Steel bridge inclined strut node fatigue assessment hot spot stress method based on machine learning

Abstract

The invention belongs to the technical field of bridge construction, and particularly relates to a steel bridge diagonal bracing node fatigue assessment hot spot stress method based on machine learning. By constructing a hot spot stress concentration coefficient Gaussian regression process proxy model of the steel bridge inclined strut nodes, a mapping relation is established among geometric parameters of the steel bridge inclined strut nodes, welding seam type input variables and hot spot stress concentration coefficient output, so that the hot spot stress of different inclined strut nodes on different steel bridges is quickly determined. And in combination with a hot spot stress S-N curve and a random traffic flow loading method, realizing fatigue performance evaluation of the steel bridge diagonal bracing node. The method is suitable for various steel bridge structure systems including diagonal bracing nodes, including truss girders, box girders, long cantilever combined structures and the like, and has good engineering adaptability and popularization value.

Description

Technical Field

[0001] This invention belongs to the field of bridge construction technology, specifically relating to a hot spot stress method for fatigue assessment of steel bridge brace nodes based on machine learning. Background Technology

[0002] In modern steel bridge structures, diagonal bracing is widely used in main beam forms such as steel truss beams, diagonally braced box girders, and cross-braced composite beams to enhance lateral stiffness, control torsional deformation, and meet the stress requirements under complex load conditions. Diagonal bracing is connected to key components such as the main beam through welding or bolting. The joints are structurally complex, with concentrated stress paths, often accompanied by geometrical abrupt changes in welds, weld legs, and plate edges, easily forming localized stress concentration zones. Under long-term alternating vehicle loads and environmental effects, the joints are repeatedly stressed, making them highly susceptible to fatigue crack initiation and propagation, posing a significant risk of bridge structural failure. Numerous engineering studies have demonstrated that diagonal bracing joints are high-risk areas for fatigue cracking. Therefore, developing a fatigue reliability analysis method for joints that can be widely applied to steel beam diagonal bracing systems is of significant engineering importance for ensuring the long-term service safety of steel bridge structures.

[0003] Currently, the commonly used fatigue assessment methods in engineering mainly include the nominal stress method, the hot spot stress method, and the notch stress method. The nominal stress method is based on the average stress of the cross section for fatigue calculation. While simple, it cannot reflect the local stress concentration effect at the brace node, resulting in a conservative assessment. The hot spot stress method superimposes membrane stress and bending stress on the nominal stress, better characterizing the local stress concentration effect caused by geometric discontinuities. It has become a widely adopted method in engineering fields both domestically and internationally. The notch stress method further introduces nonlinear stress and considers the influence of details such as weld size and notch shape, enabling more accurate fatigue assessment of complex structural details. While theoretically sound, it requires extremely high precision in finite element modeling and geometric modeling, limiting its applicability.

[0004] However, the traditional hot spot stress method still has some limitations in practical engineering applications. For diagonal bracing nodes with diverse and complex structures, it is necessary to establish finite element models for different nodes and conduct tests to calibrate stress concentration factors. This results in a large workload and low efficiency in modeling, making it difficult to meet the engineering needs of rapid evaluation of multiple nodes, thus limiting the development of fatigue evaluation of diagonal bracing nodes in steel bridge systems. Summary of the Invention

[0005] The purpose of this invention is to establish a fatigue load and resistance model for steel bridge bracing nodes through hot spot stress, and to develop a method that can be widely applied to the fatigue reliability assessment of various bridge bracing components.

[0006] This invention provides the following technical solution: a hot spot stress method for fatigue assessment of steel bridge bracing nodes based on machine learning. By constructing a Gaussian regression proxy model for the hot spot stress concentration coefficient of steel bridge bracing nodes, a mapping relationship is established between the geometric parameters and weld type input variables of the steel bridge bracing nodes and the output of the hot spot stress concentration coefficient. This allows for the rapid determination of the magnitude of the hot spot stress of different bracing nodes on different steel bridges. Combined with the hot spot stress SN curve and the random traffic flow loading method, the fatigue performance assessment of steel bridge bracing nodes is achieved.

