Pi-GPR-based welded joint fatigue life prediction method and system

Abstract

The invention relates to the technical field of welding heads, in particular to a Pi-GPR-based welding head fatigue life prediction method and system, and the method comprises the steps: constructing an experiment system; welding materials are selected, welding parameters are set, and a cross section image of the welding test piece is collected; different gap sizes are set, stress-cycle number curve data are obtained, and fatigue testing is conducted on the welding test piece; performing correlation coefficient and total stress model analysis on the area and length characteristics of the welding seam; and constructing a Pi-GPR model, designing a Matern covariance function, and optimizing Gaussian parameters and covariance function hyper-parameters by using a logarithm marginal likelihood function. The problems that a traditional physical model is high in calculation complexity, long in analysis period and difficult to comprehensively cover physical phenomena related to fatigue fracture are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of welding heads, and particularly to a method and system for predicting the fatigue life of welding heads based on Pi-GPR. Background Art

[0002] The welding process is widely used in many industries such as automobile manufacturing, shipbuilding, and construction. However, due to factors such as stress concentration caused by geometric discontinuity, residual stress generated by heat input, and material inhomogeneity in the welded joint, fatigue fracture is extremely likely to occur, seriously threatening the reliability and safety of engineering structures. Therefore, accurately predicting the fatigue life of welded joints is crucial for ensuring the normal operation of engineering structures.

[0003] Traditional fatigue life prediction methods mainly include physical models and data-driven models. Among them, physical models such as the finite element method (FEM) can simulate the complex geometric shape of welded joints based on physical principles and have relatively high prediction accuracy, but they have a large computational load, a long analysis period, and it is difficult to cover all physical phenomena related to fatigue fracture. Data-driven models use experimental data to predict fatigue life. Although they have high computational efficiency, their accuracy highly depends on a large amount of experimental data, and the quality of experimental data has a significant impact on the prediction results. In addition, existing models are difficult to simultaneously handle the non-linear characteristics of the welding process and quantify the uncertainty of fatigue life prediction. Summary of the Invention

[0004] Aiming at the deficiencies of the existing methods, the present invention solves the problems of high computational complexity, long analysis period, and difficulty in comprehensively covering physical phenomena related to fatigue fracture of traditional physical models; effectively improves the defects of excessive dependence of data-driven models on a large amount of experimental data and inability to accurately quantify prediction uncertainty; by deeply integrating physical information and Gaussian process regression technology, gives full play to the advantages of the Pi-GPR model, realizes high-precision prediction of the fatigue life of welded joints, provides a solid and reliable basis for the design, maintenance, and safety assessment of engineering structures, and thus effectively guarantees the stability and reliability of various engineering structures during actual operation, and reduces the safety risks and economic losses caused by fatigue failure of welded joints.

[0005] The technical solution adopted by the present invention is that the method for predicting the fatigue life of a welding head based on Pi-GPR includes the following steps:

[0006] Step 1: Construct an experimental system; select welding materials, set welding parameters, and collect cross-sectional images of welded specimens.

[0007] As a preferred embodiment of the present invention, a cold metal transfer welding process is used to construct an experimental system including a welding machine, an industrial robot, and a welding fixture.

[0008] As a preferred embodiment of the present invention, welding materials are selected using stress values and stress ratios.

[0009] As a preferred embodiment of the present invention, the welding material is HSGS.

[0010] Step 2: Set different gap sizes, obtain stress-cycle number curve data, and conduct fatigue tests on the welded specimens.

[0011] As a preferred embodiment of the present invention, the fatigue test is evaluated using the percentage error of the fatigue life.

[0012] Step 3: Conduct correlation coefficient and total stress model analyses on the cross-sectional area and length characteristics of the weld.

[0013] As a preferred embodiment of the present invention, the correlation coefficient analysis uses the Spearman correlation coefficient method.

[0014] As a preferred embodiment of the present invention, the correlation coefficient yields the first cross-sectional area, the first length characteristic, the second length characteristic, and the third length characteristic.

