CN113776764B - Random vibration acceleration test excitation signal generation method based on kurtosis transfer rule - Google Patents
Random vibration acceleration test excitation signal generation method based on kurtosis transfer rule Download PDFInfo
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Abstract
The invention relates to a random vibration acceleration test excitation signal generation method based on a kurtosis transfer rule, which comprises the following steps: obtaining the natural frequency and damping ratio of the test structure; calculating half-power bandwidth of the structure based on the natural frequency and the damping ratio, and obtaining PSD of vibration excitation of the structure; generating a stationary gaussian excitation signal having the same PSD as the vibration excitation using inverse fourier transform; setting the response kurtosis required by the structure; selecting a corresponding bandwidth in the excitation signal based on the natural frequency and the half-power bandwidth of the structure, and modulating the phase in the bandwidth until the kurtosis value of the decomposition signal of the excitation signal in the corresponding bandwidth reaches a set response kurtosis; and performing inverse Fourier transform on the Fourier transform amplitude and the modulated phase in the full frequency band of the excitation signal, and generating the required vibration acceleration test excitation signal. The scheme enables the structural response of the vibration acceleration test to have the characteristic of high kurtosis, and the vibration acceleration test is high in efficiency.
Description
Technical Field
The invention relates to the technical field of product life and reliability, in particular to a random vibration acceleration test excitation signal generation method based on kurtosis transfer rules.
Background
With the continuous improvement of the reliability level of products, the service life evaluation of a product with long service life and high reliability becomes a troublesome problem. It is often difficult to do so in a short time if evaluated according to conventional life test techniques. In addition, due to the rapid development of science and technology, the speed of updating products is also continuously increased, and people hope to obtain life information of the products in a shorter time. Therefore, research on accelerated life test technology is particularly important.
In the aspect of product reliability test, a durability vibration test is a main means for checking whether a product structure can reach the expected service life under the action of a service dynamic environment. The actual service dynamic environment of the product is generally a random vibration environment, so that a random vibration acceleration test method is generally adopted in engineering to evaluate the vibration fatigue life of the product structure. When an excitation signal of a random vibration acceleration test is designed, the excited power spectral density PSD in the product service process is usually obtained first. Currently, in order to cause the same fatigue damage in a shorter time, the following 2 methods are generally adopted: the power spectral density PSD level of the whole vibration acceleration test excitation signal is increased proportionally on the basis of the power spectral density PSD level of the actual service vibration environment excitation signal, or the generated random excitation signal is changed into an ultra-high-intensity excitation signal from the Gaussian excitation signal by a kurtosis control method on the premise of keeping the power spectral density PSD spectrum shape of the actual service vibration environment unchanged. This is because numerous studies have shown that the kurtosis response signal can accelerate the vibration fatigue damage accumulation process of the structure.
For the method of increasing the magnitude of the actual excitation signal power spectral density PSD proportionally, if the magnitude of the excitation signal power spectral density PSD is increased too high, the product failure in the test can not be fatigue failure any more, and at the same time, the increase of the root mean square value of the excitation signal can lead to nonlinear response of the product, so that the fatigue damage model is inapplicable. An increase in the magnitude of the power spectral density PSD may result in loads below the fatigue limit that would otherwise not damage the product exceeding the fatigue limit of the product, thereby damaging the product such that the life expectancy is lower than the practical life expectancy.
In the method of changing the excitation signal into the ultra-high-intensity excitation by the kurtosis control, the method of generating the ultra-high-intensity excitation signal by the vibrating table by the kurtosis control can generate a larger amplitude of the excitation signal while keeping the power spectrum density unchanged, but the following problems also exist: firstly, sudden large-amplitude impact signals existing in ultra-high excitation can have a certain influence on the service life of a vibrating table; secondly, the non-Gaussian excitation generated by the kurtosis control method at present is generally a stable ultra-Gaussian excitation signal, and related documents show that the fatigue life of a product under the stable ultra-Gaussian excitation is not significantly different from that under the stable Gaussian excitation, and the root cause is that the kurtosis characteristic of the stable ultra-Gaussian excitation signal is not easily conducted to the dynamic response of a structure, so that the generated acceleration effect is limited.
