represents time;
then, using wavelet coherence to describe the local correlation degree of the two unsteady signals in the region with energy common concentration, and giving the amplitude relation and the phase relation of the time-frequency domain, defining the wavelet coherence spectrum of the two unsteady signals x (t) and y (t) as follows:
Figure BDA0003024227230000081
the above formula represents the amplitude cross product between two non-steady-state signals at a certain frequency
Figure BDA0003024227230000082
With the amplitude product of the two signals
Figure BDA0003024227230000083
The ratio of (A) to (B); wherein S is a smoother, and the expression is: s (W) ═ SS(St(Wn(l) ); wherein S istIndicating smoothing on the time axis; sSIndicating smoothing on the scale axis; the smoothing function is embodied as
Figure BDA0003024227230000084
And SS(W)＝Wn(l)×c2Π (0.6 l); wherein, c1And c2Are all normalized coefficients; Π is a rectangular function; t is time;
Figure BDA0003024227230000085
representing the magnitude of the correlation between two non-stationary signals; n marks the wavelet coherence spectrum of two non-stationary signals x (t) and y (t) using non-orthogonal Morlet wavelet basis functions; l represents a scale factor of the continuous wavelet transform;
Figure BDA0003024227230000086
represents the cross wavelet power spectrum of two non-stationary signals x (t) and y (t); x represents an unsteady state inputSignal x (t); y represents an unsteady state output signal Y (t);
Figure BDA0003024227230000087
a continuous wavelet transform representing the input signal x (t);
Figure BDA0003024227230000088
a continuous wavelet transform representing an input signal y (t);
carrying out wavelet coherence processing on an unsteady input signal x (t) and an output signal y (t) through a wavelet coherence spectrum formula, then calculating and solving a wavelet coherence coefficient graph and a phase graph between the unsteady input signal x (t) and the output signal y (t), merging the wavelet coherence coefficient graph and the phase graph to obtain a wavelet coherence time-frequency graph between the two signals, and then testing the two signals under a preset confidence level by adopting a Monte Carlo method; if the detection is qualified, the obtained wavelet coherence time-frequency diagram is adopted, and if the detection is unqualified, the signal data and the calculation process need to be checked for errors, so that the accuracy and reliability of the power spectrum calculation result are ensured;
4.3 if the original structure vibration input signal of the determined plate measuring point contains both steady-state and unsteady-state signals, comprehensively analyzing the input signal; firstly, a method of combining the partial coherence analysis and the contribution of the metal plate is adopted for a steady-state signal to obtain a partial coherence function of the contribution of each vibration input signal to a sound pressure output signal; then, a wavelet coherence time-frequency diagram among all vibration signals is obtained by adopting the method of combining the wavelet coherence analysis and the metal plate contribution amount on the unsteady-state signals;
and step five, drawing a coherence coefficient graph and drawing a coherence coefficient graph according to a result obtained by analyzing the input signal, namely drawing the coherence coefficient graph according to a partial coherence function and a wavelet coherence time-frequency graph, determining a plate with the largest contribution to structural vibration and noise, and completing the whole coherence analysis overall process.
In a further improvement, in the second step, a frequency response function curve of each plate structure is obtained by a hammering method.
In the third step, the input of the signal adopts a multi-input single-output system, and the multi-input single-output system automatically judges the type of the signal according to the characteristics of the signal, namely, the type of the signal is a steady-state signal, a type of an unsteady-state signal, and the type of the signal simultaneously contains the steady-state signal and the unsteady-state signal.
In the third step, a magnitude sequence is performed on the structural vibration signals of the final plate measuring points by using a normal coherence function method, and the specific steps are as follows: firstly, calculating a constant coherence function between every two input signals, drawing the constant coherence function obtained by solving in a coordinate system, calculating the area enclosed by the constant coherence function and a coordinate axis in a concerned frequency band, determining the priority according to the size of the area, wherein the larger the area is, the more the ranking is, otherwise, the more the ranking is, and ranking all the input signals from high to low according to the priority.
