A method for fatigue reliability analysis of welded structures under non-Gaussian random loads

Abstract

The present invention discloses a method for fatigue reliability analysis of a welded structure under non-Gaussian random loads, including: quantifying various parameters of the pipeline welded structure to obtain a plurality of quantization samples representing the uncertainties of various parameters of the welded structure; according to the quantization samples, performing finite element analysis on the pipeline welded structure in finite element software to determine the critical points in the pipeline welded structure; obtaining the fatigue life corresponding to the critical points; constructing a database based on the quantization samples and the fatigue life, and training a support vector regression model according to the database in combination with the Bayesian optimization method; using the support vector regression model to obtain the fatigue life of the target pipeline welded structure, and based on the fatigue life of the target pipeline welded structure, in combination with the UIS-RC method, realizing the reliability analysis of the target pipeline welded structure. Through this method, the reliability analysis of the pipeline welded structure under non-Gaussian loads can be carried out under uncertain conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of pipeline fatigue strength reliability analysis, and more specifically, to a method for analyzing the fatigue reliability of welded structures under non-Gaussian random loads. Background Art

[0002] Pipeline transportation, together with railway, highway, aviation and water transportation, is collectively referred to as the five major transportation industries. Its basic function is to transport the specified medium to the using location, which is the most economical and simple transportation method. In many industries such as chemical engineering, nuclear energy, and water conservancy, pipelines play a crucial role. In pipelines, welding is of vital importance. As a relatively vulnerable part of the pipeline structure, whether it is the long-distance transportation pipeline of West-East Gas Pipeline or the nuclear power unit pipeline in a nuclear power plant, there are high requirements for welding. Currently, the main pipeline connection welding methods are butt welding and insert welding. In butt welding, the interfaces of two pipes are heated to the melting state and then fused together, and a strong connection is formed after cooling. During the welding process, appropriate welding materials are required to fill the interfaces to ensure the firmness and tightness of the connection. In insert welding, the pipe is inserted into the valve body for welding, and the formed shape is similar to the external shape of an internal thread connection. Different from butt welding, the weld seam used in insert welding is a fillet weld, with relatively lower requirements. Welded structures have a strong ability to withstand static loads, but their fatigue resistance is relatively weak. Welded joints usually break suddenly when the working stress is much lower than the static strength stress. Research results show that fatigue fracture at the weld seam is one of the main reasons for the failure of welded structures.

[0003] Since the filling material needs to be melted and the base material needs to bear a severe thermal load during the welding process, local non-uniform microstructures are formed in the materials around the weld seam, resulting in different mechanical properties, and stress concentration and welding residual tensile stress occur at the weld seam. Therefore, the fatigue strength at the weld seam is usually lower than that of the base material and is prone to fatigue failure. In addition, in actual engineering, due to factors such as manufacturing processes, material properties, and working environment loads, the actual performance of structural materials shows a certain degree of dispersion. Any slight change in the above-mentioned uncertain variables may lead to a reduction in the reliability of its structure or even premature failure. According to the viewpoint of fracture mechanics, the fatigue failure of a structural member is caused by the internal crack expanding to a critical size. This means that the life of the structure depends on the initiation and propagation of cracks at the dangerous parts of the structure. Affected by many internal and external uncertain factors, the fatigue crack propagation behavior shows extremely strong randomness. Therefore, in order to formulate the optimal design scheme for the pipeline welded structure under a given safety level, it is necessary to start from reliable monitoring and accurate characterization of random uncertainties, fully grasp the propagation direction of uncertainties in fatigue, accurately obtain the dispersion characteristics of the structural response under random uncertainties, and finally determine the optimal solution that meets the reliability index based on the limit state equation.

[0004] Therefore, how to conduct reliability analysis on pipeline welding structures under uncertain conditions is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above problems, the present invention provides a fatigue reliability analysis method for welding structures under non-Gaussian random loads to at least solve some of the technical problems mentioned in the above background art.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a fatigue reliability analysis method for welding structures under non-Gaussian random loads, including the following steps:

[0008] S1. Quantify each parameter of the pipeline welding structure to obtain a plurality of quantization samples representing the uncertainty of each parameter of the welding structure;

[0009] S2. According to the quantization samples, conduct finite element analysis on the pipeline welding structure in finite element software to determine the dangerous points in the pipeline welding structure;

[0010] S3. Use the notch stress method and the critical plane method to extract the non-Gaussian equivalent stress power spectrum of the dangerous points, and combine the Gaussian mixture model and the time-frequency domain hybrid method to obtain the fatigue life corresponding to the dangerous points;

[0011] S4. Construct a database according to the quantization samples and the fatigue life, and train a support vector regression model according to the database in combination with the Bayesian optimization method;

[0012] S5. Use the support vector regression model to obtain the fatigue life of the target pipeline welding structure, and based on the fatigue life of the target pipeline welding structure, combine the UIS-RC method to realize the reliability analysis of the target pipeline welding structure.

[0013] Further, it further includes:

[0014] S6. Based on the reliability analysis results, obtain the sensitivity factors corresponding to each parameter of the pipeline welding structure; and based on the sensitivity factors, obtain the influence degree of each parameter on the reliability of the pipeline welding structure.

[0015] Further, each parameter of the pipeline welding structure includes: geometric dimension parameters, material parameters, and non-Gaussian random load parameters of the pipeline welding structure.

