Angle steel connecting piece shear strength prediction method and system based on physical information neural network, electronic equipment and storage medium thereof

Abstract

The invention discloses an angle steel connecting piece shear strength prediction method and system based on a physical information neural network, electronic equipment and a storage medium thereof. The method comprises the following steps: establishing a database containing a plurality of groups of test data based on a numerical simulation result of an angle steel connecting piece finite element model verified by a push-out test; embedding an angle steel connecting piece shear bearing capacity physical constraint condition based on an elastic foundation beam theory into a loss function of the data-driven neural network model DNN; training the neural network embedded with the physical constraint condition by using a database, and adjusting and selecting a physical item weight factor and a model learning rate so as to construct a shear bearing capacity prediction model of a physical information neural network (PINN); predicting the shear strength of the angle steel connecting piece by using the trained physical information neural network (PINN) shear capacity prediction model; according to the prediction method and system, the electronic equipment and the storage medium thereof provided by the invention, the accuracy and reliability of the shear resistance prediction of the angle steel connecting piece can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of angle steel connector design and performance prediction, and particularly relates to an angle steel connector shear strength prediction method and system based on a physical information neural network, an electronic device and a storage medium thereof. BACKGROUND

[0002] In a steel-concrete composite structure, a shear connector is the key to ensuring the collaborative work of a steel beam and concrete, and its connection performance directly affects the overall stiffness, bearing capacity and durability of the composite beam. The commonly used shear connectors in engineering include stud connectors, PBL connectors and angle steel connectors. Among the many shear connectors, the angle steel connector is widely used in steel-concrete composite structures due to its simple structure, easy manufacturing, flexible installation, high shear bearing capacity and large connection stiffness.

[0003] Although the mechanical properties of angle steel connectors have been studied, there are still deficiencies in the current research. The amount of experimental data in existing literature is limited and the parameter combinations are relatively single, making it difficult to fully reflect the performance changes of the connector under various working conditions in actual engineering. The existing design calculation methods are mostly based on assumptions, and the theoretical models are mostly based on elastic theory or empirical formulas, and their applicability is limited by the model assumption conditions. In addition, the shear bearing capacity calculation formula used in engineering specifications often introduces a large safety factor to ensure safety, and the design result is relatively conservative. SUMMARY

[0004] The purpose of the present application is to overcome the deficiencies in the prior art and provide an angle steel connector shear strength prediction method and system based on a physical information neural network, an electronic device and a storage medium thereof, which can improve the accuracy and reliability of angle steel shear performance prediction.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions.

[0006] In a first aspect, the present application provides an angle steel connector shear strength prediction method based on a physical information neural network, comprising the steps of: establishing a database containing a plurality of test data based on the numerical simulation results of the angle steel connector finite element model verified by the push-out test; embedding the shear bearing capacity physical constraint conditions of the angle steel connector based on the elastic foundation beam theory into the loss function of the data-driven neural network model DNN; training the neural network embedded with the physical constraint conditions using the database, adjusting the selection of the physical item weight factor and the model learning rate, to construct a shear bearing capacity prediction model of the physical information neural network PINN; using the trained physical information neural network PINN shear bearing capacity prediction model to predict the shear bearing capacity of the angle steel connector.

[0007] Further, a database is established based on the numerical simulation results of the finite element model, including: The hot-rolled equal angle steel is used as the shear connector, and the angle steel connector is symmetrically connected to the two side flange plates of the H-shaped steel through single-sided fillet welds; Based on the symmetry of the geometric shape and the load action, a 1 / 2 finite element model is established to ensure calculation accuracy and reduce calculation cost; The H-shaped steel girder, concrete, and angle steel connector are all modeled using eight-node reduced integration solid elements; Based on the grid sensitivity analysis, the concrete grid size is determined to be 15mm, and the H-shaped steel and angle steel connector, as the main force-bearing components, are divided into a finer grid size of 10mm; Hard contact is used between the angle steel connector and the concrete to simulate compression and contact separation behavior; and binding constraints are used between the angle steel and the H-shaped steel beam to ensure deformation coordination at the connection; Symmetric boundary conditions are applied to the symmetric surface of the model, full fixed constraints are applied to the bottom surface of the concrete to restrict its translational freedom in three directions, and the load is applied to the top of the H-shaped steel beam through displacement control; Push-out tests of the angle steel connector are carried out, and the finite element verification is based on the push-out test results to obtain numerical simulation results under different conditions.

[0008] Further, the angle steel connector and the steel beam both use an ideal elastic-plastic double-line constitutive model, and the material strengthening effect is considered: before yielding, it shows linear elasticity, with an elastic modulus of 206 GPa and a Poisson's ratio of 0.3, the yield stress σ ys =400Mpa, after reaching the yield point, it enters the plastic stage and shows certain strain hardening characteristics, and finally reaches the ultimate strength σ us =500MPa.