Compared with the prior art: the invention has the advantages that:
1. the method can automatically judge the type of the signal according to the characteristics of the signal, can accurately and effectively identify the steady-state signal, the unsteady-state signal and the signal containing both the steady state and the unsteady state, solves the problem that the traditional simulation method is not suitable for solving the problem that the continuous peak frequency section occurs in the specific signal, and is more convenient and faster in operation and more accurate and reliable in analysis result.
2. The method can self-adaptively adopt a corresponding method to carry out sequencing analysis on the metal plate contribution amount aiming at the low frequency band in which the energy of a plurality of plate structure vibration signals is concentrated together, namely, the coherent analysis is introduced into the plate contribution amount analysis, so that the analysis of a steady-state signal, an unsteady-state signal and a signal containing both a steady state and an unsteady state is self-adaptively realized, and the plate structure with the largest structural vibration and noise contribution amount is determined.
Description of the drawings:
FIG. 1 is a schematic flow diagram of the system of the present invention;
FIG. 2 is a multiple-input-single-output model under the condition input adopted by the signal input in the present invention;
FIG. 3-1 is a schematic diagram showing a reasonable arrangement of sensors in the plate structure according to the embodiment;
FIG. 3-2 is a schematic diagram of a second embodiment of a reasonable arrangement of sensors in a plate structure;
FIG. 4 is a frequency response function curve of a part of a plate structure obtained by hammering method in an embodiment;
FIG. 5 is a flowchart of an iterative solution procedure for partial coherence analysis in accordance with the present invention;
FIG. 6 is a wavelet time-frequency coherence diagram of a certain measuring point obtained by analyzing an unsteady state signal in the embodiment;
FIG. 7 is a final histogram of partial correlation coefficients of the low frequency band of the plate structure in steady state according to the embodiment;
fig. 8 is a diagram of the wavelet coherence coefficients of the low frequency band at unsteady state finally obtained in the embodiment.
The specific implementation mode is as follows:
in order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
Example 1
As shown in the attached figure 1, the invention discloses a coherent analysis method for low-frequency structure vibration correlation characteristics adaptive to steady-state noise and unsteady-state noise, which comprises the following steps:
(1) preparation process of experimental coherence analysis: according to a plate structure of a certain automobile, dividing a region and a measuring point: because the vibration condition of each plate structure is different, the more the division of the metal plate region is, the more accurate the positioning of the vibration measuring points is, but the larger the calculated amount is, so that important signals are omitted in the test process, and the three-way acceleration sensors are reasonably and uniformly arranged on each plate, as shown in the attached drawing 3. The sensor selects a corresponding sensitivity when acquiring the structural vibration signal. Finally, LMS SCADAS the installation and initialization of the data acquisition system are carried out.
(2) Collecting a plate structure vibration signal: the method for obtaining the frequency response function curve of each plate structure by adopting the hammering method comprises the following steps: firstly, knocking the plate structure at each measuring point of the divided plate structure by a force hammer, acquiring signals after setting a sampling frequency f and a sampling time T in an LMS data acquisition system, then processing the plate by data of LMS software to obtain a frequency response function curve of each plate structure, wherein the frequency response function curve is shown in figure 4, and the measuring point with an obvious peak value in a low frequency band of the frequency response function of the plate structure is selected as a final plate measuring point. And finally, acquiring a vibration signal of the vehicle plate structure under the running working condition.
(3) Inputting a structural vibration signal and judging the signal property, and automatically judging the type of the signal according to the characteristics of the signal in a Matlab program;
the input of the structural vibration signal takes a multiple-input single-output model, as shown in fig. 2. The input signals are sorted according to a certain rule, and when the sorted input signals replace the original input signals, the multi-input single-output system is changed into a multi-input single-output system under the condition input.
