Non-stationary and non-Gaussian fatigue time-frequency domain conjoint analysis method

Abstract

The invention provides a non-stationary and non-Gaussian fatigue time-frequency domain conjoint analysis method. The method comprises the following steps: acquiring a frequency domain amplitude and a frequency domain phase of a non-stationary and non-Gaussian excitation signal; obtaining an amplitude frequency response curve of the structure; calculating the frequency domain amplitude of the structural stress response; calculating the power spectrum density of the structural stress response based on the frequency domain amplitude of the structural stress response; in combination with the frequency domain phase of the non-stationary and non-Gaussian excitation signal and the frequency domain amplitude of the structural stress response, obtaining a reconstructed structural vibration fatigue stress response through inverse Fourier transform; calculating the b-order moment of the vibration fatigue stress response absolute value of the reconstructed structure, and judging the relative magnitude of fatigue damage caused by different non-stationary and non-Gaussian excitation signals to the structure based on the b-order moment of the vibration fatigue stress response absolute value of the reconstructed structure. According to the method, the evaluation process is greatly simplified, and the relative magnitude of fatigue can be quickly evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue damage assessment, and particularly to a non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method. Background Art

[0002] In the engineering field, fatigue damage is one of the important reasons for structural failure. With the development of modern industry, the working environment faced by mechanical equipment is becoming increasingly complex, and vibration excitation often exhibits non-stationary and non-Gaussian characteristics. Accurately analyzing fatigue damage under such complex excitation is crucial for ensuring the reliability and safety of equipment. In early research, fatigue damage under stationary Gaussian excitation was mainly analyzed, and the relevant theories and methods were relatively mature. However, the excitation conditions in actual working conditions far exceed this scope, and the emergence of non-stationary and non-Gaussian excitation has brought great challenges to fatigue damage analysis.

[0003] The frequency domain method for fatigue damage calculation is a method for analyzing fatigue damage based on the frequency characteristics of signals. It is mainly used for calculating stationary Gaussian fatigue damage. However, the frequency domain method has significant deficiencies in dealing with non-stationary and non-Gaussian excitation; since the frequency components of non-stationary signals change with time, while the frequency domain method assumes that the signal is stationary during analysis, it is difficult to capture this time-varying characteristic, resulting in the loss of key frequency information in the signal and affecting the accuracy of fatigue damage analysis. For non-Gaussian excitation, the analysis model based on the Gaussian distribution assumption of the frequency domain method is no longer applicable. Since non-Gaussian excitation has a complex probability distribution different from the Gaussian distribution, and the frequency domain method does not combine the time-domain amplitude of the response to capture the non-Gaussian characteristics of the structural response, the existing analysis model cannot accurately describe non-Gaussian excitation, resulting in a large deviation in fatigue damage estimation and being unable to accurately describe the complex probability distribution of non-Gaussian excitation.

[0004] In addition, when dealing with complex multi-frequency component signals, the frequency domain method has a large amount of calculation and low calculation efficiency, and it is difficult to meet the requirements of quickly processing a large amount of data in actual engineering.

[0005] Therefore, there is an urgent need for a technical solution to effectively analyze non-stationary and non-Gaussian fatigue damage. Summary of the Invention

[0006] In view of the defects existing in the prior art, the present invention provides a non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method.

[0007] To achieve the above technical objectives, the specific technical solutions adopted by the present invention are as follows: On the one hand, the present invention provides a non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method, including the following steps: Obtain the frequency domain amplitude and frequency domain phase of the non-stationary and non-Gaussian excitation signal; Obtain the amplitude-frequency response curve of the structure; Based on the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal and the amplitude-frequency response curve of the structure, calculate the frequency-domain amplitude of the structural stress response; Calculate the power spectral density of the structural stress response based on the frequency-domain amplitude of the structural stress response; Combined with the frequency-domain phase of the non-stationary non-Gaussian excitation signal and the frequency-domain amplitude of the structural stress response, obtain the reconstructed structural vibration fatigue stress response through inverse Fourier transform

[0008]

[0009] where, is the frequency-domain amplitude of the structural stress response; is the frequency-domain phase of the non-stationary non-Gaussian excitation signal; N is the number of discrete sampling points; k is the frequency index value; n is the discrete time index; Calculate the b -th moment of the absolute value of the reconstructed structural vibration fatigue stress response

[0010] where, b is the structural material S-N fatigue index of the curve; Based on the value, judge the relative magnitudes of the fatigue damages caused by different non-stationary non-Gaussian excitation signals to the structure.