[0009] Further, the concrete constitutive refers to the uniaxial stress-strain relationship under compression and tension in the Concrete Structure Design Specification (GB50010); In the compression stage, the stress-strain curve of the concrete shows nonlinear characteristics, with linear growth in the initial stage, and the initial elastic modulus is calculated by =0.0033; f cr The axial compressive strength of the concrete is ε cr =0.002, and the ultimate compressive strain is ε cu =0.0033; In the tension stage, the concrete shows brittle characteristics, and the stress-strain relationship rises to the peak tensile stress f trTake 0.1 times the axial compressive strength, that is f tr =0.1 f cr Corresponding peak tensile strain ε tr =0.0001, the tensile stress reaches its peak value and then drops rapidly, with the drop segment adopting an exponential decreasing method.

[0010] Furthermore, all input features and output results in the database are normalized to ensure they are distributed within the [0,1] interval, thus avoiding interference with the training process due to differences. Input features include angle steel length, side length, thickness, concrete strength, and steel strength, while output results are shear bearing capacity. After processing, the data is randomly divided into a training set (used to evaluate the model's generalization ability) and a test set, with a ratio of 8:2.

[0011] Furthermore, the loss function of the neural network with embedded physical constraints is expressed as: ; In the formula, Indicates the target value. For the first i The neural network prediction value for each sample. n The total number of samples, v i This represents the predicted value from the physical formula; V The shear bearing capacity of angle steel is expressed as , f c For concrete compressive strength, L The length of the angle steel. K v These are parameters related to the geometric properties of the cross-section. K c This is a coefficient related to the elastic modulus of concrete.

[0012] Furthermore, the physics term weighting factor and model learning rate are adjusted to ensure a balance between model prediction accuracy and physical consistency, as follows: physics term weighting factor λ The value range is 10~15, preferably. λ= 15; Model learning rate η The value should not exceed 0.01, preferably. η = 0.005.

[0013] Secondly, the present invention provides a shear strength prediction system for angle steel connectors based on a physical information neural network, comprising: The data construction module is a database containing several sets of experimental data, built based on the numerical simulation results of the finite element model of the angle steel connectors that have been tested and verified. The physical constraint module is configured to embed the shear capacity physical constraint condition of the angle steel connector based on the elastic foundation beam theory into a loss function of a data-driven neural network model (DNN). The model construction module is configured to train the neural network embedded with the physical constraint condition by using a database, adjust a physical item weight factor and a model learning rate, and construct a physical information neural network (PINN) shear capacity prediction model. The model prediction module is configured to predict the shear capacity of the angle steel connector by using the trained PINN shear capacity prediction model.

[0014] In a third aspect, the present application provides an electronic device, comprising: a processor; a memory for storing instructions executable by the processor; The processor is configured to execute the instructions to implement the method for predicting the shear strength of the angle steel connector based on the physical information neural network according to any one of the first aspect.

[0015] In a fourth aspect, the present application provides a computer-readable storage medium, when the instructions in the storage medium are executed by the processor of an electronic device, the electronic device can execute the method for predicting the shear strength of the angle steel connector based on the physical information neural network according to any one of the first aspect.

[0016] Compared with the prior art, the present application has the following beneficial effects: the method, system, electronic device and storage medium for predicting the shear strength of the angle steel connector based on the physical information neural network provided by the present application carry out a push-out test, perform a finite element analysis based on the test results to construct a database for training a model, embed a calculation formula of the shear capacity of the angle steel connector based on the elastic foundation beam into a loss function of the physical information neural network based on a data-driven neural network, determine an optimal weight factor of a physical item, and the like, train and construct a physical information-guided neural network model for shear capacity prediction, improve the accuracy and reliability of the prediction of the shear performance of the angle steel, and improve the explainability of the neural network model. In addition, the prediction error distribution of the physical information neural network prediction model provided by the present application is more concentrated, the error distribution range is narrower, the symmetry is stronger, the overall distribution conforms to the normal distribution, the kernel density curve shows a clear unimodal peak, indicating that the system error and volatility of the physical information neural network are small, and the physical information neural network is used to guide the design of the angle steel connector, optimize the size of the structural member, improve the safety of the structure, and promote the development of the engineering design in the direction of intelligentization. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 The flowchart of the method for predicting the shear strength of the angle steel connector based on the physical information neural network provided by the present application is shown.

[0018] Figure 2 A schematic diagram of the hot-rolled equal angle steel provided by the embodiment of the present application.

[0019] Figure 3 A schematic diagram of the angle steel connecting piece push-out test piece provided by the embodiment of the present application.

[0020] Figure 4 A schematic diagram of the appearance change of the push-out test piece provided by the embodiment of the present application.

[0021] Figure 5 A schematic diagram of the finite element model of the push-out test piece provided by the embodiment of the present application.

