A diesel engine connecting rod structure reliability analysis method and system

Abstract

The application discloses a diesel engine connecting rod structure reliability analysis method and system, and relates to the technical field of computer-aided engineering simulation, which comprises the following steps: collecting connecting rod data, constructing a parameterized finite element model and a simulation parameter space; selecting sample combinations and performing static force analysis to generate a finite element stress sample set; training an improved PI-DeepONet to generate a stress prediction field; training a Kriging residual error model to correct the maximum stress and output a prediction variance; dividing safe combinations and failure combinations to construct an initial failure boundary; screening supplementary combinations and recalculating and updating to generate a convergent failure boundary; and determining the state of random samples to calculate the failure probability and reliability. The improved PI-DeepONet and Kriging residual error correction are introduced, high-precision prediction of the stress field of the diesel engine connecting rod, iterative positioning of the failure boundary and rapid analysis of the structural reliability are realized.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering simulation technology, and in particular to a method and system for reliability analysis of diesel engine connecting rod structures. Background Technology

[0002] As diesel engines develop towards higher power density, higher speed, and lighter weight, connecting rods are subjected to combustion pressure, reciprocating inertial forces, and alternating loads during operation. Stress concentrations easily occur in the large-end bore area, small-end bore area, rod body area, and transition fillet area. The reliability of the connecting rod structure directly affects the operational stability of the diesel engine. Existing diesel engine connecting rod structure analysis typically establishes a finite element model based on a three-dimensional model of the connecting rod, sets material parameters, load conditions, and constraints, and performs static analysis under typical speed, maximum burst pressure, and equivalent inertial force conditions. Then, the connecting rod structural state is determined based on the maximum equivalent stress and material bearing capacity threshold. Some methods use response surface methodology, neural networks, or Kriging models to establish the mapping relationship between structural parameters, material parameters, operating condition parameters, and maximum stress, reducing redundant finite element solutions, and combining random sampling and limit state functions to calculate failure probability and reliability.

[0003] Existing methods largely rely on a limited number of typical operating conditions and finite element samples, making it difficult to fully cover the parameter space formed by the combined parameters of the connecting rod structure, material parameters, and diesel engine operating conditions. Prediction bias is prone to occur in sparse sample regions and dangerous areas with large stress gradients. Traditional surrogate models mainly fit the numerical relationship between input parameters and stress results, lacking constraints on the load transmission path within the connecting rod, nodal force balance, and local dangerous areas, making it difficult to accurately characterize stress changes at transition fillets, hole edges, and abrupt cross-sectional changes. Single surrogate models have limited ability to characterize prediction residuals and uncertainties, and the maximum stress error can affect the distinction between safe and failure combinations. Existing failure boundaries are usually directly fitted from initial samples, lacking targeted supplementary sampling and finite element recalculation of the boundary neighborhood, which can easily lead to boundary position shifts; directly increasing the finite element sample size increases computational load, making it difficult to balance stress prediction accuracy, failure boundary convergence, and reliability analysis efficiency.

[0004] Therefore, how to provide a reliability analysis method and system for diesel engine connecting rod structures is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] One objective of this invention is to propose a reliability analysis method and system for diesel engine connecting rod structures. This invention employs parametric finite element modeling, improved PI-DeepONet stress prediction, Kriging residual correction, failure boundary iteration, and random sampling reliability calculation methods to construct a connecting rod simulation parameter space and a finite element stress sample set. The stress field of the connecting rod is predicted through load path competition allocation, node residual force feedback iteration, and self-generated query of hazardous areas. Based on the finite element maximum stress correction prediction results, safe combinations and failure combinations are divided. Supplementary sampling is performed in the neighborhood of the failure boundary, and finite element recalculation is executed to generate a convergent failure boundary, calculating the connecting rod failure probability and reliability. Compared with traditional finite element analysis and single surrogate models, this invention has the advantages of high stress prediction accuracy, sufficient characterization of hazardous areas, accurate failure boundary location, and high reliability analysis efficiency.

[0006] A reliability analysis method for a diesel engine connecting rod structure according to an embodiment of the present invention includes:

[0007] Obtain diesel engine connecting rod data, construct a parametric finite element model, and generate a simulation parameter space;

[0008] Sample combinations are selected from the simulation parameter space, and static analysis is performed through the parameterized finite element model to generate a finite element stress sample set;

[0009] The improved PI-DeepONet is trained using the aforementioned finite element stress sample set. The improved PI-DeepONet includes a load path competition allocation layer, a node residual force feedback iteration layer, and a hazardous area self-generated query head to generate a stress prediction field.

[0010] Extract the corresponding maximum stress from the stress prediction field and the finite element stress sample set, calculate the stress residual and train the Kriging residual model to generate the corrected maximum stress and prediction variance;

[0011] By comparing the corrected maximum stress with the material bearing capacity threshold, the corresponding sample combinations are divided into safe combinations and failure combinations, and an initial failure boundary is constructed.

[0012] Candidate combinations are generated in the neighborhood of the initial failure boundary. Supplementary combinations are selected according to the predicted variance and the nearest sample distance. The parameterized finite element model is used to recalculate and update the finite element stress sample set, improve PI-DeepONet and Kriging residual model, and iteratively generate the convergent failure boundary.

[0013] Random samples are extracted from the simulation parameter space, the failure state is determined based on the convergent failure boundary, the failure probability and reliability are calculated, and the reliability analysis results of the diesel engine connecting rod structure are generated.

[0014] Optionally, the diesel engine connecting rod data specifically includes the connecting rod three-dimensional model, connecting rod length, large end bore diameter, small end bore diameter, rod body thickness, transition fillet radius, material density, elastic modulus, Poisson's ratio, material load-bearing threshold, diesel engine speed, maximum burst pressure, equivalent inertial force, load location, and constraint location.

[0015] Optionally, the step of constructing a parametric finite element model and generating a simulation parameter space includes:

[0016] The diesel engine connecting rod 3D model is subjected to non-designed hole closure, repeated surface merging and surface repair. The center of the big end hole and the center of the small end hole are connected to form an axial baseline. The big end hole area, small end hole area, rod body area and transition fillet area are divided to generate the connecting rod geometric partition model.

[0017] The link length, large end diameter, small end diameter, link thickness, and transition fillet radius are written into the link geometric partition model. The dimensions and region boundaries are updated according to the parameter values ​​to generate a parametric link model.

[0018] The parametric link model is meshed into a finite element model, and the material density, elastic modulus and Poisson's ratio are configured. The load position and constraint position are mapped to the node to generate the parametric finite element model.

[0019] Write the diesel engine speed into the operating condition field, write the maximum burst pressure and equivalent inertial force into the load field, limit the value range of structural parameters, material parameters and operating condition parameters, and generate a simulation parameter configuration table.

[0020] According to the simulation parameter configuration table, the parameter values ​​are combined, and parameter combinations with size conflicts and load boundary overlaps are eliminated. The retained parameter combinations are associated with the parameterized finite element model to generate the simulation parameter space.

[0021] Optionally, generating the finite element stress sample set includes:

[0022] The range of each parameter value in the simulation parameter space is divided into layers. Parameter values ​​are extracted from each layer and rearranged and combined to generate an initial sample combination.

[0023] Calculate the normalized parameter distance between each initial sample combination, remove the initial sample combination whose minimum distance is less than the distance threshold, and re-extract the parameter values ​​in the corresponding parameter layer to generate sample combinations and number them.

[0024] The sample combinations are written into the parametric finite element model one by one, and the linkage structure dimensions, material properties, working condition fields, load fields and constraint nodes are updated to generate the sample finite element model.

[0025] Assemble the stiffness matrix and load vector of the sample finite element model, solve the nodal displacements, calculate the element strain, element stress and nodal equivalent stress based on the nodal displacements, and generate the sample stress results.

[0026] A finite element stress sample set is generated by associating the node coordinates, equivalent stress, maximum stress, and maximum stress location with the sample combination number.

[0027] Optionally, generating the stress prediction field includes:

[0028] An improved PI-DeepONet is constructed, which includes a load path competition allocation layer, a node residual force feedback iteration layer, and a dangerous area self-generated query head. The finite element stress sample set is associated with the element connection, stiffness matrix, and load vector of the corresponding sample finite element model according to the sample combination number to generate model training samples.

[0029] The load path competition allocation layer receives model training samples, connects candidate unit paths from load nodes to constraint nodes, calculates the cumulative length, equivalent stiffness, and minimum cross-sectional area of ​​each candidate unit path, normalizes the ratio of equivalent stiffness to cumulative length to obtain the initial load ratio, multiplies the minimum cross-sectional area by the material bearing capacity threshold and subtracts the initial allocated load to obtain the path bearing capacity margin, adjusts the initial load ratio according to the path bearing capacity margin, and outputs the path load characterization.

[0030] The node residual force feedback iteration layer receives the path load characterization and node coordinates, and generates the initial node displacement by fusing the branch network and the backbone network. The stiffness matrix is ​​multiplied by the node displacement to obtain the node internal force, and the node residual force is obtained by subtracting the node internal force from the load vector. The node residual force is distributed to adjacent elements according to the element connection and aggregated to the node feature. The displacement correction amount is generated and the node displacement is iteratively updated to output the equilibrium displacement field.

[0031] The hazardous area self-generated query head receives the equilibrium displacement field, calculates the equivalent stress of the nodes and the ratio of the difference in equivalent stress between adjacent nodes to the node distance to obtain the stress gradient, merges adjacent nodes whose equivalent stress is not less than the stress threshold or whose stress gradient is not less than the gradient threshold, generates a hazardous area, sets the midpoint of adjacent nodes and the stress gradient direction interpolation point in the hazardous area, and calculates the corresponding stress through the fusion of the branch network and the backbone network, and outputs the hazardous area query stress.

[0032] The query stress in the dangerous area is mapped back to the node according to the element it belongs to, and then fused with the equivalent stress of the node corresponding to the equilibrium displacement field to generate the current predicted stress field. The difference between the predicted stress field and the equivalent stress of the finite element node is used to obtain the dangerous area mapping error.

[0033] The improved PI-DeepONet is trained, and the node equivalent stress prediction error, node residual force balance error, path load conservation error, and dangerous area reflection error are weighted to obtain a joint loss value. The parameters of the load path competition allocation layer, node residual force reflection iteration layer, dangerous area self-generated query head, branch network, and backbone network are iteratively updated, and the current predicted stress field is refreshed. When the change of the joint loss value in 6 consecutive training rounds is less than 0.001, the stress prediction field is generated.

[0034] Optionally, generating the corrected maximum stress and predicted variance includes:

[0035] Extract the maximum stress of the stress prediction field and the finite element stress sample set according to the sample combination number. Subtract the predicted maximum stress from the finite element maximum stress to obtain the stress residual. Associate the corresponding link structure parameters, material parameters and working condition parameters to generate residual training samples.

[0036] The parameter values ​​in the residual training samples are normalized, and the normalized parameter vector is used as input and the stress residual is used as output to train the Kriging residual model.

[0037] Input the parameter combination corresponding to the stress prediction field into the Kriging residual model to calculate the prediction residual and prediction variance;

[0038] The predicted residual is added to the corresponding predicted maximum stress to obtain the corrected maximum stress. The corrected maximum stress and the predicted variance are then correlated according to the parameter combination.

[0039] Optionally, the construction of the initial failure boundary includes:

[0040] The maximum stress and material bearing capacity threshold are correlated by parameter combination. The maximum stress is then subtracted from the maximum stress to obtain the limit state value of the linkage structure.

[0041] The parameter combinations with limit state values ​​greater than zero are defined as safe combinations, and the parameter combinations with limit state values ​​not greater than zero are defined as failure combinations, thus generating a set of safe combinations and a set of failure combinations.