[0011] Furthermore, it also includes: Based on rainflow counting, the structural material S-N curve, and linear fatigue damage accumulation, calculate the fatigue damage value of the reconstructed structural stress response, specifically calculated according to the following formula

[0012] where, is the fatigue damage value of the structure; C is the structural material S-N fatigue strength of the curve; V p is the peak frequency; T is the excitation signal time; is the probability density distribution of the structural stress amplitude obtained by the rainflow counting method; is the stress amplitude; is the power spectral density of the structural stress response; f is the frequency; is the n -th moment of the signal.

[0013] Further, the frequency-domain amplitude and frequency-domain phase of the non-stationary non-Gaussian excitation signal are obtained according to the following formula:

[0014]

[0015]

[0016] wherein, is the complex-valued spectrum of the non-stationary non-Gaussian excitation signal; is the sampling frequency of the non-stationary non-Gaussian excitation signal; is the frequency; is the non-stationary non-Gaussian sequence; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal; is the frequency-domain phase of the non-stationary non-Gaussian excitation signal; is the real part of; is the imaginary part of.

[0017] Further, the methods for obtaining the amplitude-frequency response curve of the structure include the finite element method and on-site actual testing.

[0018] Further, the frequency-domain amplitude of the structural stress response is calculated according to the following formula:

[0019] wherein, is the frequency-domain amplitude of the structural stress response; is the amplitude-frequency response curve of the structure; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal.

[0020] Further, the power spectral density of the structural stress response is calculated according to the following formula:

[0021] wherein, is the frequency-domain amplitude of the structural stress response.

[0022] Compared with the prior art, the beneficial technical effects of the present invention are as follows: The present invention provides a non-stationary non-Gaussian fatigue time-frequency domain joint analysis method. By considering the phase of the excitation signal, the complete information of the signal frequency and amplitude changing with time is obtained, so as to effectively track the frequency dynamic evolution of the non-stationary signal, accurately capture its non-stationary characteristics, improve the ability to extract key frequency information in the non-stationary signal, and further improve the accuracy of fatigue damage analysis.

[0023] The present invention combines the frequency-domain phase of the excitation with the frequency-domain amplitude of the response to more comprehensively analyze the non-Gaussian characteristics of the structural response, constructs an analysis model that better fits the complex probability distribution of the non-Gaussian excitation, reduces the deviation in the process of fatigue damage estimation, and realizes the accurate analysis of fatigue damage under non-Gaussian excitation.

[0024] Through a unique time-frequency hybrid analysis method, the present invention effectively integrates the phase information of the excitation signal and the frequency-domain amplitude information of the response, combines the advantages of accurate time-domain and efficient frequency-domain, skips the rain-flow counting to evaluate the relative magnitude of fatigue damage, optimizes the calculation process, reduces unnecessary calculation steps, thereby improving the calculation efficiency, meeting the needs of quickly processing a large amount of data in practical engineering, and providing a more efficient analysis tool for engineering applications.

[0025] Specifically, the present invention innovatively combines the advantages of the two, uses the frequency-domain amplitude of the structural stress response obtained efficiently by the frequency-domain analysis method C n , and then fuses the phase information of the non-stationary non-Gaussian excitation signal that is sensitive to the time-varying characteristics of the signal . Through the mathematical tool of inverse Fourier transform, the frequency-domain information is converted back to the time-domain, thereby realizing the efficient reconstruction of the structural stress response. This reconstruction method not only gives full play to the computational efficiency advantage of the frequency-domain analysis method but also absorbs the advantages of the time-domain analysis method in describing signal details and accurately reflecting the true characteristics of the signal. The reconstructed structural stress response obtained through this step can more accurately reflect the actual stress state of the structure under non-stationary non-Gaussian random excitation, providing a more reliable data basis for subsequent steps such as rain-flow counting and fatigue damage calculation. On the other hand, the present invention quickly evaluates the relative magnitude of non-stationary non-Gaussian fatigue based on the b order moment of the absolute value of the reconstructed structural stress response, avoiding the traditional rain-flow counting process. The traditional rain-flow counting process is relatively time-consuming and complex, and the present invention greatly simplifies the evaluation process and can quickly evaluate the relative magnitude of fatigue.

[0026] Therefore, the present invention can significantly improve the accuracy and reliability of the entire fatigue analysis process, which is of great significance for accurately evaluating the fatigue life and safety of structures under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0028] Figure 1Schematic diagram of the non-stationary non-Gaussian fatigue time-frequency domain joint analysis method provided for an embodiment.

