A method for predicting multiaxial fatigue life of structures under random vibration loads

Abstract

The present invention provides a method for predicting the multi-axial fatigue life of a structure under a random vibration load, comprising: decomposing the power spectrum density function of a non-Gaussian random vibration load into third-order Gaussian components through a Gaussian mixture model, loading each order component into a structural model as a load, extracting the stress component power spectrum density function for a dangerous position, calculating the maximum variance value of the equivalent stress power spectrum density function of a spatial plane based on a multi-axial fatigue criterion and a maximum variance method, and determining the position of a critical plane. Based on a critical plane frequency domain method, the multi-axial power spectrum density function of a dangerous point is processed into a uniaxial equivalent power spectrum density function, and the third-order non-Gaussian mixture probability density function of the equivalent stress power spectrum density function is calculated according to the Dirlik method to predict the fatigue damage and life of the structure. The present invention takes into account the influence of the multi-axial stress state on the fatigue life of the structure, so that the problem of predicting the fatigue life of the structure is more in line with the fatigue damage mechanism. The method is simple and has better universality.

Description

Technical Field

[0001] The invention belongs to the technical field of structural fatigue life prediction and relates to a method for predicting fatigue life of a structure under a random vibration load and in a multi-axial stress state. Background Art

[0002] The strategic importance of high-end equipment such as modern aero engines, hypersonic vehicles, and advanced missiles has become increasingly prominent. Predicting the fatigue life of these equipment structures has become one of the most active and challenging areas in the field of mechanical strength. Many structures are subject to a variety of loads during service, including internal and external pressure differentials, high and low temperatures, vibration, and impact. These complex conditions can easily lead to stress concentration in weak areas, a contributing factor to fatigue failure.

[0003] Harsh service environments are an important factor leading to fatigue failure of structures. Random vibration loads cause complex stress states in local parts of the structure, making fatigue failure more likely to occur. Most of the random vibration loads encountered in engineering are non-Gaussian random loads. However, in practice, most of these loads are calculated and analyzed as if they were Gaussian random loads. This results in large deviations in the results of random vibration fatigue life analysis using the Gaussian assumption, which poses a huge safety hazard to the equipment during service or use. As a result, some key structures still suffer unexpected fatigue failures during use under harsh conditions in the field after passing Gaussian random vibration tests, failing to meet the expected life and reliability indicators. Therefore, researchers hope to find a method that can accurately and reliably predict structural fatigue damage and life under non-Gaussian random vibration loads.

[0004] Frequency-domain and time-domain methods are the two primary approaches to addressing these types of problems. While time-domain methods offer excellent computational accuracy, they are computationally intensive and unsuitable for practical engineering analysis. Regarding frequency-domain methods, since current frequency-domain methods are designed for Gaussian random loads, directly using frequency-domain methods to calculate damage under non-Gaussian random vibration loads will result in significant errors. Furthermore, structures under random vibration loads are subject to a multiaxial stress state, and current research on frequency-domain problems under these multiaxial conditions is insufficient.

[0005] Therefore, how to effectively reduce the fatigue life prediction error of the structure under the multi-axial stress state of random vibration load is an urgent problem that technicians in this field need to solve. Summary of the Invention

[0006] In view of this, the present invention proposes a method for predicting the multiaxial fatigue life of structures under random vibration loads, which solves the problem of large errors in fatigue life prediction of multiaxial stress states of structures under non-Gaussian random vibration loads based on the frequency domain method.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] The present invention discloses a method for predicting the multi-axial fatigue life of a structure under random vibration load, comprising the following steps:

[0009] S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectrum density function frequency domain load through Fourier transform;

[0010] S2: Calculating high-order spectral moment parameters of the power spectral density function frequency domain load, and decomposing the power spectral density function frequency domain load into third-order Gaussian component loads using a Gaussian mixture model based on the high-order spectral moment parameters;

[0011] S3: Load the structural model with the third-order Gaussian component load three times, each time applying the same-order Gaussian component load to the X, Y, and Z axes of the structural model. Perform random vibration analysis on each loading operation, calculate the Von Mises root mean square stress of each node, and determine the node position with the maximum Von Mises root mean square stress as the dangerous point of the structure.