[0007] Furthermore, the training method for the Gaussian regression surrogate model of the hot spot stress concentration factor is as follows:

[0008] Using the thickness of the gusset plate, the thickness of the flange plate, the diameter of the weld hole, and the weld height at the steel bridge brace joint as model parameter variables, and through a method of completely randomized design plus orthogonal design, m training sample sets are set to establish corresponding m finite element models of steel bridge brace joints; m is an integer > 0;

[0009] Eccentric pressure was applied to the finite element model of each of the m steel bridge bracing nodes. The nominal stress at the weld hole on the eccentrically compressed side of the steel bridge bracing node was controlled to 1 MPa. The maximum hot spot stress was obtained by calculation using finite element software, which is the corresponding hot spot stress concentration factor SCF.

[0010] The finite element models of m steel bridge bracing nodes and their corresponding SCF values ​​are organized into input-output samples. The input variables are standardized with zero mean and unit variance. Using a 5-fold cross-validation method, the samples are divided into 5 parts according to the 5-fold cross-validation principle, with the first 5 parts serving as the validation set and the remaining 4 parts as the training set, ensuring that each evaluation covers the entire spatial distribution. The performance of the squared exponential kernel, the Matern5 / 2 kernel, and the exponential kernel with automatic correlation length scaling in terms of simulation error is verified and compared. In the validation set of each fold, the trained Gaussian regression process surrogate model is used to predict the SCF. The root mean square error and prediction interval coverage of each fold are calculated, and the results of the 5 folds are averaged. The kernel function with the smallest average root mean square error and the average coverage closest to the target value is selected as the final covariance function and determined as the final kernel function.

[0011] Using a finite element model of m steel bridge bracing nodes, a Gaussian regression process surrogate model for hot spot stress concentration coefficients is retrained under a selected kernel function to obtain the final hyperparameters. Then, the pre-reserved FE samples are used to verify that the overall root mean square error and confidence interval coverage meet the design requirements, thus establishing a Gaussian regression process surrogate model.

[0012] Furthermore, a machine learning-based method for assessing hot spot stress in the fatigue evaluation of steel bridge brace nodes includes the following steps:

[0013] S1: Establish the overall finite element model of the bridge;

[0014] S2: Determine the nominal stress influence surface of the steel bridge brace node by applying a unit moving dynamic load to the overall finite element model of the bridge;

[0015] S3: By sampling, the parameter characteristics of the vehicle type of each vehicle in the daily random traffic flow sequence are assigned; with a fixed traffic flow loading step frequency, the corresponding coordinate set of each loading of the traffic flow is obtained, the traffic flow coordinates under each step frequency are input into the nominal stress influence surface, the stress generated by each vehicle is superimposed to obtain the stress time history curve, and the nominal stress spectrum of the sample day is obtained by rain flow counting method.

[0016] S4: Input the parameters affecting the stress concentration factor, such as the gusset plate thickness, flange plate thickness, weld hole diameter, and weld height of the steel bridge bracing node, into the Gaussian regression process proxy model for the hot spot stress concentration factor, and output the stress concentration factor SCF of the steel bridge bracing node under study.

[0017] S5: The nominal stress in the daily nominal stress spectrum of the sample is converted into hot spot stress amplitude by formula (1);

[0018] σ h =σ n ×SCF Equation (1);

[0019] In the formula, SCF is the hot spot stress concentration factor, σ h For the hot spot stress at the weld toe, σ n The nominal stress at the weld toe;

[0020] The equivalent damage calculation is performed using equation (2) to determine the equivalent hot spot stress amplitude S. eq And the equivalent number of loops N d ;

[0021]

[0022] In the formula, Δσ D For constant amplitude fatigue limit, n i n j These represent the number of stress cycles above and below the constant amplitude fatigue limit, respectively; K C K D These are the fatigue strength coefficients when the fatigue limit is above and below the constant amplitude fatigue limit, respectively.