Disclosure of Invention
The invention aims to provide a random vibration acceleration test excitation signal generation method.
In order to achieve the above object, the present invention provides a method for generating a random vibration acceleration test excitation signal based on kurtosis transfer rule, comprising:
s1, obtaining the natural frequency f and damping ratio xi of a test structure;
s2, calculating half-power bandwidth of the test structure based on the natural frequency f and the damping ratio xi;
s3, obtaining the power spectral density PSD of the vibration excitation actually applied to the test structure;
s4, generating a stable Gaussian excitation signal g (t) with the same power spectral density PSD as the vibration excitation actually applied to the test structure by using inverse Fourier transform;
s5, setting the required response kurtosis K of the test structure r ；
S6, based on the natural frequency f and the half-power bandwidth of the test structure, selecting phases in the half-power bandwidth of the stationary Gaussian excitation signal g (t) which is preset multiple times at the natural frequency of the test structure, and modulating until the kurtosis value of the decomposition signal of the stationary Gaussian excitation signal g (t) in the selected bandwidth reaches the set response kurtosis K r ；
S7, recombining the Fourier transform amplitude value in the full frequency range of the stable Gaussian excitation signal g (t) with the phase after the modulation process, and carrying out inverse Fourier transform to generate a required vibration acceleration test excitation signal a (t).
According to one aspect of the present invention, in step S6, in the step of selecting the phase of the stationary gaussian excitation signal g (t) within a half power bandwidth of a preset multiple at the natural frequency of the test structure for modulation, the preset multiple is 3 times.
According to one aspect of the invention, in step S5, a desired response kurtosis K of the test structure is set r In the step (a), the response kurtosis K is determined under the condition of ensuring that the test structure is subjected to fatigue failure without overstressing failure r Selecting a larger value within its allowable range, and the response kurtosis K r The larger the setting, the more remarkable the acceleration effect of random vibration.
According to one aspect of the present invention, in the step S2 of calculating the half-power bandwidth of the test structure based on the natural frequency f and the damping ratio ζ, a calculation formula based on the natural frequency f and the damping ratio ζ is expressed as:
W H ＝2ξf；
wherein W is H Representing the half power bandwidth of the test structure.
According to one aspect of the invention, in step S6, the phase of the stationary Gaussian excitation signal g (t) within a half-power bandwidth preset by a multiple at the natural frequency of the test structure is selected for modulation until the kurtosis value of the decomposed signal of the stationary Gaussian excitation signal g (t) within the selected bandwidth reaches the set response kurtosis K r In the step (a), after completing the modulation of the phase within the bandwidth, the kurtosis of the decomposed signal of the bandwidth is greater than or equal to the response kurtosis K r 。
According to one aspect of the invention, in step S5, the response kurtosis K r Greater than 3.
According to the scheme, from the time domain waveform characteristics, the acceleration test excitation signal generated by the method is similar to the stable Gaussian excitation signal, but the structural response of the vibration acceleration test can be ensured to have high kurtosis, so that the efficiency of the vibration acceleration test is effectively improved.
According to the scheme of the invention, the vibration fatigue acceleration excitation signal generated by the invention can not only keep the power spectral density PSD of the actual vibration excitation environment of the product, but also integrally present the characteristic of stable Gaussian in the time domain, can effectively protect the service life of the vibrating table, and can 'customize' the kurtosis of the response signal of the structure under the action of the vibration fatigue acceleration test excitation signal before the test, thereby ensuring that the high kurtosis response signal with the acceleration test effect can be generated, being beneficial to the accurate control of the vibration fatigue acceleration test and the calculation and analysis of the test result, and having good feasibility and wide application value.
According to the scheme, the random vibration acceleration test excitation signal generated based on the kurtosis transfer rule is close to a stable Gaussian signal from the aspect of the global signal characteristic, but the local high kurtosis characteristic of the excitation signal can be effectively transferred to the response signal, so that the acceleration test effect is effectively ensured.