[0042] The parameter values ​​of safe and failed combinations are normalized, the parameter distance between combinations is calculated, and the heterogeneous combinations with the smallest distance are paired to generate safe-fail combination pairs.

[0043] Boundary points are determined based on the limit state values ​​of the safety combination and failure combination in the safety failure combination pair. Each boundary point is fitted and the safety side and failure side are calibrated to generate the boundary function and the initial failure boundary.

[0044] Optionally, the iterative generation of convergence failure boundaries includes:

[0045] Centered on the boundary point of the current failure boundary, the parameter values ​​are adjusted in the neighborhood of each parameter dimension, and parameter combinations that exceed the simulation parameter space and overlap with existing samples are eliminated to generate candidate combinations.

[0046] Each candidate combination is input into the Kriging residual model to obtain the predicted variance. The parameter distance between each candidate combination and the nearest sample in the finite element stress sample set is calculated, normalized and weighted to obtain the supplementary score, and supplementary combinations are selected according to the supplementary score.

[0047] The supplementary combination is written into the parametric finite element model to perform static analysis, extract the nodal equivalent stress, maximum stress and maximum stress location, and incorporate them into the finite element stress sample set;

[0048] The improved PI-DeepONet was trained using the updated finite element stress sample set. The stress residuals were recalculated and the Kriging residual model was updated. The corrected maximum stress was calculated, safe combinations and failure combinations were divided, and the failure boundary was updated.

[0049] Calculate the minimum parameter distance from each boundary point of the current failure boundary to the previous failure boundary, and take the maximum value as the boundary change. If the boundary change is greater than the boundary convergence threshold, continue to perform boundary neighborhood sampling, finite element recalculation and model update until the boundary change is no greater than the boundary convergence threshold, and generate a converged failure boundary.

[0050] Optionally, the generation of reliability analysis results for the diesel engine connecting rod structure includes:

[0051] According to the value range defined by the simulation parameter space, the connecting rod structure parameters, material parameters and diesel engine operating parameters are uniformly sampled, and a random sample set is generated and numbered.

[0052] The random samples are input one by one into the boundary function corresponding to the convergence failure boundary. The random samples located on the failure side are marked as failure samples, and the random samples located on the safe side are marked as safe samples.

[0053] The total number of random samples and the number of failed samples are counted. The failure probability is obtained by dividing the number of failed samples by the total number of random samples. The reliability is obtained by subtracting the failure probability from one.

[0054] The reliability analysis results of the diesel engine connecting rod structure are generated by associating the connecting rod structural parameters, material parameters, diesel engine operating parameters, and failure states with random sample numbers, and encapsulating them with failure probability and reliability.

[0055] A diesel engine connecting rod structure reliability analysis system according to an embodiment of the present invention includes the following modules:

[0056] The parameter space construction module is used to process diesel engine connecting rod data to form a parametric finite element model and simulation parameter space;

[0057] The finite element simulation module is used to filter parameter combinations and perform static solutions to form a finite element stress sample set.

[0058] The stress prediction module is used to process finite element stress sample sets by improving PI-DeepONet and output the stress prediction field;

[0059] The residual correction module is used to establish the residual relationship between the predicted maximum stress and the finite element maximum stress, and outputs the corrected maximum stress and the prediction variance.

[0060] The failure boundary construction module is used to divide safe combinations and failure combinations to form the initial failure boundary;

[0061] The boundary iteration module is used to filter supplementary combinations of boundary neighborhoods, update the finite element stress sample set, improve PI-DeepONet and Kriging residual models, and form convergent failure boundaries.

[0062] The reliability calculation module is used to determine the failure state of random samples, calculate the failure probability and reliability, and output the reliability analysis results of the diesel engine connecting rod structure.

[0063] The beneficial effects of this invention are:

[0064] This invention proposes a reliability analysis method and system for diesel engine connecting rod structures. By constructing a parametric finite element model, a finite element stress sample set, and a simulation parameter space, it achieves joint analysis of connecting rod structural parameters, material parameters, and diesel engine operating condition parameters. Compared to methods that only perform finite element calculations for a few typical operating conditions, this invention can cover a wider range of parameter combinations, reduce the limitations of results caused by single-condition analysis, and provide a unified data foundation for connecting rod stress prediction, failure state determination, and reliability calculation.

[0065] This invention improves the PI-DeepONet for predicting the stress field of connecting rods by introducing a load path competition allocation layer, a node residual force feedback iteration layer, and a self-generated query head for hazardous areas. It can extract stress characteristics of hazardous areas in connecting rods by combining load transfer paths, node force balance, and local stress gradients, thus improving the stress prediction accuracy in areas such as large-end hole areas, small-end hole areas, transition fillet areas, and locations of abrupt cross-section changes. By correcting the predicted maximum stress using a Kriging residual model and outputting the prediction variance, it can reduce the prediction bias caused by a single surrogate model in sparse sample regions, improving the accuracy of safe and failure combination classification.

[0066] This invention constructs an initial failure boundary based on the corrected maximum stress, and then selects supplementary combinations in the boundary neighborhood by combining the predicted variance and the nearest sample distance. Finally, it generates a convergent failure boundary through finite element recalculation and model update iterations, avoiding the computational burden caused by directly expanding the finite element sample size in the full parameter space. Based on the convergent failure boundary, failure determination is performed on random samples, enabling the calculation of the failure probability and reliability of diesel engine connecting rods, balancing stress prediction accuracy, failure boundary location accuracy, and reliability analysis efficiency. Attached Figure Description

[0067] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0068] Figure 1 This is a flowchart of a reliability analysis method for diesel engine connecting rod structure proposed in this invention;

[0069] Figure 2 This is a schematic diagram of the improved PI-DeepONet network structure for a diesel engine connecting rod structure reliability analysis method proposed in this invention.

[0070] Figure 3 This is a schematic diagram of a diesel engine connecting rod structure reliability analysis system proposed in this invention. Detailed Implementation

[0071] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0072] refer to Figure 1 and Figure 2 A reliability analysis method for diesel engine connecting rod structures, comprising:

[0073] Obtain diesel engine connecting rod data, construct a parametric finite element model, and generate a simulation parameter space;

[0074] Sample combinations are selected from the simulation parameter space, and static analysis is performed through the parameterized finite element model to generate a finite element stress sample set;

[0075] The improved PI-DeepONet is trained using the aforementioned finite element stress sample set. The improved PI-DeepONet includes a load path competition allocation layer, a node residual force feedback iteration layer, and a hazardous area self-generated query head to generate a stress prediction field.

[0076] Extract the corresponding maximum stress from the stress prediction field and the finite element stress sample set, calculate the stress residual and train the Kriging residual model to generate the corrected maximum stress and prediction variance;

[0077] By comparing the corrected maximum stress with the material bearing capacity threshold, the corresponding sample combinations are divided into safe combinations and failure combinations, and an initial failure boundary is constructed.

[0078] Candidate combinations are generated in the neighborhood of the initial failure boundary. Supplementary combinations are selected according to the predicted variance and the nearest sample distance. The parameterized finite element model is used to recalculate and update the finite element stress sample set, improve PI-DeepONet and Kriging residual model, and iteratively generate the convergent failure boundary.

[0079] Random samples are extracted from the simulation parameter space, the failure state is determined based on the convergent failure boundary, the failure probability and reliability are calculated, and the reliability analysis results of the diesel engine connecting rod structure are generated.

[0080] In this embodiment, the diesel engine connecting rod data specifically includes the connecting rod three-dimensional model, connecting rod length, large end bore diameter, small end bore diameter, rod body thickness, transition fillet radius, material density, elastic modulus, Poisson's ratio, material load-bearing threshold, diesel engine speed, maximum burst pressure, equivalent inertial force, load location, and constraint location.

[0081] In this embodiment, the construction of the parameterized finite element model and the generation of the simulation parameter space include:

[0082] The 3D model of the diesel engine connecting rod is subjected to non-designed hole closure, repeated surface merging, and surface repair. An axial baseline is formed by connecting the centers of the large-end hole and the small-end hole. The model is then divided into large-end hole area, small-end hole area, rod body area, and transition fillet area, generating a connecting rod geometric partition model. Among these:

[0083] Generate the link geometry partitioning model, specifically:

[0084] Extract the three-dimensional model of the diesel engine connecting rod and the hole design dimensions from the diesel engine connecting rod data. Form hole feature records based on hole position, hole diameter and axial depth, and match them with each hole type surface. Identify unmatched hole type surfaces as non-designed holes, fit and fill the surface along the hole boundary and stitch it with the adjacent surface.

[0085] Compare the boundary coordinates, overlap range, and normal parallelism of each surface. Surfaces with overlapping boundaries are identified as repeating surfaces. One surface is retained and the topological connectivity is transferred. Unclosed boundary lines are extracted. The surface is fitted and repaired between the corresponding boundary points until there are no unclosed boundary lines.

[0086] Extract the cylindrical boundary points of the large-end hole and the small-end hole, perform circle fitting on them respectively, and obtain the center of the large-end hole and the center of the small-end hole. Connect the two hole centers to form an axial reference line.

[0087] The cylindrical surface of the large end hole, as well as the end face and outer edge curved surface that share the boundary with the cylindrical surface of the large end hole, are divided into the large end hole area. The cylindrical surface of the small end hole, as well as the end face and outer edge curved surface that share the boundary with the cylindrical surface of the small end hole, are divided into the small end hole area. The curved surface that extends along the axial reference line between the two hole areas is divided into the rod body area. The fillet connecting curved surface that is adjacent to both the hole area and the rod body area is divided into the transition fillet area.

[0088] Write region identifiers for each surface and record the axial baseline, hole center, region boundary line and surface topology connection relationship to generate a link geometry partition model;

[0089] The connecting rod length, large end bore diameter, small end bore diameter, rod thickness, and transition fillet radius are written into the connecting rod geometric partition model. The dimensions and region boundaries are updated according to the parameter values ​​to generate a parametric connecting rod model, wherein:

[0090] Generate a parametric link model, specifically:

[0091] The length of the connecting rod corresponds to the center distance between the two holes. The diameters of the large and small holes correspond to the cylindrical surface diameters of the large and small holes, respectively. The thickness of the rod body corresponds to the distance between the outer surfaces on both sides of the rod body area along the thickness direction. The radius of the transition fillet corresponds to the radius of curvature of the connecting surface between the hole area and the rod body area.

[0092] Using the center of the large end hole as a fixed point, calculate the difference between the connecting rod length parameter value and the current center distance between the two holes, move the small end hole area along the axial baseline, and adjust the rod body area surface along the axial direction according to the ratio of the center distance between the two holes before and after the update.

[0093] Calculate the difference between the large end diameter and small end diameter parameter values ​​and the current diameter, respectively, and use half of the difference as the radial offset to move the hole surface and hole edge boundary along the normal of the corresponding hole cylindrical surface;

[0094] Calculate the difference between the shaft thickness parameter value and the current shaft thickness, and move the outer surfaces on both sides of the shaft area by half of the difference along opposite normal directions;

[0095] Delete the original connecting surface between the hole area and the shaft area, refit the connecting surface based on the updated hole edge boundary, shaft boundary and transition fillet radius, update the boundary lines, area identifiers and topological connection relationships of each geometric partition, and generate a parametric link model;

[0096] The parametric link model is meshed using finite element methods, and material density, elastic modulus, and Poisson's ratio are configured. Load and constraint locations are mapped to nodes to generate the parametric finite element model, wherein:

[0097] Generate a parametric finite element model, specifically as follows:

[0098] Set the mesh size separately for the large-end hole area, small-end hole area, rod body area and transition rounded corner area. Use a smaller mesh size than the rod body area in the hole edge and transition rounded corner area. Discretize the surface of each partition into a surface mesh, reuse the nodes on the shared boundary of adjacent partitions, and fill the interior of the model with tetrahedral elements.