[0023] S6: Repeat steps S3 to S5 to simulate m' random traffic sequences and generate m' equivalent hotspot stress amplitudes S for each sample. eq And the equivalent number of loops N d , and fit the corresponding probability distribution functions respectively; m' is an integer > 0;

[0024] S7: Perform m'*m' random samplings on the random variable in equation (3) to solve the bridge failure probability g(X) under different service years;

[0025]

[0026] In the formula, Δ follows a log-normal distribution with a mean of 1 and a coefficient of variation of 0.3; n is the service life of the bridge structure;

[0027] The fatigue reliability index β of the bridge can be further solved using equation (4);

[0028]

[0029] In the formula, It is the inverse function of the standard normal distribution function.

[0030] Compared with the prior art, the advantages of the present invention are:

[0031] This invention, based on the hot spot stress method, considers the geometric discontinuities and stress concentration effects at the weld toe of the brace joint, enabling a more accurate reflection of the fatigue stress characteristics of the structure under actual service conditions. By constructing a Gaussian regression proxy model for the hot spot stress concentration factor (SCF), a mapping relationship between the node's geometric parameters and the stress concentration effect is established, replacing the traditional point-by-point modeling and simulation process. This Gaussian regression proxy model is applicable to steel bridge brace joints of different forms, scales, and complexities. Users only need to input the basic structural parameters of the joint to quickly obtain the hot spot stress concentration factor for fatigue reliability analysis, significantly improving the efficiency and versatility of fatigue assessment. This method is applicable to various steel bridge structural systems containing brace joints, including truss beams, box girders, and long cantilever composite structures, possessing good engineering adaptability and promotional value. Simultaneously, it can be used for fatigue performance optimization and structural design adjustments during the design phase, as well as for health status assessment and maintenance strategy formulation during bridge operation, providing effective technical support for improving the safety and maintainability of bridges throughout their entire life cycle. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the nominal stress influence surface;

[0033] Figure 2 This is a map showing the distribution characteristics of vehicle models.

[0034] Figure 3 This is a map showing the coordinate distribution of random traffic flow at a given moment.

[0035] Figure 4 The nominal stress spectrum for the sample day;

[0036] Figure 5 This is a probability distribution diagram of the stress amplitude of the hot spots in the sample.

[0037] Figure 6 This is a probability distribution diagram of the equivalent number of cycles;

[0038] Figure 7 This is a schematic diagram of the hot spot stress method for fatigue assessment of steel bridge brace nodes based on machine learning.

[0039] Figure 8 This is a schematic diagram of the fatigue reliability assessment results using the nominal stress method. Detailed Implementation

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] A machine learning-based method for assessing hot spot stress in the fatigue evaluation of steel bridge brace joints includes the following steps:

[0042] S1: Based on the bridge parameters, a finite element model of the entire bridge was established using finite element software. A single-wheel, dual-tire moving load with an area of ​​200mm (longitudinal) × 600mm (transverse) and a pressure of 1KN was applied to the center positions of each lane using a finite element subroutine. The stress influence lines of the steel bridge brace nodes for the corresponding lanes were extracted. Using a MATLAB program, with the transverse and longitudinal positions as independent variables and the stress influence values ​​of the steel bridge brace nodes as dependent variables, the stress influence lines were interpolated and fitted to form a nominal stress influence surface. The results of the nominal stress influence surface are as follows: Figure 1 As shown;

[0043] S2: Traffic information characteristics of the bridge under study are obtained through dynamic weighing. After screening, vehicles weighing less than 3t are removed. The corresponding vehicle type distribution characteristics are obtained from the screened vehicles. The distribution characteristics are as follows: Figure 2 As shown; based on vehicle type classification, statistically fit the probability distribution functions of vehicle type proportion and parameters such as vehicle weight, wheelbase, driving distance, and lane ratio for each vehicle type;