[0022] Figure 6 A schematic diagram of the material hardening effect of the ideal elastic-plastic double-line constitutive model of concrete provided by the embodiment of the present application.

[0023] Figure 7 A schematic diagram of the uniaxial stress-strain relationship of the steel constitutive provided by the embodiment of the present application.

[0024] Figure 8 A schematic diagram of the contact relationship of the finite element model provided by the embodiment of the present application.

[0025] Figure 9 A schematic diagram of the boundary condition of the finite element model provided by the embodiment of the present application.

[0026] Figure 10 An equivalent stress nephogram provided by the embodiment of the present application.

[0027] Figure 11 An equivalent plastic strain distribution diagram provided by the embodiment of the present application.

[0028] Figure 12 A test piece crack morphology comparison diagram provided by the embodiment of the present application.

[0029] Figure 13 A comparison diagram of the finite element and test load-displacement curves provided by the embodiment of the present application.

[0030] Figures 14 to 18 An angle steel geometric parameter and material strength distribution histogram provided by the embodiment of the present application.

[0031] Figure 19 A BP neural network structure diagram provided by the embodiment of the present application.

[0032] Figure 20 A diagram showing the influence of physical loss weight on physical error under different learning rates provided by the embodiment of the present application.

[0033] Figure 21A figure showing the influence of different physical loss weights provided by the embodiment of the present application on the physical consistency of the model.

[0034] Figure 22 A residual histogram and its kernel density estimation (KDE) curve diagram provided by the embodiment of the present application.

[0035] Figures 23 to 28 A distribution diagram of the predicted values and the true values of the data-driven model and the physical information neural network on the training set and the test set under different training times provided by the embodiment of the present application. DETAILED DESCRIPTION

[0036] The present application will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0037] As shown in Figure 1 , the embodiment of the present application provides a shear strength prediction method for angle steel connecting piece based on physical information neural network, comprising the steps of: establishing a database containing several groups of test data based on the numerical simulation results of the finite element model of the angle steel connecting piece verified by the push-out test; embedding the shear bearing capacity physical constraint condition of the angle steel connecting piece based on the elastic foundation beam theory into the loss function of the data-driven neural network model DNN; training the neural network embedded with the physical constraint condition by using the database, adjusting and selecting the physical item weight factor and the model learning rate, to construct a physical information neural network PINN shear bearing capacity prediction model; using the trained physical information neural network PINN shear bearing capacity prediction model to predict the shear bearing capacity of the angle steel connecting piece.

[0038] In the present embodiment, based on the data-driven neural network, the physical equation is embedded into the loss function, aiming to improve the accuracy and reliability of the angle steel shear performance prediction, and improve the interpretability of the neural network model. In order to make up for the deficiency of the existing angle steel connecting piece push-out test database, first, the shear member push-out test is carried out, and the finite element analysis and verification are carried out based on the test results, a database containing several hundred groups of data is established, and then a physical information guided neural network model is constructed for shear bearing capacity prediction and determination of the optimal weight factor of the physical item.

[0039] For the purpose and requirement of angle steel connector push-out test, the phenomenon of the test specimen is analyzed and the test model for shear strength prediction is constructed. In the model test of the embodiment, hot-rolled isosceles angle steel is used as the shear connector, the length B of the angle steel limb is 180 mm, the thickness t is 16 mm, and the length L is 320 mm. Two holes with a radius of 25 mm are opened at a distance of 110 mm from the flange of the angle steel web, as shown in Figure 2 .

[0040] Specifically, the push-out specimen is composed of three parts, the middle part is an H-shaped steel with a flange width of 150 mm, a thickness of 20 mm, and a web height of 600 mm, and the two sides are concrete blocks with a width of 350 mm, a length of 500 mm, and a height of 700 mm. The angle steel connector is welded to the flange plate of the H-shaped steel by single-sided fillet welding, as shown in Figure 3 .

[0041] Among them, the steel members used are Q345B steel, with a yield strength of 400 MPa, a tensile strength of 520 MPa, and an elastic modulus of 1.95 x 10 5 MPa. The 28-day compressive strength of the concrete cube specimen with a size of 150 mm x 150 mm x 150 mm is 40.3 MPa; the mix ratio is cement: slag powder: fly ash: sand: crushed stone: additive: water = 359: 103: 51: 713: 1070: 7.18: 154.

[0042] In this embodiment, through the prediction and analysis of the shear loading model of the push-out specimen, at the initial stage of loading, the overall specimen shows linear elastic response, and no obvious signs of damage are observed. As the load continues to increase, the concrete member gradually enters the nonlinear deformation stage, and small longitudinal cracks first appear at the bottom. These cracks usually develop along the stress concentration areas on both sides of the position where the angle steel connector is located, indicating that this area is a weak link in the structure. In the subsequent loading process, the cracks gradually expand upwards, and the crack width and number increase, indicating that the concrete has entered the plastic damage stage.