[0016] Further, in step S1, the UIS-RC method is used to quantify the geometric dimension parameters and material parameters of the pipeline welding structure; specifically including:

[0017] (1) Obtain the random variable distribution information of the pipeline welding structure, expressed as:

[0018]

[0019] Among them, Lower represents the lower sampling boundary; Upper represents the upper sampling boundary; F -1 (·) represents the inverse function of the cumulative distribution probability function; p represents the selected sampling probability value; represents the sample center of the i-th parameter x i ;

[0020] (2) Generate quantization samples of geometric dimension parameters and material parameters according to the random variable distribution information of the pipeline welding structure; expressed as:

[0021] X = Lower + (Upper - Lower) * rand(L)

[0022] Among them, X represents the quantization sample; rand represents a random number uniformly distributed in the interval [0, 1]; L represents the number of quantization samples; different quantization samples correspond to different geometric parameters and material parameters;

[0023] (3) Obtain the weight of each sample point in the quantization sample X, expressed as:

[0024]

[0025] Among them, W K represents the weight of the K-th sample point; f xi represents the probability density function of the i-th parameter; X i,K represents the value of the K-th sample point corresponding to the i-th parameter;

[0026] (4) Compare the weight of each sample point with a constant threshold:

[0027] If the weight of the sample point is greater than the threshold C, retain the corresponding sample point, and update the weight of the retained sample point to W K *p c ; Among them, p c represents the regularization coefficient;

[0028] If the weight of the sample point is less than the threshold C, compare W K / C with the random number r: If W K / C is greater than the random number r, retain the corresponding sample point, and update the weight of the retained sample point to W K *p c ; Otherwise, resample; where, r ∈ (0, 1);

[0029] (5) Repeat the above steps of quantizing geometric dimension parameters and material parameters until the number of retained sample points meets the preset sample size.

[0030] Furthermore, in step S1, the non-Gaussian random load parameters of the pipeline welding structure are quantified by a non-linear method; specifically including:

[0031] (1) Introduce a non-linear transformation function to relate the non-Gaussian process to the Gaussian process, expressed as:

[0032]

[0033] where Z(t) represents the non-Gaussian process; X(t) represents the Gaussian process; G(·) represents the transformation function; g -1 (·) represents the inverse transformation function, and G(·) = g -1 (·);

[0034] (2) Use the Hermite transformation function based on the third moment to expand the signal through the Hermite polynomial to generate the non-Gaussian random load of the pipeline welding structure that conforms to the actual engineering situation; expressed as:

[0035]

[0036] where Z0 represents the standardized non-Gaussian random load; X0 represents the standardized Gaussian random load; κ represents the constant coefficient; h3 represents the coefficient related to the third moment; μ Z represents the mean value of the non-Gaussian process Z(t); δ Z represents the standard deviation of the non-Gaussian process Z(t); μ x represents the mean value of the Gaussian process X(t); δ x represents the standard deviation of the Gaussian process X(t); G1(·) represents the Hermite transformation function based on the third moment.

[0037] Furthermore, step S3 specifically includes:

[0038] S3.1. Extract the power spectra of each stress component at the critical point from the finite element analysis results through the notch stress method and the critical plane method; and synthesize the power spectra of each stress component into the non-Gaussian equivalent stress power spectrum of the critical point on the critical plane;

[0039] S3.2. Use the Gaussian mixture model to convert the non-Gaussian equivalent stress power spectrum into a combination of multiple Gaussian components;

[0040] S3.3. Use the time-frequency domain conversion method and the rainflow counting method to calculate the fatigue damage of each Gaussian component to the pipeline welding structure and obtain the fatigue life.

[0041] Furthermore, step S3.1 specifically includes:

[0042] S3.11. Extract the dynamic responses at the critical points in the pipeline welding structure by the notch stress method; and determine the concentration positions of each stress component based on the dynamic responses as the positions of the critical points.

[0043] S3.12. Determine the critical plane of the critical point based on the critical plane method.

[0044] S3.13. Obtain the non-Gaussian equivalent stress power spectrum of the critical point on the critical plane.

[0045] Further, the step S3.3 specifically includes:

[0046] S3.31. Convert each Gaussian component from the frequency-domain signal to the time-domain signal by the time-frequency domain conversion method.

[0047] S3.32. Obtain the fatigue damage caused by each Gaussian component in the time domain by the rainflow counting method.

[0048] S3.33. Use the Miner criterion to accumulate the fatigue damage of each Gaussian component to obtain the total fatigue damage and the corresponding fatigue life.

[0049] Further, in step S5, the reliability analysis of the target pipeline welding structure is realized by combining the UIS-RC method according to the fatigue life of the target pipeline welding structure, which specifically includes:

[0050] (1) Input the fatigue life of the target pipeline welding structure into the load-life fatigue interference model to obtain the corresponding performance index; the load-life fatigue interference model is expressed as:

[0051] G2 = lgN f -lgN d

[0052] where G2 represents the performance index; N f represents the fatigue life of the target pipeline welding structure; N d represents the preset life.

[0053] (2) Obtain the corresponding indicative value according to the performance index, which is expressed as:

[0054]

[0055] where I represents the indicative value.

[0056] (3) Obtain the failure probability of the target pipeline welding structure according to the indicative value, which is expressed as:

[0057]

[0058] where P fdenotes the failure probability; N denotes the quantization sample size; is the final weight of the Kth sample point;

[0059] (4) According to the failure probability, obtain the reliability of the target pipeline welding structure, expressed as:

[0060] R = 1 - P f

[0061] where R denotes the reliability.

[0062] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a fatigue reliability analysis method for a welding structure under non-Gaussian random loads, which has the following beneficial effects:

[0063] The structural reliability analysis method adopted by the present invention is the uniform importance sampling method based on rejection-control (UIS-RC method). This method improves the efficiency of the original method by introducing rejection control into the uniform importance sampling and discarding samples with lower weights. This method can obtain efficient and accurate results without the information of the most probable point, and realizes the efficient and robust solution of the structural reliability analysis problem.

[0064] The present invention uses the Gaussian mixture model (GMM model) to decompose the non-Gaussian equivalent power spectrum into a combination of Gaussian components, and combines the time-frequency domain hybrid method to obtain the fatigue life of the pipeline welding structure. By combining the advantages of the time-frequency domain method, it accurately calculates the fatigue life of the pipeline welding structure under non-Gaussian loads, and at the same time avoids a large amount of calculations.