[0012] S4: extracting the stress component power spectrum density function at the dangerous point position, calculating the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multi-axial fatigue criterion and the maximum variance method, and determining the orientation coefficient of the critical plane;

[0013] S5: Based on the orientation coefficient of the critical plane, the power spectrum density matrix in the random process is introduced, and the multiaxial stress power spectrum density function is equivalently treated as a uniaxial stress power spectrum density function;

[0014] S6: Calculate the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method, combine the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function, and predict the fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function.

[0015] Preferably, the S2 includes:

[0016] S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameter of the zero-mean Gaussian process is expressed as a function of the standard deviation:

[0017]

[0018] Where m j is the j-th order spectral moment parameter, α i (i=1,2,3) is the weight coefficient of the third-order Gaussian component, σ i(i=1,2,3) is the standard deviation of the third-order Gaussian component stress;

[0019] S22: Based on the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α1, α2, α3, σ1, σ2, σ3;

[0020] S23: Determine the magnitude of the third-order power spectral density function components (G1(f), G2(f), G3(f)) with Gaussian characteristics:

[0021] G1(f)=eta1G(f), G2(f)=eta2G(f), G3(f)=eta3G(f);

[0022] Where G(f) is the frequency domain load of the power spectrum density function, η1, η2 and η3 are proportional constants, is the variance of the non-Gaussian random process:

[0023]

[0024] Preferably, in said S3: calculate the root mean square δ of the Von Mises stress of each node eq :

[0025]

[0026] Where, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz are the shear stresses in the three axes X, Y, and Z.

[0027] Preferably, the S4 includes:

[0028] S41: Extract the power spectrum density function of stress components for nodes at dangerous locations (G xx ,G yy ,G zz ,G xy ,G xz ,G yz );

[0029] S42: Determine the maximum stress variance expression based on the power spectrum density function of the stress component:

[0030]

[0031] Where, stress variance μ kl for:

[0032]

[0033] When k=1, G kl (f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross-power spectral density function;

[0034] a k 、a l ∈[a1,a2,a3,a4,a5.a6] is the row vector of orientation coefficients determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated using the cosines of the principal stress directions represented by the three Euler angles;

[0035] S43: Rotate the three Euler angles incrementally at every unit angle, calculate the maximum variance of the equivalent stress of the plane obtained by all angle combinations in space, calculate the orientation coefficient and stress variance of the equivalent power spectrum density function at the maximum variance value, and complete the determination of the critical plane position.

[0036] Preferably, in said S5: the equivalent stress power spectrum density function G eq (f) is:

[0037] Where G kk (f) is the autopower spectral density function, a k is the critical plane orientation coefficient determined when the variance of equivalent stress is maximum.

[0038] Preferably, the step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 includes:

[0039]

[0040] Where,

[0041] Where m0, m1, m2, and m4 are the four moments of inertia of the power spectrum density function, and their expressions are:

[0042]

[0043] Preferably, the step of combining the three stress amplitude probability density functions with a Gaussian mixture model to calculate a third-order non-Gaussian mixture probability density function in S6 includes:

[0044] f GMM (s)=α1p1(s1)+α2p2(s2)+α3p3(s3);

[0045] Where, f GMM(s) is the stress amplitude probability density function of the Gaussian mixture model, p1(s), p2(s), p3(s) are the three stress amplitude probability density functions of the Gaussian components, α i is the weight coefficient of the Gaussian component.