[0043] When the load approaches the ultimate bearing capacity, the cracks quickly penetrate the entire concrete height, forming a typical through damage mode. At this time, the local crushing phenomenon of the concrete is obvious, especially in the area where the angle steel root contacts the concrete, the relative slip and extrusion between materials intensify the damage at this part.

[0044] After loading, the appearance of the specimen can be observed that the angle steel member has obvious deformation, showing a tendency to open upwards, indicating that it has borne a large pressure during the shearing process. In addition, obvious local cracking phenomenon appears at the root of the angle steel, i.e., near the connection with the steel beam, as shown in Figure 4 , which indicates that the stress concentration at the root of the angle steel is obvious.

[0045] To predict and verify the comparison of the shear capacity of angle steel, in the embodiments of the present application, two types of neural network models are developed: one is a data-driven neural network (DNN), which mainly relies on existing test data and finite element analysis results for model fitting, and the data-driven model used is a classic back propagation neural network (BP neural network); the other is the physical information neural network (PINN) used in the technical solution of the present application, that is, the physical constraint condition is introduced in the training process, and the formula for calculating the shear capacity of the angle steel connector based on the elastic foundation beam theory is embedded in the loss function, thereby enhancing the physical consistency and prediction accuracy of the model.

[0046] In order to compare the performance of the two models fairly, DNN and PINN use the same network structure and training strategy, including consistent input and output parameters, hidden layer settings, activation functions, and optimization algorithms. By comparing and analyzing the performance of the two types of models in terms of prediction accuracy, physical consistency, and generalization ability, the effectiveness of physical constraints in improving the prediction performance of neural networks is verified.

[0047] Currently, there are limited experimental studies on the shear performance of angle steel connectors, and the publicly available data resources are scarce, making it difficult to meet the requirements of neural network modeling in terms of sample size and parameter diversity. In order to make up for the lack of database and improve the reliability and generalization ability of model training, in the embodiments of the present application, first, numerical simulation is carried out based on the finite element model verified by push-out tests, to provide data basis for the training and evaluation of subsequent neural network models.

[0048] Considering the symmetry of the test piece in geometry and load action, a 1 / 2 finite element model is established to reduce the computational cost while ensuring calculation accuracy, as shown in Figure 5 .

[0049] Specifically, the steel beam, concrete, and angle steel connector are modeled using eight-node reduced integration solid elements (C3D8R), which have high computational efficiency and good numerical stability, and can effectively capture the stress and deformation of the structure during loading.

[0050] In addition, the C3D8R element is suitable for handling nonlinear problems, especially in complex conditions such as large deformation, contact, and material damage. Grid sensitivity analysis is carried out to determine the concrete grid size of 15mm. In comparison, H-shaped steel and angle steel connectors are the main force components, so finer grid division (10mm) is adopted.

[0051] The angle steel connector and the steel beam both adopt an ideal elastic-plastic double-line constitutive model, and the strengthening effect of the material is considered. As shown in Figure 6As shown, the material exhibits linear elasticity before yielding, with an elastic modulus of 206 GPa and a Poisson's ratio of 0.3, a yield stress of 400 MPa, and a plastic stage after reaching the yield point, exhibiting certain strain hardening characteristics, and finally reaching an ultimate strength of 500 MPa. σ ys σ us

[0052] To accurately reflect the nonlinear mechanical properties of concrete, the concrete constitutive model refers to the uniaxial stress-strain relationship of concrete under compression and tension in the Code for Design of Concrete Structures (GB50010), as shown. Figure 7

[0053] In the compression stage, the stress-strain curve of concrete shows nonlinear characteristics, with a linear increase in the initial stage, and the initial elastic modulus is calculated by f cr where fc is the axial compressive strength of concrete, and ε cr =0.002 is the peak strain, and ε cu =0.0033 is the ultimate compressive strain.

[0054] In the tension stage, concrete exhibits obvious brittle characteristics, and the stress-strain relationship rises to the peak tensile stress f tr , which is 0.1 times the axial compressive strength, i.e. f tr =0.1 f cr , corresponding to the peak tensile strain ε tr =0.0001, and the tensile stress rapidly decreases after reaching the peak value, with an exponential decrease in the descending segment.

[0055] In this embodiment, two types of contact relationships are set in the push-out specimen test model: 1) Hard contact between the angle steel connector and the concrete, used to simulate compression and contact separation behavior, which can accurately reflect the true physical response of the connection surface under stress state during loading, and avoid unreasonable penetration; 2) Binding constraint between the angle steel and the H-shaped steel beam to ensure deformation coordination at the connection, reflecting the actual working condition that the two are welded and do not slip relative to each other, as shown. Figure 8

[0056] ​​​​​In terms of boundary conditions, symmetric boundary conditions are applied on the symmetric plane of the model to effectively reduce the amount of calculation by taking advantage of the symmetry of geometry and load; fixed constraints are applied on the bottom surface of the concrete to limit its translational freedom in three directions, which is used to simulate the limited state of the test specimen placed on the rigid bearing platform in the test; the load is applied on the top of the H-shaped steel beam by displacement control, as shown in Figure 9 .