[0065] Based on the Bayesian optimization theory and K-fold cross-validation, the present invention trains a support vector regression model to replace the finite element analysis for reliability evaluation, reduces the calculation cost, and the established machine learning model has small prediction result dispersion and high accuracy.

[0066] The technical solutions of the present invention will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] 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 the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0068] Figure 1 is a schematic flow chart of the fatigue reliability analysis method for a welding structure under non-Gaussian random loads provided by an embodiment of the present invention.

[0069] Figure 2 Schematic diagram of the insertion welding structure of a 304L stainless steel pipeline provided by an embodiment of the present invention.

[0070] Figure 3 Schematic diagram of the simulation results of non-Gaussian loads provided by an embodiment of the present invention.

[0071] Figure 4 Schematic diagram of the process for extracting the power spectrum of the equivalent stress at the dangerous point of the pipeline welding structure by combining the notch stress method and the critical plane method provided by an embodiment of the present invention.

[0072] Figure 5 Schematic diagram of the relationship between the critical plane and the direction cosine at the dangerous point of the pipeline welding structure provided by an embodiment of the present invention.

[0073] Figure 6 Schematic diagram of the power spectral density of the equivalent stress at the dangerous point provided by an embodiment of the present invention.

[0074] Figure 7 Schematic diagram of the power spectrum of the Gaussian decomposition stress provided by an embodiment of the present invention.

[0075] Figure 8 Schematic diagram of the training process of the support vector regression model provided by an embodiment of the present invention.

[0076] Figure 9 Schematic diagram of the prediction accuracy of the surrogate model provided by an embodiment of the present invention.

[0077] Figure 10 Schematic diagram of the calculation results of the fatigue reliability of the pipeline insertion welding structure provided by an embodiment of the present invention.

[0078] Figure 11 Schematic diagram of the sensitivity analysis results of each parameter of the pipeline provided by an embodiment of the present invention. Specific implementation manners

[0079] 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. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0080] An embodiment of the present invention discloses a fatigue reliability analysis method for a welded structure under non-Gaussian random loads. Refer to Figure 1 As shown, the method includes the following steps:

[0081] S1. Quantify each parameter of the pipeline welding structure to obtain a plurality of quantization samples representing the uncertainty of each parameter of the welding structure;

[0082] S2. Based on the quantified samples, perform finite element analysis on the pipeline welding structure in finite element software to determine the dangerous points in the pipeline welding structure;

[0083] S3. Use the notch stress method and the critical plane method to extract the non-Gaussian equivalent stress power spectrum of the dangerous points, and combine the Gaussian mixture model and the time-frequency domain hybrid method to obtain the fatigue life corresponding to the dangerous points;

[0084] S4. Construct a database based on the quantified samples and the fatigue life, and train a support vector regression model according to the database combined with the Bayesian optimization method;

[0085] S5. Use the support vector regression model to obtain the fatigue life of the target pipeline welding structure, and based on the fatigue life of the target pipeline welding structure, combine the UIS-RC method to realize the reliability analysis of the target pipeline welding structure;

[0086] S6. Based on the reliability analysis results, obtain the sensitivity factors corresponding to each parameter of the pipeline welding structure; and based on the sensitivity factors, obtain the influence degree of each parameter on the reliability of the pipeline welding structure.

[0087] Next, each of the above steps will be described in detail.

[0088] In the above step S1, each parameter of the pipeline welding structure is quantified to obtain multiple quantified samples representing the uncertainty of each parameter of the welding structure;

[0089] Among them, each parameter of the pipeline welding structure includes: geometric dimension parameters, material parameters, and non-Gaussian random load parameters of the pipeline welding structure; for example, for the in-line welding structure of a pipeline made of 304L stainless steel under non-Gaussian load, fatigue reliability analysis based on parameter uncertainty quantification can be referred to Figure 2 as shown. The performance parameters of this 304L stainless steel are shown in Table 1.

[0090] Table 1: Static material parameters and fatigue parameters of 304L stainless steel

[0091]

[0092] Based on this, when quantifying each parameter of the pipeline welding structure, it includes the following two parts:

[0093] 1. Use the uniform importance sampling method based on rejection-control (UIS-RC method) to quantify the geometric dimension parameters and material parameters of the pipeline welding structure; for example, select the material parameters E, ρ, and Poisson's ratio v e and the geometric dimension parameters as uncertain quantification samples, and their distributions are shown in Table 2.

[0094] Table 2 Random parameter distribution

[0095] Material parameters Mean value Standard deviation Elastic modulus of Weld 1 (GMPa) 190 9.5 Poisson's ratio of Weld 1 0.31 0 Elastic modulus of Weld 2 (GMPa) 204 10.2 Poisson's ratio of Weld 2 0.305 0.01525 Elastic modulus of base metal area (GMPa) 206 10.3 Poisson's ratio of base metal area 0.3 0.015 Density (uniform) (kg / m3) 7890 394.5 <![CDATA[Limit gap h1 (mm)]]> 0.0001 0.00033 times the mean value <![CDATA[Radius r1 (mm) of Weld 1]]> 0.0004 0.00033 times the mean value <![CDATA[Penetration depth h2 (mm)]]> 0.00045 0.00033 times the mean value

[0096] This method adds rejection control on the basis of the original uniform importance sampling method, specifically including:

[0097] (1) Obtain the distribution information of random variables of the pipeline welding structure, expressed as:

[0098]

[0099] where, Lower represents the lower boundary of sampling; Upper represents the upper boundary of sampling; F -1 (·) represents the inverse function of the cumulative distribution probability function; p represents the selected sampling probability value; represents the sample center of the i-th parameter x i ;