[0015] As a preferred embodiment of the present invention, the formula for the total stress model is:

[0016] M secondary =F axial ×e (6)

[0017]

[0018] where y is the perpendicular distance from the neutral axis to the cross-section, I inertia is the moment of inertia of the neutral axis, e is the inherent plate eccentricity generated by the geometric characteristics of the single-angle lap welded joint, and e is defined as the sum of the base metal thicknesses t and δ; M secondary is the accidental secondary bending moment during the test; F axial is the axial force applied by the fatigue testing machine to the welded joint during the fatigue test; σ force is the stress caused by F axial ; σ moment is the stress caused by M secondary and is used to calculate the cross-sectional area A cross-section .

[0019] Step 4: Construct a Pi-GPR model, and train the Pi-GPR model using the weld area and length characteristics; design a Matern covariance function, and optimize the Gaussian parameters and covariance function hyperparameters using the log marginal likelihood function.

[0020] As a preferred embodiment of the present invention, step 4 specifically includes:

[0021] First, for any two input points x and x', set the mean function and covariance function of the random variable f(x);

[0022] Secondly, according to the prior distribution of the function value f represented by the observed data point (X, y'), X represents the input variable of the Pi-GPR model during training, and y' represents the actual fatigue life measured in the fatigue test; f models the relationship between X and y', and the variance added to the function value f is Gaussian noise;

[0023] Next, predict the new input data point X * The function value f * The distribution of , we get the covariance equation between the training points and the test points;

[0024] Secondly, the regression model is introduced to select the observation data points and input data points;

[0025] Secondly, the Matern covariance function is improved by using sine Bessel to quantify the similarity between function values ​​at different input data points;

[0026] The improved Matern covariance function formula is:

[0027]

[0028] Among them, K ν represents the sine Bessel function, Γ(ν) is the gamma function, ν is the smoothness parameter, and l represent the variance and length scale, respectively;

[0029] As a preferred embodiment of the present invention, the logarithmic marginal likelihood function is used to calculate the hyperparameters of the Gaussian parameters and the Matern covariance function. To optimize, the formula is:

[0030]

[0031] Where n is the number of iterations,

[0032] As a preferred embodiment of the present invention, a welding head fatigue life prediction system based on Pi-GPR includes: a memory for storing instructions executable by a processor; and a processor for executing instructions to implement a welding head fatigue life prediction method based on Pi-GPR.

[0033] Beneficial effects of the present invention:

[0034] 1. The Pi-GPR model adopts the Matern covariance function, improves the Matern function using the sine Bessel function, and optimizes the Gaussian parameters and covariance function hyperparameters using the log marginal likelihood function to prevent model overfitting and enhance robustness.

[0035] 2. Improve prediction accuracy: By integrating physical information, key factors such as geometric features and stress distribution during the welding process are deeply considered. The weld cross-sectional area and its related length features of the welded joint cross-section are analyzed to establish a close connection with the fatigue life. These physical features reflect the actual structural characteristics of the welded joint, enabling the model to accurately simulate the physical process of fatigue failure. Verified by a large amount of experimental data, its prediction results are highly consistent with the actual fatigue life. Compared with traditional models, it can more accurately judge the fatigue life of welded joints under different working conditions, effectively reduce prediction errors, and provide a reliable guarantee for the safety design of engineering structures.

[0036] 3. Reduce data dependence: The physically informed Gaussian process regression model uses easily measurable length-related physical features, which contain rich internal information of the welded joint. Based on the fatigue fracture mechanics principle, they can replace the role of some experimental data to a certain extent. Through comparative experiments, it is found that even when the proportion of training data is low, the prediction performance of the model still remains within an acceptable range. This not only reduces the cost of data collection and processing but also improves the prediction efficiency, making fatigue life prediction more feasible and practical in actual engineering.