[0057] In this embodiment, the finite element analysis results of the push-out specimen in different states are compared and analyzed with the phenomenon of the push-out specimen, as shown in Figure 10 , the equivalent stress nephogram shows that there is obvious stress concentration at the intersection of the flange and the angle steel, which also shows obvious deformation in the test, verifying the accuracy of the finite element model in predicting stress distribution. Figure 11 The comparison of equivalent plastic strain distribution and test failure phenomenon is shown, the finite element result shows that the equivalent plastic strain at the root area of the angle steel is close to 0.2, reaching the critical value of material failure, and obvious shear phenomenon is also observed at this position in the test, indicating that the finite element accurately simulates the failure position and failure mode in the test. Figure 12 The crack prediction results based on the tensile direction damage variable are given and compared with the crack morphology of the specimen, from the finite element analysis results, the cracks mainly show longitudinal cracks extending from the H-shaped steel flange and transverse cracks near the flange, similar crack morphology is also observed in the test, further verifying the reliability of the finite element model in predicting the direction of crack propagation.

[0058] In addition, the comparison of finite element and test load-displacement curves is shown in Figure 13 , in the initial stage, the two curves are basically coincided, indicating that the finite element model has good stiffness prediction ability in the elastic stage, as the load increases, the specimen enters the plastic stage, when the displacement is 1-3mm, the load increases slowly, the finite element curve is slightly higher than the test data, when reaching the ultimate bearing capacity, the peak load and displacement are basically consistent, after the peak, the curve drops relatively slowly, the finite element curve drops faster. Overall, the finite element shows good prediction ability in bearing capacity.

[0059] In this embodiment, about 117 groups of database are used for extended analysis based on the finite element model to make up for the lack of experimental data. The database covers key influencing factors such as geometric parameters of connecting components and concrete performance, and its distribution is shown in Figures 14 to 18 .

[0060] As shown in the figure, the length distribution of angle steel is concentrated in the 300-350 mm range, accounting for nearly one-third, while there are also a considerable number of samples between 100-250 mm, ensuring the model's adaptability to different component lengths. The side length distribution is relatively uniform, with samples distributed in the 80-240 mm range, which can well cover the common structural design range.

[0061] The thickness is mainly concentrated in the range of 12-20 mm, showing a certain degree of skewed distribution, but it is still representative overall. The distribution of axial compressive strength of concrete is relatively concentrated, with most samples concentrated around 48 MPa, and a small number of samples distributed in the ranges of 30-40 MPa and 56-60 MPa.

[0062] Based on this, in order to improve the efficiency of neural network training and prediction stability, all input features and output results are normalized to be distributed in the [0,1] interval, so as to avoid interference to the training process due to the two differences. The input features include angle steel length, side length, thickness, concrete strength, and steel strength, and the output is shear bearing capacity. The data is randomly divided into training set (80% of the data) and test set (20% of the data) to evaluate the generalization ability of the model.

[0063] In this embodiment, in the DNN-based prediction model, the thickness (t), length (L), leg length (B), steel strength, and concrete strength of the angle steel are the main factors affecting its shear capacity, and there is a significant nonlinear relationship among these factors. Therefore, based on the actual situation of the angle steel connectors, a BP neural network consisting of one input layer, one hidden layer, and one output layer was established. The input layer has five nodes, corresponding to the five factors affecting the shear capacity of the angle steel. The BP neural network structure is as follows: Figure 19 As shown.

[0064] Specifically, the data-driven neural network uses mean squared error as the loss function to measure the error between the predicted value and the actual shear capacity. Its expression is: ; in, R i For the first i The true shear bearing capacity of each sample This represents the target value of the i-th sample. For the first i The neural network prediction value for each sample. n This represents the total number of samples. During model training, R i The smaller the error, the better the model's predictive performance, as the objective function is to find its minimum value.

[0065] On the basis of the data-driven model, a shear capacity calculation formula obtained based on the elastic foundation beam theory is introduced, and the physical formula is embedded into the loss function, so that the model meets the statistical law and also meets the physical constraint, improves the prediction accuracy and physical interpretability. The neural network loss function of the physical constraint is expressed as: L i =R i + λV i ; ; The total loss of the physical information neural network is composed of two parts: data item loss and physical item loss, R i is the mean square error; V i is the physical loss term, which represents the error between the predicted value and the physical formula V u ; λ is the weight factor, which represents the influence of the data item and the physical constraint item on the model. If λ= 0 ， The model degenerates into a data-driven neural network, and if λ is larger, it reflects the training process dominated by the physical constraint.