[0044] S3: Using MATLAB programming, generate random traffic flow sequences. Assign parameter characteristics to the vehicle type of each vehicle in the daily random traffic flow sequence through sampling. Using a traffic flow loading step frequency of 1 m, obtain the corresponding coordinate set for each loading step. The random traffic flow coordinate distribution at a certain moment is as follows: Figure 3As shown, the traffic flow coordinates at each step frequency are input into the nominal stress influence surface. The stresses generated by each vehicle are superimposed to obtain the stress time history curve. The nominal stress spectrum of the sample day is obtained by rainflow counting method. The obtained nominal stress spectrum of the sample day is as follows. Figure 4 As shown;

[0045] S4: Input the parameters affecting the stress concentration factor, such as the gusset plate thickness, flange plate thickness, weld hole diameter, and weld height of the steel bridge bracing node, into the Gaussian regression process proxy model for the hot spot stress concentration factor, and output the stress concentration factor SCF of the steel bridge bracing node under study.

[0046] S5: The nominal stress in the daily nominal stress spectrum of the sample is converted into hot spot stress amplitude by formula (1);

[0047] σ h =σ n ×SCF Equation (1);

[0048] In the formula, SCF is the hot spot stress concentration factor, σ h For the hot spot stress at the weld toe, σ n The nominal stress at the weld toe;

[0049] The equivalent damage calculation is performed using equation (2) to determine the equivalent hot spot stress amplitude S. eq And the equivalent number of loops N d ;

[0050]

[0051] In the formula, Δσ D For constant amplitude fatigue limit, S i and S j They are greater than and less than Δσ, respectively. D The stress amplitude, n i n j These represent the number of stress cycles above and below the constant amplitude fatigue limit, respectively; K C K D These are the fatigue strength coefficients when the fatigue limit is above and below the constant amplitude fatigue limit, respectively.

[0052] S6: Repeat steps S3 to S5 to simulate 1000 random traffic flow sequences and generate 1000 samples of equivalent hotspot stress amplitude S. eq And the equivalent number of loops N d And fit the corresponding probability distribution functions respectively; equivalent hot spot stress amplitude S eq And the equivalent number of loops N d The probability distribution is as follows Figure 5 and Figure 6 As shown;

[0053] S7: Perform 1,000,000 random samplings on the random variable in equation (3) to solve the bridge failure probability g(X) under different service years;

[0054]

[0055] In the formula, Δ follows a log-normal distribution with a mean of 1 and a coefficient of variation of 0.3; n is the service life of the bridge structure;

[0056] The fatigue reliability index β of the bridge can be further solved using equation (4);

[0057]

[0058] In the formula, It is the inverse function of the standard normal distribution function.

[0059] This example assumes a design service life of 100 years and a bridge fatigue reliability index β of 2.0 (corresponding to a failure probability of 2%). Figure 7 The results show that when the bridge's service life reaches 76 years, the structural fatigue reliability index is lower than the bridge fatigue reliability index β; that is, the risk of fatigue failure is high, and targeted bridge structural inspection and reinforcement maintenance plans need to be developed to ensure the safety and stability of the structure within its design service life.

[0060] To compare and analyze the accuracy of the method of this invention in assessing the fatigue reliability of steel bridge bracing joints compared to the traditional nominal stress method, the fatigue reliability of steel bridge bracing joints under the nominal stress method is calculated according to the above steps. In steps S4 and S5, the conversion of hot spot stress is not required; the remaining steps are the same as in this invention. The determined fatigue reliability results are as follows: Figure 8 As shown in the image analysis, when the bridge's service life reaches 139 years, the structural fatigue reliability index is lower than the bridge fatigue reliability index β. By comparing the fatigue reliability results obtained by the two methods, it can be seen that the fatigue reliability assessment result without considering the stress concentration effect of the steel bridge bracing joint (nominal stress method) is too high, while the fatigue reliability assessment result of the steel bridge bracing joint calculated by considering the hot spot stress method is safer and more in line with the actual engineering situation, and can provide accurate reference data for bridge maintenance and design.