The multiple-input single-output system at conditional input is represented as:
Figure BDA0003024227230000111
when using Y ═ Xq+1When the output signal Y is replaced and the previous r (r ≦ q) ordered condition inputs are taken into consideration, the above equation is modified to
Figure BDA0003024227230000112
After replacing r with (r-1), the calculation yields: xj·r！＝Xj·(r-1)！-LrjXr·(r-1)！. Wherein the capital X represents the fourier transform of the respective signal. Xi·(i-1)！Representing the original signal XiHas removed X1，X2，...，Xi-1The associated impact on it. In this case, the input signals in the system are independent of each other. L is1y，L2y，...，LqyExpressed as the system optimum frequency response function with the input subscript preceding the output subscript. And N is environmental interference. Y is the output signal.
In the Matlab program, according to the characteristics of the input structural vibration signal, the multi-input single-output system adopts a substitute data method to automatically judge the type of the signal, namely, substitute data is introduced, and the stationarity and the non-stationarity of the original vibration signal are judged according to the characteristics of the substitute data.
Suppose there is a Gaussian process { xl(t) } (- ∞ < t < + ∞), in which xl(t) is a sample function. Let E be the sign of the averaging, then μx(t)＝E[xl(t)]The global average at time t is arbitrarily determined. While r (t)1,t2)＝E[xl(t1)xl(t2)]Referred to as the autocorrelation function. For a steady state process, its mux(t) and r (t)1,t2) Are time-invariant or time-independent. Thus having μx(t)＝const，r(t1,t2)＝E[xl(t+τ)xl(t)]R (τ). Where τ is t1-t2Known as latency. For steady state Gaussian process xl(t), its autocorrelation function or its power spectral density function (PSD) is:
Figure BDA0003024227230000121
this may determine its nature. On the other hand, if xl(t) is unstable, its mux(t) and r (t)1,t2) Is time-varying or time-dependent such that its power spectral density function should be analyzed in the time-frequency domain. The time-frequency distribution is mainly used for analyzing the power spectrum of the unsteady random signal. Because the power spectrum of the unsteady random signal is time-varying, a time axis is introduced on the basis of the original power spectrum to form time-frequency distribution. The time-frequency distribution can show the change of the power spectrum of the signal along with time. Time-frequency distribution S of signal x (t)x,K(t, f) can be expressed as:
Figure BDA0003024227230000122
in the formula hk(t) is a Hermite function of order k. Wherein
Figure BDA0003024227230000123
In the formula Hk(t) is a Hermite polynomial of order k.
The 'substitute data' adopted in the matalb program is steady, and meanwhile, the second-order statistical characteristics of the original data and the amplitude value of the power spectrum and the like are kept unchanged. According to Wiener-Khintchin theory, the work of the signalThe rate spectrum is equal to the square of the magnitude of its fourier transform, thus keeping the power spectrum magnitude value of the signal, or the magnitude value of its fourier transform, constant. Assuming the original data is x (t), its Fourier transform is taken as
Figure BDA0003024227230000124
The substitute data s (t) is composed of
Figure BDA0003024227230000125
And (4) generating. Wherein the content of the first and second substances,
Figure BDA0003024227230000126
is in the range of [ - π, π]The uniformly distributed random phases ensure that s (t) and x (t) have the same fourier transform magnitude. The stationary effect is on the fluctuation of the frequency spectrum with time, namely for a steady signal, the frequency spectrum does not change with time; whereas for non-stationary signals, the frequency spectrum may change over time. Therefore, the stationarity of the signal can be judged by comparing the similarity degree of the frequency spectrums at different time points. The distance of the spectrum from the average of the spectrum at different points in time is defined as:
Figure BDA0003024227230000131
is composed of
Figure BDA0003024227230000132
In the formula: symbol'<>"means averaging. The distance here is defined as:
Figure BDA0003024227230000133
in the formula: the symbols "" denote the normalization functions of the corresponding functions. Distance between two adjacent plates
Figure BDA0003024227230000134
Fluctuation with time theta1Is defined as
Figure BDA0003024227230000135
The variance of (a), namely:
Figure BDA0003024227230000136
to replace data
Figure BDA0003024227230000137
The fluctuation with time is denoted as Θ0. By comparison of Θ1And Θ0The stationarity of the original data can be determined. I.e. theta0The probability density function of (c) is denoted as f (Θ)0) Selecting an appropriate threshold gamma, if f (theta)0) If the gamma is less than gamma, judging the signal to be an unsteady random signal; if f (theta)0) If the signal is more than gamma, judging the signal to be an unsteady random signal; if the input vibration signal has a certain section f (theta) in the data0) < gamma, another segment f (theta)0) If the signal is more than gamma, the signal is judged to contain both steady-state and non-steady-state random signals.
