CN115791052A - Multi-input multi-output non-stationary random vibration environment test system and control method - Google Patents
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Abstract
The invention discloses a multi-input multi-output non-stationary random vibration test system and a control method. The control method comprises the steps of setting reference information, generating a pseudo-reference random signal and a reference non-stationary signal, generating a driving signal through a frequency domain inverse system, and responding to the non-stationary random vibration signal by a vibration test subsystem. According to the multi-input multi-output non-stable random vibration test system and the control method, good control over the power spectral density and the kurtosis can be achieved at the same time, a real engineering environment is simulated accurately, the test conditions are closer to the actual engineering conditions, and the test results have practical reference significance.
Description
Technical Field
The invention belongs to the technical field of mechanical vibration environment tests, and particularly relates to a multi-input multi-output non-stationary random vibration test system and a control method.
Background
The environmental test is to reproduce the actual working environment, boundary and load of the product through ground tests such as static force, vibration, comprehensive environment, aerodynamic heat and the like, so as to predict, verify and verify the mechanical and thermal properties and reliability of the product, and provide a basis for design verification, improvement and optimization of the product.
In most cases, the real vibration environment in practical engineering is random, and at this time, a random vibration environment test is indispensable for testing the reliability, safety and comfort of products under random excitation. The random vibration environment test can be divided into a single-input single-output vibration test and a multiple-input multiple-output vibration test. The multiple-input multiple-output vibration test can simulate a more complex vibration environment. The random vibration environment test can be divided into a stationary random vibration test and a non-stationary random vibration test according to the type of the random signal. At present, signals reproduced by random vibration tests are mainly smooth Gaussian signals, however, in practical engineering application, many random vibration environments are not smooth. The stable signal is greatly different from the vibration environment of the actual engineering, so that the simulated test is far from the actual engineering application.
Disclosure of Invention
The invention aims to solve the technical problem of providing a multi-input multi-output non-stationary random vibration test system and a control method thereof, and the system and the method can provide a non-stationary random signal generation method and a non-stationary random signal control strategy matched with the non-stationary random signal generation method for use, so that a random vibration test is closer to a real engineering environment.
In order to realize the purpose, the invention adopts the following technical scheme:
a multi-input multi-output non-stationary random vibration test system comprises a digital control subsystem, a digital signal generation and acquisition subsystem and a vibration test subsystem. The vibration test subsystem is connected to the digital control subsystem through the digital signal generation and acquisition subsystem. The digital subsystem is implemented by a computer that includes an algorithm module. The digital signal generation and acquisition subsystem comprises a control module, a signal input module and a signal output module, wherein the control module is connected with the computer, and the signal input module and the signal output module are both connected with the control module. The vibration test subsystem comprises an excitation device, a power amplifier, an acceleration sensor, a clamp and a test piece.
Further, the method for controlling the multi-input multi-output non-stationary random vibration signal adopted by the algorithm module comprises the following steps:
1) Setting reference information including setting reference spectrum S rr And a reference kurtosis. To S rr Cholesky decomposition was performed:
wherein the superscript H represents the complex conjugate transpose.
2) Adding random phase to obtain the frequency spectrum of the required reference pseudo-random signal x (t):
X＝LΘ(44)
wherein L is a spectrum correction matrix, and the initial L before being corrected is L r (ii) a Θ is a random phase matrix, and is as follows:
wherein, theta i (i =1,2, \ 8230;, n) is a value in the range [ - π, π]And n is the number of control points in the experiment.
3) The inverse fourier transform of the signal spectrum X yields the desired reference pseudo-random signal X (t), and an appropriate amplitude modulation function a (t) is selected from the reference kurtosis, where the parameter t represents the time series of the signal.
4) Calculating the frequency spectrum of each frame of driving signal by a frequency domain inverse system method:
D i ＝ZX i (46)
wherein D is i For the ith frame drive signal spectrum, Z is the impedance matrix of the test system, X i For reference to pseudo-random signal x for ith frame i (t) a signal spectrum obtained by Fourier transform. To D i Performing inverse Fourier transform to obtain the required driving signal d for each frame i (t)。
5) By means of an improved time-domain randomization method,generating a reference non-stationary random signal x with time-varying root mean square value and controllable kurtosis Ref-NS And (t), obtaining the non-stationary driving signal d (t) required by the test through the frequency domain inverse system in the step 4). Generating a reference stationary random signal x by a classical time domain randomization method Ref-S (t)。
6) The driving signal d (t) is output through the signal output module and drives the vibration of the vibration test subsystem to control the vibration of the test object.