Drawings
FIG. 1 is a block diagram schematically illustrating steps of a method for generating a random vibration acceleration test excitation signal according to one embodiment of the present invention;
FIG. 2 is a PSD plot schematically illustrating the power spectral density of an excitation signal according to one embodiment of the invention;
FIG. 3 is a graph schematically illustrating a stationary Gaussian excitation signal according to an embodiment of the invention;
FIG. 4 is a flow chart schematically illustrating phase modulation according to one embodiment of the present invention;
fig. 5 is a diagram schematically illustrating an acceleration test excitation signal generated after phase modulation according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the drawings and the specific embodiments, which are not described in detail herein, but the embodiments of the present invention are not limited to the following embodiments.
As shown in fig. 1, according to an embodiment of the present invention, a method for generating a random vibration acceleration test excitation signal based on a kurtosis transfer rule of the present invention includes:
s1, obtaining the natural frequency f and damping ratio xi of a test structure;
s2, calculating half-power bandwidth of the test structure based on the natural frequency f and the damping ratio xi,
s3, obtaining the power spectral density PSD of the vibration excitation actually applied to the test structure;
s4, generating a stable Gaussian excitation signal g (t) with the same power spectral density PSD as the vibration excitation actually applied to the test structure by using an inverse Fourier transform or other random signal generation methods;
s5, setting the required response kurtosis K of the test structure r ；
S6, based on the natural frequency and the half-power bandwidth of the test structure, selecting the phase (Fourier phase) in the half-power bandwidth of the stationary Gaussian excitation signal g (t) which is in the preset multiple of the natural frequency of the test structure, and modulating until the kurtosis value of the decomposition signal of the stationary Gaussian excitation signal g (t) in the selected bandwidth reaches the set response kurtosis K r ；
S7, recombining the Fourier transform amplitude in the full frequency range of the stable Gaussian excitation signal g (t) with the phase after the modulation process, and carrying out inverse Fourier transform to generate a required vibration acceleration test excitation signal a (t).
According to an embodiment of the present invention, in the step S2 of calculating the half-power bandwidth of the test structure based on the natural frequency f and the damping ratio ζ, a calculation formula based on the natural frequency f and the damping ratio ζ is expressed as:
W H ＝2ξf；
wherein W is H Representing the half power bandwidth of the test structure.
In step S3, the PSD refers to a power spectral density, which is a physical quantity characterizing the relation between the power energy and the frequency of the signal, according to an embodiment of the present invention. Which is often used in applications to study random vibration signals. Furthermore, the gaussian random vibration signal can be fully described since only one parameter of the power spectral density PSD. The method is also a reason for describing the test section by adopting a power spectral density function in various random vibration test standards at home and abroad at present. The power spectral density PSD, the amplitude probability density function PDF and the time history signal of a typical Gaussian random vibration signal are combined. From its time domain signal characteristics, it can be seen that the gaussian signal has a 99.74% amplitude distribution within ±3σ, which is a fundamental feature of the gaussian signal amplitude distribution.
In step S4, according to an embodiment of the present invention, in the step of generating the stationary gaussian excitation signal g (t) having the same power spectral density PSD as the vibration excitation using inverse fourier transform, the stationary gaussian excitation signal g (t) may also be generated by using another random signal generation method.
According to one embodiment of the present invention, in step S5, a required response kurtosis K of the test structure is set r In the step (a), under the condition that fatigue failure of a test structure is ensured without overstress failure, the response kurtosis K r Selecting a larger value within the allowable range and responding to the kurtosis K r The larger the setting, the more remarkable the acceleration effect of random vibration.
According to one embodiment of the present invention, in step S5, a required response kurtosis K of the test structure is set r In the step (a), response kurtosis K r Significantly greater than 3. In the present embodiment, the kurtosis is a numerical statistic reflecting the distribution characteristics of random variables, and is a 4-order cumulative amount. The kurtosis is equal to 3 and represents Gaussian distribution, the kurtosis is larger than 3 and represents ultra-high Gaussian distribution, and the kurtosis is smaller than 3 and represents sub-Gaussian distribution. The ultra-high-s distribution represents a signal with more and greater amplitude, so if the response kurtosis of a structure under an excitation signal can be significantly greater than 3 (i.e., more and greater amplitude can be present in the response signal), the structure will fail and break in a shorter time. Furthermore, in the scheme, the response kurtosis of the structure under the modulated excitation signal is obviously more than 3 by modulating the phase of the specific frequency band of the excitation signal so as to accelerate the fatigue failure of the structure and achieve the aim of accelerating the test, for example, the response kurtosis K r The optional settings are 4, 5, 6, 7, etc., and the corresponding settings can be made according to the needs.