[0046] Preferably, the step of predicting fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function in S6 includes:

[0047] Find the fatigue damage of a structural model under non-Gaussian loading:

[0048]

[0049] Where, ν P is the frequency at which the stress amplitude crosses zero; k, C are power function forms NS k = SN curve parameter of C; T0 is the total loading time;

[0050] The fatigue life T of the structural model is:

[0051]

[0052] It can be seen from the above technical solution that, compared with the prior art, the beneficial effects of the present invention include:

[0053] (1) The present invention establishes a set of prediction methods for estimating the multiaxial fatigue life of structures under non-Gaussian random vibration loads, solving the problem of using frequency domain methods to predict the multiaxial fatigue life of structures under non-Gaussian random vibration loads. The third-order Gaussian mixture model improves the accuracy of the calculation results.

[0054] (2) The present invention uses the maximum variance method to find the critical plane at the dangerous point of the structure, and calculates the equivalent stress power spectrum density function on the critical plane of the dangerous position based on the multi-axis frequency domain method of the maximum shear stress criterion. The calculation process is relatively simple and the effect is good;

[0055] (3) The present invention combines the characteristics of accurate results of the time domain method and simple calculation of the frequency domain method. Based on the damage equivalence principle, the equivalent power spectrum density function is converted into a time domain result through inverse Fourier transform, and a hybrid frequency-time domain process is established. Compared with the frequency domain method based on the critical plane, the amount of calculation is greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only embodiments of the present invention. Those skilled in the art can also derive other drawings based on the provided drawings without inventive effort.

[0057] Figure 1 A flow chart of a method for predicting multi-axial fatigue life of a structure under random vibration loads provided by an embodiment of the present invention;

[0058] FIG2( a ) is a front view of a structural model provided by an embodiment of the present invention;

[0059] FIG2( b ) is a top view of the structural model provided by an embodiment of the present invention;

[0060] FIG3( a ) is a schematic diagram of the time domain form of a random vibration load provided by an embodiment of the present invention;

[0061] FIG3( b ) is a schematic diagram of the frequency domain form of random vibration load provided by an embodiment of the present invention;

[0062] FIG4( a ) is a schematic diagram of the autopower spectral density function of the stress component at the dangerous point provided by an embodiment of the present invention;

[0063] FIG4( b ) is a schematic diagram of the power spectrum density function of the equivalent stress at the dangerous point provided by an embodiment of the present invention;

[0064] Figure 5 A schematic diagram comparing the lifespan prediction results using frequency domain and time domain processing methods provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0066] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting multi-axial fatigue life of a structure under random vibration load, comprising the following steps:

[0067] S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectrum density function frequency domain load through Fourier transform;

[0068] S2: Calculate the high-order spectral moment parameters of the power spectral density function frequency domain load, and use the Gaussian mixture model based on the high-order spectral moment parameters to decompose the power spectral density function frequency domain load into third-order Gaussian component loads;

[0069] S3: Load the structural model with the third-order Gaussian component load three times, each time applying the same-order Gaussian component load to the X, Y, and Z axes of the structural model. Perform random vibration analysis on each loading operation, calculate the Von Mises root mean square stress of each node, and determine the node position with the maximum Von Mises root mean square stress as the dangerous point of the structure.

[0070] S4: Extract the power spectrum density function of the stress component at the dangerous point position, calculate the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multiaxial fatigue criterion and the maximum variance method, and determine the orientation coefficient of the critical plane;

[0071] S5: Based on the orientation coefficient of the critical plane, the power spectrum density matrix in the random process is introduced, and the multiaxial stress power spectrum density function is equivalently treated as the uniaxial stress power spectrum density function;

[0072] S6: The stress amplitude probability density function of the uniaxial stress power spectrum density function is calculated according to the frequency domain Dirlik method. The three stress amplitude probability density functions are combined with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function. The fatigue damage and life of the structural model under non-Gaussian load are predicted based on the third-order non-Gaussian mixture probability density function.