[0099] According to the mesh quality inspection rules for tetrahedral elements, the upper limit of the mesh aspect ratio is set to 5, the lower limit of the minimum dihedral angle is set to 15°, and the lower limit of the minimum normalized Jacobian value is set to 0.2.

[0100] Calculate the aspect ratio, minimum dihedral angle, and minimum normalized Jacobian value of each element. Element elements with an aspect ratio greater than 5, a minimum dihedral angle less than 15°, or a minimum normalized Jacobian value less than 0.2 are identified as unqualified elements. The mesh of the local area where the unqualified element is located is removed and re-meshed. Record the node number, node coordinates, element number, and element connection relationship.

[0101] Write the material density into the element mass attribute, and write the elastic modulus and Poisson's ratio into the element constitutive parameters to generate the element material parameter record;

[0102] Based on the correspondence between geometric surfaces and surface elements, the surface elements corresponding to the load and constraint positions are extracted, and the nodes contained in each surface element are marked as load nodes and constraint nodes, respectively.

[0103] By associating the parametric link model, finite element mesh, material parameters, load node set, constraint node set, and mesh size of each partition, a parametric finite element model is generated.

[0104] The diesel engine speed is written into the operating condition field, and the maximum burst pressure and equivalent inertial force are written into the load field. The value ranges of structural parameters, material parameters, and operating condition parameters are limited to generate a simulation parameter configuration table, in which:

[0105] Generate a simulation parameter configuration table, specifically as follows:

[0106] Based on the design dimensions and dimensional tolerances of the connecting rod, determine the lower and upper limits of the values ​​for the connecting rod length, large end diameter, small end diameter, rod thickness, and transition fillet radius;

[0107] Based on the allowable deviations in material properties, determine the lower and upper limits of the values ​​for material density, elastic modulus, and Poisson's ratio;

[0108] The speed range is determined based on the diesel engine operating boundary, and the range of maximum burst pressure and equivalent inertial force is determined based on the load boundary. These ranges are then written into the operating condition field and the load field, respectively.

[0109] The value intervals of each parameter are determined according to the dimensional tolerance resolution, material parameter adjustment accuracy, and working condition sampling step size. The parameter name, field type, lower limit of value, upper limit of value, value interval, and unit of measurement are written into the parameter record to generate a simulation parameter configuration table.

[0110] According to the parameter configuration table, after combining the parameter values, parameter combinations with conflicting dimensions and overlapping load boundaries are eliminated. The remaining parameter combinations are then associated with the parameterized finite element model to generate a simulation parameter space, where:

[0111] The simulation parameter space is generated as follows:

[0112] Candidate values ​​are generated based on the lower limit, upper limit, and value interval of each field. These are then combined into parameter records in the order of structural parameters, material parameters, working condition fields, and load fields, and a combination number is assigned to each parameter record.

[0113] Substitute each structural parameter into the parametric link model, update the bore cylindrical surface, the outer surface of the link body and the transition fillet surface, calculate the minimum wall thickness from the bore cylindrical surface to the corresponding outer surface, and detect the intersection relationship between non-adjacent surfaces; mark parameter combinations with minimum wall thickness not greater than 0 or with intersection lines between non-adjacent surfaces as size conflict combinations;

[0114] Update the spatial positions of load boundaries and constraint boundaries based on structural parameters, calculate the geometric intersection of load boundaries and constraint boundaries, and mark parameter combinations with non-empty geometric intersections as load boundary overlap combinations;

[0115] Delete combinations with conflicting dimensions and combinations with overlapping load boundaries, and write the combination number, structural parameters, material parameters, load field values, load field values, load boundary identifiers, and constraint boundary identifiers of the remaining combinations into the same parameter record;

[0116] The simulation parameter space is generated by associating each parameter record with the parametric finite element model, the mesh size of each partition, the element material parameter record, the region identifier, and the correspondence between the geometric surface and the surface element.

[0117] In this embodiment, generating the finite element stress sample set includes:

[0118] The simulation parameter space is divided into layers based on the range of parameter values. Parameter values ​​are extracted from each layer and rearranged to generate an initial sample combination, wherein:

[0119] The initial sample combination is generated as follows:

[0120] The number of structural parameters, material parameters, working condition fields, and load fields in the simulation parameter space is counted. Ten times the total number of parameter fields is determined as the initial sample size. If the calculation result is greater than the total number of parameter records in the simulation parameter space, the total number of parameter records is determined as the initial sample size.

[0121] Based on the initial number of samples, the range of values ​​for each parameter is divided into a corresponding number of parameter layers, and the lower limit, upper limit, and layer number of each parameter layer are recorded.

[0122] One parameter value is extracted from the candidate values ​​contained in each parameter layer. If there is no candidate value in the parameter layer, the candidate value with the smallest absolute value of the difference from the center of the parameter layer is selected to obtain the hierarchical extraction value sequence of each parameter.

[0123] The extraction values ​​of the first parameter are retained, and the extraction values ​​of the remaining parameters are shuffled. The extraction values ​​of different parameters are combined according to the same order to obtain the sample records.

[0124] Each sample record is matched field by field with the parameter record in the simulation parameter space. When there is no completely consistent parameter record, the parameter difference between the sample record and each unselected parameter record is calculated. Each difference is divided by the width of the corresponding parameter value range, the sum of squares is calculated and the square root is taken. The unselected parameter record with the smallest calculation result is selected to replace the sample record and generate the initial sample combination.

[0125] Calculate the normalized parameter distance between each initial sample combination, remove initial sample combinations whose minimum distance is less than the distance threshold, and re-extract parameter values ​​at the corresponding parameter layer to generate sample combinations and assign them numbers, where:

[0126] Generate and number sample combinations, specifically as follows:

[0127] Subtract the corresponding lower limit from each parameter value, and then divide by the difference between the upper and lower limits to obtain the normalized parameter value with a range of 0 to 1.

[0128] For any two initial sample combinations, calculate the difference in normalized parameter values ​​for the same parameter, add the squares of each difference and take the square root to obtain the normalized parameter distance between the two initial sample combinations.

[0129] Let N be the number of initial samples and M be the number of parameter fields. Calculate N to the power of negative M and take half of the result as the distance threshold. Extract the minimum distance between each initial sample combination and the other initial sample combinations.

[0130] When the minimum distance is less than the distance threshold, the initial sample combination with the earlier combination order is retained, and the initial sample combination with the later combination order is deleted. Candidate combinations that match the simulation parameter space are generated in the parameter layer corresponding to the deleted combination, and the minimum normalized parameter distance between each candidate combination and the retained combination is calculated respectively.

[0131] Compare the minimum normalized parameter distance of each candidate combination, select the candidate combination with the largest minimum normalized parameter distance to replace the deleted combination, and after all combinations are replaced, write the sample combination number in the order of combination generation to generate the sample combination.

[0132] The sample combinations are written into the parametric finite element model one by one, and the linkage structure dimensions, material properties, working condition fields, load fields and constraint nodes are updated to generate the sample finite element model.

[0133] Assemble the stiffness matrix and load vector of the sample finite element model, solve for the nodal displacements, calculate the element strain, element stress, and nodal equivalent stress based on the nodal displacements, and generate the sample stress results, wherein:

[0134] The sample stress results are generated as follows:

[0135] The element volume and strain matrix are calculated based on the nodal coordinates of the tetrahedral element. The material constitutive matrix is ​​constructed based on the elastic modulus and Poisson's ratio. The element stiffness matrix is ​​obtained by multiplying the transpose of the strain matrix, the material constitutive matrix, the strain matrix and the element volume in sequence. The elements are then superimposed according to the nodal degrees of freedom to form the overall stiffness matrix.

[0136] Multiply the maximum burst pressure by the area of ​​each load surface triangular element to obtain the pressure load borne by each surface triangular element, and divide the pressure load equally to the three vertex nodes along the outer normal of the surface.

[0137] The element mass is obtained by multiplying the volume of each tetrahedral element by the material density. The total mass is obtained by summing the masses of each element. The equivalent inertial force is divided by the total mass to obtain the equivalent inertial acceleration. The axial reference line direction is determined according to the sign of the equivalent inertial force. The element inertial load is obtained by multiplying the element mass by the equivalent inertial acceleration and then equally distributed to the four element nodes. The pressure load and inertial load of each node are superimposed to form the overall load vector.

[0138] Set the translational degrees of freedom corresponding to the constrained nodes to zero, eliminate the corresponding rows and columns from the global stiffness matrix and global load vector, solve for the nodal displacements of the remaining degrees of freedom, and backfill the zero displacements to the constrained nodes;

[0139] Extract the displacement components of each element containing nodes, multiply them with the corresponding strain matrix to obtain the element strain, and then multiply the material constitutive matrix with the element strain to obtain the element normal stress and shear stress.

[0140] The three normal stress components and three shear stress components of the node are obtained by weighted averaging of the stresses of the elements associated with the same node by the adjacent element volumes. The three normal stress components are subtracted from each other and squared respectively. The sum of the squares of the three differences is divided by 2, and then 3 times the sum of the squares of the three shear stress components is added. The square root of the result is used to obtain the equivalent stress of the node.

[0141] Compare the equivalent stress at each node, record the maximum equivalent stress at the node as the maximum stress, mark the corresponding node coordinates as the location of the maximum stress, and associate the node number, node coordinates, element strain, element stress, equivalent stress at the node, maximum stress, and location of the maximum stress to generate sample stress results;

[0142] A finite element stress sample set is generated by associating the node coordinates, equivalent stress, maximum stress, and maximum stress location with the sample combination number.

[0143] In this embodiment, generating the stress prediction field includes:

[0144] An improved PI-DeepONet is constructed, comprising a load path competition allocation layer, a node residual force feedback iteration layer, and a hazardous area self-generated query head. The finite element stress sample set is associated with the element connections, stiffness matrices, and load vectors of the corresponding sample finite element models according to the sample combination number to generate model training samples, wherein:

[0145] The improved PI-DeepONet is constructed as follows:

[0146] Based on the traditional PI-DeepONet's branch network, backbone network, feature inner product layer, and physical residual constraint structure, a load path competition allocation layer is added between the branch network output and the feature inner product layer to fuse the element connection, stiffness matrix, and load vector encoding results of the finite element model with the branch features.

[0147] A new node residual force feedback iteration layer is added between the output end of the feature inner accumulation layer and the stress output end to feed back the physical residual constraint calculation results to the stress feature;

[0148] The fixed node coordinate query terminal of the backbone network is improved into a self-generated query head for dangerous areas. The node coordinate representation is connected with the initial stress space representation formed by the first calculation of the feature inner layer to generate query features.

[0149] The load path competition allocation layer, the node residual force feedback iteration layer, and the dangerous area self-generated query head are respectively connected to the branch feature transmission path, the physical residual feedback path, and the trunk query path to obtain the improved PI-DeepONet;

[0150] The load path competition allocation layer receives model training samples, concatenates candidate element paths from load nodes to constraint nodes, calculates the cumulative length, equivalent stiffness, and minimum cross-sectional area of ​​each candidate element path, normalizes the ratio of equivalent stiffness to cumulative length to obtain the initial load ratio, multiplies the minimum cross-sectional area by the material bearing capacity threshold and subtracts the initial allocated load to obtain the path bearing capacity margin, adjusts the initial load ratio according to the path bearing capacity margin, and outputs the path load characterization, wherein:

[0151] The load path contention allocation layer includes:

[0152] Cell adjacency index table: stores cell adjacency relationships, common nodes, and effective cross-sectional area;

[0153] Candidate path expansion queue: Connects candidate element paths from load nodes to constraint nodes;

[0154] Path parameter accumulator: calculates cumulative length, equivalent stiffness, and minimum cross-sectional area;

[0155] Initial proportional normalizer: Calculates the initial load proportion for each path;

[0156] Load margin register: stores the initial allocated load and path load margin;

[0157] Competition Proportion Updater: Adjusts and normalizes the load proportions of each path;

[0158] Path representation output buffer: Output path load representation;

[0159] The processing procedure of the load path contention allocation layer is as follows:

[0160] The load path competition allocation layer extracts node coordinates from the finite element stress sample records in the model training samples, and receives element connections, stiffness matrices and load vectors, while also receiving branch features output by the branch network.