According to an embodiment of the present invention, in the step S6, the preset multiple may be set to 3 times in the step of selecting the phase of the stationary gaussian excitation signal g (t) within the half-power bandwidth of the preset multiple at the natural frequency of the test structure for modulation.
According to one embodiment of the invention, in step S6, the phase of the stationary Gaussian excitation signal g (t) within a half-power bandwidth preset by a multiple at the natural frequency of the test structure is selected to be modulated until the kurtosis value of the decomposition signal of the stationary Gaussian excitation signal g (t) within the selected bandwidth reaches a set response kurtosis K r In the step (a), after completing the modulation of the phase within the bandwidth, the kurtosis of the decomposed signal of the bandwidth is greater than or equal to the response kurtosis K r 。
It should be noted that, the phase modulation refers to that the amplitude and the phase of the signal after being decomposed in the frequency domain can be obtained after the signal is subjected to fourier transformation, and in this scheme, the amplitude distribution characteristic of the excitation signal is changed by changing the phase (the amplitude is not changed, so as to ensure that the power spectral density PSD of the signal is not changed) so that the phase meets a certain condition.
According to one embodiment of the present invention, in the process of executing step S7, the effect achieved is that the fourier transform amplitude in the full frequency band of the stationary gaussian excitation signal g (t) is combined with the phase after the modulation process to perform the inverse fourier transform again, so as to generate the final acceleration test excitation signal a (t).
By the arrangement, from the time domain waveform characteristics, the acceleration test excitation signal generated by the method is similar to the stable Gaussian excitation signal, but the structural response can be ensured to have high kurtosis, so that the vibration acceleration test efficiency is effectively improved.
For further explanation of the present invention, the present embodiment is exemplified with reference to the accompanying drawings.
S1, obtaining a test structure with a natural frequency f of 40Hz and a damping ratio xi of 0.04;
s2, calculating half-power bandwidth W of test structure based on natural frequency f and damping ratio xi H Is 3.2Hz.
S3, obtaining the power spectral density PSD of the vibration excitation actually applied to the test structure, wherein the PSD is shown in FIG. 2;
s4, generating a stable Gaussian excitation signal g (t) with the same power spectral density PSD as the vibration excitation actually applied to the test structure by using inverse Fourier transform, wherein the signal g (t) is shown in FIG. 3;
s5, setting the required response kurtosis K of the test structure r 7 (note that the greater the acceleration effect it sets, the more pronounced it is, but provided that the structure is guaranteed to undergo fatigue failure without overstress failure);
s6, selecting corresponding bandwidths in the stable Gaussian excitation signals based on the natural frequency and the half-power bandwidth of the test structure, and modulating Fourier phases positioned in the bandwidths until kurtosis values of decomposition signals of the stable Gaussian excitation signals in the corresponding bandwidths reach set response kurtosis. In this embodiment, the phase of the stationary Gaussian excitation signal g (t) within the 3-half power bandwidth at the natural frequency of the test structure (i.e., the phase within 35.2-44.8 Hz) is continuously modulated until the kurtosis of the decomposed signal of the 3-half power bandwidth at the natural frequency of the test structure reaches the set response kurtosis K r See fig. 4;
in this embodiment, the kurtosis of the modulated decomposed signal is 7.30. It should be noted that the kurtosis of the decomposed signal increases after each modulation and the added value is different each time, so the kurtosis of the modulation is slightly larger than the kurtosis of the target.