[0100] (2) Generate quantization samples of geometric dimension parameters and material parameters according to the distribution information of random variables of the pipeline welding structure; expressed as:

[0101] X = Lower + (Upper - Lower) * rand(L)

[0102] where, X represents the quantization sample; rand represents a random number uniformly distributed in the interval [0, 1]; L represents the number of quantization samples; different quantization samples correspond to different geometric parameters and material parameters;

[0103] (3) Obtain the weight of each sample point in the quantization sample X, expressed as:

[0104]

[0105] where, W K represents the weight of the K-th sample point; f xi represents the probability density function of the i-th parameter; X i,K represents the value of the K-th sample point corresponding to the i-th parameter;

[0106] (4) Compare the weight of each sample point with a constant threshold:

[0107] If the weight of the sample point is greater than the threshold C, retain the corresponding sample point, and update the weight of the retained sample point to W K *p c ; where, p c represents the regularization coefficient;

[0108] If the weight of the sample point is less than the threshold C, compare W K / C with the random number r: If W KIf / C is greater than the random number r, the corresponding sample points are retained, and the weights of the retained sample points are updated to W K *p c ; otherwise, resampling is performed; where r ∈ (0, 1);

[0109] (5) Repeat the above steps of quantifying geometric size parameters and material parameters until the number of retained sample points meets the preset sample size (which can be set to 1000).

[0110] 2. Quantify the non-Gaussian random load parameters of the pipeline welding structure through a non-linear method; specifically including:

[0111] (1) Introduce a non-linear transformation function to relate the non-Gaussian process to the Gaussian process, expressed as:

[0112]

[0113] Among them, Z(t) represents the non-Gaussian process; X(t) represents the Gaussian process; G(·) represents the transformation function; g -1 (·) represents the inverse transformation function, and G(·) = g -1 (·); if the transformation function G(·) is a monotonically increasing function, the Gaussian process X(t) and its corresponding transformed Z(t) have the same average up-crossing rate, peaks, and valleys at the same moment. This means that the transformation function only changes the amplitude and average value of the rainflow counting cycle, but does not change the number and order of the cycles;

[0114] (2) Use the Hermite transformation function based on the third moment, which expands the signal through Hermite polynomials (orthogonal polynomials) and can effectively capture the high-order statistical characteristics of the signal, especially the third moment (i.e., skewness) information. Generate non-Gaussian random loads for the pipeline welding structure that conform to the actual engineering situation; expressed as:

[0115]

[0116] Among them, Z0 represents the standardized non-Gaussian random load; X0 represents the standardized Gaussian random load; κ represents the constant coefficient; h3 represents the coefficient related to the third moment; μ Z represents the mean of the non-Gaussian process Z(t); δ Z represents the standard deviation of the non-Gaussian process Z(t); μ x represents the mean of the Gaussian process X(t); δ x represents the standard deviation of the Gaussian process X(t); G1(·) represents the Hermite transformation function based on the third moment;

[0117] In the embodiments of the present invention, a first-order approximation model coefficient is adopted, expressed as follows:

[0118]

[0119] However, the model coefficients can only ensure an appropriate representation of very mild non - linearities.

[0120] Winterstein and Kashef developed an empirical formula for the model coefficients to minimize the differences in the target skewness and kurtosis from the Hermite model; expressed as:

[0121]

[0122] In this formula, γ3 represents the skewness of the non - Gaussian random load; γ4 represents the kurtosis of the non - Gaussian random load; h4 represents the coefficient related to the fourth - moment; h 40 represents the base coefficient related to the fourth - moment; the developed model coefficients can be used in certain regions of skewness and kurtosis, with the range as follows:

[0123]

[0124] Figure 3 A non - Gaussian random process with a skewness of 0 and a kurtosis of 5 after being transformed by the Hermite function and its power spectral density.

[0125] In the above model coefficient formula, the skewness γ3 and kurtosis γ4 are the deviations of non - Gaussianity, defined as:

[0126]

[0127] In this formula, E(·) is the expected - value operator; μ Z represents the mean of the non - Gaussian process Z(t); δ Z represents the standard deviation of the non - Gaussian process Z0; that is, when the skewness γ3 is zero, the distribution is symmetric with respect to the mean. The kurtosis γ4 refers to the concentration of the PDF near the mean. If the kurtosis γ4 is greater than 3, the tails of the non - Gaussian distribution are longer than those of the Gaussian distribution. On the contrary, a kurtosis γ4 value less than 3 indicates that the non - Gaussian distribution is concentrated around the mean and has short tails. In actual operation, the skewness γ3 and kurtosis γ4 of the Gaussian process X0 can be set to 0 and 3 respectively.

[0128] The above results show that the simulation process of non - Gaussian random signals based on the non - linear transformation method can accurately control the skewness and kurtosis values of the simulated signals and can also accurately simulate the spectral shapes of various power spectral densities.

[0129] In the above step S2, according to the quantization samples, a finite - element analysis of the pipeline welding structure is carried out in finite - element software to determine the dangerous points in the pipeline welding structure, that is, the positions where stress concentration or fatigue damage is most likely to occur under specific load conditions.

[0130] Taking the 304L stainless steel mentioned above and Figure 3 as an example, it specifically includes:

[0131] (1) Establish a three-dimensional model according to the parameters of the slender pipeline solid model, and reasonably simplify the model on the premise of not affecting the analysis results while reducing the calculation amount. In the analysis of the dynamic response of the pipeline structure, in order to avoid large stress concentration at the connection position, the welding modeling method - the notch stress method is adopted to model the welded connection part with tetrahedron elements.