(4) The method for realizing the combination of the coherent analysis and the metal plate contribution amount in the Matlab program comprises the following steps: aiming at the low frequency band in which the energy of a plurality of structural vibration signals is concentrated together, and carrying out corresponding analysis in a self-adaptive mode according to the type of an input signal, namely if the input signal is a steady-state signal, a system correspondingly adopts a method of combining partial coherent analysis and metal plate contribution; if the input signal is an unsteady signal, the system correspondingly adopts a method of combining wavelet coherence analysis and metal plate contribution; if the signals contain both steady-state and unsteady-state signals, the system can correspondingly perform comprehensive coherent analysis, namely, firstly, a method of combining partial coherent analysis and the contribution of the sheet metal is adopted for the steady-state signals, then, a method of combining wavelet coherent analysis and the contribution of the sheet metal is adopted for the unsteady-state signals, and finally, the results are comprehensively analyzed.
The working conditions of the embodiment of the invention are as follows: in a steady state, the running speed of the vehicle is at a constant speed of 70 km/h; and in the unsteady state, the running speed of the vehicle is 60-70 km/h. The corresponding analysis is performed adaptively according to the following method.
1. If the input signal is a steady-state signal, a method combining partial coherent analysis and the contribution of the metal plate is adopted.
As shown in fig. 5, the input signals and the output signals of the board structure are tested and collected, and the input signals are prioritized, and it is generally considered that the greater the influence of a certain input signal on the output signals, the higher the priority of the input signal ranking is, the higher the priority is. The method comprises the following steps of firstly, calculating a normal coherence function between every two input signals, drawing the solved normal coherence function in a coordinate system, calculating the area enclosed by the normal coherence function in a concerned frequency band, determining the priority according to the size of the area, wherein the larger the area is, the more the sequence is forward, otherwise, the more the sequence is backward, and sequencing all the input signals according to the priority of the rule; second, impulse response function method; and thirdly, a Hilbert transform method. In order to be suitable for the condition that plate structure measuring points are more, a normal coherence function method is adopted to sequence input signals. And then, by utilizing a least square method and through optimal selection of a frequency response function, the mutual coupling influence of other input signals on a certain input signal is eliminated one by one.
With conditional input, the self-power spectral density function of all signals is: gjj·r！＝Gjj·(r-1)！-Lrj 2Grr·r！. Then, the self-spectrum of the input signals and the cross-spectrum between each input signal and each output signal are solved one by one, and the obtained partial coherence function expression is as follows:
Figure BDA0003024227230000141
the partial coherence function for accurately calculating the contribution of each vibration input signal to the sound pressure output signal through an iterative algorithm is as follows:
Figure BDA0003024227230000142
wherein: gii·(i-1)！(f) Is xi(t) removal of x(i-1)(t) conditional self-spectra after their influence; gyy·(i-1)！(f) Is y (t) by removing x(i-1)(t) conditional self-spectra after their influence; giy·(i-1)！(f) Is x(i-1)(t) after removing the influence on both, xi(t) and y (t). L isijExpressed as the optimal frequency response function of the multi-input single-output system.
2. If the input signal is an unsteady signal, a method combining wavelet coherence analysis and the contribution of the metal plate is adopted.