[0161] The node coordinates and element connections are passed to the element adjacency index table. The output of the element adjacency index table is passed to the candidate path expansion queue. The node coordinates, stiffness matrix, load vector and candidate element path are passed to the path parameter accumulator. The load vector and path parameters are passed to the initial scaling normalizer.

[0162] Let the number of nodes be N, the number of elements be E, the branch feature dimension be D, the node coordinate matrix size be N×3, the element connection matrix size be E×4, the overall stiffness matrix size be 3N×3N, the load vector size be 3N×1, and the branch feature size be 1×D;

[0163] Compare the node numbers of each tetrahedral element, register the elements that share three nodes as adjacent elements, calculate the area of ​​the shared triangular face and the unit normal vector based on the three common nodes, connect the centroids of two adjacent elements and normalize the connection vector to obtain the unit path direction, multiply the area of ​​the shared triangular face by the absolute value of the dot product of the unit normal vector and the unit path direction to obtain the effective cross-sectional area between adjacent elements, and write it into the element adjacency index table.

[0164] The candidate path expansion queue starts from the load node associated element, and adds elements that do not appear in the current path step by step along the element adjacency relationship. The expansion stops after connecting to the constraint node associated element, resulting in P candidate element paths.

[0165] The path parameter accumulator adds the centroid distances of adjacent elements within each candidate element path to obtain the cumulative length, extracts the nodes and corresponding stiffness submatrices contained in the path, sets the load nodes in the element at the beginning of the path to unit displacement along the direction of the resultant load force, sets the constraint nodes in the element at the end of the path to zero displacement, sets linearly decreasing displacements according to the proportion of the cumulative length from the element to the beginning of the path to the other path nodes, and forms a path displacement template. The path displacement template is transposed, the stiffness submatrices are multiplied sequentially with the path displacement template, and then divided by the sum of squares of the components of the path displacement template to obtain the equivalent stiffness. The effective cross-sectional areas within the path are compared to obtain the minimum cross-sectional area.

[0166] The initial proportional normalizer calculates the ratio of the equivalent stiffness to the cumulative length of each candidate element path, and then divides it by the sum of the corresponding ratios of all candidate element paths to obtain the initial load ratio. The nodal load components in the load vector are accumulated according to the three coordinate directions to obtain the three resultant force components. The three resultant force components are squared, summed, and the square root is taken to obtain the load resultant force. The load resultant force is multiplied by the initial load ratio to obtain the initial distributed load.

[0167] The load margin register associates the corresponding material record with the sample combination number, extracts the corresponding material load threshold from the diesel engine connecting rod data, multiplies the minimum cross-sectional area with the material load threshold to obtain the path load, and then subtracts the initial allocated load to obtain the path load margin.

[0168] The competitive ratio updater divides the path load margin by the sum of all path loads and adds it to the initial load ratio. It sets the calculation result less than 0 to 0, and then divides the calculation result of each path by the sum of the calculation results of all paths to obtain the adjusted load ratio. When all calculation results are 0, the adjusted load ratio is determined according to the ratio of the load of each path to the total load of all paths.

[0169] The path representation output buffer arranges the cumulative length, equivalent stiffness, minimum cross-sectional area, path load margin, and adjusted load ratio into a path parameter matrix of size P×5. The path parameter matrix is ​​multiplied by the path feature mapping matrix of size 5×D to obtain a path feature matrix of size P×D. The P path features are weighted and summed column by column according to the adjusted load ratio to obtain a path load representation of size 1×D. This representation is then added element by element to the branch features of size 1×D to form an enhanced branch feature, which is then passed into the feature inner product layer.

[0170] The path feature dimension D is consistent with the branch network output dimension. The path feature mapping matrix is ​​uniformly initialized by Xavier and updated with model training. The number of nodes N and the number of units E are determined according to the corresponding model training samples. The number of candidate unit paths P is determined according to the output results of the candidate path expansion queue.

[0171] The node residual force feedback iteration layer receives path load representations and node coordinates, fuses them with the branch network and the backbone network to generate initial node displacements, multiplies the stiffness matrix by the node displacements to obtain the node internal forces, subtracts the node internal forces from the load vectors to obtain the node residual forces, distributes the node residual forces to adjacent elements according to element connections and aggregates them to node features, generates displacement corrections and iteratively updates the node displacements, and outputs the equilibrium displacement field, where:

[0172] The node residual force feedback iteration layer includes:

[0173] Initial displacement buffer: stores the initial node displacements generated by the fusion of the branch network and the backbone network;

[0174] Nodal force multiplier: Calculates the product of the stiffness matrix and the nodal displacements;

[0175] Nodal residual force register: stores the difference between the load vector and the nodal internal force;

[0176] Unit residual force return table: Distributes the node residual force to adjacent units according to the unit connection;

[0177] Node feature aggregator: Aggregates the residual force features of adjacent elements;

[0178] Displacement correction generator: Generates displacement correction amounts based on the aggregated node features;

[0179] Displacement Iteration Register: Superimposes displacement corrections and updates node displacements;

[0180] Equilibrium displacement output buffer: Outputs the equilibrium displacement field after iteration;

[0181] The process of the node residual force feedback iteration layer is as follows:

[0182] The node residual force feedback iteration layer receives a 1×D path load representation and N×3 node coordinates, and connects the 3N×3N stiffness matrix, 3N×1 load vector and E×4 element in the model training sample according to the sample combination number. The backbone network maps the node coordinates to N×D node coordinate features and copies the path load representation to N×D path load features. The two types of features are multiplied element by element and then multiplied with the D×3 displacement mapping matrix to generate N×3 initial node displacements. The constrained node displacements are set to 0 and written to the initial displacement buffer.

[0183] The nodal internal force multiplier expands the nodal displacements into 3N×1 displacement vectors according to the nodal number and the three coordinate directions, and multiplies them with a 3N×3N stiffness matrix to obtain a 3N×1 nodal internal force vector.

[0184] The nodal residual force register subtracts the nodal internal force vector from the load vector to obtain a 3N×1 nodal residual force vector, and restores it to an N×3 nodal residual force matrix, setting the constraint nodal residual force to 0;

[0185] The element residual force return table is based on the number of associated elements of each node according to the element connection of E×4. The node residual force is evenly distributed to the corresponding associated elements to form an E×4×3 element node residual force matrix. The distributed residual forces of the four nodes in the element are added in each coordinate direction to obtain the element residual force characteristics of E×3.

[0186] The node feature aggregator calculates the centroid of each element and the distance from the node within the element to the centroid. It normalizes the inverse of the distance to the return weight, assigns the element residual force features to the corresponding nodes and sums them to obtain N×3 node return residual forces. It connects the current node displacement, node residual force and node return residual force in columns to form N×9 node aggregate features.

[0187] The displacement correction generator multiplies the node aggregation features sequentially with the 9×D residual force feature mapping matrix and the D×3 correction gain matrix, and processes them with the Sigmoid function to obtain the N×3 correction gain. It extracts the diagonal stiffness of each node in three directions from the stiffness matrix, divides the node's back-in residual force by the corresponding diagonal stiffness, and multiplies it element by element with the correction gain to obtain the displacement correction amount. When the diagonal stiffness is 0, the corresponding displacement correction amount is set to 0.

[0188] The displacement iteration register multiplies the displacement correction by 0.5 and adds it to the current node displacement to update the node displacement. It also recalculates the node internal forces, node residual forces, and displacement correction. After each iteration, the constrained node displacement is kept at 0.

[0189] The ratio of the L2 norm of the nodal residual force vector to the L2 norm of the load vector is calculated. The iteration stops when the ratio is not greater than 0.0001. If the condition is not met after 8 iterations, the nodal displacement of the 8th iteration is retained.

[0190] The equilibrium displacement output buffer is arranged according to the node number, and the N×3 node displacements at the time of stopping iteration are generated to form an equilibrium displacement field.

[0191] The parameters of the node residual force feedback iteration layer include the number of nodes N, the number of elements E, the feature dimension D, the iteration coefficient, the maximum number of iterations, the convergence ratio, the displacement mapping matrix, the residual force feature mapping matrix, and the correction gain matrix;

[0192] The number of nodes N and the number of units E are determined based on the corresponding model training samples. The feature dimension D is consistent with the path load representation dimension. The three types of mapping matrices are uniformly initialized by Xavier and updated with the training of the improved PI-DeepONet.

[0193] The hazardous region self-generated query head receives the equilibrium displacement field, calculates the equivalent stress at the nodes and the ratio of the difference in equivalent stress between adjacent nodes to the node distance to obtain the stress gradient, merges adjacent nodes whose equivalent stress is not less than the stress threshold or whose stress gradient is not less than the gradient threshold, generates a hazardous region, sets the midpoint of adjacent nodes and the stress gradient direction interpolation point in the hazardous region, and calculates the corresponding stress through fusion of the branch network and the backbone network, outputting the hazardous region query stress, where:

[0194] The self-generated query header for dangerous areas includes:

[0195] Nodal stress calculator: Calculates the equivalent stress at nodes based on the equilibrium displacement field;

[0196] Stress gradient register: stores the stress gradient of adjacent nodes;

[0197] Dangerous Node Screening Table: Screens nodes that have reached the stress threshold or gradient threshold;

[0198] Dangerous area merging queue: Merges adjacent dangerous nodes and generates dangerous areas;

[0199] Adjacent Node Midpoint Generator: Calculates the coordinates of the midpoint between adjacent nodes within the hazardous area;

[0200] Gradient interpolation point generator: Generates interpolation point coordinates along the stress gradient direction;

[0201] Query Feature Fuder: Fuses query point coordinate features and branch features;

[0202] Query stress output buffer: Output the query stress in the dangerous area;

[0203] The process of handling self-generated query headers in dangerous areas is as follows:

[0204] The hazardous area self-generated query head receives an N×3 equilibrium displacement field and associates it with the N×3 node coordinates, E×4 element connections, material elastic modulus, Poisson's ratio, and material bearing capacity threshold according to the sample combination number. It then constructs a 6×6 material constitutive matrix based on the material elastic modulus and Poisson's ratio.

[0205] Let M be the number of adjacent node pairs, R be the number of dangerous areas, Q be the number of query points, and D be the feature dimension;

[0206] The nodal stress calculator extracts the nodal coordinates and equilibrium displacements of each tetrahedral element according to the element connection, and arranges them into a 12×1 element displacement vector. A 6×12 strain-displacement matrix is ​​calculated based on the nodal coordinates. Multiplying it with the element displacement vector yields a 6×1 element strain, which is then multiplied with the material constitutive matrix to obtain the element stress. The sum of the squares of the three normal stresses obtained by subtracting each pair of them and multiplying by 0.5, and then adding this sum to three times the sum of the squares of the three shear stresses and taking the square root, yields the element von Mises equivalent stress. The equivalent stress of adjacent elements is weighted and averaged according to the element volume to obtain the N×1 nodal equivalent stress.

[0207] The stress gradient register extracts M sets of non-repeating adjacent nodes from the element connection to form an M×2 node pair index. The absolute value of the equivalent stress difference of each node pair is divided by the node distance to obtain an M×1 node pair stress gradient. The maximum value of the associated gradient of each node is taken to form an N×1 node stress gradient.