[0132] (2) Mesh the finite element model. The swept hexahedron mesh is selected. When meshing, follow the principle of dense meshing in important parts and sparse meshing in unimportant parts, so as to ensure the accuracy of the results in key parts and reduce the overall operation amount and improve the operation efficiency. The weld and the area near the weld root are important parts of this model, and the mesh size is 0.25mm; the thin-walled pipe is an unimportant part, and the mesh size is 1mm.

[0133] (3) Apply Figure 3 the simulated load in, define the boundary conditions, conduct finite element analysis, and obtain that the dangerous point of the pipeline inserted welding structure is at the weld toe.

[0134] In the above step S3, the non-Gaussian equivalent stress power spectrum of the dangerous point is extracted by using the notch stress method and the critical plane method, and the fatigue life corresponding to the dangerous point is obtained by combining the Gaussian mixture model and the time-frequency domain hybrid method;

[0135] This step mainly uses the EMD decomposition method to process the non-Gaussian random load. In the finite element analysis software, based on the notch stress method in the pipeline structure fatigue life analysis method combined with the critical plane method, the equivalent stress power spectral density function curve and the root mean square value of the critical plane are obtained. The Gaussian mixture model (GMM) is used to describe the probability statistical characteristics of the stress response at the dangerous point, specifically including:

[0136] S3.1. Extract the power spectra of each stress component at the dangerous point from the finite element analysis results through the notch stress method and the critical plane method; and synthesize the power spectra of each stress component into the non-Gaussian equivalent stress power spectrum of the dangerous point on the critical plane; see Figure 4 shown, specifically including:

[0137] S3.11. Extract the dynamic response at the dangerous point in the pipeline welding structure through the notch stress method. Here, the dynamic response refers to the change of the stress component with time in the pipeline welding structure under the action of random load; then determine the concentrated position of each stress component based on this dynamic response as the position of the dangerous point;

[0138] S3.12. Determine the critical plane of the dangerous point based on the critical plane method; specifically:

[0139] The failure criterion corresponding to the above critical plane method is expressed as:

[0140] σ eq (t) = {σ km (t), P, ψ}

[0141] Among them, σ eq (t) represents the equivalent stress; σ km (t) represents the stress or strain components of the critical points in different directions solved by finite element analysis; P represents the critical plane parameter; ψ represents the material property. The form of the equivalent stress is related to the selection of the critical plane position. In the present invention, the position of the maximum principal stress is selected as the critical plane, and the relationship between the critical plane position and the direction cosine is as Figure 5 shown, and the expression of the equivalent stress is:

[0142]

[0143] Among them, σ xx (t) represents the principal stress in the X-axis direction; σ yy (t) represents the principal stress in the Y-axis direction; σ zz (t) represents the principal stress in the Z-axis direction; σ xy (t) represents the principal stress in the direction of the angle between the X-axis and the Y-axis; σ xz (t) represents the principal stress in the direction of the angle between the X-axis and the Z-axis; σ yz (t) represents the principal stress in the direction of the angle between the Y-axis and the Z-axis; l1 represents the average direction cosine of σ xx (t); m1 represents the average direction cosine of σ yy (t); n1 represents the average direction cosine of σ zz (t); l1, m1, n1 satisfy the orthogonality condition as follows:

[0144]

[0145] The equivalent stress is expressed by stress components as:

[0146]

[0147] Among them, a η represents the coefficient in the fatigue failure criterion of the ηth stress component;

[0148] The present invention uses the maximum variance method to determine the critical plane position of the critical point. This method is based on the maximum principal stress equivalent criterion, calculates the variance of the power spectral density of the equivalent stress of each plane at the weak position of the structure, and the plane with the maximum variance is the critical plane.

[0149] The unilateral power spectral density matrix of the pipeline welding structure in the frequency domain is as follows:

[0150]

[0151] Among them, G km (f) represents the cross-power spectral density function of σ(t) (k, m = 1, ..., 6); G kk (f) represents the auto-power spectral density function of σ(t), obtained from the power spectrum of the stress components calculated by finite element analysis, and G km (f) has a negligible impact on the result.

[0152] The covariance matrix μ in the frequency domain xst can be calculated by the following formula:

[0153]

[0154] Among them, μ xst is the covariance matrix of the stress tensor of the pipeline welding structure; the stress tensor is expressed as: σ(t) = [σ xx (t), σ yy (t), σ zz (t), σ xy (t), σ xz (t), σ yz (t)]; the covariance matrix is expressed in matrix form as:

[0155]

[0156] Among them, μ km represents the cross-stress component power spectral density variance of the kth stress component and the mth stress component (k, m = 1, ..., 6); μ kk represents the stress component power spectral density variance of the kth stress component;

[0157] The equivalent stress power spectral density variance is defined as follows:

[0158]

[0159] Among them, μ eq represents the equivalent stress power spectral density variance; a k represents the coefficient in the fatigue failure criterion of the kth stress component; a m represents the coefficient in the fatigue failure criterion of the mth stress component;

[0160] By changing the magnitudes of the direction cosines l1, m1, n1 to change the position, the power spectral density variances at different positions are statistically analyzed, and the position with the maximum value is selected as the critical plane

[0161] S3.13. Based on the critical plane obtained in step S3.12, obtain the non-Gaussian equivalent stress power spectrum of the dangerous point on this critical plane; expressed as:

[0162]

[0163] Among them, G eq (f) represents the non-Gaussian equivalent stress power spectrum; a k represents the coefficient in the fatigue failure criterion of the k-th stress component; a m represents the coefficient in the fatigue failure criterion of the m-th stress component; G km (f) represents the cross-power spectral density function of the k-th stress component and the m-th stress component;

[0164] Since the influence of the cross-spectrum power spectral density on the fatigue life result is negligible when using the frequency-domain critical plane method for analysis, the equivalent stress power spectrum on the critical plane can be simplified and calculated as follows, and the result is as Figure 6 shown:

[0165]