7) And acquiring a vibration response signal y by using the acceleration sensor and the signal input module.
8) And extracting a non-stationary envelope of the acquired vibration response signal. The non-stationary envelope of the vibration response signal is defined as:
x e ＝x Ref-NS -x Refs-S (47)
the resulting stationary signal is:
y st ＝y-x e (48)
response power spectral density is then calculated:
S yy ＝YY H (49)
wherein Y is a stationary signal Y st The superscript H represents the complex conjugate transpose.
9) And carrying out dual control on the non-stationary characteristic and the stationary characteristic of the acquired response signal. The non-stationary characteristic is controlled by adjustment of the amplitude modulation function. And controlling the stationary characteristic of the response signal, namely controlling the power spectral density of the non-stationary random signal after envelope extraction, wherein the algorithm for controlling the response signal adopts the algorithm for controlling the response signal by matrix power. Response spectral density S to stationary signals yy Performing Cholesky decomposition:
calculating a correction matrix delta:
10 ) judging the error between the power spectral density and the kurtosis and the target value, if so, quitting the control, otherwise, continuing to correct, and entering the step 11).
11 Calculate a new spectral modification matrix:
L new ＝Δ η L (52)
wherein eta is convergence power exponent, and can control convergence rate, and has a value range of (0,1)]. Will calculate the obtained L new And replacing to the step 2), calculating a new driving signal.
Further, the improved time domain randomization method is as follows: and introducing an amplitude modulation function, and controlling the non-stationary characteristic of the generated signal by adjusting the statistical characteristic of the amplitude modulation function. According to the improved time domain randomization principle, the generated non-stationary random signal expression can be obtained:
wherein A is i (t) is an amplitude modulation function, w i (t) is a window function and l is a superposition factor. Generated non-stationary random signal x Ref-NS The kurtosis formula of (t) is:
wherein K x For the kurtosis of the pseudo-random signal x (t), the coefficients a, b, c are defined as:
where T is the time length of the pseudo-random signal x (T). When the three parameters of the amplitude modulation function, the window function and the superposition factor are determined, the coefficients a, b, c will be constant, so that the pseudo-random signal x (t) and the generated true random signal x will be constant Ref-NS The kurtosis relationship between (t) is linear.
Let the superposition factor be 2 (l = 2), which is also for the sake of superposition. The kurtosis of a sufficiently long non-stationary random signal generated can also be further reduced to:
K NS ＝αK A K x +β(58)
in the above formula K A For the kurtosis of the amplitude modulation function, the coefficients α and β are defined as:
a method for controlling a multi-input multi-output non-stationary random vibration signal by adopting the test system comprises the following steps:
1) Setting reference information including setting reference spectrum S rr And a reference kurtosis. To S rr Performing Cholesky decomposition:
wherein the superscript H represents the complex conjugate transpose.
2) Adding random phase to obtain the frequency spectrum of the required reference pseudo-random signal x (t):
X＝LΘ(65)
wherein L is a spectrum correction matrix, and the initial L before being corrected is L r (ii) a Θ is a random phase matrix, and is as follows:
wherein, theta i (i =1,2, \ 8230;, n) is a value in the range [ - π, π]And n is the number of control points in the experiment.
3) The inverse fourier transform of the signal spectrum X yields the desired reference pseudo-random signal X (t), and an appropriate amplitude modulation function a (t) is selected from the reference kurtosis, where the parameter t represents the time series of the signal.
4) Calculating the frequency spectrum of each frame of driving signal by a frequency domain inverse system method:
D i ＝ZX i (67)
wherein D is i For the ith frame drive signal spectrum, Z is the impedance matrix of the test system, X i For reference to pseudo-random signal x for ith frame i (t) a signal spectrum obtained by Fourier transform. To D i Performing inverse Fourier transform to obtain the required driving signal d for each frame i (t)。
5) Generating a reference non-stationary random signal x with time-varying root mean square value and controllable kurtosis by an improved time domain randomization method Ref-NS And (t), obtaining the non-stationary driving signal d (t) required by the test through the frequency domain inverse system in the step 4). Generating a reference stationary random signal x by a classical time domain randomization method Ref-S (t)。
6) The driving signal d (t) is output through the signal output module to drive the vibration control test object of the vibration test subsystem to vibrate.
7) And acquiring a vibration response signal y by using the acceleration sensor and the signal input module.