[0208] The critical node screening table uses 0.8 times the material bearing capacity threshold as the stress threshold, determines the 90th percentile from the stress gradients of node pairs greater than 0 and uses it as the gradient threshold, and marks nodes with equivalent stress not less than the stress threshold or stress gradient not less than the gradient threshold as critical nodes; if there is no stress gradient of node pairs greater than 0, only stress threshold screening is performed.

[0209] The dangerous area merging queue establishes the adjacency relationship of dangerous nodes according to the unit connection. Starting from the unmerged dangerous node, dangerous nodes of the shared unit are continuously added until there are no more unadded adjacent dangerous nodes, resulting in R dangerous areas. The node number and adjacent node pairs in the area are recorded.

[0210] The adjacent node midpoint generator extracts adjacent node pairs within the danger zone where both ends are danger nodes. It then averages the coordinates of the two nodes component by component to obtain the midpoint of the adjacent nodes.

[0211] The gradient interpolation point generator moves 0.25 times the distance from the node with lower equivalent stress along the direction of the node with higher equivalent stress to obtain the interpolation point in the stress gradient direction. When the equivalent stress of two nodes is the same, no corresponding interpolation point is generated.

[0212] Merge the midpoints of adjacent nodes and the interpolation points of the stress gradient direction, delete duplicate coordinate points, and arrange them according to the danger zone number and the coordinates of the query point to form a Q×3 danger zone query coordinate. When there is no danger zone composed of adjacent danger nodes, record R and Q as 0 and directly output the empty danger zone query stress.

[0213] The query feature fusion unit inputs the query coordinates of the hazardous area into the backbone network to obtain Q×D query coordinate features, inputs the 1×D path load characterization into the branch network to obtain 1×D query branch features, and copies them to Q×D. The query branch features are multiplied element-wise with the query coordinate features, and then multiplied with the D×1 query stress mapping vector to obtain the Q×1 query equivalent stress. The query stress mapping vector is initialized uniformly by Xavier and updated with the improved PI-DeepONet training.

[0214] The query stress output buffer is associated with the hazardous area number, query point coordinates and query equivalent stress by query point number, generating Q×5 hazardous area query stress;

[0215] The parameters of the self-generated query head for hazardous areas include the number of nodes N, the number of elements E, the number of adjacent node pairs M, the number of hazardous areas R, the number of query points Q, the feature dimension D, the stress threshold, the gradient threshold, and the interpolation ratio.

[0216] N and E are determined based on the model training samples, M, R and Q are determined based on the node adjacency relationship, the dangerous area merging result and the query point generation result, respectively, and D is consistent with the path load representation dimension, with an interpolation ratio of 0.25.

[0217] The queried stress in the hazardous area is mapped back to the node according to the element it belongs to, and fused with the equivalent stress of the node corresponding to the equilibrium displacement field to generate the current predicted stress field. The difference between this predicted and the equivalent stress of the finite element nodes is used to obtain the hazardous area mapping error, where:

[0218] The error in the dangerous area reflection is as follows:

[0219] The tetrahedral element containing the query point is determined based on the query point coordinates and element connections. The centroid coordinates of the query point relative to the four element nodes are calculated and used as the node reflection weight. When the query point is located on a common face or common edge, all elements containing the query point are retained.

[0220] Multiply the query equivalent stress by the reflection weights greater than 0 and write it to the corresponding node. Divide the sum of the weighted stresses received by each node by the sum of the weights to obtain the node query stress.

[0221] The node query stress is averaged with the node equivalent stress corresponding to the equilibrium displacement field to obtain the node predicted stress in the dangerous area. The original node equivalent stress is retained for nodes that have not received query stress. The current predicted stress field is generated by arranging them according to the node number. When the query stress in the dangerous area is empty, the original node equivalent stress is directly used as the current predicted stress field.

[0222] According to the sample combination number and node number, the current predicted stress field is aligned with the equivalent stress of the finite element node node node by node. The equivalent stress of the finite element node is subtracted from the current predicted stress to obtain the reflection error of the dangerous area.

[0223] The improved PI-DeepONet is trained by weighting the node equivalent stress prediction error, node residual force balance error, path load conservation error, and dangerous area reflection error to obtain a joint loss value. The parameters of the load path competition allocation layer, node residual force reflection iteration layer, dangerous area self-generated query head, branch network, and backbone network are iteratively updated, and the current predicted stress field is refreshed. When the change in the joint loss value over six consecutive training rounds is less than 0.001, a stress prediction field is generated, where:

[0224] The improved PI-DeepONet is trained as follows:

[0225] Eight model training samples are selected for each batch. Sample combination parameters, node coordinates, element connections, stiffness matrix, load vectors and equivalent stress of finite element nodes are extracted and input into the improved PI-DeepONet to generate path load characterization, equilibrium displacement field, query stress of dangerous area and current predicted stress field, and finite element node equivalent stress is aligned according to sample combination number and node number.

[0226] The sum of the squares of the differences between the equivalent stress at the nodes corresponding to the equilibrium displacement field and the equivalent stress at the finite element nodes is divided by the sum of the squares of the equivalent stress at the finite element nodes and 0.00000001 to obtain the prediction error of the equivalent stress at the nodes. The load vector is subtracted after multiplying the stiffness matrix with the displacement vector expanded from the equilibrium displacement field to eliminate the constrained degrees of freedom. The sum of the squares of the remaining differences is divided by the sum of the squares of the unconstrained degree of freedom loads and 0.00000001 to obtain the residual force balance error at the nodes. The average of the current predicted stress of the nodes in each candidate element path is multiplied by the minimum cross-sectional area to obtain the path-transferred load. The adjusted load ratio is multiplied by the resultant load force to obtain the path-distributed load. The sum of the squares of the differences between the two types of loads is divided by the sum of the squares of the path-distributed loads and 0.00000001 to obtain the path load conservation error. The average of the squares of the dangerous area reflection error of the node receiving the queried stress is taken to obtain the dangerous area reflection error. When the dangerous area query stress is empty, the dangerous area reflection error is set to 0.

[0227] The average values ​​of the four types of errors within the batch are multiplied by 0.40, 0.25, 0.20, and 0.15 respectively and then summed to obtain the joint loss value. The parameters of the load path competition allocation layer, node residual force return iteration layer, danger area self-generated query head, branch network, and backbone network are updated using the Adam optimizer with an initial learning rate of 0.001, and the current predicted stress field is refreshed. Training stops when the absolute value of the difference between the joint loss values ​​of adjacent training rounds is less than 0.001 for 6 consecutive rounds. The model training samples are input into the converged improved PI-DeepONet, and the current predicted stress field is summarized according to the sample combination number to generate the stress prediction field.

[0228] This invention structurally optimizes the traditional PI-DeepONet by introducing a load path competition allocation layer, enabling the model to distinguish different load paths based on structural force transmission characteristics, reducing load allocation distortion, and improving the prediction accuracy of the overall stress distribution of the diesel engine connecting rod.

[0229] To address the issue that the predicted results may deviate from the nodal force equilibrium, a nodal residual force feedback iteration layer is introduced. The displacement characterization is corrected by feedback through the nodal residual force. Since the nodal residual force can reflect the deviation between the predicted state and the mechanical equilibrium conditions, it can enhance the physical consistency and stability of the predicted stress field.

[0230] To address stress concentration in rounded transition zones, hole edges, and abrupt cross-sectional areas, a self-generated query head for hazardous areas is introduced to supplement local query information for high-stress and high-gradient regions. This improves the spatial resolution of hazardous areas and reduces the omission of peak stress and excessive smoothing of local stress.

[0231] The improved PI-DeepONet not only retains the original operator mapping and stress field prediction capabilities, but also achieves deep integration of diesel engine connecting rod load transfer relationships, nodal mechanical balance and local stress changes in dangerous areas, which greatly improves the physical consistency, local resolution and maximum stress prediction accuracy of connecting rod stress under complex working conditions.

[0232] In this embodiment, generating the corrected maximum stress and predicted variance includes:

[0233] The maximum stress is extracted from the stress prediction field and the finite element stress sample set according to the sample combination number. The maximum stress is obtained by subtracting the predicted maximum stress from the maximum stress in the finite element set. The stress residual is then associated with the corresponding link structure parameters, material parameters, and working condition parameters to generate residual training samples, where:

[0234] The residual training samples are generated as follows:

[0235] According to the sample combination number, the nodal predicted stress in the stress prediction field and the finite element nodal equivalent stress in the finite element stress sample set are summarized respectively. The maximum value of each sample combination is taken to obtain the predicted maximum stress and the finite element maximum stress.

[0236] The stress residual is obtained by subtracting the predicted maximum stress of the same sample combination from the maximum stress of the finite element method.

[0237] Based on the sample combination number, the link structure parameters, material parameters, and working condition parameters are associated. The link structure parameters, material parameters, and working condition parameters are arranged in sequence to form a parameter vector. The sample combination number, parameter vector, predicted maximum stress, finite element maximum stress, and stress residual are encapsulated into residual training records and summarized to generate residual training samples.

[0238] The parameter values ​​in the residual training samples are normalized, and the normalized parameter vector is used as input and the stress residual as output to train the Kriging residual model, wherein:

[0239] Training the Kriging residual model involves the following steps:

[0240] The minimum and maximum values ​​of each field of the linkage structure parameters, material parameters, and working condition parameters are calculated separately. The difference between the parameter value and the corresponding minimum value is divided by the difference between the maximum value and the minimum value to obtain the normalized parameter value. When the maximum value and the minimum value are equal, the corresponding normalized parameter value is set to 0.

[0241] The normalized parameter values ​​are organized according to the order of the linkage structure parameters, material parameters, and working condition parameters to form a residual training parameter vector, and then the parameter vector matrix and stress residual vector are formed according to the sample combination number.

[0242] Set an initial value of 1 and a value greater than 0 for each parameter dimension. Calculate the squared difference between any two residual training parameter vectors in each parameter dimension and divide them by the square of the corresponding length scale parameter. Sum the results and convert them into sample correlation coefficients through a Gaussian correlation function to generate a sample correlation matrix. Add 0.00000001 to the main diagonal.

[0243] The sample correlation matrix is ​​solved using the all-one vector and the stress residual vector as right-hand terms, respectively, to obtain the mean solution vector and the residual solution vector. The inner product of the all-one vector and the residual solution vector is divided by the inner product of the all-one vector and the mean solution vector to obtain the global residual mean. The stress residual vector is subtracted from the global residual mean to obtain the residual bias vector. The sample correlation matrix is ​​solved again using the residual bias vector as the right-hand term. The inner product of the residual bias vector and the solution result is divided by the number of residual training records to obtain the process variance.

[0244] The negative log-likelihood value is calculated based on the determinant of the process variance and the sample correlation matrix. The maximum likelihood estimation is used to adjust each length scale parameter within the range where the length scale parameter is greater than 0. The sample correlation matrix, global residual mean, and process variance are then regenerated.

[0245] Training stops when the absolute value of the difference between the negative log-likelihood values ​​of two consecutive iterations is less than 0.0001 for five consecutive iterations. The parameter field order, normalization upper and lower limits, residual training parameter vector, stress residual vector, length scale parameter, sample correlation matrix, global residual mean and process variance are saved to obtain the Kriging residual model.

[0246] The parameter combination corresponding to the stress prediction field is input into the Kriging residual model to calculate the prediction residual and prediction variance, where:

[0247] The prediction residuals and prediction variance are calculated as follows:

[0248] According to the parameter field order and normalization upper and lower limits saved in the Kriging residual model, each parameter combination is normalized to form a parameter vector to be corrected. The normalized value of the parameter field with the same maximum and minimum value is set to 0.