[0166] Among them, G kk (f) represents the power spectral density function of the k-th stress component;

[0167] S3.2. Use the Gaussian mixture model (GMM model) to convert the non-Gaussian equivalent stress power spectral density into a combination of multiple Gaussian components, which is expressed as:

[0168] f NG (x) = α1f1(x) + α2f2(x) +... + α v-1 f v-1 (x) + α v f v (x)

[0169]

[0170] Among them, f NG (x) represents the probability density function of the non-Gaussian process; f v (x) represents the probability density function of the v-th Gaussian component σ v , α v represents the weight coefficient of f v (x); and α1 + α2 +... α v = 1; x represents the non-Gaussian random load variable;

[0171] The present invention uses a third-order Gaussian mixture model. To solve the fatigue life of the welded structure, the GMM model can decompose the non-Gaussian process (the equivalent stress power spectrum based on the critical plane) into Gaussian processes with different weight coefficients, and further use higher-order statistics to decompose the non-Gaussian equivalent stress power spectral density (PSD) into three PSDs with different magnitudes, introducing the Gaussian decomposition characteristics into the frequency domain. The variance of the non-Gaussian equivalent stress power spectrum is:

[0172]

[0173] For three Gaussian components, there are:

[0174]

[0175] where S1(f), S2(f), and S3(f) are the PSDs of the three Gaussian components, are the variances of the three Gaussian processes, then there are:

[0176]

[0177] G eq (f) = α1S1(f) + α2S2(f) + α3S3(f)

[0178] To derive the rainflow distribution of a non-Gaussian process based on frequency-domain data, it is necessary to determine the magnitudes of S1(f), S2(f), and S3(f). Assume that their sum is proportional along the frequency axis:

[0179] G eq (f) = η1S X (f), G eq (f) = η2S X (f), G eq (f) = η3S X (f)

[0180] where η1, η2, and η3 are proportionality constants. By solving the above two equations simultaneously, we get:

[0181]

[0182] At this time, there are 6 unknowns α1, α2, α3, σ1, σ2, and σ3. Therefore, 6 equations need to be constructed to solve for the unknowns. The true values of the higher-order statistics of non-Gaussian random loads in engineering practice are unknown, and substitute values are generally used. The second-order, fourth-order, sixth-order, eighth-order, and tenth-order statistical moments of non-Gaussian random loads can be obtained by the following formula.

[0183]

[0184] where m represents the statistical moment of the non-Gaussian load, the subscript represents the order; m' represents the estimated value of the statistic;

[0185] When T is large enough, the approximate value will approach the true value. According to the GMM formula, the higher-order moments of the Gaussian process can be expressed as a function of the standard deviation. Therefore, there are:

[0186]

[0187] The first 10 high-order moments are obtained from the power spectral density function results as follows:

[0188] m2 = 2.025×10^1

[0189] m4 = 2.308×10^3

[0190] m6 = 5.961×10^5

[0191] m8 = 2.607×10^8

[0192] m 10 = 1.639×10^11

[0193] Substitute the above results into the above formula, and the coefficient and the mean square value of the Gaussian component are obtained by solving the system of equations:

[0194] α1 = 0.0602, α2 = 0.4249, α3 = 0.5149

[0195]

[0196] Find the values of the proportionality constants η1, η2, and η3 according to the above results:

[0197]

[0198] According to the Gaussian component proportionality coefficient and the response power spectrum, a schematic diagram of the third-order Gaussian decomposition model can be drawn, as Figure 7 shown.

[0199] S3.3. Use the time-frequency domain conversion method and the rainflow counting method to calculate the fatigue damage of each Gaussian component to the pipeline welding structure and obtain the fatigue life; specifically including:

[0200] S3.31. Convert each Gaussian component from the frequency-domain signal to the time-domain signal through the time-frequency domain conversion method; specifically:

[0201] Use the inverse Fourier transform to convert the Gaussian component from the frequency-domain signal to the time-domain signal; expressed as:

[0202]

[0203] where X(f) represents the frequency-domain signal corresponding to the Gaussian component; x(t) represents the time-domain signal corresponding to the Gaussian component; f represents the frequency; j represents the imaginary unit.

[0204] S3.32. Obtain the fatigue damage caused by each Gaussian component in the time domain through the rainflow counting method;

[0205] The rain - flow counting method is used to calculate the fatigue damage caused by each Gaussian component. The original stress - time series is converted into an extreme - value series, the peaks and valleys in the load are identified, and according to the extreme - value series, combined with Matlab, the rain - flow counting method is used to extract each cycle and record the amplitude and direction.

[0206] For each cycle, calculate the fatigue damage it causes according to the S - N curve. According to Miner's rule, the fatigue damage caused by a single Gaussian component is estimated as:

[0207]

[0208] where D γ represents the damage degree caused by the γ - th Gaussian component; N a represents the counting times of the h - th cycle; N f,h is the fatigue life corresponding to the h - th cycle.

[0209] S3.33. Use Miner's criterion to accumulate the fatigue damage of each Gaussian component to obtain the total fatigue damage and the corresponding fatigue life; which is expressed as:

[0210]

[0211] where D GMM represents the total fatigue damage; T represents the fatigue life;

[0212] In the above step S4, construct a database according to the quantization samples and the fatigue life, and train a support vector regression model in combination with the Bayesian optimization method; including:

[0213] (1) Initialize the quantization samples, and perform training after normalizing the initialized quantization samples;

[0214] (2) Set the parameters to be optimized (penalty coefficient and kernel function parameter) and the corresponding value ranges;

[0215] (3) Define the objective function to evaluate the performance of the parameters to be optimized;

[0216] (4) Set the maximum number of iterations for optimization, which can be set to 100;

[0217] (5) Use the Bayesian optimization method to optimize the parameters to be optimized in the support vector regression model in the current round; the optimization process is as Figure 8 shown;

[0218] (6) After the optimization ends, set the obtained best feasible solution as the optimal parameter into the support vector regression model;

[0219] (7) Verify the results through simulation experiments to prove the effectiveness of the optimization algorithm. The comparison between the model calculation results and the simulation experiment verification results is as Figure 9 shown; in the embodiment of the present invention, the prediction results are all within twice the band, meeting the accuracy requirements, which proves the effectiveness of the optimization algorithm.