8) And extracting a non-stationary envelope of the acquired vibration response signal. The non-stationary envelope of the vibration response signal is defined as:
x e ＝x Ref-NS -x Refs-S (68)
the resulting stationary signal is:
y st ＝y-x e (69)
response power spectral density is then calculated:
S yy ＝YY H (70)
wherein Y is a stationary signal Y st The superscript H represents the complex conjugate transpose.
9) And carrying out dual control of non-stationary characteristic and stationary characteristic on the acquired response signal. The non-stationary characteristic is controlled by adjustment of the amplitude modulation function. And controlling the stationary characteristic of the response signal, namely controlling the power spectral density of the non-stationary random signal after envelope extraction, wherein the algorithm for controlling the response signal adopts the algorithm for controlling the response signal by matrix power. Response spectral density S to stationary signals yy Cholesky decomposition was performed:
calculating a correction matrix delta:
10 ) determining the power spectral density and the error between the kurtosis and the target value, if the power spectral density and the kurtosis reach the target value, exiting the control, otherwise, continuing to correct, and entering the step 11).
11 Calculate a new spectral modification matrix:
L new ＝Δ η L (73)
where η is the convergence power exponent, canThe convergence rate is controlled to be in the range of (0, 1)]. Will calculate the obtained L new And replacing to the step 2), calculating a new driving signal.
Further, the improved time domain randomization method is as follows: and introducing an amplitude modulation function, and controlling the non-stationary characteristic of the generated signal by adjusting the statistical characteristic of the amplitude modulation function. According to the improved time domain randomization principle, the generated non-stationary random signal expression can be obtained:
wherein A is i (t) is an amplitude modulation function, w i (t) is a window function and l is a superposition factor. Generated non-stationary random signal x Ref-NS The kurtosis formula of (t) is:
wherein K x For the kurtosis of the pseudo-random signal x (t), the coefficients a, b, c are defined as:
where T is the time length of the pseudo-random signal x (T). When the three parameters of the amplitude modulation function, the window function and the superposition factor are determined, the coefficients a, b, c will be constant, so that the pseudo-random signal x (t) and the generated true random signal x Ref-NS The kurtosis relationship between (t) is linear.
Let the superposition factor be 2 (l = 2), which is also for the sake of superposition. The kurtosis of a sufficiently long non-stationary random signal generated can also be further reduced to:
K NS ＝αK A K x +β(79)
in the above formula K A For the kurtosis of the amplitude modulation function, the coefficients α and β are defined as:
according to the multi-input multi-output non-stable random vibration test system and the control method, good control over the power spectral density and the kurtosis can be achieved at the same time, a real engineering environment is simulated accurately, the test conditions are closer to the actual engineering conditions, and the test results have practical reference significance.
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FIG. 1 is a flow chart of the operation of a multi-input multi-output non-stationary random vibration test system according to the present invention;
FIG. 2 is a block diagram of a flow chart of a multi-input multi-output non-stationary random vibration test method of the present invention;
FIG. 3 is a block diagram of a multi-input multi-output non-stationary random vibration testing system according to an embodiment of the present invention;
FIG. 4 is a graph illustrating the effect of controlling the power spectral density in response to a non-stationary random signal in the X control direction according to an embodiment of the present invention;
FIG. 5 is a graph illustrating the effect of controlling the power spectral density in response to non-stationary random signals in the Y control direction according to an embodiment of the present invention;
FIG. 6 is a graph illustrating the effect of kurtosis control in response to non-stationary random signals in the X and Y control directions according to an embodiment of the present invention.
Detailed Description
The following describes a multi-input multi-output non-stationary random vibration test system and a test algorithm in detail with reference to the accompanying drawings. In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper", "lower", "bottom", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
This example shows a two-input two-output non-stationary random vibration control test.
As shown in fig. 1 and 3, in the present embodiment, a table top of a Shinken G-6080-3HT-020 triaxial vibration table is used as a non-stationary random vibration test object, and a VXI signal sending and collecting system and a computer are used to analyze and process a non-stationary response signal, so as to realize non-stationary random vibration control.
The Shinken G-6080-3HT-020 triaxial shaker is a small, motorized shaker capable of providing simultaneous X, Y and Z translation. The size of the vibration table is 0.2 multiplied by 0.2m, the frequency range is 5-1000Hz, and the maximum displacement is 20mm. The maximum load of the vibration table is 20kg, and the maximum acceleration in no load is 52.9m/s 2 The maximum acceleration at 20kg full load was 22.6m/s 2 . Agilent VXI signal sending and collecting systemThe method mainly comprises the following three parts: EX2500A, VT1436 and VT 1434A. The EX2500A is connected with a computer through a network cable, the data transmission speed can reach 40MB/s, the computer can process data quickly, and the information interaction between a data acquisition module in a VXI signal sending and acquisition system and the computer is played.