[0073] The structural model used in this embodiment is shown in Figure 2, where Figure (a) is the main view of the structural model and Figure (b) is the top view of the structural model, with units in mm. In the figure, L is the length of the sample, W is the width, H is the height, b4 is the notch width, and θ is the notch opening angle. The structural model size parameters are: L = 180mm, W = 16mm, H = 1.8mm, b1 = 45mm, b2 = 1.8mm, b3 = 20mm, b4 = 7mm, θ = 60°, through hole for

[0074] In the embodiment, random vibration analysis is performed on the aluminum alloy specimen under non-Gaussian random vibration load. In the analysis, the left end of the aluminum alloy specimen is fixedly constrained.

[0075] The material used for the structural model in the embodiment may be aluminum alloy 6061-T6, wherein the test piece is tested at room temperature.

[0076] In one embodiment, in S1, the non-Gaussian random vibration time domain load x(t) with a certain kurtosis and skewness is converted into the corresponding power spectrum density function frequency domain load G(f) through Fourier transform, where the kurtosis value of the non-Gaussian random vibration load is taken as 5 and the skewness value is taken as 0.01. The calculation expressions of kurtosis γ3 and skewness γ4 are:

[0077]

[0078] Where E[·] is the expected value operator, μ x and δ x are the mean and standard deviation of x(t), respectively. Skewness γ3 represents the degree of asymmetry in the random process amplitude distribution, and kurtosis γ4 characterizes the sharpness of the peak and width of the tail of the random process amplitude probability density function curve. Figure 3 shows a non-Gaussian random vibration load and its power spectral density function.

[0079] In one embodiment, S2 includes:

[0080] S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameters of the zero-mean Gaussian process are expressed as a function of the standard deviation:

[0081]

[0082] Where m j is the j-th order spectral moment parameter, α i (i=1,2,3) is the weight coefficient of the third-order Gaussian component, σ i (i=1,2,3) is the standard deviation of the third-order Gaussian component stress;

[0083] S22: Based on the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α1, α2, α3, σ1, σ2, σ3;

[0084] S23: Determine the magnitude of the third-order power spectral density function components (G1(f), G2(f), G3(f)) with Gaussian characteristics:

[0085] G1(f)=eta1G(f), G2(f)=eta2G(f), G3(f)=eta3G(f);

[0086] Where G(f) is the frequency domain load of the power spectrum density function, η1, η2 and η3 are proportional constants, is the variance of the non-Gaussian random process:

[0087]

[0088] In this embodiment, the specific steps for calculating the high-order spectral moment parameters of the non-Gaussian load are as follows:

[0089] Since the non-Gaussian power spectrum load needs to be decomposed into the third-order Gaussian component power spectrum density function, it is necessary to calculate the 2nd, 4th, 6th, 8th, and 10th (m2, m4, m6, m8, m 10 )-order high-order spectral moment parameters. The calculation formula of high-order spectral moment parameters is:

[0090]

[0091] The specific steps for calculating the weight coefficient of the Gaussian component in combination with the Gaussian mixture model are:

[0092] The power spectral density function of the non-Gaussian load is decomposed into three-order power spectral density function components (G1(f), G2(f), G3(f)) with Gaussian characteristics.

[0093] According to the Gaussian mixture model formula, the higher-order moments of the zero-mean Gaussian process can be expressed as a function of the standard deviation, so:

[0094]

[0095] Where, α i (i=1,2,3) is the Gaussian component coefficient, σ i (i=1,2,3) is the standard deviation of Gaussian component stress. Since the Gaussian component coefficient has the following relationship:

[0096] α1+α2+α3=1

[0097] According to the above equations, the unknown parameters α1, α2, α3, σ1, σ2, and σ3 can be solved.

[0098] In this step, the Gaussian mixture model is used to decompose the non-Gaussian process into Gaussian processes with different weight coefficients. The weight coefficients represent the probability of the three Gaussian components appearing in the time domain.