[0037] 4. Quantify prediction uncertainty and enhance the robustness of the system: Different welding conditions and material properties will lead to certain uncertainties in fatigue life. By calculating the mean and variance of the prediction results and the design of the Pi-GPR model and giving the confidence interval, the model quantifies this uncertainty, making the system have a certain degree of robustness, improving the reliability and stability of the system, and allowing engineers to intuitively understand the reliability of the prediction results.

[0038] 5. Good generalization ability: Thanks to the physical principles integrated in the Pi-GPR model and the carefully selected input features, they have a certain degree of universality and adaptability. Under different welding processes and structural scenarios, the model can quickly adjust and accurately predict the fatigue life, providing a unified and reliable method for the fatigue analysis of various engineering structures, greatly expanding the application scope of the model, and meeting the complex and changing needs in actual engineering. Brief Description of the Drawings

[0039] Figure 1 is the flowchart of the welding joint fatigue life prediction method based on Pi-GPR of the present invention;

[0040] Figure 2Schematic diagram of the welding experimental device;

[0041] Figure 3 For x 1 = 0.2, x 2 = 0.5 fatigue test specimen and stress-time graph;

[0042] Figure 4 Schematic diagram of the cross-section and length characteristics of the welded joint;

[0043] Figure 5 For increasing A 1 Cross-section diagram of the welded specimen after fatigue fracture with related length characteristics;

[0044] Figure 6 Pi-GPR model prediction result graph, scatter plot of predicted values and actual values (left) and confidence interval (right). Specific implementation manners

[0045] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, so it only shows the components related to the present invention.

[0046] As Figure 1 shown, the method for predicting the fatigue life of a welded joint based on Pi-GPR includes the following steps:

[0047] Step 1: Establish experimental data and conduct welding experiments. Select the cold metal transfer (CMT) welding process, build an experimental system including a welding machine, an industrial robot, and a welding fixture, use high-strength galvanized steel (HSGS) as the welding material, set different welding parameters (such as gap size, wire feeding speed, welding speed, etc.) for welding, preprocess the welded specimen and then collect the cross-sectional image of the welded specimen. As Figure 2 shown, it shows the layout of the welding machine, robot, fixture, and specimen; select six different stress values, which respectively correspond to 10% - 60% of the ultimate tensile strength (UTS) of the HSGS base material, and the stress ratio is fixed at 0.1. This precise stress parameter setting helps to systematically study the fatigue performance of the welded joint under different stress levels; the fatigue test strictly processes and tests the CMT welded specimen in accordance with the ASTM E466 standard to ensure the standardization of the test and the reliability of the results, making the data under different experimental conditions comparable; the applied stress uses a sine function to precisely control the stress value range σ range and stress ratio σ ratio , and the specific formula is as follows:

[0048] σ range = σ max - σ min (1)

[0049] σ ratio = σ max / σ min (2)

[0050] Wherein, σ range is the stress value range; σ ratio is the stress ratio; σ max is the maximum stress; σ min is the minimum stress.

[0051] Step 2: Data preprocessing. Conduct fatigue tests. Process the welded specimens to meet the standards. Use a universal axial fatigue testing machine. Set different stress value ranges and stress ratios for testing. Conduct multiple repeated tests under each condition to obtain stress-cycle number (S-N) curve data;

[0052] As Figure 3 shown, select x 1 = 0.2, x 2 = 0.5, and conduct fatigue life tests at different wire feeding speeds and welding speeds. Explain the specimen structure and test stress parameters to obtain the percentage error of fatigue life at different gap sizes. The formula is:

[0053]

[0054] Wherein, x 1 , x 2 are the gap sizes; N represents the number of cycles; Fatiguelife represents the fatigue life, expressed on a logarithmic scale of 10.

[0055] Obtain S-N curve data using the test data, which provides key experimental basis for subsequent model training and verification. It is the foundation for establishing an accurate fatigue life prediction model, can comprehensively evaluate the prediction performance of the Pi-GPR model and other comparison models. By comparing the differences between the predicted values and the actual test values, it helps to verify the applicability and generalization ability of the model under various working conditions, ensuring that the model can be applied to different scenarios in actual engineering and providing a reliable tool for predicting the fatigue life of engineering structures.