VT1436 is a data acquisition board card, which has a total of 16 acquisition channels. The board card has a certain DSP function, and can play roles in conditioning sensor signals, anti-mixing filtering and the like. VT1436 also has 32MB FIFO memory, which buffers consecutive signals, thus preventing data loss.
VT1434A is a signal source board card in VXI, with 4 signal source channels. The VT1434A carries many signal source patterns, including random and sinusoidal patterns. Meanwhile, the signal source mode can also be set as a self-defined signal, and the mode is adopted in random vibration control tests, so that a specified driving signal can be sent.
The table top of the triaxial vibration table is taken as a vibration control test object, and the directions of the response control points are the horizontal X and Y directions on the table top of the vibration table.
As shown in FIG. 2, the test mainly comprises the following steps:
1. and setting reference information of a non-stationary random vibration control test. Wherein the reference information comprises a reference spectrum and a reference kurtosis. In this example, the frequency bandwidth of the control is 20-2000Hz, the alarm limit of the reference spectrum is set to + -3 dB, the parking limit is set to + -6 dB, and the amplitude modulation function distribution satisfies zero mean Gaussian distribution.
2. And measuring a frequency response function matrix of the vibration control test object. H in method for estimating frequency response function matrix of control test object from frequency response function 1 And the estimation method is used for storing the measured frequency response function matrix for subsequently generating a driving signal required in the vibration control test.
3. The test was started. The amplitude modulation function is added to generate the non-stationary drive signal required for the test, which in this example is then applied to both the X and Y directions of the table top of the tri-axial vibration table.
4. Acceleration signals of two control directions of the table top of the vibration table are acquired through the acceleration sensor. And transmitting the acquired non-stationary response signals to a computer control system for analysis and processing, and simultaneously controlling the power spectral density and the kurtosis of the non-stationary response signals.
5. And judging errors between the power spectrum and the kurtosis and the target value, if the errors do not meet the requirement of test control, continuing to perform iterative control, and if not, quitting the control.
The control effect of the multi-axis non-stationary random vibration control test of the present example is shown in fig. 4 to 6. In fig. 4 and 5, the solid line at the outermost side represents a parking limit of ± 6dB of the reference spectrum, the dotted line at the second outer side represents an alarm limit of ± 3dB, the dotted line at the middle is a reference line, and the solid line is a response power line, and it can be seen from the figures that the lines of the response power spectrum in both directions of the vibration table are within the alarm limit of ± 3dB of the reference spectrum, and the control effect is very good. As can be seen from FIG. 6, the kurtosis of the non-stationary signal in response in two directions of the vibration table is completely controlled near the kurtosis value of the target in the control iteration process, and the fluctuation is very small.
Based on the description of the preferred embodiments of the present invention, it should be clear that the invention as defined by the appended claims is not limited to the specific details set forth in the above description, but that many obvious modifications thereof are possible without departing from the spirit or scope thereof.
Claims (5)
1. A multi-input multi-output non-stationary random vibration test system is characterized by comprising a digital control subsystem, a digital signal generation and acquisition subsystem and a vibration test subsystem; the vibration testing subsystem is connected to the digital control subsystem through the digital signal generating and collecting subsystem; the digital subsystem is implemented by a computer, the computer including an algorithm module; the digital signal generating and collecting subsystem comprises a control module, a signal input module and a signal output module, the control module is connected with the computer, and the signal input module and the signal output module are both connected with the control module; the vibration test subsystem comprises an excitation device, a power amplifier, an acceleration sensor, a clamp and a test piece.