[0066] The shear capacity of the angle steel connecting piece is mainly affected by the geometric characteristics of the angle steel and the material strength. The following shear capacity calculation formula is used in the embodiment of the application: ; In the formula, V is the shear capacity of the angle steel, f c is the compressive strength of the concrete, L is the length of the angle steel, K v is a parameter related to the geometric characteristics of the cross section, K c is a coefficient related to the elastic modulus of the concrete.

[0067] In the physical information neural network, reasonable selection of the weight factor λ and the learning rate η is of great significance to achieve the balance between the prediction accuracy and the physical consistency of the model. In order to analyze the influence of different λ values and learning rates on the performance of the model, different learning rates η=0.005, 0.01, 0.02, 0.05 are selected in this embodiment, and the neural network is trained respectively and the average absolute error MAE of the physical item with the weight factor λ and the absolute value of the physical item residual are recorded on the test set.

[0068] Figure 20 different learning rates (η ) the physical loss weight ( λ ) on the physical error. As can be seen from the figure, as λ increases, the trend of the physical error changes significantly at different learning rates.

[0069] When the learning rate is small ( η = 0.005 and 0.01), the physical error remains at a low level and changes little within the entire λ range, especially the curve of η = 0.005 remains almost flat, indicating that the model can better balance data loss and physical constraints at this time.

[0070] When the learning rate increases to η = 0.02 and 0.05, the physical error becomes extremely sensitive to λ, showing a sudden shock, especially after λ increases to a certain extent, the error rises sharply. In particular, the curve of η = 0.05, when λ approaches 8, the physical error jumps rapidly and maintains at a high level, indicating that an excessively large learning rate may lead to instability in the training process, making the physical constraint unable to effectively play a role.

[0071] Therefore, a smaller learning rate helps the physics-guided neural network to optimize the physical consistency stably, while an excessively large learning rate may destroy the balance in the training process, leading to a significant increase in the physical error.

[0072] Figure 21 The influence of different physical loss weights ( λ ) on the physical consistency of the model is given, taking the mean absolute error (MAE) of the physical residual and the percentage of the physical error as the measurement indicators, and the error bar reflects the volatility and stability of the experimental results of each group.

[0073] As can be seen from the figure, when λ = 0, that is, the model does not introduce any physical constraints, the physical residual MAE reaches the highest value, exceeding 230kN, the physical error percentage also exceeds 22%, and the error bar is long, indicating that the physical consistency of the model is poor and the results are unstable at this time.

[0074] With the gradual increase of λ , the physical error decreases rapidly, especially during the process of increasing λ from 0 to 10, the MAE and error percentage are significantly reduced, respectively to about 120kN and 12%, and the error bar is also significantly shortened, indicating that the model not only improves the physical consistency after introducing appropriate physical constraints, but also the prediction results are more stable.

[0075] Further observation can find that when λ increases to 15, the physical residual MAE reaches the minimum value, close to 100 kN, the corresponding error percentage also drops to the minimum, about 11%, and the error bar is the shortest, indicating that the model at this time shows the best accuracy and robustness, indicating that the physical loss and the data loss reach a good trade-off.

[0076] However, when λ Continuing to increase to 20 and 25, although the error remains at a low level, it begins to show a rebound trend, and the error bar is slightly lengthened, reflecting an increase in the uncertainty of the model's prediction. This may be due to the physical term having too high a proportion in the loss function, limiting the ability to fit the data and thus affecting the overall performance.

[0077] The above study reveals the influence of the weight of the physical loss on the effect of the physics-guided neural network, indicating that the model can achieve the best physical consistency and prediction stability when λ is in the interval of 10~15. λ

[0078] In this embodiment, in order to further evaluate the accuracy and stability of the model's prediction results, the residual distribution of the data-driven neural network model (DNN) and the physics information neural network model (PINN) is compared and analyzed, and the results are shown in Figure 22 The figure shows the residual histogram and its kernel density estimation (KDE) curve of the two models in the prediction of shear strength, revealing the concentration of the model's prediction error, systematic bias and distribution pattern.

[0079] From Figure 22 , it can be seen that the residual of the DNN model is right-biased, with residual values mainly concentrated in 200 kN to 400 kN, and there are many positive residuals greater than 400 kN, indicating that the model has a significant overestimation on most samples. At the same time, its residual distribution range is wide, from about -600 kN to +600 kN, indicating that the model's prediction fluctuates greatly under different input samples, and its stability is poor. Its KDE curve is relatively flat and does not form a significant peak, further indicating that the model has a large error dispersion, and the prediction results lack consistency and robustness.