[0249] The differences between the parameter vector to be corrected and each residual training parameter vector are calculated in each parameter dimension. The correlation coefficient is obtained by combining the length scale parameter and the Gaussian correlation function, and then arranged in the order of the residual training records to form the predicted correlation vector.

[0250] Subtract the global residual mean from the stress residual vector to obtain the residual deviation vector. Solve the system of linear equations formed by the sample correlation matrix and the residual deviation vector to obtain the residual correlation weights.

[0251] The predicted residual is obtained by multiplying the predicted correlation vector with the residual correlation weights one by one, summing the results, and adding the sum to the global residual mean.

[0252] Solve the sample correlation matrix using the predicted correlation vector and the all-1 vector as right-hand terms respectively to obtain the correlation response vector and the mean response vector. Subtract the inner product of the predicted correlation vector and the correlation response vector from 1, and add the square of the difference between 1 and the sum of the components of the correlation response vector divided by the sum of the components of the mean response vector. Multiply the result with the process variance to obtain the prediction variance. When the prediction variance is less than 0, set the prediction variance to 0.

[0253] The predicted residual is added to the corresponding predicted maximum stress to obtain the corrected maximum stress. The corrected maximum stress and the predicted variance are then correlated according to the parameter combination.

[0254] In this embodiment, constructing the initial failure boundary includes:

[0255] The maximum stress and material bearing capacity threshold are correlated by parameter combination. The maximum stress is then subtracted from the maximum stress to obtain the limit state value of the linkage structure.

[0256] The parameter combinations with limit state values ​​greater than zero are defined as safe combinations, and the parameter combinations with limit state values ​​not greater than zero are defined as failure combinations, thus generating a set of safe combinations and a set of failure combinations.

[0257] The parameter values ​​of safe and failed combinations are normalized, the parameter distances between combinations are calculated, and the heterogeneous combinations with the smallest distances are paired to generate safe-failure combination pairs, where:

[0258] Generate security failure combination pairs, specifically:

[0259] Calculate the minimum and maximum values ​​of each parameter field in all safety and failure combinations. Divide the parameter value by the corresponding minimum value and then divide by the difference between the maximum and minimum values ​​to obtain the normalized parameter value. When the maximum and minimum values ​​are equal, set the corresponding normalized parameter value to 0.

[0260] The normalized values ​​of the linkage structure parameters, material parameters, and operating condition parameters are arranged in sequence to form a safety combination parameter vector and a failure combination parameter vector;

[0261] The parameter vector of each safety combination is subtracted from the parameter vector of each failure combination. The square root of the sum of the squared differences of each dimension is obtained to obtain the parameter distance. The failure combination with the smallest distance is paired with the corresponding safety combination. When the distances are the same, the combination with the smaller sum of the absolute values ​​of the extreme state values ​​at both ends is selected.

[0262] The safety combination number, failure combination number, safety combination parameter vector, failure combination parameter vector, extreme state values ​​at both ends and parameter distance are encapsulated into a combination pair record. The combination pair records are summarized and the minimum and maximum values ​​of each parameter field are associated to generate a safety failure combination pair.

[0263] Boundary points are determined based on the limit state values ​​of the safety combination and failure combination in the safety-failure combination pair. Each boundary point is fitted, and the safety side and failure side are calibrated to generate the boundary function and initial failure boundary, wherein:

[0264] The boundary function and initial failure boundary are generated as follows:

[0265] Extract the safety combination parameter vector, failure combination parameter vector, and limit state values ​​at both ends from each safety failure combination pair. Divide the safety limit state value by the difference between the safety limit state value and the failure limit state value to obtain the boundary interpolation ratio. Multiply the difference between the two parameter vectors by the boundary interpolation ratio and add it to the safety combination parameter vector to obtain the normalized boundary parameter vector.

[0266] The normalized boundary parameter vector is restored based on the minimum and maximum values ​​of each parameter field, and the boundary points composed of the linkage structure parameters, material parameters and working condition parameters are obtained. The corresponding limit state values ​​are then set to 0.

[0267] The safety combination parameter vector, failure combination parameter vector, and normalized boundary parameter vector are combined to form the boundary fitting parameter vector. The corresponding limit state values ​​are used to form the fitting target vector. The parameter distance between each boundary fitting parameter vector is calculated. The median of the non-zero parameter distance is determined as the radial scale. The parameter distance is converted into a distance response through the Gaussian radial basis function to generate the fitting matrix.

[0268] Add 0.00000001 to the main diagonal of the fitting matrix, solve the linear equation system formed by the fitting matrix and the fitting target vector, and obtain the radial basis weights.

[0269] The parameter field order, the minimum and maximum values ​​of each parameter field, the boundary fitting parameter vector, the radial scale, and the radial basis weights are encapsulated into a boundary function.

[0270] The parameter region with boundary function values ​​greater than 0 is designated as the safe side, the parameter region with boundary function values ​​not greater than 0 is designated as the failure side, and the set of parameters with boundary function values ​​equal to 0 within the parameter value range is determined as the initial failure boundary.

[0271] In this embodiment, the iterative generation of convergence failure boundaries includes:

[0272] Centered on the boundary point of the current failure boundary, the parameter values ​​are adjusted within the neighborhood of each parameter dimension. Parameter combinations that exceed the simulation parameter space or overlap with existing samples are eliminated, generating candidate combinations, where:

[0273] The candidate combinations are generated as follows:

[0274] In the first round, the initial failure boundary is determined as the current failure boundary. The minimum, maximum and allowable values ​​of each parameter field in the simulation parameter space are extracted. The link structure parameters, material parameters and working condition parameters of each boundary point of the current failure boundary are arranged in sequence to form a boundary parameter vector.

[0275] The neighborhood step size is determined by 3% of the range of values ​​of each continuous parameter. The neighborhood step size is added or subtracted from the boundary parameter values ​​respectively. Discrete parameters take the allowed values ​​adjacent to the boundary parameter values. One or two parameter dimensions are adjusted each time, while the other parameters remain unchanged, forming the boundary neighborhood parameter vector.

[0276] Remove boundary neighborhood parameter vectors whose parameter values ​​are less than the corresponding minimum value, greater than the corresponding maximum value, or do not belong to the allowed values. Normalize the remaining boundary neighborhood parameter vectors and the existing parameter combinations in the finite element stress sample set according to the minimum and maximum values ​​of each parameter field. When the maximum value is equal to the minimum value, set the corresponding normalized parameter value to 0.

[0277] Calculate the parameter distance between each boundary neighborhood parameter vector and each existing parameter combination, and remove the boundary neighborhood parameter vectors whose minimum parameter distance is no greater than 0.005;

[0278] Arrange the remaining boundary neighborhood parameter vectors in the order of generation, retain the first record, calculate the parameter distance between the remaining records and all retained records in turn, retain the records with the minimum parameter distance greater than 0.005, number the retained parameter combinations, and generate candidate combinations.

[0279] Each candidate combination is input into the Kriging residual model to obtain the predicted variance. The parameter distance between each candidate combination and the nearest sample in the finite element stress sample set is calculated, normalized, and weighted to obtain a supplementary score. Supplementary combinations are then selected based on the supplementary score, where:

[0280] The selection and supplementary combinations are as follows:

[0281] According to the parameter field order and normalization upper and lower limits saved in the Kriging residual model, each candidate combination is normalized and input into the Kriging residual model to obtain the corresponding prediction variance.

[0282] According to the parameter normalization rule used when generating candidate combinations, the parameter distance between each candidate combination and all parameter combinations in the finite element stress sample set is calculated, and the minimum value is determined as the nearest sample distance.

[0283] Calculate the minimum and maximum values ​​of prediction variance and nearest sample distance for all candidate combinations. Subtract each value from the corresponding minimum value and divide by the difference between the maximum and minimum values ​​to obtain the normalized prediction variance and normalized nearest sample distance. When the maximum and minimum values ​​are equal, set the corresponding normalized value to 0.5.

[0284] Multiply the normalized prediction variance by 0.6 and the normalized nearest sample distance by 0.4, and sum them to obtain the supplementary score. Arrange the candidate combinations in descending order of the supplementary score. When the scores are the same, select the candidate combinations with larger prediction variance and larger nearest sample distance in order. Select the top 10 as supplementary combinations. If there are fewer than 10 candidate combinations, retain all of them.

[0285] The supplementary combination is written into the parametric finite element model to perform static analysis, extracting the nodal equivalent stress, maximum stress, and maximum stress location, and incorporating them into the finite element stress sample set, wherein:

[0286] Perform static analysis, specifically:

[0287] Extract the link structure parameters, material parameters, and working condition parameters from the supplementary combination one by one, write them into the corresponding fields of the parametric finite element model, update the geometric dimensions, material properties, and working condition loads, and perform finite element static analysis using the established element type, mesh generation rules, constraint type, load application method, and solution accuracy.

[0288] Extract the equivalent stress of nodes by node number, take the maximum equivalent stress of nodes as the maximum stress, and record the corresponding node coordinates as the location of the maximum stress. When the maximum stresses are the same, record the coordinates of the node with the smallest node number.

[0289] The supplementary combination number, parameter combination, nodal equivalent stress, maximum stress and maximum stress location are encapsulated as finite element stress samples and written into the finite element stress sample set.

[0290] The improved PI-DeepONet was trained using the updated finite element stress sample set. The stress residuals were recalculated and the Kriging residual model was updated. The corrected maximum stress was calculated, safe combinations and failure combinations were divided, and the failure boundary was updated.

[0291] Calculate the minimum parameter distance from each boundary point of the current failure boundary to the previous failure boundary, and take the maximum value as the boundary change. If the boundary change is greater than the boundary convergence threshold, continue to perform boundary neighborhood sampling, finite element recalculation, and model update until the boundary change is no greater than the boundary convergence threshold, generating a converged failure boundary, where:

[0292] Generate the convergence failure boundary, specifically as follows:

[0293] The initial failure boundary is saved as the failure boundary of the previous round. After each update of the failure boundary, the boundary points of the current failure boundary and the previous failure boundary are normalized according to the minimum and maximum values ​​of each parameter field in the simulation parameter space to form the current boundary parameter vector and the previous boundary parameter vector. When the maximum value is equal to the minimum value, the corresponding normalized parameter value is set to 0.

[0294] The difference between each current boundary parameter vector and all previous boundary parameter vectors is calculated. The square root of the sum of the squares of the differences in each dimension is then used to obtain the parameter distance between boundary points. The minimum parameter distance for each current boundary point is taken, and the maximum value among all the minimum values ​​is determined as the boundary change.

[0295] Set the boundary convergence threshold to 0.01. When the boundary change is greater than 0.01, save the current failure boundary as the previous failure boundary for the next round, and determine the current failure boundary as the sampling center of the boundary neighborhood for the next round. Then, re-execute the candidate combination generation, supplementary combination screening, finite element static analysis and model update to obtain the current failure boundary for the next round.

[0296] Iteration stops when the boundary change is no greater than 0.01, and the boundary points, boundary functions, safe side, failure side, and boundary change of the current failure boundary are encapsulated into a convergent failure boundary.

[0297] In this embodiment, the generation of reliability analysis results for the diesel engine connecting rod structure includes:

[0298] Based on the value range defined by the simulation parameter space, the connecting rod structure parameters, material parameters, and diesel engine operating parameters are uniformly sampled, combined to generate random sample sets, and numbered, where:

[0299] Generate and number a random sample set, specifically as follows:

[0300] Extract the minimum and maximum values ​​of each continuous parameter and the allowable values ​​of each discrete parameter in the simulation parameter space, and set the number of random samples to 100,000.