2. The multiple-input multiple-output non-stationary random vibration testing system according to claim 1, wherein the method for controlling the multiple-input multiple-output non-stationary random vibration signal employed by the algorithm module comprises the steps of:
1) Setting reference information including setting reference spectrum S rr And a reference kurtosis; to S rr Cholesky decomposition was performed:
wherein, the superscript H represents complex conjugate transpose;
2) Adding random phase to obtain the frequency spectrum of the required reference pseudo-random signal x (t):
X＝LΘ (2)
wherein L is a spectrum correction matrix, and the initial L before being corrected is L r (ii) a Θ is a random phase matrix, and is as follows:
wherein, theta i (i =1,2, \8230;, n) is in the range of [ - π, π]N is the number of control points of the test;
3) Performing inverse Fourier transform on a signal frequency spectrum X to obtain a required reference pseudo-random signal X (t), and selecting a proper amplitude modulation function A (t) according to a reference kurtosis, wherein a parameter t represents a time sequence of the signal;
4) Calculating the frequency spectrum of each frame of driving signal by a frequency domain inverse system method:
D i ＝ZX i (4)
wherein D is i For the ith frame drive signal spectrum, Z is the impedance matrix of the test system, X i For referencing pseudo-random signal x to ith frame i (t) performing a Fourier transform to obtain a signal spectrum; to D i Performing inverse Fourier transform on the signalTo obtain the required driving signal d for each frame i (t)；
5) Generating a reference non-stationary random signal x with time-varying root mean square value and controllable kurtosis by an improved time domain randomization method Ref-NS (t), obtaining a non-stationary driving signal d (t) required by the test through the frequency domain inverse system in the step 4); generating a reference stationary random signal x by a classical time domain randomization method Ref-S (t)；
6) The driving signal d (t) is output through the signal output module and drives the vibration of the vibration test subsystem to control the vibration of the test object;
7) Collecting a vibration response signal y by using an acceleration sensor and a signal input module;
8) Extracting non-stationary envelope of the collected vibration response signal; the non-stationary envelope of the vibration response signal is defined as:
x e ＝x Ref-NS -x Refs-S (5)
the resulting stationary signal is:
y st ＝y-x e (6)
response power spectral density is then calculated:
S yy ＝YY H (7)
wherein Y is a stationary signal Y st The superscript H represents the complex conjugate transpose;
9) Carrying out dual control of non-stationary characteristic and stationary characteristic on the collected response signal; the non-stationary characteristic is controlled by adjusting an amplitude modulation function; controlling the stationary characteristic of the response signal, namely controlling the power spectral density of the non-stationary random signal after envelope extraction, wherein the algorithm for controlling the response signal adopts the algorithm for controlling the response signal by matrix power; response spectral density S to stationary signals yy Cholesky decomposition was performed:
calculating a correction matrix delta:
10 Judging the error between the power spectral density and the kurtosis and the target value, if so, exiting the control, otherwise, continuing to correct, and entering the step 11);
11 Calculate a new spectral modification matrix:
L new ＝Δ η L (10)
wherein eta is convergence power exponent, and can control convergence rate, and has a value range of (0,1)](ii) a Will calculate the obtained L new And replacing to the step 2), calculating a new driving signal.
3. The multiple-input multiple-output non-stationary random vibration testing system according to claim 1, wherein said improved time-domain randomization method is: introducing an amplitude modulation function, and controlling the non-stationary characteristic of a generated signal by adjusting the statistical characteristic of the amplitude modulation function; according to an improved time domain randomization principle, obtaining a generated non-stationary random signal expression:
wherein A is i (t) is an amplitude modulation function, w i (t) is a window function, l is a superposition factor; generated non-stationary random signal x Ref-NS The kurtosis formula of (t) is:
wherein K x For the kurtosis of the pseudo-random signal x (t), the coefficients a, b, c are defined as:
wherein T is the time length of the pseudo-random signal x (T); when the three parameters of the amplitude modulation function, the window function and the superposition factor are determined, the coefficients a, b, c will be constant, so that the pseudo-random signal x (t) and the generated true random signal x Ref-NS (t) the kurtosis relationship between is linear;
let the superposition factor be 2 (l = 2), which is also for convenience of superposition; the kurtosis of a sufficiently long non-stationary random signal generated can also be further reduced to:
K NS ＝αK A K x +β (16)
in the above formula K A For the kurtosis of the amplitude modulation function, the coefficients α and β are defined as:
4. a method of controlling a multiple-input multiple-output non-stationary random vibration signal for use in the testing system of claim 1, comprising the steps of:
1) Setting reference information including setting reference spectrum S rr And a reference kurtosis; to S rr Performing Cholesky decomposition:
wherein, the superscript H represents complex conjugate transpose;
2) Adding random phase to obtain the frequency spectrum of the required reference pseudo-random signal x (t):