[0220] In the above step S5, a support vector regression model is used to obtain the fatigue life of the target pipeline welding structure, and the reliability analysis of the target pipeline welding structure is realized according to the fatigue life of the target pipeline welding structure; specifically including:

[0221] (1) Input the fatigue life of the target pipeline welding structure into the load-life fatigue interference model to obtain the corresponding performance index; the load-life fatigue interference model is expressed as:

[0222] G2 = lgN f -lgN d

[0223] wherein, G2 represents the performance index; N f represents the fatigue life of the target pipeline welding structure; N d represents the preset life;

[0224] (2) Obtain the corresponding indicative value according to the performance index, which is expressed as:

[0225]

[0226] wherein, I represents the indicative value;

[0227] (3) Obtain the failure probability of the target pipeline welding structure according to the indicative value, which is expressed as:

[0228]

[0229] wherein, P f represents the failure probability; N represents the quantization sample size; is the final weight of the Kth sample point;

[0230] (4) Obtain the reliability of the target pipeline welding structure according to the failure probability, which is expressed as:

[0231] R = 1 - P f

[0232] wherein, R represents the reliability. The solution result of the reliability of the pipeline welding structure is as Figure 10 shown.

[0233] In step S6 above, based on the reliability analysis results, obtain the sensitivity factor corresponding to each quantization sample; and obtain the influence degree of each quantization sample on the reliability of the pipeline welding structure based on the sensitivity factor; and obtain the parameters with greater influence on the results.

[0234] In the embodiment of the present invention, based on the Monte Carlo method for sensitivity analysis of each parameter, the mean and variance of the pipeline insertion welding structure can be obtained when the design life is 10 8 s, and the sensitivity of its basic random parameters {E1, E2, E3, υ1, υ2, υ3, ρ, h1, r1, h2} relative to the failure probability P f is expressed as:

[0235]

[0236] Where is the probability density function of the i-th parameter x i , is the sample center of the i-th parameter, is the sample standard deviation of the i-th parameter.

[0237] Considering that the physical units of these 10 basic random parameters {E1, E2, E3, υ1, υ2, υ3, ρ, h1, r1, h2} are different, the obtained sensitivity cannot directly reflect the magnitude of the influence of the parameters on the results.

[0238] To solve this problem, it is necessary to perform a dimensionless treatment on the calculated sensitivity, which is expressed as:

[0239]

[0240] Where α i and η i respectively represent the sensitivities of the mean and standard deviation of each basic random parameter to the failure probability of the pipeline welding structure after dimensionless treatment.

[0241] Using the dimensionless sensitivity data, the sensitivity factor of each random variable relative to the pipeline insertion welding structure can be calculated, and thus the ranking of the influence magnitudes of each basic random parameter can be obtained. Its expression is as follows:

[0242]

[0243] Where s i is the sensitivity gradient of each basic random parameter. The sensitivity factor λ i can be calculated using s i :

[0244]

[0245] Where It is the sum of the sensitivity gradients of each basic random parameter.

[0246] By calculation, the sensitivity factors of the basic random parameters {E1, E2, E3, υ1, υ2, υ3, ρ, h1, r1, h2} are shown in Table 3 and Figure 11 as follows.

[0247] Table 3 Sensitivity Factors

[0248] Sensitivity category Sensitivity factor Sorting <![CDATA[Radius r1 of Weld 1]]> 0.393500 1 <![CDATA[Limiting gap h1]]> 0.317400 2 <![CDATA[Penetration depth h2]]> 0.186800 3 Elastic modulus of Weld 1 0.024500 4 Poisson's ratio of Weld 2 0.022100 5 Elastic modulus of Weld 2 0.022000 6 Poisson's ratio of Weld 1 0.020738 7 Poisson's ratio of base metal 0.001500 8 Elastic modulus of base metal 0.010799 9 Density 0.000506 10

[0249] From Figure 11 it can be seen that the influence proportions of the basic parameters {h1, h2, r1} are very large. The order of the influence on the failure probability of the pipeline insertion welding structure is: r1 > h1 > h2 > others. This means that the uncertainty of geometric dimensions has a greater impact on the failure probability of the pipeline welding structure, and sufficient attention should be paid to these three parameters when conducting reliability design for pipeline welding.

[0250] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other.

[0251] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fatigue reliability analysis method for welded structures under non-Gaussian random loads, characterized in that, It includes the following steps: S1. Quantify each parameter of the pipeline welding structure to obtain multiple quantization samples representing the uncertainty of each parameter of the welding structure; S2. According to the quantization samples, perform finite element analysis on the pipeline welding structure in finite element software to determine the dangerous points in the pipeline welding structure; S3. Use the notch stress method and the critical plane method to extract the non-Gaussian equivalent stress power spectrum of the dangerous points, and combine the Gaussian mixture model and the time-frequency domain hybrid method to obtain the fatigue life corresponding to the dangerous points; S4. Construct a database according to the quantization samples and the fatigue life, and train a support vector regression model according to the database combined with the Bayesian optimization method; S5. Use the support vector regression model to obtain the fatigue life of the target pipeline welding structure, and according to the fatigue life of the target pipeline welding structure, combine the UIS-RC method to realize the reliability analysis of the target pipeline welding structure; The specific steps of step S3 include: S3.