[0061] The training method for the Gaussian regression surrogate model of the hot spot stress concentration factor is as follows:

[0062] To obtain the stress concentration coefficients of different steel bridge brace nodes, a Gaussian regression surrogate model needs to be pre-trained. Existing research indicates that fatigue cracking of steel bridge brace nodes mainly occurs in the following areas: weld throat direction, gusset plate location, weld leading edge, and weld hole location, exhibiting significant stress concentration. The stress concentration effect is extremely sensitive to these four types of geometric parameters. A completely stochastic design method was used to establish finite element models of 300 steel bridge brace nodes, with gusset plate thicknesses ranging from 16mm to 32mm and flange plate thicknesses ranging from 12mm to 28mm. The diameter of the through-hole ranges from 50mm to 90mm, and the weld height ranges from 14mm to 22mm. 300 sample sequences were established, and each sequence was uniformly sampled from four types of parameters to generate 300 finite element models of steel bridge bracing nodes. An eccentric pressure of 58mm was applied to each of the 300 finite element models of steel bridge bracing nodes, and the nominal stress at the through-hole on the eccentrically compressed side of the steel bridge bracing node was controlled to 1MPa. The maximum hot spot stress was obtained by calculation using finite element software, which is the corresponding hot spot stress concentration factor (SCF).

[0063] The finite element models of 300 steel bridge bracing nodes and their corresponding SCF values ​​were compiled into an input-output sample. The input variables were standardized with zero mean and unit variance. Using a 5-fold cross-validation method, the sample was divided into 5 parts, one as the validation set and the other 4 as the training set, ensuring that each evaluation covered the entire spatial distribution. The performance of the squared exponential kernel, the Matern5 / 2 kernel, and the exponential kernel with automatic correlation length scaling in terms of simulation error was verified and compared. In the validation set of each fold, the trained Gaussian regression process surrogate model was used to predict the SCF. The root mean square error and prediction interval coverage of each fold were calculated, and the results of the 5 folds were averaged. The kernel function with the smallest average root mean square error and the average coverage closest to the target value was selected as the final covariance function.

[0064] Using a finite element model of 300 steel bridge brace nodes, a Gaussian regression surrogate model for hot spot stress concentration coefficients was retrained under a selected kernel function to obtain the final hyperparameters. The model was then validated using pre-reserved FE samples to confirm that the overall root mean square error and confidence interval coverage met the design requirements, thus establishing the Gaussian regression surrogate model.

[0065] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A hot spot stress method for fatigue assessment of steel bridge brace joints based on machine learning, characterized in that: A Gaussian process regression surrogate model for the hot spot stress concentration coefficient of steel bridge bracing nodes is constructed based on machine learning. A mapping relationship is established between the geometric parameters and weld type input variables of the steel bridge bracing nodes and the output hot spot stress concentration coefficient, thereby quickly determining the magnitude of hot spot stress of different bracing nodes on different steel bridges. Combined with the hot spot stress SN curve and the random traffic flow loading method, the fatigue performance of steel bridge bracing nodes can be evaluated.