[0080] ​In contrast, the residual distribution of the PINN model is more concentrated, and the overall trend is symmetrical. The KDE curve shows a clear unimodal feature, and the main peak is near the residual of 0, indicating that the deviation between the predicted value and the actual value is small, and the systematic error is significantly reduced. The residual range of PINN is roughly concentrated in -200 kN to +200 kN, the number of extreme error samples is significantly reduced, and the residual density concentration is higher, the prediction result is more stable and reliable. In addition, although its KDE curve has a slight multimodal phenomenon, which may be related to the extreme samples in the data set, the overall distribution pattern is close to normal distribution, which meets the ideal error distribution assumption.

[0081] In summary, the PINN model with physical information constraints has stronger prediction ability and better generalization performance in shear strength prediction. Its residual distribution is more concentrated and symmetrical, and the systematic error and volatility are significantly smaller than those of the traditional DNN model. This shows that in the modeling of shear connectors, the neural network method that integrates physical constraints has more advantages than the pure data-driven model, which can improve the physical consistency and credibility of the model while ensuring the prediction accuracy.

[0082] In this embodiment, Figures 23 to 28 The distribution of the predicted values and the true values of the data-driven model (λ=0) and the physical information neural network (λ=15) on the training set and the test set under different training times (epoch = 10, 100 and 500) is shown. It can be seen that with the increase of training times, the prediction accuracy of both types of models improves, but the model with physical constraints is significantly better than the pure data-driven model in fitting effect.

[0083] In the early training (epoch = 10), the prediction points of both models are relatively discrete, and the data rules have not been effectively learned; when the training reaches epoch = 100, the prediction results of the physical information neural network model are obviously close to the ideal prediction line, while the pure data-driven model still has many deviations; after sufficient training (epoch = 200), the prediction values of the physical information neural network model are basically distributed along the ideal line, indicating that it not only performs well on the training set, but also shows good generalization ability on the test set. This shows that the introduction of physical equations can effectively improve the learning efficiency and accuracy of neural networks in the shear strength of angle steel connectors.

[0084] Notably, at epoch = 200, the R² on the test set reached 0.9088 with an RMSE of 127.0 kN, while the R² on the training set was 0.8562 with an RMSE of 176.3 kN, i.e., the model's prediction performance on the test set was better than on the training set. The reason is that the training set contains some extreme values or outliers, which have a greater impact on the loss function, but this does not affect the overall fitting ability of the model. The model shows high fitting accuracy on both the training and test sets, and as the training rounds increase, the prediction results gradually converge, the R² continuously improves, and the RMSE continuously decreases, reflecting good stability and generalization ability.

[0085] In the embodiments of the present application, for the shear bearing capacity prediction problem of angle steel connectors, a physical information neural network (PINN) model combining mechanical theory and data-driven methods is proposed and constructed to predict the shear strength of angle steel connectors, i.e., by introducing physical calculation formulas into the network training process, the physical consistency and high precision of structure performance prediction are realized. The performance of the prediction model is systematically evaluated from multiple aspects such as model accuracy, physical loss weight influence, error distribution characteristics, and engineering application potential, effectively improving the accuracy and reliability of angle steel shear performance prediction.

[0086] The calculation formula of the shear bearing capacity of the angle steel shear key obtained based on the elastic foundation beam is embedded in the loss function of the physical information neural network, and the physical information neural network model shows higher precision in shear bearing capacity prediction. Compared with traditional data-driven models, the physical information neural network has obvious improvement in mean absolute error (MAE) and absolute coefficient (R²).

[0087] The physical loss weight has a significant impact on the physical error and the physical consistency of the model. At a smaller learning rate (η = 0.005 and 0.01), the physical error is relatively stable, and as λ increases, the model can better balance the data loss and physical constraints, maintaining a lower physical error. At a larger learning rate (η = 0.02 and 0.05), the physical error is more sensitive to changes in λ, which may lead to instability during training and affect the physical consistency From the error distribution, compared with data-driven neural networks, the prediction error distribution of the physical information neural network is more concentrated, the error distribution range is narrower, the symmetry is stronger, the overall distribution conforms to the normal distribution, and the kernel density curve shows a clear unimodal peak, indicating that the systematic error and volatility of the physical information neural network are smaller than those of the data-driven neural network.

[0088] Compared with traditional empirical formula, the high-precision prediction and physical consistency of the physical information neural network provide support for structural engineering design. Application of the physical information neural network established in the embodiment to shear bearing capacity prediction can realize more reasonable design, optimize structural member size, improve structural safety, and promote the development of engineering design towards intelligence.

[0089] The embodiment of the present application provides a shear strength prediction system for angle steel connecting piece based on a physical information neural network, comprising: A data construction module is configured to establish a database containing a plurality of groups of push-out tests based on finite element simulation verification tests of the angle steel connecting piece push-out test; A physical constraint module is configured to embed shear bearing capacity physical constraint conditions of the angle steel connecting piece based on the elastic foundation beam theory into a loss function of a data-driven neural network model DNN; A model construction module is configured to train the neural network embedded with the physical constraint conditions by using the database, adjust and select a physical item weight factor and a model learning rate, so as to construct a physical information neural network PINN shear bearing capacity prediction model; A model prediction module is configured to predict the shear bearing capacity of the angle steel connecting piece by using the trained physical information neural network PINN shear bearing capacity prediction model.