[0301] For each continuous parameter, independent and uniform sampling is performed 100,000 times between the corresponding minimum and maximum values. For each discrete parameter, independent and equal probability sampling is performed 100,000 times from the corresponding allowed values ​​to obtain the sampling sequence of each parameter field.

[0302] According to the same sampling order, the sampled values ​​of connecting rod structural parameters, material parameters and diesel engine operating parameters are combined into a random sample;

[0303] Random samples are numbered sequentially from 1 to 100000. The random sample numbers, connecting rod structural parameters, material parameters, and diesel engine operating parameters are encapsulated to generate a random sample set.

[0304] Each random sample is input into the boundary function corresponding to the convergent failure boundary. Random samples located on the failure side are marked as failure samples, and random samples located on the safe side are marked as safe samples, wherein:

[0305] The failure samples and safe samples are labeled as follows:

[0306] According to the order of the parameter fields stored in the boundary function, the linkage structure parameters, material parameters and diesel engine operating parameters in each random sample are arranged in sequence, and normalized according to the minimum and maximum values ​​of each parameter field stored in the boundary function to form a random sample parameter vector. When the maximum value is equal to the minimum value, the corresponding normalized parameter value is set to 0.

[0307] Calculate the parameter distance between the random sample parameter vector and each boundary fitted parameter vector, and convert it into a distance response using the Gaussian radial basis function in combination with the radial scale. Multiply each distance response by the corresponding radial basis weight and sum them to obtain the boundary function value.

[0308] When the boundary function value is not greater than 0, the corresponding random sample is marked as a failed sample and the failure state is set to 1; when the boundary function value is greater than 0, the corresponding random sample is marked as a safe sample and the failure state is set to 0.

[0309] Write the failure status into the corresponding random sample to complete the labeling of failure samples and safety samples;

[0310] The total number of random samples and the number of failed samples are counted. The failure probability is obtained by dividing the number of failed samples by the total number of random samples. The reliability is obtained by subtracting the failure probability from one.

[0311] The reliability analysis results of the diesel engine connecting rod structure are generated by associating the connecting rod structural parameters, material parameters, diesel engine operating parameters, and failure states with random sample numbers, and encapsulating them with failure probability and reliability.

[0312] refer to Figure 3 A reliability analysis system for diesel engine connecting rod structures includes the following modules:

[0313] The parameter space construction module is used to process diesel engine connecting rod data to form a parametric finite element model and simulation parameter space;

[0314] The finite element simulation module is used to filter parameter combinations and perform static solutions to form a finite element stress sample set.

[0315] The stress prediction module is used to process finite element stress sample sets by improving PI-DeepONet and output the stress prediction field;

[0316] The residual correction module is used to establish the residual relationship between the predicted maximum stress and the finite element maximum stress, and outputs the corrected maximum stress and the prediction variance.

[0317] The failure boundary construction module is used to divide safe combinations and failure combinations to form the initial failure boundary;

[0318] The boundary iteration module is used to filter supplementary combinations of boundary neighborhoods, update the finite element stress sample set, improve PI-DeepONet and Kriging residual models, and form convergent failure boundaries.

[0319] The reliability calculation module is used to determine the failure state of random samples, calculate the failure probability and reliability, and output the reliability analysis results of the diesel engine connecting rod structure.

[0320] Example 1: To verify the feasibility of this invention in practice, it was applied to the design finalization and verification of a connecting rod for a high-reliability diesel power unit. This connecting rod suffers from problems such as insufficient finite element sample coverage, large deviations in stress prediction in critical areas, and difficulty in accurately determining the failure boundary due to the combined effects of structural dimensional deviations, material property fluctuations, and changes in operating conditions. The analysis object is an alloy steel connecting rod with a length of 260 mm, a large end bore diameter of 102 mm, a small end bore diameter of 48 mm, a rod thickness of 31 mm, and a transition fillet radius of 6.5 mm; the material density is 7850 kg / m³, the elastic modulus is 210 GPa, the Poisson's ratio is 0.30, and the material load-bearing threshold is 690 MPa; the diesel engine speed range is 1400–2200 r / min, the maximum burst pressure range is 14.0–19.5 MPa, and the equivalent inertial force range is 52–92 kN. In this embodiment, the method of the present invention is used to establish a parametric finite element model, predict the stress field of the connecting rod and iteratively determine the failure boundary, and calculate the failure probability and reliability of the connecting rod.

[0321] After receiving the 3D model of the connecting rod, the system repaired 3 undesigned holes, 7 sets of repeated surfaces, and 11 surface breaks. It connected the centers of the large-end hole and the small-end hole to form an axial baseline and divided the model into large-end hole area, small-end hole area, rod body area, and transition fillet area. Before repair, the maximum gap on the model surface was 0.42 mm, which decreased to 0.03 mm after repair. The system set the connecting rod length, large-end hole diameter, small-end hole diameter, rod body thickness, and transition fillet radius as adjustable parameters, and divided the connecting rod model into a tetrahedral mesh, forming 186,420 nodes and 112,760 elements. The average side length of the elements in the inner fillet area of ​​the large-end hole was 1.2 mm, and the average side length of the elements in the rod body area was 2.5 mm.

[0322] The connecting rod length was set to 257.5–262.5 mm, the large end bore diameter to 100.8–103.2 mm, the small end bore diameter to 47.4–48.6 mm, the rod thickness to 28.5–33.5 mm, the transition fillet radius to 5.0–8.0 mm, and the elastic modulus to 204–216 GPa. The system divided each parameter range into 12 layers, extracted parameter values ​​from each layer, and rearranged them to generate 160 initial samples. Normalized distance calculations showed that the minimum distance between 9 samples was less than 0.08. The system resampled at the corresponding parameter layers, increasing the minimum normalized distance between samples to 0.091 and improving the parameter space coverage from 86.3% to 94.7%.

[0323] One by one, 160 sets of samples were written into the parametric finite element model, updating the connecting rod structure dimensions, material properties, diesel engine speed, maximum burst pressure, equivalent inertial force, and constraint nodes. The average time for each set of samples to complete model update, stiffness matrix assembly, load vector generation, and static solution was 8.7 min. The maximum nodal equivalent stress of the 160 sets of samples ranged from 438.6 to 771.2 MPa, with an average of 612.4 MPa. Among them, 96 sets were below the material bearing capacity threshold, and 64 sets were not below the material bearing capacity threshold. Among the locations of maximum stress, 115 sets were located at the inner fillet of the large end hole, 29 sets were located at the edge of the small end hole, and 16 sets were located in the cross-sectional change region of the rod.

[0324] The model processing procedure is demonstrated using sample S087. S087 has a connecting rod length of 261.4 mm, a large-end bore diameter of 101.6 mm, a small-end bore diameter of 48.3 mm, a rod thickness of 29.3 mm, a transition fillet radius of 5.5 mm, an elastic modulus of 207.8 GPa, a rotational speed of 2050 r / min, a maximum burst pressure of 18.8 MPa, and an equivalent inertial force of 86.7 kN. Finite element analysis yielded a maximum nodal equivalent stress of 706.4 MPa, a maximum nodal displacement of 0.306 mm, and the maximum stress was located at the inner fillet of the connection between the large-end bore and the rod body. This sample is considered a failure sample.

[0325] After S087 enters the load path competition allocation layer, six candidate element paths are formed by connecting the load nodes to the constraint nodes. The cumulative lengths of the six paths range from 176.4 to 228.6 mm, and the minimum cross-sectional areas range from 558 to 814 mm². The initial load ratios obtained based on the path equivalent stiffness and cumulative length are 0.30, 0.24, 0.18, 0.13, 0.09, and 0.06, which are adjusted to 0.27, 0.24, 0.20, 0.14, 0.09, and 0.06 based on the path bearing capacity margin. After adopting the adjusted load ratios, the load expression error of the main bearing path decreases from 12.6% to 4.1%.

[0326] Path loads are input to the branch network, and node coordinates are input to the backbone network. The initial node displacements are generated by fusing these two types of features. The stiffness matrix is ​​multiplied by the node displacements to obtain the nodal internal forces, and the load vector is subtracted from the nodal internal forces to obtain the nodal residual forces. The initial mean square value of the nodal residual forces was 0.084. After four rounds of nodal residual force feedback and displacement correction, the mean square value of the nodal residual forces successively decreased to 0.034, 0.016, 0.009, and 0.005. The maximum displacement of the final equilibrium displacement field was 0.302 mm, differing from the finite element result by 0.004 mm, with a relative error of 1.31%.

[0327] The hazardous area self-generated query head calculates the equivalent stress and stress gradient of nodes based on the equilibrium displacement field, merging adjacent nodes with an equivalent stress of not less than 580 MPa or a stress gradient of not less than 18 MPa / mm. Two hazardous areas are formed in S087: the rounded corner area inside the large-end hole contains 174 nodes, and the lower edge area of ​​the small-end hole contains 74 nodes. The system generates 318 query points at the midpoints of adjacent nodes and along the stress gradient direction. Without performing the hazardous area query, the model predicts a maximum stress of 679.5 MPa, lower than the material bearing capacity threshold, and the average absolute error of the hazardous area nodes is 21.3 MPa. After completing the query stress calculation, node reflection, and stress fusion, the maximum predicted stress increases to 697.8 MPa, and the average absolute error of the hazardous area nodes decreases to 7.1 MPa.

[0328] Of the 160 samples, 112 were used as training samples, 24 as validation samples, and 24 as test samples. The joint loss of the improved PI-DeepONet decreased from 0.391 to 0.016, and updates ceased after the loss change was less than 0.001 for six consecutive training rounds. For S087, the maximum stress output by the improved PI-DeepONet was 697.8 MPa, and the difference between the maximum stress in the finite element method and the predicted maximum stress was 8.6 MPa. The Kriging residual model output a predicted residual of 7.7 MPa and a prediction variance of 15.6 MPa², yielding a corrected maximum stress of 705.5 MPa, which differed from the finite element result by 0.9 MPa, with a relative error of 0.13%. The failure state determination result was consistent with the finite element analysis.

[0329] Based on the corrected maximum stress and material bearing capacity threshold of 160 samples, 96 safe combinations and 64 failure combinations were obtained. The system calculated the normalized distance between the safe and failure combinations, forming 58 safe-failure combination pairs, and fitted them to obtain the initial failure boundary. When using 30 independent samples for verification, 4 misjudgments occurred in the initial failure boundary, 3 of which were located in the parameter region where the transition fillet radius was less than 5.8 mm and the maximum burst pressure was greater than 18.3 MPa.

[0330] The system generates 480 candidate combinations in the neighborhood of the initial failure boundary. The prediction variance of the candidate combinations ranges from 4.2 to 38.7 MPa², and the normalized distance to the nearest finite element sample ranges from 0.03 to 0.26. After an initial screening of 18 supplementary combinations for finite element recalculation, the boundary change is 0.061. After a second screening of 14 supplementary combinations, the boundary change decreases to 0.023. After a third screening of 10 supplementary combinations, the boundary change decreases to 0.008, below the boundary convergence threshold of 0.01. The finite element stress sample set is expanded from 160 to 202 sets, and the number of misclassifications in 30 independent samples decreases from 4 to 1 set.

[0331] The system uniformly extracts 100,000 random samples from the simulation parameter space. Upon convergence to the failure boundary, 2,874 samples are identified as failure samples, yielding a failure probability of 2.874% and a reliability of 97.126%. An additional 600 random samples are selected for finite element verification. Of these, 18 samples actually failed. This invention identifies 17 failures, the traditional Kriging method identifies 14 failures, and the non-iterative initial failure boundary identifies 13 failures.

[0332] In the same batch of 24 test samples, the maximum mean absolute error of stress was 27.1 MPa for the traditional Kriging method, 18.4 MPa for the ordinary DeepONet, and 9.6 MPa for the present invention before residual correction and 5.8 MPa after residual correction.