[0029] Figure 2 The double-degree-of-freedom system and its frequency response curve diagram provided for an embodiment, where Figure 2 (a) is a schematic diagram of the double-degree-of-freedom system, Figure 2 (b) is the frequency response curve diagram of the double-degree-of-freedom system; Figure 3 Schematic diagram of the non-stationary non-Gaussian signal provided for an embodiment, where Figure 3 (a) is the non-stationary non-Gaussian signal 1 with a kurtosis of 10; Figure 3 (b) is the non-stationary non-Gaussian signal 2 with a kurtosis of 10; Figure 3 (c) is the non-stationary non-Gaussian signal 3 with a kurtosis of 10. Detailed implementation manner

[0030] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0031] Referring to Figure 1 , an embodiment provides a non-stationary non-Gaussian fatigue time-frequency domain joint analysis method, including the following steps: Obtain the frequency-domain amplitude and frequency-domain phase of the non-stationary non-Gaussian excitation signal; Obtain the amplitude-frequency response curve of the structure; Based on the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal and the amplitude-frequency response curve of the structure, calculate the frequency-domain amplitude of the structural stress response; Calculate the power spectral density of the structural stress response based on the frequency-domain amplitude of the structural stress response; Combining the frequency-domain phase of the non-stationary non-Gaussian excitation signal and the frequency-domain amplitude of the structural stress response, obtain the reconstructed structural vibration fatigue stress response through inverse Fourier transform

[0032]

[0033] Wherein, is the frequency-domain amplitude of the structural stress response; is the frequency-domain phase of the non-stationary non-Gaussian excitation signal; N is the number of discrete sampling points; k is the frequency index value; n is the discrete time index; Calculate the b order moment of the absolute value of the structural vibration fatigue stress response of the reconstruction

[0034] wherein, b is the fatigue index of the structural material S-N curve; Based on values to judge the relative magnitudes of the fatigue damages caused by different non-stationary non-Gaussian excitation signals to the structure.

[0035] Obtain the frequency-domain amplitude and frequency-domain phase of the non-stationary non-Gaussian excitation signal according to the following formula:

[0036]

[0037]

[0038] wherein, is the complex-valued spectrum of the non-stationary non-Gaussian excitation signal; is the sampling frequency of the non-stationary non-Gaussian excitation signal; is the frequency; is the non-stationary non-Gaussian sequence; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal; is the frequency-domain phase of the non-stationary non-Gaussian excitation signal; is the real part of; is the imaginary part of.

[0039] The methods for obtaining the amplitude-frequency response curve of the structure include the finite element method and actual field tests.

[0040] The frequency-domain amplitude of the structural stress response is calculated according to the following formula:

[0041] wherein, is the frequency-domain amplitude of the structural stress response; is the amplitude-frequency response curve of the structure; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal.

[0042] The power spectral density of the structural stress response is calculated according to the following formula:

[0043] wherein, is the frequency-domain amplitude of the structural stress response.

[0044] In one embodiment, the non-stationary non-Gaussian fatigue time-frequency domain joint analysis method further includes calculating the fatigue damage value of the reconstructed structural stress response based on rainflow counting, the structural material S-N curve, and linear fatigue damage accumulation. Specifically, it is calculated according to the following formula

[0045] where is the fatigue damage value of the structure; C is the structural material S-N curve fatigue strength; V p is the peak frequency; T is the excitation signal time; is the probability density distribution of the structural stress amplitude obtained by the rainflow counting method; is the stress amplitude; is the power spectral density of the structural stress response; f is the frequency; is the n order moment of the signal.

[0046] In one embodiment, a two-degree-of-freedom system is selected as the object. By experimental comparison, the fatigue damage calculated by the non-stationary non-Gaussian fatigue time-frequency domain joint analysis method provided by the present invention is compared with the fatigue damage calculated by the frequency domain method, and compared with the true fatigue damage of the system to verify the accuracy and correctness of the method described in the present invention.

[0047] Since the two-degree-of-freedom system has wide representativeness in the engineering field, its dynamic characteristics are relatively complex and can reflect the characteristics of many actual structures. The two-degree-of-freedom system is selected as the object, referring to Figure 2 , the two-degree-of-freedom system and its frequency response curve diagram selected for this embodiment.

[0048] Referring to Figure 3 , for the non-stationary non-Gaussian signal received by the two-degree-of-freedom system, where Figure 3 (a) is non-stationary non-Gaussian signal 1 with a kurtosis of 10; Figure 3 (b) is non-stationary non-Gaussian signal 2 with a kurtosis of 10; Figure 3 (c) is non-stationary non-Gaussian signal 3 with a kurtosis of 10.