The wavelet coherence analysis method is wavelet transform combined coherence analysis. First, a suitable wavelet basis function is selected, here a non-orthogonal Morlet wavelet basis function is selected, which is defined in the time and frequency domains as:
Figure BDA0003024227230000151
wherein the center frequency omega0And 6, taking.
Wavelet coherence is adopted to describe the local correlation degree of two unsteady signals in a common energy concentration area, and the amplitude relation and the phase relation of a time frequency domain are given. Defining the wavelet coherence spectrum of two unsteady signals x (t) and y (t) as:
Figure BDA0003024227230000152
wherein, S is a smoothing device,
Figure BDA0003024227230000153
representing the magnitude of the correlation between the two non-stationary signals.
The wavelet coherence time-frequency diagram of a certain measuring point obtained by calculation is shown in figure 6. The light and shade of the color in the figure represents the degree of correlation between the input signal and the output signal, the brighter the color, the stronger the correlation between the two, and the darker the color, the weaker the correlation between the two. Higher correlation procedures indicate greater contribution of the panel structure to noise. The results of this analysis were also examined using the monte carlo method at a certain confidence level.
3. If the signal contains both steady-state and unsteady-state signals, the method of combining partial coherent analysis and sheet metal contribution is firstly adopted for the steady-state signals according to the method, and the plate structure with the largest noise contribution in the steady state is determined. And based on the result, adopting a method of combining wavelet coherence analysis and metal plate contribution to the unsteady-state signal, and finally integrating the results of partial coherence analysis and wavelet coherence to obtain the magnitude of the comprehensive contribution of the plate structure vibration to the noise.
(5) And (4) drawing a coherence coefficient graph in a steady state and a non-steady state according to the analysis result of the step (4) as shown in the attached fig. 7 and 8, and determining the plate with the largest contribution to the structural vibration and noise according to the coherence coefficient graph.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (4)

1. A coherent analysis method for vibration correlation characteristics of a low-frequency structure is characterized by comprising the following steps:
step one, a preparation process of test coherence analysis: dividing regions and measuring points according to the plate structure; arranging a three-way acceleration sensor at each measuring point, and installing a data acquisition system;
step two, collecting a vibration signal of the plate structure: firstly, obtaining a frequency response function curve of each plate structure at each measuring point of the divided plate structure through a data acquisition system, and selecting a plurality of measuring points with obvious peak values in the frequency response function curve of the plate structure as final plate measuring points; finally, collecting a final structural vibration signal of a plate measuring point under a driving working condition;
inputting the final structural vibration signals of the plate measuring points under the driving working condition into a multi-input single-output model, and sorting the final structural vibration signals of the plate measuring points under the driving working condition; when the sequenced input signals are used as the input signals of the multi-input single-output system, the multi-input single-output system is changed into a multi-input single-output system under the condition input;
the expression of the multi-input single-output system at the time of conditional input is as follows:
Figure FDA0003541897050000011
wherein Y' represents the total output signal; x' represents the fourier transform of the respective signal;q represents the number of input signals; n represents an nth input signal; n denotes the ambient interference noise, Xn·(n-1)！Representing an input signal XnHas removed X1，X2，...，Xn-1To XnThe correlation effect of (1), i.e. when the input signals in the system are independent of each other; l isnyThe optimal frequency response function of the nth system is obtained;
according to the characteristics of the input structural vibration signal, the multi-input single-output system under the condition of input automatically judges the type of the signal by adopting a substitute data method; the method comprises the following specific steps:
suppose there is a Gaussian process { xl(t) } -infinity < t < + > infinity, wherein xl(t) is the first sample function having a Gaussian process, t represents time, [ alpha ], [ beta ], [ alpha ], [ beta ], [ alpha ] is a]To find the sign of the average, then μx(t)＝E[xl(t)]The global average at time t is determined arbitrarily; while r (t)1,t2)＝E[xl(t1)xl(t2)]，r(t1,t2) Representing the sample function at t1And t2Value of autocorrelation function of time, where t1And t2Each represents an arbitrary specified time, and ∞ t2＜t1＜+∞；
The structural vibration signal is stationary for a steady state process, i.e. the final plate measurement point, of which μx(t) and r (t)1,t2) Are all time independent, and therefore have μx(t)＝const，r(t1,t2)＝E[xl(t+τ)xl(t)]R (τ); where τ is t1-t2Is time delay;
wherein const represents a constant;
for steady state Gaussian process { xl(t)}-∞＜t＜+∞，xlThe power spectral density function of (t) is:
Figure FDA0003541897050000021
wherein Sxx(ω) represents the power spectral density; ω represents frequency; x represents a sample function xl(t)；rxxRepresenting a sample function xl(t) fromA correlation function value; e represents a natural constant; i represents an imaginary number; d τ represents the derivation of τ; thus determining the nature of the structural vibration signal of the final plate measuring point, namely the nature is stationarity or non-stationarity;
if { xl(t) } is unsteady, i.e. the structural vibration signal at the final plate measurement point is non-stationary, the mu of the structural vibration signal at the final plate measurement pointx(t) and r (t)1,t2) The time is correlated, so that the power spectral density function of the structural vibration signal of the final plate measuring point is analyzed in a time-frequency domain to obtain the property of the structural vibration signal of the final plate measuring point;
the time-frequency distribution is used for analyzing the power spectrum of the unsteady random signal, and because the power spectrum of the unsteady random signal is time-varying, a time axis is introduced on the basis of the original power spectrum to form time-frequency distribution, and the change condition of the power spectrum of the signal along with the time is displayed through the time-frequency distribution; time-frequency distribution S of structural vibration signals x (t) of final plate measuring pointx,K(t, f) is expressed as:
Figure FDA0003541897050000031
wherein x represents x (t), namely a structural vibration signal of a final plate measuring point; k represents the order; f represents a frequency; s represents the time of substitution data s (t); x(s) represents substitution data s (t); t represents a time; i represents an imaginary unit; ds2Representing the derivation of the secondary derivative for the substitution data s (t); pi represents a circumferential ratio; h isk(t) is a Hermite function of order k, wherein
Figure FDA0003541897050000032
In the formula Hk(t) is a Hermite polynomial of order k; k! Represents a factorial of k;
setting the final structural vibration signal of the plate measuring point as x (t), and then Fourier transform of the structural vibration signal
X(f)＝∫e-i2πtfx(t)dt；
Wherein dt represents the derivation of t; f represents a frequency;
the substitute data s (t) is composed of
Figure FDA0003541897050000033
Generating; wherein the content of the first and second substances,
Figure FDA0003541897050000034
is in the range of [ - π, π]Uniformly distributed random phases for ensuring that s (t) and x (t) have the same fourier transform magnitude;
the stationarity of the signal is judged by comparing the similarity degree of the frequency spectrums at different time points; the distance of the spectrum from the average of the spectrum at different points in time is defined as:
Figure FDA0003541897050000035
Figure FDA0003541897050000036
in the formula: symbol'<>"means averaging; k represents the distance of the spectrum from the average value of the spectrum at different time points; sx,KRepresenting a power spectral density function; k represents the order; (t)nMeans time points, °); t is tnRepresents the nth time, wherein N ═ 1,2, …, N "; by degree representing the phase of signal x (t)
Figure FDA0003541897050000037
N "represents the length of signal x (t);
distance of frequency spectrum from average value of frequency spectrum at different time points
Figure FDA0003541897050000038
Is defined as:
Figure FDA0003541897050000039
wherein the symbols "" represent the normalization functions of the corresponding functions; g (f) represents a power spectral density function; h (f) represents a Hermite polynomial;
Figure FDA0003541897050000041