[0056] Step 3: Physical feature extraction. Analyze the geometric features of the cross-section of the welded joint. For example Figure 4 select the first cross-sectional area A 1 of the weld, the second cross-sectional area A 2 , the third cross-sectional area A 3 , as well as the first length feature L 1 related to the shape, the second length feature L 2 , the third length feature L 3 , the fourth length feature L 4 and the fifth length feature L 5, the sixth length feature L 6 ; Use the Spearman rank correlation coefficient SRCC to analyze the correlation between cross-sectional area, shape features and fatigue life;

[0057] The welded metal (i.e., welding material) has three intersection points P 1 , P 4 , P 5 , P 1 is the left intersection point of the first substrate and the welded metal, P 4 is the right intersection point of the first substrate and the welded metal, P 5 is the lowest intersection point of the first substrate and the welded metal; the welded metal has one intersection point P 2 with the second substrate, and the highest point of the welding material is P 3 ; P 1 P 2 is the first length feature, P 2 P 3 is the second length feature, P 1 P 3 is the third length feature, P 2 P 4 is the fourth length feature, P 4 P 5 is the fifth length feature, P 1 P 5 is the sixth length feature; P 1 P 2 P 3 constitutes the first cross-sectional area, P 1 P 2 P 4 constitutes the second cross-sectional area, P 1 P 4 P 5 constitutes the third cross-sectional area.

[0058] Taking the extracted physical features as the input variables of the Pi-GPR model can significantly improve the prediction accuracy compared with the model that only uses system features such as welding process parameters and fatigue test parameters;

[0059] The Spearman formula is as follows:

[0060]

[0061] Among them, ρ is the correlation coefficient, r is the correlation coefficient calculated from the actual data values, d i represents the rank difference between two variables, n is the total number of observed data, x i represents the value of the x variable in the sample, corresponds to the mean value of the x variable, y” i represents the value of the y” variable in the sample, Represents the mean value of the "y" variable, where "y" refers to the actual fatigue life measured from the samples.

[0062] It has more advantages than the traditional Pearson correlation coefficient (PCC) method in dealing with non - linear data such as fatigue tests of welded specimens, and can more accurately screen out the features strongly correlated with fatigue life. Select the cross - sectional area A of the weld 1 and the length feature L 1 , L 2 , L 3 .

[0063] Analyze the physical mechanisms by which the selected physical features affect fatigue life. For example, the relevant length features can extend fatigue life by changing stress distribution and increasing load - bearing capacity; as Figure 5 shown, increasing A 1 and the relevant length L 1 to L 3 features, A cross-section and I inertia increase, the total stress σ total decreases, the stress concentration phenomenon reduces, the stress borne by the welded joint during fatigue loading is more uniform, effectively delaying the initiation and propagation of fatigue cracks, and ultimately extending the fatigue life;

[0064] The formula for the total stress is:

[0065] M secondary = F axial ×e (6)

[0066]

[0067] where y is the perpendicular distance from the neutral axis to the cross - section, I inertia is the moment of inertia of the neutral axis, e is the inherent plate eccentricity caused by the geometric characteristics of the single - angle lap welded joint, and e is defined as the sum of the base metal thicknesses t and δ; M secondary is the accidental secondary bending moment during the test process; F axial is the axial force applied by the fatigue testing machine to the welded joint during the fatigue test; σ force is the stress caused by F axial ; σ moment is the stress caused by M secondary , and is used to calculate the cross - sectional area A cross-section of the welded joint in the x - axis and z - axis planes.

[0068] The present invention constructs a total stress model to analyze the selected physical features.

[0069] The selected physical features enable the model input to have data with practical physical significance and representativeness, thereby establishing a reasonable mapping relationship between the input and the output (fatigue life), allowing the model to make predictions based on physical principles and actual data laws, rather than relying solely on the statistical correlation of the data, and improving the reliability and interpretability of the model.