[0099] The non-Gaussian power spectrum density function is further decomposed into three power spectrum density functions of Gaussian components of different magnitudes using high-order statistics, and the Gaussian decomposition characteristics are introduced into the frequency domain. The specific execution steps are as follows:

[0100] Variance of a non-Gaussian random process It can be expressed as:

[0101]

[0102] To derive the Gaussian component power spectral density function based on frequency domain data, it is necessary to determine the values ​​of G1(f), G2(f), and G3(f). Assuming that they are proportional along the frequency axis, that is:

[0103] G1(f)=eta1G(f), G2(f)=eta2G(f), G3(f)=eta3G(f);

[0104] Where η1, η2 and η3 are proportional constants, and the calculation formula is:

[0105]

[0106] In one embodiment, the structural model in S3 is loaded with the same first-order Gaussian component load in the three directions XYZ each time, and a finite element analysis is performed each time until the loading analysis of the three-order Gaussian component loads is completed, that is, a total of three finite element analyses are performed: the root mean square δ of the Von Mises stress at each node is calculated. eq :

[0107]

[0108] Where, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz are the shear stresses in the three axes X, Y, and Z.

[0109] In this embodiment, the material parameters of the aluminum alloy 6061-T6 used in the specimen model are detailed in Table 1.

[0110] Table 1 Material parameters of aluminum alloy 6061-T6

[0111] parameter value Young's modulus 68.9GPa density 2849Kg / m3 Poisson's ratio 0.33 Yield strength 275MPa Ultimate tensile strength 310MPa

[0112] In one embodiment, S4 includes:

[0113] S41: Extract the power spectrum density function of stress components for nodes at dangerous locations (G xx ,G yy ,G zz ,G xy ,G xz ,G yz ), the maximum stress variance value is calculated based on the power spectrum density function. Figure 4(a) shows the corresponding autopower spectrum density function of the stress component.

[0114] S42: Determine the maximum stress variance expression based on the power spectrum density function of the stress component:

[0115]

[0116] Where, stress variance μ kl for:

[0117]

[0118] When k=1, G kl (f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross-power spectral density function;

[0119] a k 、a l∈[a1,a2,a3,a4,a5.a6] is the row vector of orientation coefficients determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated using the cosines of the principal stress directions represented by the three Euler angles;

[0120] S43: The three Euler angles are rotated incrementally at every unit angle, such as a unit angle of 0.5°, and the maximum variance value of the equivalent stress of the plane obtained by all angle combinations in space is calculated. The orientation coefficient and stress variance of the equivalent power spectrum density function at the maximum variance value are calculated to complete the determination of the critical plane position.

[0121] In this embodiment, S42 includes the following specific execution steps:

[0122] Azimuth coefficient a k 、a l =[a1,a2,a3,a4,a5,a6] can be expressed as:

[0123]

[0124] a4=2(l1m1-l3m3), a5=2(l1n1-l3n3), a6=2(n1m1-n3m3);

[0125] Where, l i ,m i ,n i The direction cosines of the principal stresses can be expressed by the three Euler angles φ, θ, and ψ:

[0126] l1=cosψcosφ-cosθcosψsinφ, m1=sinψcosφ+cosθcosψsinφ,

[0127] n1=sinθsinφ, l2=-cosψcosφ-cosθcosψcosφ,

[0128] m2=-sinψcosφ+cosθcosψcosφ, n2=sinθcosφ,

[0129] l3=sinθsinψ, m3=-sinθcosψ, n3=cosθ

[0130] In the formula, (0≤θ<π, 0≤ψ<π, 0≤φ<2π).

[0131] In one embodiment, in S5: the expression of the equivalent power spectrum density function is:

[0132]

[0133] Where G kk(f) represents the autopower spectral density function, G kl (f) represents the cross-power spectral density function, a k 、a l The critical plane orientation coefficient determined when the equivalent stress variance is maximum.

[0134] When using the frequency domain critical surface method, the effect of the cross-spectral power spectrum density on the fatigue life results can be ignored. Therefore, the equivalent stress power spectrum density function can be simplified to:

[0135]

[0136] Where G kk (f) is the autopower spectral density function, a k is the critical plane orientation coefficient determined when the equivalent stress has the maximum variance. Figure 4(b) shows the power spectrum density function of the equivalent stress.