X＝LΘ (23)
wherein L is a spectrum correction matrix, and the initial L before being corrected is L r (ii) a Θ is a random phase matrix, and is as follows:
wherein, theta i (i =1,2, \ 8230;, n) is a value in the range [ - π, π]N is the number of control points of the test;
3) Carrying out inverse Fourier transform on a signal frequency spectrum X to obtain a required reference pseudo-random signal X (t), and selecting a proper amplitude modulation function A (t) according to a reference kurtosis, wherein a parameter t represents a time sequence of the signal;
4) Calculating the frequency spectrum of each frame of driving signal by a frequency domain inverse system method:
D i ＝ZX i (25)
wherein D is i For the ith frame drive signal spectrum, Z is the impedance matrix of the test system, X i For reference to pseudo-random signal x for ith frame i (t) performing a Fourier transform to obtain a signal spectrum; to D i Performing inverse Fourier transform to obtain the required driving signal d for each frame i (t)；
5) Generating a reference non-stationary random with time-varying root mean square value and controllable kurtosis by an improved time domain randomization methodSignal x Ref-NS (t), obtaining a nonstationary driving signal d (t) required by the test through the frequency domain inverse system in the step 4); generating a reference stationary random signal x by a classical time domain randomization method Ref-S (t)；
6) The driving signal d (t) is output through the signal output module and drives the vibration of the vibration test subsystem to control the vibration of the test object;
7) Collecting a vibration response signal y by using an acceleration sensor and a signal input module;
8) Extracting non-stationary envelope of the collected vibration response signal; the non-stationary envelope of the vibration response signal is defined as:
x e ＝x Ref-NS -x Refs-S (26)
the resulting stationary signal is:
y st ＝y-x e (27)
response power spectral density is then calculated:
S yy ＝YY H (28)
wherein Y is a stationary signal Y st The superscript H represents the complex conjugate transpose;
9) Carrying out dual control of non-stationary characteristic and stationary characteristic on the collected response signal; the non-stationary characteristic is controlled by adjusting an amplitude modulation function; controlling the stationary characteristic of the response signal, namely controlling the power spectral density of the non-stationary random signal after envelope extraction, wherein the algorithm for controlling the response signal adopts the algorithm for controlling the response signal by matrix power; response spectral density S to stationary signals yy Performing Cholesky decomposition:
calculating a correction matrix delta:
10 Judging the error between the power spectral density and the kurtosis and the target value, if so, quitting the control, otherwise, continuing to correct, and entering the step 11);
11 Calculate a new spectral modification matrix:
L new ＝Δ η L (31)
wherein eta is convergence power exponent, and can control convergence rate, and has a value range of (0,1)](ii) a Will calculate the obtained L new And replacing to the step 2), calculating a new driving signal.
5. The method of controlling a multiple-input multiple-output non-stationary random vibration signal as claimed in claim 4, wherein said improved time domain randomization method is: introducing an amplitude modulation function, and controlling the non-stationary characteristic of a generated signal by adjusting the statistical characteristic of the amplitude modulation function; according to an improved time domain randomization principle, obtaining a generated non-stationary random signal expression:
wherein A is i (t) is an amplitude modulation function, w i (t) is a window function, l is a superposition factor; generated non-stationary random signal x Ref-NS The kurtosis formula of (t) is:
wherein K x For the kurtosis of the pseudo-random signal x (t), the coefficients a, b, c are defined as:
wherein T is the time length of the pseudo-random signal x (T); when the three parameters of the amplitude modulation function, the window function and the superposition factor are determined, the coefficients a, b, c will be constant, so that the pseudo-random signal x (t) and the generated true random signal x will be constant Ref-NS (t) the kurtosis relationship between is linear;
let the superposition factor be 2 (l = 2), which is also for convenience of superposition; the kurtosis of a sufficiently long non-stationary random signal generated can also be further reduced to:
K NS ＝αK A K x +β (37)
in the above formula K A For the kurtosis of the amplitude modulation function, the coefficients α and β are defined as:
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|---|---|---|---|---|
| CN117191311A (en) * | 2023-08-14 | 2023-12-08 | 暨南大学 | Accelerated vibration test method for product under non-stationary and non-Gaussian vibration of logistics |
| CN117191311B (en) * | 2023-08-14 | 2024-05-24 | 暨南大学 | Accelerated vibration test method for product under non-stationary and non-Gaussian vibration of logistics |
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2022
- 2022-12-20 CN CN202211639292.4A patent/CN115791052A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117191311A (en) * | 2023-08-14 | 2023-12-08 | 暨南大学 | Accelerated vibration test method for product under non-stationary and non-Gaussian vibration of logistics |
| CN117191311B (en) * | 2023-08-14 | 2024-05-24 | 暨南大学 | Accelerated vibration test method for product under non-stationary and non-Gaussian vibration of logistics |
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