[0070] Step 4: Construct a Pi-GPR model to predict the fatigue life of the welded joint. By calculating the mean and variance of the prediction results, a confidence interval is given. This feature enables the Pi-GPR model to quantitatively evaluate the reliability of the prediction while providing the prediction results, allowing users to clearly understand the degree of uncertainty of the prediction results and providing more comprehensive information for engineering decisions.

[0071] The Pi-GPR (Physics Information-driven Gaussian Process Regression) model includes:

[0072] First, for any two input points x and x' starting from the input point x, set the mean function m(x) and covariance function k(x, x') of the random variable f(x). The formulas are:

[0073] f = [f(x 1 ), f(x 2 ), …, f(x n )], m(x) = E[f(x)] (8)

[0074] k(x, x') = E[(f(x) - m(x))(f(x') - m(x'))] (9)

[0075] Among them, E() is the average value.

[0076] Secondly, using the characteristics of GP, represent the prior distribution of the function value f according to the observed data points (X, y'). X represents the input variable of the Pi-GPR model during training, y' represents the actual fatigue life measured in the fatigue test, f models the relationship between X and y', and Gaussian noise with a variance of is added to the function value f:

[0077] f(x) ~ GP(m(x), k(x, x')) (10)

[0078]

[0079] Among them, f represents the function value modeled by the Gaussian process (GP); ε is Gaussian noise that follows a normal distribution ; is the variance of the noise.

[0080] Thirdly, predict the new input data point X* The function value f * is distributed according to a joint Gaussian distribution, and the covariance equation between the training points and the test points is obtained:

[0081]

[0082] where K * represents the covariance between the training points and the test points, and K ** represents the variance between the test points.

[0083] Secondly, a regression model is introduced to select the observed data points and the input data points for predicting the fatigue life distribution;

[0084]

[0085] Secondly, the similarity between the function values on different input data points is quantified, and a suitable covariance function is selected: The present invention selects the Matern covariance function, and uses the log marginal likelihood function to optimize the Gaussian parameters and the covariance function hyperparameters The smoothness parameter ν included in the Matern covariance function has low sensitivity to noise data and shows strong robustness in preventing overfitting, and can effectively handle the uncertainty and complexity in the experimental data, providing a guarantee for accurate prediction. The formula:

[0086]

[0087] where K ν represents the sine Bessel function, Γ(ν) corresponds to the gamma function, and l represent the variance and the length scale respectively; n is the number of iterations; when the length scale is L 1 it is l.

[0088] where I is the Bessel function, and - is the sign change.

[0089] As Figure 6 shown, the gap size is fixed at 0.5 mm, the welding speed is set at 60 and 80 cm / min, the wire feeding speed is defined as 7.0 m / min, and the representative values in the σ range are defined as uts - 20%, uts - 40%, and uts - 60%. The prediction result graph of the Pi - GPR model is obtained, including the scatter plot (left) of the predicted value and the actual value and the confidence interval (right), showing the prediction effect of the model from two perspectives of data distribution and uncertainty quantification, which is convenient for evaluating the reliability of the model.

[0090] To compare the effects of the root mean square error (RMSE) and its square as prediction performance metrics, the same training and test data sets were used for evaluation to ensure that the comparison process was both fair and effective;

[0091] By comparing the prediction performance metrics of the root mean square error (RMSE) and the coefficient of determination R-squared, and evaluating them with the same training data and test data, the fairness and effectiveness of the comparison were ensured, highlighting the advantages of the physics-informed Gaussian process regression model in terms of prediction accuracy and the ability to explain the variance of actual fatigue life. The formulas for the root mean square error (RMSE) and the coefficient of determination R-squared are as follows:

[0092]

[0093] where n represents the number of samples, represents the predicted value, and y i corresponds to the actual value, represents the average value of the actual values.