a normalization function representing a power spectral density function, namely:
Figure FDA0003541897050000042
Figure FDA0003541897050000043
a normalization function representing a Hermite polynomial, namely:
Figure FDA0003541897050000044
f represents a frequency;
Figure FDA0003541897050000045
fluctuation with time theta1Is defined as
Figure FDA0003541897050000046
The variance of (a), namely:
Figure FDA0003541897050000047
of substitution data s (t) determined above
Figure FDA0003541897050000048
The fluctuation with time is denoted as Θ0By comparison of theta1And Θ0Determining the stability of the structural vibration signal of the final plate measuring point; i.e. theta0The probability density function of (c) is denoted as f (Θ)0) Setting a threshold gamma, if f (theta)0) If the gamma is less than gamma, judging the signal to be an unsteady random signal; if f (theta)0) If the signal is more than gamma, judging the signal to be an unsteady random signal; if a certain section f (theta) of the input vibration signal data0) < gamma, another segment f (theta)0) If the signal is more than gamma, judging that the signal contains both steady-state and unsteady-state random signals;
step four, determining an analysis method of the input signal according to the property of the vibration input signal and analyzing the input signal:
4.1 if the final structural vibration signal of the plate measuring point is a steady-state signal, analyzing by adopting a method combining partial coherence analysis and metal plate contribution:
the self-power spectral density function of all vibration input signals is: gjj·r！＝Gjj·(r-1)！-|Lrj|2Grr·(r-1)！；
Wherein G isjj·(r-1)！Structure vibration input signal x independent of each other in terms of representing condition inputj(t) removal of x(r-1)(t) to xj(t) the self-power spectral density after correlation; l isrjRepresenting an optimal frequency response function of the multi-input single-output system when the condition is input; grr·(r-1)！Structure vibration input signal x independent of each other in terms of representing condition inputr(t) removal of x(r-1)(t) to xr(t) the correlated contribution self-power spectral density; r represents the total number of vibration input signals; j represents the jth structural vibration input signal, where j is 1, 2.
Then, the self spectrum of the vibration input signals and the cross spectrum between each input signal and the vibration input signals are solved one by one, and the obtained partial coherence function expression is as follows:
Figure FDA0003541897050000051
wherein the content of the first and second substances,
Figure FDA0003541897050000052
representing structural vibration input signal xi(t) and output signal y (t) removing x(r-1)(t) magnitude of partial coherence function after correlation with y (t); gamma ray2(f) Representing the magnitude of the partial coherence function; i denotes the ith structural vibration input signal, where i ═ 1, 2.., r; y represents the output signal y (t);
the partial coherence function for accurately calculating the contribution of each vibration input signal to the sound pressure output signal through an iterative algorithm is as follows:
Figure FDA0003541897050000053
wherein: gii·(i-1)！(f) Is xi(t) removal of x(i-1)(t) to xi(t) conditioned self-spectra; gyy·(i-1)！(f) Is y (t) by removing x(i-1)(t) a conditional self-spectrum after influence on y (t), y (t) representing the output signal; giy·(i-1)！(f) Inputting a signal x for structural vibrationi(t) and output signal y (t) removing x(r-1)After the relevant influence of (t) on y (t), xi(t) and y (t) are conditional cross spectra; l isijExpressing the optimal frequency response function of the multi-input single-output system;
4.2 if the final structural vibration signal of the plate measuring point is an unsteady state signal, adopting a method combining wavelet coherence analysis and metal plate contribution:
selecting non-orthogonal Morlet wavelet basis functions, the definition of the non-orthogonal Morlet wavelet basis functions in time domain and frequency domain being:
Figure FDA0003541897050000054
wherein the center frequency omega0Taking 6; t represents time;
then, using wavelet coherence to describe the local correlation degree of the two unsteady signals in the region with energy common concentration, and giving the amplitude relation and the phase relation of the time-frequency domain, defining the wavelet coherence spectrum of the two unsteady signals x (t) and y (t) as follows:
Figure FDA0003541897050000061