[0333] The failure state determination accuracies of the traditional Kriging method, the ordinary DeepONet, and the present invention are 91.7%, 95.8%, and 99.2%, respectively.

[0334] Traditional uniform supplemental sampling requires 360 finite element analysis (FEM) calculations, while this invention requires only 202 calculations, reducing the FEM computation by 43.9% and shortening the overall analysis time from 8.1 hours to 4.7 hours.

[0335] As can be seen from Example 1, the present invention can improve the stress prediction accuracy of the critical area of ​​the connecting rod, reduce the maximum stress deviation by using residual correction, and reduce the number of state misjudgments and finite element solutions by supplementing sampling in the neighborhood of the failure boundary, thereby improving the accuracy and computational efficiency of the reliability analysis of the diesel engine connecting rod structure.

[0336] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A reliability analysis method for a diesel engine connecting rod structure, characterized in that, include: Obtain diesel engine connecting rod data, construct a parametric finite element model, and generate a simulation parameter space; Sample combinations are selected from the simulation parameter space, and static analysis is performed through the parameterized finite element model to generate a finite element stress sample set; The improved PI-DeepONet is trained using the aforementioned finite element stress sample set. The improved PI-DeepONet includes a load path competition allocation layer, a node residual force feedback iteration layer, and a hazardous area self-generated query head to generate a stress prediction field. Extract the corresponding maximum stress from the stress prediction field and the finite element stress sample set, calculate the stress residual and train the Kriging residual model to generate the corrected maximum stress and prediction variance; By comparing the corrected maximum stress with the material bearing capacity threshold, the corresponding sample combinations are divided into safe combinations and failure combinations, and an initial failure boundary is constructed. Candidate combinations are generated in the neighborhood of the initial failure boundary. Supplementary combinations are selected according to the predicted variance and the nearest sample distance. The parameterized finite element model is used to recalculate and update the finite element stress sample set, improve PI-DeepONet and Kriging residual model, and iteratively generate the convergent failure boundary. Random samples are extracted from the simulation parameter space, the failure state is determined based on the convergent failure boundary, the failure probability and reliability are calculated, and the reliability analysis results of the diesel engine connecting rod structure are generated.

2. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The diesel engine connecting rod data specifically includes the connecting rod's three-dimensional model, connecting rod length, large end bore diameter, small end bore diameter, rod body thickness, transition fillet radius, material density, elastic modulus, Poisson's ratio, material load-bearing threshold, diesel engine speed, maximum burst pressure, equivalent inertial force, load location, and constraint location.

3. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The construction of the parametric finite element model and the generation of the simulation parameter space include: The three-dimensional model of the diesel engine connecting rod is subjected to non-designed hole closure, repeated surface merging and surface repair. The center of the big end hole and the center of the small end hole are connected to form an axial baseline. The big end hole area, small end hole area, rod body area and transition fillet area are divided to generate the connecting rod geometric partition model. The link length, large end diameter, small end diameter, link thickness, and transition fillet radius are written into the link geometric partition model. The dimensions and region boundaries are updated according to the parameter values ​​to generate a parameterized link model. The parametric link model is meshed into a finite element model, and the material density, elastic modulus and Poisson's ratio are configured. The load position and constraint position are mapped to the node to generate the parametric finite element model. Write the diesel engine speed into the operating condition field, write the maximum burst pressure and equivalent inertial force into the load field, limit the value range of structural parameters, material parameters and operating condition parameters, and generate a simulation parameter configuration table. According to the simulation parameter configuration table, parameter combinations with size conflicts and load boundary overlaps are eliminated. The remaining parameter combinations are associated with the parameterized finite element model to generate a simulation parameter space.

4. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The generation of the finite element stress sample set includes: The range of each parameter value in the simulation parameter space is divided into layers. Parameter values ​​are extracted from each layer and rearranged and combined to generate an initial sample combination. Calculate the normalized parameter distance between each initial sample combination, remove the initial sample combination whose minimum distance is less than the distance threshold, and re-extract the parameter values ​​in the corresponding parameter layer to generate sample combinations and number them. The sample combinations are written into the parametric finite element model one by one, and the linkage structure dimensions, material properties, working condition fields, load fields and constraint nodes are updated to generate the sample finite element model. Assemble the stiffness matrix and load vector of the sample finite element model, solve the nodal displacements, calculate the element strain, element stress and nodal equivalent stress based on the nodal displacements, and generate the sample stress results. A finite element stress sample set is generated by associating the node coordinates, equivalent stress, maximum stress, and maximum stress location with the sample combination number.

5. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The generation of the stress prediction field includes: An improved PI-DeepONet is constructed, which includes a load path competition allocation layer, a node residual force feedback iteration layer, and a dangerous area self-generated query head. The finite element stress sample set is associated with the element connection, stiffness matrix, and load vector of the corresponding sample finite element model according to the sample combination number to generate model training samples. The load path competition allocation layer receives model training samples, connects candidate unit paths from load nodes to constraint nodes, calculates the cumulative length, equivalent stiffness, and minimum cross-sectional area of ​​each candidate unit path, normalizes the ratio of equivalent stiffness to cumulative length to obtain the initial load ratio, multiplies the minimum cross-sectional area by the material bearing capacity threshold and subtracts the initial allocated load to obtain the path bearing capacity margin, adjusts the initial load ratio according to the path bearing capacity margin, and outputs the path load characterization. The node residual force feedback iteration layer receives the path load characterization and node coordinates, and generates the initial node displacement by fusing the branch network and the backbone network. The stiffness matrix is ​​multiplied by the node displacement to obtain the node internal force, and the node residual force is obtained by subtracting the node internal force from the load vector. The node residual force is distributed to adjacent elements according to the element connection and aggregated to the node feature. The displacement correction amount is generated and the node displacement is iteratively updated to output the equilibrium displacement field. The hazardous area self-generated query head receives the equilibrium displacement field, calculates the equivalent stress of the nodes and the ratio of the difference in equivalent stress between adjacent nodes to the node distance to obtain the stress gradient, merges adjacent nodes whose equivalent stress is not less than the stress threshold or whose stress gradient is not less than the gradient threshold, generates a hazardous area, sets the midpoint of adjacent nodes and the stress gradient direction interpolation point in the hazardous area, and calculates the corresponding stress through the fusion of the branch network and the backbone network, and outputs the hazardous area query stress. The stress in the dangerous area is mapped back to the node according to the element it belongs to, and then fused with the equivalent stress of the node corresponding to the equilibrium displacement field to generate the current predicted stress field. The difference between the current predicted stress field and the equivalent stress of the finite element node is used to obtain the dangerous area mapping error. The improved PI-DeepONet is trained, and the node equivalent stress prediction error, node residual force balance error, path load conservation error, and dangerous area reflection error are weighted to obtain a joint loss value. The parameters of the load path competition allocation layer, node residual force reflection iteration layer, dangerous area self-generated query head, branch network, and backbone network are iteratively updated, and the current predicted stress field is refreshed. When the change of the joint loss value in 6 consecutive training rounds is less than 0.001, the stress prediction field is generated.

6. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The generation of the corrected maximum stress and prediction variance includes: Extract the maximum stress of the stress prediction field and the finite element stress sample set according to the sample combination number. Subtract the predicted maximum stress from the finite element maximum stress to obtain the stress residual. Associate the corresponding link structure parameters, material parameters and working condition parameters to generate residual training samples. The parameter values ​​in the residual training samples are normalized, and the normalized parameter vector is used as input and the stress residual is used as output to train the Kriging residual model. Input the parameter combination corresponding to the stress prediction field into the Kriging residual model to calculate the prediction residual and prediction variance; The predicted residual is added to the corresponding predicted maximum stress to obtain the corrected maximum stress. The corrected maximum stress and the predicted variance are then correlated according to the parameter combination.

7. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The construction of the initial failure boundary includes: The maximum stress and material bearing capacity threshold are correlated by parameter combination. The maximum stress is then subtracted from the maximum stress to obtain the limit state value of the linkage structure. The parameter combinations with limit state values ​​greater than zero are defined as safe combinations, and the parameter combinations with limit state values ​​not greater than zero are defined as failure combinations, thus generating a set of safe combinations and a set of failure combinations. The parameter values ​​of safe and failed combinations are normalized, the parameter distance between combinations is calculated, and the heterogeneous combinations with the smallest distance are paired to generate safe-fail combination pairs. Boundary points are determined based on the limit state values ​​of the safety combination and failure combination in the safety failure combination pair. Each boundary point is fitted and the safety side and failure side are calibrated to generate the boundary function and the initial failure boundary.

8. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The iterative generation of convergence failure boundaries includes: Centered on the boundary point of the current failure boundary, the parameter values ​​are adjusted in the neighborhood of each parameter dimension, and parameter combinations that exceed the simulation parameter space and overlap with existing samples are eliminated to generate candidate combinations. Each candidate combination is input into the Kriging residual model to obtain the predicted variance. The parameter distance between each candidate combination and the nearest sample in the finite element stress sample set is calculated, normalized and weighted to obtain the supplementary score, and supplementary combinations are selected according to the supplementary score. The supplementary combination is written into the parametric finite element model to perform static analysis, extract the nodal equivalent stress, maximum stress and maximum stress location, and incorporate them into the finite element stress sample set; The improved PI-DeepONet was trained using the updated finite element stress sample set. The stress residuals were recalculated and the Kriging residual model was updated. The corrected maximum stress was calculated, safe combinations and failure combinations were divided, and the failure boundary was updated. Calculate the minimum parameter distance from each boundary point of the current failure boundary to the previous failure boundary, and take the maximum value as the boundary change. If the boundary change is greater than the boundary convergence threshold, continue to perform boundary neighborhood sampling, finite element recalculation and model update until the boundary change is no greater than the boundary convergence threshold, and generate a converged failure boundary.

9. The reliability analysis method for a diesel engine connecting rod structure according to claim 1, characterized in that, The reliability analysis results of the generated diesel engine connecting rod structure include: According to the value range defined by the simulation parameter space, the connecting rod structure parameters, material parameters and diesel engine operating parameters are uniformly sampled, and a random sample set is generated and numbered. The random samples are input one by one into the boundary function corresponding to the convergence failure boundary. The random samples located on the failure side are marked as failure samples, and the random samples located on the safe side are marked as safe samples. The total number of random samples and the number of failed samples are counted. The failure probability is obtained by dividing the number of failed samples by the total number of random samples. The reliability is obtained by subtracting the failure probability from one. The reliability analysis results of the diesel engine connecting rod structure are generated by associating the connecting rod structure parameters, material parameters, diesel engine operating parameters, and failure states with the random sample number, and then encapsulating them with the failure probability and reliability.

10. A reliability analysis system for a diesel engine connecting rod structure, comprising executing the reliability analysis method for a diesel engine connecting rod structure as described in any one of claims 1 to 9, characterized in that, Includes the following modules: The parameter space construction module is used to process diesel engine connecting rod data to form a parametric finite element model and simulation parameter space; The finite element simulation module is used to filter parameter combinations and perform static solutions to form a finite element stress sample set. The stress prediction module is used to process finite element stress sample sets by improving PI-DeepONet and output the stress prediction field; The residual correction module is used to establish the residual relationship between the predicted maximum stress and the finite element maximum stress, and outputs the corrected maximum stress and the prediction variance. The failure boundary construction module is used to divide safe combinations and failure combinations to form the initial failure boundary; The boundary iteration module is used to filter supplementary combinations of boundary neighborhoods, update the finite element stress sample set, improve PI-DeepONet and Kriging residual models, and form convergent failure boundaries. The reliability calculation module is used to determine the failure state of random samples, calculate the failure probability and reliability, and output the reliability analysis results of the diesel engine connecting rod structure.

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