[0094] This comparison aimed to highlight the advantages of the Pi-GPR model in terms of prediction accuracy and its excellent ability to explain the variance of actual fatigue life; in addition, the performance of the Pi-GPR model under different training data ratios (TDR) was evaluated to determine the degree of dependence of the model on experimental data and to test its prediction efficacy under limited data conditions; by gradually reducing the ratio of training data, the changes in the model's prediction performance metrics were observed, and then the stability and reliability of the model under data-scarce conditions were analyzed. These analyses provided useful guidance on how to reasonably utilize limited experimental data in practical applications.

[0095] Inspired by the above ideal embodiments of the present invention, through the above description, relevant staff can completely make various changes and modifications without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for predicting fatigue life of welded joints based on Pi-GPR, characterized in that: The following steps are involved: Step 1: Build the experimental system; select welding materials, set welding parameters, and collect cross-sectional images of welding specimens; Step 2: Set different gap sizes, obtain stress-cycle number curve data, and perform fatigue test on the welding specimen; Step 3: Analyze the correlation coefficient and total stress model of the weld area and length characteristics; Step 4: Construct the Pi-GPR model and train the Pi-GPR model using the weld area and length features; design the Matern covariance function and use the logarithmic marginal likelihood function to optimize the Gaussian parameters and covariance function hyperparameters.

2. The Pi-GPR-based welding joint fatigue life prediction method according to claim 1 is characterized in that: Step 4 specifically includes: First, for any two input points x and x', set the mean function and covariance function of the random variable f(x); Secondly, according to the prior distribution of the function value f represented by the observed data point (X, y'), X represents the input variable of the Pi-GPR model during training, and y' represents the actual fatigue life measured in the fatigue test; f models the relationship between X and y', and the variance added to the function value f is Gaussian noise; Next, predict the new input data point X * The function value f * The distribution of , we get the covariance equation between the training points and the test points; Secondly, the regression model is introduced to select the observation data points and input data points; Secondly, the Matern covariance function is improved by using sine Bessel to quantify the similarity between function values ​​at different input data points; The improved Matern covariance function formula is: Among them, K ν represents the sine Bessel function, Γ(ν) is the gamma function, ν is the smoothness parameter, and l represent variance and length scale, respectively; 3. The Pi-GPR-based welding joint fatigue life prediction method according to claim 2 is characterized in that: Use the log-marginal likelihood function to determine the hyperparameters of the Gaussian parameters and the Matern covariance function To optimize, the formula is: Where n is the number of iterations, 4. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: The formula for the total stress model is: Where y is the vertical distance from the neutral axis to the cross section, I inertia is the moment of inertia about the neutral axis, e is the inherent plate eccentricity produced by the geometric characteristics of the single-angle lap weld joint, and e is defined as the sum of the parent material thickness t and δ; M secondary It is the unexpected secondary bending moment caused during the test; F axial The axial force applied by the fatigue testing machine to the welded joint during the fatigue test; σ force F axial The stress caused by moment M secondary The stress caused is used to calculate the cross-sectional area A of the weld joint on the x-axis and z-axis planes cross-section .

5. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: The correlation coefficient analysis was performed using the Spearman correlation coefficient method.

6. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: The first cross-sectional area, the first length characteristic, the second length characteristic and the third length characteristic are obtained through the correlation coefficient.

7. The Pi-GPR-based welding joint fatigue life prediction method according to claim 1, characterized in that: An experimental system including a welding machine, an industrial robot and a welding fixture was constructed using the cold metal transfer welding process.

8. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: Use stress values ​​and stress ratios to select welding materials.

9. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: The welding material is HSGS.

10. The method for predicting fatigue life of welding joints based on Pi-GPR according to claim 1, characterized in that: Fatigue tests are evaluated using the percentage error of fatigue life.

11. The welding joint fatigue life prediction system based on Pi-GPR is characterized by: include: a memory for storing instructions executable by a processor; A processor, used for executing instructions to implement the Pi-GPR-based welding joint fatigue life prediction method as described in any one of claims 1 to 10.

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