1. Through the notch stress method and the critical plane method, extract the power spectrum of each stress component at the dangerous points from the finite element analysis results; and synthesize the power spectra of each stress component into the non-Gaussian equivalent stress power spectrum of the dangerous points on the critical plane; S3.

2. Use the Gaussian mixture model to convert the non-Gaussian equivalent stress power spectrum into a combination of multiple Gaussian components; S3.

3. Use the time-frequency domain conversion method and the rain flow counting method to calculate the fatigue damage of each Gaussian component to the pipeline welding structure and obtain the fatigue life; The specific steps of step S3.1 include: S3.

11. Extract the dynamic response at the dangerous points in the pipeline welding structure through the notch stress method; and based on the dynamic response, determine the concentration position of each stress component as the position of the dangerous points; S3.

12. Determine the critical plane of the dangerous points based on the critical plane method; S3.

13. Obtain the non-Gaussian equivalent stress power spectrum of the dangerous points on the critical plane; In step S5, the reliability analysis of the target pipeline welding structure is realized by combining the UIS-RC method according to the fatigue life of the target pipeline welding structure, specifically including: (1) Input the fatigue life of the target pipeline welding structure into the load-life fatigue interference model to obtain the corresponding performance index; the load-life fatigue interference model is expressed as: G2 = lgN f -lgN d Among them, G2 represents a performance index; N f represents the fatigue life of the welded structure of the target pipeline; N d represents a preset life; (2) According to the performance index, obtain the corresponding characteristic value, expressed as: where I represents the characteristic value; (3) According to the characteristic value, obtain the failure probability of the target pipeline welding structure, expressed as: Among them, P f represents the failure probability; N represents the quantization sample size; is the final weight of the Kth sample point; (4) According to the failure probability, obtain the reliability of the target pipeline welding structure, expressed as: R = 1 - P f where R represents the reliability.

2. The fatigue reliability analysis method of a welded structure under non-Gaussian random loads according to claim 1, characterized in that It also includes: S6. Based on the reliability analysis results, obtain the sensitivity factors corresponding to each parameter of the pipeline welding structure; and based on the sensitivity factors, obtain the influence degree of each parameter on the reliability of the pipeline welding structure.

3. A fatigue reliability analysis method for a welded structure under non-Gaussian random loads according to claim 1, characterized in that The parameters of the pipeline welding structure include: geometric dimension parameters, material parameters and non-Gaussian random load parameters of the pipeline welding structure.

4. A method for analyzing the fatigue reliability of a welded structure under a non-Gaussian random load according to claim 3, characterized in that In step S1, the UIS-RC method is used to quantify the geometric dimension parameters and material parameters of the pipeline welding structure; specifically including: (1) Obtain the distribution information of random variables of the pipeline welding structure, expressed as: Among them, Lower represents the lower boundary of sampling; Upper represents the upper boundary of sampling; F -1 (·) represents the inverse function of the cumulative distribution probability function; p represents the selected sampling probability value; represents the sample center of the i-th parameter x i ; (2) Generate quantization samples of geometric dimension parameters and material parameters according to the distribution information of random variables of the pipeline welding structure; expressed as: X = Lower + (Upper - Lower) * rand(L) where X represents the quantization sample; rand represents a random number uniformly distributed in the interval [0, 1]; L represents the number of quantization samples; different quantization samples correspond to different geometric parameters and material parameters respectively; (3) Obtain the weight of each sample point in the quantization sample X, expressed as: Among them, W K represents the weight of the K-th sample point; represents the probability density function of the i-th parameter; X i,K represents the value of the i-th parameter corresponding to the K-th sample point; (4) Compare the weight of each sample point with a constant threshold: If the weight of a sample point is greater than the threshold C, the corresponding sample point is retained, and the weight of the retained sample point is updated to W K *p c ; where p c represents the regularization coefficient; If the weight of a sample point is less than the threshold C, then compare W K / C with a random number r: if W K / C is greater than the random number r, then retain the corresponding sample point and update the weight of the retained sample point to W K *p c ; otherwise, resample; where r ∈ (0, 1); (5) Repeat the above steps of quantizing geometric dimension parameters and material parameters until the number of remaining sample points meets the preset sample capacity.

5. A method for analyzing the fatigue reliability of a welded structure under non-Gaussian random loads according to claim 3, characterized in that In step S1, the non-Gaussian random load parameters of the pipeline welding structure are quantized by a non-linear method; specifically including: (1) Introduce a non-linear transformation function to relate the non-Gaussian process to the Gaussian process, expressed as: Among them, Z(t) represents a non-Gaussian process; X(t) represents a Gaussian process; G(·) represents a transformation function; g -1 (·) represents the inverse transformation function, and G(·) = g -1 (·); (2) Use the Hermite transformation function based on the third moment, expand the signal by the Hermite polynomial, and generate a non-Gaussian random load of the pipeline welding structure that conforms to the actual engineering situation; expressed as: Among them, Z0 represents the non-Gaussian random load after standardization; X0 represents the Gaussian random load after standardization; κ represents a constant coefficient; h3 represents the coefficient related to the third moment; μ Z represents the mean value of the non-Gaussian process Z(t); δ Z represents the standard deviation of the non-Gaussian process Z(t); μ x represents the mean value of the Gaussian process X(t); δ x represents the standard deviation of the Gaussian process X(t); G1(·) represents the Hermite transformation function based on the third moment.

6. The fatigue reliability analysis method of a welded structure under non-Gaussian random load according to claim 1, wherein The specific steps of step S3.3 include: S3.

31. Convert each Gaussian component from the frequency-domain signal to the time-domain signal through the time-frequency domain conversion method; S3.

32. Obtain the fatigue damage caused by each Gaussian component in the time domain through the rainflow counting method; S3.

33. Use the Miner criterion to accumulate the fatigue damage of each Gaussian component to obtain the total fatigue damage and the corresponding fatigue life.

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