S7, recombining the Fourier transform amplitude in the full frequency range of the stable Gaussian excitation signal g (t) with the phase after the modulation process and carrying out inverse Fourier transform to generate a required vibration acceleration test excitation signal a (t), as shown in FIG. 5. In this embodiment, the response kurtosis of the test structure at the acceleration test excitation signal a (t) is 7.37.
The foregoing is merely exemplary of embodiments of the invention and, as regards devices and arrangements not explicitly described in this disclosure, it should be understood that this can be done by general purpose devices and methods known in the art.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The method for generating the excitation signal of the random vibration acceleration test based on the kurtosis transfer rule comprises the following steps:
s1, obtaining the natural frequency f and damping ratio xi of a test structure;
s2, calculating half-power bandwidth of the test structure based on the natural frequency f and the damping ratio xi;
s3, obtaining the power spectral density PSD of the vibration excitation actually applied to the test structure;
s4, generating a stable Gaussian excitation signal g (t) with the same power spectral density PSD as the vibration excitation actually applied to the test structure by using inverse Fourier transform;
s5, setting the required response kurtosis K of the test structure r ；
S6, based on the natural frequency f and the half-power bandwidth of the test structure, selecting phases in the half-power bandwidth of the stationary Gaussian excitation signal g (t) which is preset multiple times at the natural frequency of the test structure, and modulating until the kurtosis value of the decomposition signal of the stationary Gaussian excitation signal g (t) in the selected bandwidth reaches the set response kurtosis K r ；
S7, recombining the Fourier transform amplitude value in the full frequency range of the stable Gaussian excitation signal g (t) with the phase after the modulation process, and carrying out inverse Fourier transform to generate a required vibration acceleration test excitation signal a (t).
2. The method for generating a random vibration acceleration test excitation signal according to claim 1, wherein in step S6, the phase of the stationary gaussian excitation signal g (t) within a half power bandwidth of a preset multiple at the natural frequency of the test structure is selected to be modulated, and the preset multiple is 3 times.
3. The method of generating a random vibration acceleration test excitation signal according to claim 2, wherein in step S5, a required response kurtosis K of the test structure is set r In the step (a), the response kurtosis K is determined under the condition of ensuring that the test structure is subjected to fatigue failure without overstressing failure r Selecting a larger value within its allowable range, and the response kurtosis K r The larger the setting, the more remarkable the acceleration effect of random vibration.
4. A random vibration acceleration test excitation signal generation method according to any one of claims 1 to 3, wherein in the step S2 of calculating a half power bandwidth of the test structure based on the natural frequency f and the damping ratio ζ, a calculation formula based on the natural frequency f and the damping ratio ζ is expressed as:
W H ＝2ξf；
wherein W is H Representing the half power bandwidth of the test structure.
5. A random vibration acceleration test excitation signal generation method according to any one of claims 1 to 3, characterized in that in step S6, phases in the stationary gaussian excitation signal g (t) within a half power bandwidth preset at the natural frequency of the test structure are selected for modulation until the kurtosis value of the decomposed signal of the stationary gaussian excitation signal g (t) within the selected bandwidth reaches the set response kurtosis K r In the step (a), after completing the modulation of the phase within the bandwidth, the kurtosis of the decomposed signal of the bandwidth is close to the response kurtosis K r 。
6. A random vibration acceleration test excitation signal generation method according to any one of claims 1 to 3, characterized in that in step S5, the response kurtosis K r Greater than 3.
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| CN107103162A (en) * | 2017-05-26 | 2017-08-29 | 中国人民解放军国防科学技术大学 | A kind of vibration accelerated test method and system based on Theory of The Cumulative Fatigue Damage |
| JP2018021781A (en) * | 2016-08-02 | 2018-02-08 | 地方独立行政法人大阪産業技術研究所 | Non-gaussian vibration control device |
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| JP2018021781A (en) * | 2016-08-02 | 2018-02-08 | 地方独立行政法人大阪産業技術研究所 | Non-gaussian vibration control device |
| CN107103162A (en) * | 2017-05-26 | 2017-08-29 | 中国人民解放军国防科学技术大学 | A kind of vibration accelerated test method and system based on Theory of The Cumulative Fatigue Damage |
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