[0049] In this embodiment, among the S-N curve parameters of the two-degree-of-freedom system, S-N the C curve fatigue strength S-N = 1, b the fatigue index of the

[0050] Table 1 Structural vibration fatigue damage under different excitation signals

[0051] As can be seen from the table, the data in the second column and the fifth column of Table 1 show that the two are in a direct proportional relationship, that is (the b order moment of the absolute value of the reconstructed structural vibration fatigue stress response) is directly proportional to the true fatigue damage of the system; it shows that the larger it is, the greater the true fatigue damage of the system. It shows that this relationship can be used to quickly evaluate the relative magnitudes of fatigue damage caused by different excitation signals, providing convenience for engineering analysis.

[0052] It can also be seen from Table 1 that the errors in calculating the non-stationary non-Gaussian fatigue damage by the frequency domain method are 89.46%, 55.62% and 51.53%. It can be seen that there are relatively large errors in the results of calculating the non-stationary non-Gaussian fatigue damage by the frequency domain method, which may lead to misjudgments of the structural fatigue state. While the errors in calculating the non-stationary non-Gaussian fatigue damage by the method provided by the present invention are 1.38%, 3.61% and 6.14%, the calculation errors are small, and the calculation results are closer to the true values, and can more accurately evaluate the fatigue damage of the system in actual engineering, ensuring the safety and stability of the structure.

[0053] As can be seen from the above results, the non-stationary non-Gaussian fatigue time-frequency domain joint analysis method proposed by the present invention has high correctness and reliability in calculating non-stationary non-Gaussian fatigue damage, providing a more accurate and effective evaluation means for fatigue damage assessment in related engineering fields.

[0054] Matters not covered by the present invention are well-known technologies.

[0055] The technical features of the above embodiments can be combined arbitrarily. For the sake of brief description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0056] The above-described embodiments only represent several implementation manners of the present application. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

[0057] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method, characterized in that, It includes the following steps: Obtain the frequency-domain amplitude and frequency-domain phase of the non-stationary non-Gaussian excitation signal; Obtain the amplitude-frequency response curve of the structure; Based on the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal and the amplitude-frequency response curve of the structure, calculate the frequency-domain amplitude of the structural stress response; Calculate the power spectral density of the structural stress response based on the frequency-domain amplitude of the structural stress response; Combining the frequency-domain phase of the non-stationary non-Gaussian excitation signal and the frequency-domain amplitude of the structural stress response, the reconstructed structural vibration fatigue stress response is obtained through inverse Fourier transform Among them, is the frequency-domain amplitude of the structural stress response; is the frequency-domain phase of the non-stationary and non-Gaussian excitation signal; N is the number of discrete sampling points; k is the frequency index value; n is the discrete time index; Calculating the b moment of the absolute value of the structural vibration fatigue stress response after reconstruction Among them, b is the structural material S-N fatigue index of the curve; Based on Judge the relative magnitudes of fatigue damage caused by different non-stationary and non-Gaussian excitation signals to the structure according to the values.

2. The non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method according to claim 1, characterized in that It also includes: Based on rainflow counting and structural materials S-N The fatigue damage value of the reconstructed structural stress response is calculated based on the curve and linear fatigue damage accumulation, and is specifically calculated according to the following formula Among them, is the fatigue damage value of the structure; C is the structural material S-N curve fatigue strength; V p is the peak frequency; T is the excitation signal time; is the probability density distribution of the structural stress amplitude obtained by the rainflow counting method; is the stress amplitude; is the power spectral density of the structural stress response; f is the frequency; is the n order moment of the signal.

3. A non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method according to claim 1, characterized in that Obtain the frequency-domain amplitude and frequency-domain phase of the non-stationary non-Gaussian excitation signal according to the following formula: wherein, is the complex-valued spectrum of the non-stationary non-Gaussian excitation signal; is the sampling frequency of the non-stationary non-Gaussian excitation signal; is the frequency; is the non-stationary non-Gaussian sequence; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal; is the frequency-domain phase of the non-stationary non-Gaussian excitation signal; is the real part of; is the imaginary part of.

4. A non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method as described in claim 1, characterized in that, The methods for obtaining the amplitude-frequency response curve of the structure include the finite element method and actual on-site testing.

5. A non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method according to claim 1, characterized in that, The frequency-domain amplitude of the structural stress response is calculated according to the following formula: Among them, is the frequency-domain amplitude of the structural stress response; is the amplitude-frequency response curve of the structure; is the frequency-domain amplitude of the non-stationary non-Gaussian excitation signal.

6. The non-stationary and non-Gaussian fatigue time-frequency domain joint analysis method according to claim 1, characterized in that The power spectral density of the structural stress response is calculated according to the following formula: Among them, is the frequency domain amplitude of the structural stress response.

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