2. The hot spot stress method for fatigue assessment of steel bridge brace nodes based on machine learning as described in claim 1, characterized in that, The training method for the Gaussian regression surrogate model of the hot spot stress concentration factor is as follows: Using the thickness of the gusset plate, the thickness of the flange plate, the diameter of the weld hole, and the weld height at the steel bridge brace joint as model parameter variables, m training sample sets are set up through a completely randomized design method to establish corresponding m finite element models of the steel bridge brace joints; m is an integer > 0. Eccentric pressure was applied to the finite element model of each of the m steel bridge bracing nodes. The nominal stress at the weld hole on the eccentrically compressed side of the steel bridge bracing node was controlled to 1 MPa. The maximum hot spot stress was obtained by calculation using finite element software, which is the corresponding hot spot stress concentration factor SCF. The finite element models of m steel bridge bracing nodes and their corresponding SCF values ​​are organized into input-output samples, and the input variables are standardized with zero mean and unit variance. Using a 5-fold cross-validation method, the samples are divided into 5 parts according to the 5-fold cross-validation principle. The 5 parts are used as the validation set, and the remaining 4 parts are used as the training set to ensure that each evaluation covers the distribution of the entire space. The performance of the squared exponential kernel, the Matern5 / 2 kernel, and the exponential kernel with autocorrelation length scaling in terms of simulation error is compared. In the validation set of each fold, the trained Gaussian regression process surrogate model is used to predict the SCF. The root mean square error and prediction interval coverage of each fold are calculated. Finally, the results of the 5 folds are averaged. The kernel function with the smallest average root mean square error and the average coverage closest to the target value is selected as the final covariance function. Using a finite element model of m steel bridge bracing nodes, a Gaussian regression process surrogate model for hot spot stress concentration coefficients is retrained under a selected kernel function to obtain the final hyperparameters. Then, the pre-reserved FE samples are used to verify that the overall root mean square error and confidence interval coverage meet the design requirements, thus establishing a Gaussian regression process surrogate model.

3. The hot spot stress method for fatigue assessment of steel bridge brace nodes based on machine learning as described in claim 2, characterized in that, Includes the following steps: S1: Establish the overall finite element model of the bridge; S2: Determine the nominal stress influence surface of the steel bridge brace node by applying a unit moving dynamic load to the overall finite element model of the bridge; S3: By sampling, parameter characteristics are assigned to the vehicle type of each vehicle in the daily random traffic flow sequence; With a fixed traffic flow loading step frequency, the corresponding coordinate set of traffic flow is obtained for each loading. The traffic flow coordinates under each step frequency are input into the nominal stress influence surface. The stress generated by each vehicle is superimposed to obtain the stress time history curve. The nominal stress spectrum of the sample day is obtained by rain flow counting method. S4: Input the parameters affecting the stress concentration factor, such as the gusset plate thickness, flange plate thickness, weld hole diameter, and weld height of the steel bridge bracing node, into the Gaussian regression process proxy model for the hot spot stress concentration factor, and output the stress concentration factor SCF of the steel bridge bracing node under study. S5: The nominal stress in the daily nominal stress spectrum of the sample is converted into hot spot stress amplitude by formula (1); σ h = σ n × SCF Equation (1); In the formula, SCF is the hot spot stress concentration factor, σ h For the hot spot stress at the weld toe, σ n The nominal stress at the weld toe; The equivalent damage calculation is performed using equation (2) to determine the equivalent hot spot stress amplitude S. eq And the equivalent number of loops N d ; In the formula, Δσ D For constant amplitude fatigue limit, n i n j These represent the number of stress cycles above and below the constant amplitude fatigue limit, respectively; K C K D These are the fatigue strength coefficients when the fatigue limit is above and below the constant amplitude fatigue limit, respectively. S6: Repeat steps S3 to S5 to simulate m' random traffic sequences and generate m' equivalent hotspot stress amplitudes S for each sample. eq And the equivalent number of loops N d , and fit the corresponding probability distribution functions respectively; m' is an integer > 0; S7: Perform m'*m' random samplings on the random variable in equation (3) to solve the bridge failure probability g(X) under different service years; In the formula, Δ follows a log-normal distribution with a mean of 1 and a coefficient of variation of 0.3; n is the service life of the bridge structure; The fatigue reliability index β of the bridge can be further solved using equation (4); In the formula, It is the inverse function of the standard normal distribution function.

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