[0137] It should be noted that, in this embodiment, S5 obtains three different uniaxial stress power spectrum density functions after three finite element analyses. Each uniaxial power spectrum density function is obtained by extracting the stress power spectrum density functions (G xx ,G yy ,G zz ,G xy ,G xz ,G yz ), and the expressions of the three uniaxial stress power spectrum density functions are the same. The specific calculation results are different due to the differences in the stress power spectrum density functions in the six directions of each uniaxial stress power spectrum density function.

[0138] In one embodiment, the step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 includes:

[0139]

[0140] Where,

[0141] Where m0, m1, m2, and m4 are the four moments of inertia of the power spectrum density function, and their expressions are:

[0142]

[0143] In one embodiment, the step of combining the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function in S6 includes:

[0144] f GMM(s)=α1p1(s1)+α2p2(s2)+α3p3(s3);

[0145] Where, f GMM (s) is the stress amplitude probability density function of the Gaussian mixture model, p1(s), p2(s), p3(s) are the three stress amplitude probability density functions of the Gaussian components, α i is the weight coefficient of the Gaussian component.

[0146] In one embodiment, the step of predicting fatigue damage and life of the structural model under non-Gaussian load based on a third-order non-Gaussian mixture probability density function in S6 includes:

[0147] Find the fatigue damage of a structural model under non-Gaussian loading:

[0148]

[0149] Where, ν P Indicates the frequency at which the stress amplitude crosses 0; k, C are power function forms NS k = SN curve parameter of C; T0 represents the total loading time;

[0150] The fatigue life T of the structural model is:

[0151]

[0152] Based on the damage equivalence principle, the equivalent power spectral density function in S5 is converted into time domain results through inverse Fourier transform, and a hybrid frequency-time domain process is established. The fatigue damage and life of the structure are calculated according to the Miner cumulative damage criterion and the rain flow counting method, and compared with the S6 results. Figure 5 It is a comparison chart of the frequency domain results and the time domain results based on the method of the invention. Among them, the frequency domain results are the results analyzed and calculated in step S6 of the present invention; the time domain results are the results calculated by the equivalent power spectrum converted into the time domain process in step S5 of the present invention. The life values ​​of the frequency domain results and the time domain results are within a 2-fold error band. Comparison explanation: By decomposing the power spectrum of non-Gaussian loads into multiple Gaussian components, the classical frequency domain method can be used to solve the non-Gaussian vibration problem. The prediction results combined with the multi-axial stress power spectrum equivalence criterion are close to the time domain results, which illustrates the rationality and effectiveness of the multi-axial fatigue life prediction method of structures under random vibration loads.

[0153] The above is a detailed introduction to the method for predicting the multi-axial fatigue life of structures under random vibration loads provided by the present invention. In this embodiment, specific examples are used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present invention.

[0154] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this embodiment may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown in this embodiment, but is intended to conform to the widest scope consistent with the principles and novel features disclosed in this embodiment.

Claims

1. A method for predicting the multiaxial fatigue life of a structure under random vibration load, characterized in that: The steps include: S1: The non-Gaussian random vibration time domain load containing kurtosis and skewness is converted into the corresponding power spectrum density function frequency domain load through Fourier transform; S2: Calculating high-order spectral moment parameters of the power spectral density function frequency domain load, and decomposing the power spectral density function frequency domain load into third-order Gaussian component loads using a Gaussian mixture model based on the high-order spectral moment parameters; S3: Load the structural model with the third-order Gaussian component load three times, each time applying the same-order Gaussian component load to the X, Y, and Z axes of the structural model. Perform random vibration analysis on each loading operation, calculate the Von Mises root mean square stress of each node, and determine the node position with the maximum Von Mises root mean square stress as the dangerous point of the structure. S4: extracting the stress component power spectrum density function at the dangerous point position, calculating the maximum variance value of the equivalent stress power spectrum density function of each plane in the space based on the multi-axial fatigue criterion and the maximum variance method, and determining the orientation coefficient of the critical plane; S5: Based on the orientation coefficient of the critical plane, the power spectrum density matrix in the random process is introduced, and the multiaxial stress power spectrum density function is equivalently treated as a uniaxial stress power spectrum density function; S6: Calculate the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method, combine the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function, and predict the fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function.

2. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The S2 includes: S21: According to the Gaussian mixture model formula, the higher-order spectral moment parameter of the zero-mean Gaussian process is expressed as a function of the standard deviation: Where m j is the j-th order spectral moment parameter, α i is the weight coefficient of the third-order Gaussian component, σ i is the standard deviation of the third-order Gaussian component stress, where i = 1, 2, 3; S22: Based on the standard deviation function of the high-order spectral moment parameters in S21, the simultaneous equations are solved to obtain α1, α2, α3, σ1, σ2, σ3; S23: Determine the magnitude of the third-order power spectral density function components (G1(f), G2(f), G3(f)) with Gaussian characteristics: G1(f)=eta1G(f), G2(f)=eta2G(f), G3(f)=eta3G(f); Where G(f) is the frequency domain load of the power spectrum density function, η1, η2 and η3 are proportional constants, is the variance of the non-Gaussian random process:

3. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: In S3: Calculate the root mean square δ of the Von Mises stress at each node eq : Where, δ x ,δ y ,δ z are the normal stresses in the three axes of XYZ, τ xy ,τ xz ,τ yz are the shear stresses in the three axes X, Y, and Z.

4. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The S4 includes: S41: Power spectrum density function group G for extracting stress components at dangerous location nodes xx , G yy , G zz , G xy , G xz , G yz ; S42: Determine the maximum stress variance expression based on the power spectrum density function of the stress component: Where, stress variance μ kl for: When k=1, G kl (f) represents the auto-power spectral density function, when k≠l, G kl (f) represents the cross-power spectral density function; a k 、a l ∈[a1,a2,a3,a4,a5.a6] is the row vector of orientation coefficients determined based on the maximum shear stress criterion on the critical plane in the frequency domain, and is calculated using the cosines of the principal stress directions represented by the three Euler angles; S43: Rotate the three Euler angles incrementally at every unit angle, calculate the maximum variance of the equivalent stress of the plane obtained by all angle combinations in space, calculate the orientation coefficient and stress variance of the equivalent power spectrum density function at the maximum variance value, and complete the determination of the critical plane position.

5. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: In S5: Equivalent stress power spectrum density function G eq (f) is: Where G kk (f) is the autopower spectral density function, a k is the critical plane orientation coefficient determined when the variance of equivalent stress is maximum.

6. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 1, characterized in that: The step of calculating the stress amplitude probability density function of the uniaxial stress power spectrum density function according to the frequency domain Dirlik method in S6 includes: Where, Where m0, m1, m2, and m4 are the four moments of inertia of the power spectrum density function, and their expressions are:

7. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 6, characterized in that: The step of combining the three stress amplitude probability density functions with the Gaussian mixture model to calculate the third-order non-Gaussian mixture probability density function in S6 includes: f GMM (s)=α1p1(s1)+α2p2(s2)+α3p3(s3); Where, f GMM (s) is the stress amplitude probability density function of the Gaussian mixture model, p1(s), p2(s), p3(s) are the three stress amplitude probability density functions of the Gaussian components, α i is the weight coefficient of the Gaussian component.

8. The method for predicting multiaxial fatigue life of a structure under random vibration load according to claim 7, characterized in that: The step of predicting fatigue damage and life of the structural model under non-Gaussian load based on the third-order non-Gaussian mixture probability density function in S6 includes: Find the fatigue damage of a structural model under non-Gaussian loading: Where, ν P is the frequency at which the stress amplitude crosses zero; k, C are power function forms NS k = SN curve parameter of C; T0 is the total loading time; The fatigue life T of the structural model is:

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