the above formula represents the amplitude cross product | S (l) between two non-steady-state signals at a certain frequency-1Wn XY(l))2With the respective amplitude products S (l) of the two signals-1|Wn X(l)|2)·S(l-1|Wn Y(l)|2) The ratio of (A) to (B); wherein S is a smoother, and the expression is: s (W) ═ SS(St(Wn(l) ); wherein S istIndicating smoothing on the time axis; sSIs shown in scaleSmoothing on the shaft; the smoothing function is embodied as
Figure FDA0003541897050000062
And SS(W)＝Wn(l)×c2Π (0.6 l); wherein, c1And c2Are all normalized coefficients; Π is a rectangular function; t is time; rn 2(l) Representing the magnitude of the correlation between two non-stationary signals; n marks the wavelet coherence spectrum of two non-stationary signals x (t) and y (t) using non-orthogonal Morlet wavelet basis functions; l represents a scale factor of the continuous wavelet transform; wn XY(l) Represents the cross wavelet power spectrum of two non-stationary signals x (t) and y (t); x represents an unsteady state input signal X (t); y represents an unsteady state output signal Y (t); wn X(l) A continuous wavelet transform representing the input signal x (t); wn Y(l) A continuous wavelet transform representing an input signal y (t);
carrying out wavelet coherence processing on an unsteady input signal x (t) and an output signal y (t) through a wavelet coherence spectrum formula, then calculating and solving a wavelet coherence coefficient graph and a phase graph between the unsteady input signal x (t) and the output signal y (t), merging the wavelet coherence coefficient graph and the phase graph to obtain a wavelet coherence time-frequency graph between the two signals, and then testing the two signals under a preset confidence level by adopting a Monte Carlo method; if the detection is qualified, the obtained wavelet coherence time-frequency diagram is adopted, and if the detection is unqualified, the signal data and the calculation process need to be checked for errors, so that the accuracy and reliability of the power spectrum calculation result are ensured;
4.3 if the original structure vibration input signal of the determined plate measuring point contains both steady-state and unsteady-state signals, comprehensively analyzing the input signal; firstly, a method of combining the partial coherence analysis and the contribution of the metal plate is adopted for a steady-state signal to obtain a partial coherence function of the contribution of each vibration input signal to a sound pressure output signal; then, a wavelet coherence time-frequency diagram among all vibration signals is obtained by adopting the method of combining the wavelet coherence analysis and the metal plate contribution amount on the unsteady-state signals;
and step five, drawing a coherence coefficient graph and drawing a coherence coefficient graph according to a result obtained by analyzing the input signal, namely drawing the coherence coefficient graph according to a partial coherence function and a wavelet coherence time-frequency graph, determining a plate with the largest contribution to structural vibration and noise, and completing the whole coherence analysis overall process.
2. The method for coherently analyzing vibration correlation characteristics of a low-frequency structure according to claim 1, wherein in the second step, the frequency response function curve of each plate structure is obtained by a hammering method.
3. The method for coherently analyzing the vibration correlation characteristics of a low-frequency structure according to claim 1, wherein in the third step, the input of the signal adopts a multi-input single-output system, and the multi-input single-output system automatically determines the type of the signal according to the characteristics of the signal, that is, the type of the signal is a steady-state signal, a non-steady-state signal, and the signal contains both steady-state and non-steady-state signals.
4. The coherent analysis method for the low-frequency structural vibration correlation characteristics according to claim 1, wherein in the third step, a magnitude sequence is performed on the structural vibration signals of the final plate measurement points by using a constant coherence function method, and the specific steps are as follows: firstly, calculating a constant coherence function between every two input signals, drawing the constant coherence function obtained by solving in a coordinate system, calculating the area enclosed by the constant coherence function and a coordinate axis in a concerned frequency band, determining the priority according to the size of the area, wherein the larger the area is, the more the ranking is, otherwise, the more the ranking is, and ranking all the input signals from high to low according to the priority.
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