[0090] The embodiment of the present application provides an electronic device, comprising: a processor; a memory for storing instructions executable by the processor; The processor is configured to execute the instructions to implement the shear strength prediction method for the angle steel connecting piece based on the physical information neural network as described above.

[0091] In addition, the embodiment of the present application also provides a computer-readable storage medium, when the instructions in the storage medium are executed by the processor of the electronic device, the electronic device can execute the shear strength prediction method for the angle steel connecting piece based on the physical information neural network as described above.

[0092] The above only describes the preferred embodiments of the present application, and it should be noted that for those skilled in the art, without departing from the technical principles of the present application, a number of improvements and modifications can be made, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A method for predicting the shear strength of an angle steel connector based on a physical information neural network, characterized by, The method comprises the steps of: establishing a database containing a plurality of sets of test data based on the numerical simulation results of the finite element model of the angle steel connector verified by the push-out test; embedding the physical constraint condition of the shear capacity of the angle steel connector based on the elastic foundation beam theory into the loss function of the data-driven neural network model DNN; training the neural network embedded with the physical constraint condition by using the database, adjusting and selecting a physical term weight factor and a model learning rate, to construct a physical information neural network PINN shear capacity prediction model; using the trained physical information neural network PINN shear capacity prediction model to predict the shear capacity of the angle steel connector.

2. The physical information neural network-based shear strength prediction method of an angle steel connector according to claim 1, wherein, The database is established based on the numerical simulation results of the finite element model, comprising: hot-rolled equal-angle steel is used as the shear connector, and the angle steel connector is symmetrically connected to the two side flange plates of the H-shaped steel through single-sided fillet welds; based on the symmetry of the geometric shape and the load action, a 1 / 2 finite element model is established to ensure calculation accuracy and reduce calculation cost; the H-shaped steel beam, the concrete and the angle steel connector are modeled by using eight-node reduced integration solid elements; based on the grid sensitivity analysis, the grid size of the concrete is determined to be 15mm, and the H-shaped steel and the angle steel connector, as the main force-bearing components, are divided into a finer grid size of 10mm; hard contact is used between the angle steel connector and the concrete to simulate compression and contact separation behavior, and binding constraints are used between the angle steel and the H-shaped steel beam to ensure deformation coordination at the connection; symmetric boundary conditions are applied to the model symmetric surface, the concrete bottom surface is fixedly constrained to limit its three-direction translational freedom, and the load is applied to the top of the H-shaped steel beam through displacement control; the push-out test of the angle steel connector is carried out, the finite element model is verified based on the push-out test results, and the numerical simulation results under different states are obtained. 3.The physical information neural network-based angle connection shear strength prediction method according to claim 2, characterized in that, Both angle steel connectors and steel beams are ideal elastic-plastic double-line constitutive models, and the strengthening effect of the material is considered: linear elasticity before yielding, with an elastic modulus of 206 GPa and a Poisson's ratio of 0.3, yielding stress σ ys = 400 MPa, entering the plastic stage after reaching the yield point and showing certain strain hardening characteristics, and finally reaching the ultimate strength σ us = 500 MPa.

4. The physical information neural network-based shear strength prediction method for an angle connection according to claim 3, characterized by, The concrete constitutive refers to the uniaxial stress-strain relationship under compression and tension in the Concrete Structure Design Specification (GB50010); In the compression stage, the stress-strain curve of concrete shows nonlinear characteristics, and the initial stage is linear growth, and the initial elastic modulus is The calculation is obtained, f cr The axial compressive strength of concrete is The normalized processing is performed on all input features and output results in the database to make them distributed in the [0, 1] interval, so as to avoid interference on the training process due to differences, the input features include the length, side length, thickness of the angle steel, the concrete strength and the steel strength, and the output result is the shear capacity, and after the processing, the data is randomly divided into a training set data for evaluating the generalization ability of the model and a test set in a ratio of 8:

2. cr = 0.002, the ultimate compressive strain The loss function of the neural network embedded with the physical constraint condition is represented as: cu = 0.0033; In the tensile stage, the concrete shows brittle characteristics, and the stress-strain relationship rises to the peak tensile stress f tr , take 0.1 times of the axial compressive strength, that is f tr =0.1 f cr , corresponding to the peak tensile strain The method comprises the steps of: tr =0.0001, the tensile stress decreases rapidly after reaching the peak, and the descending segment adopts exponential decline. 5.The physical information neural network-based angle connection shear strength prediction method according to claim 3, wherein, a data construction module, which establishes a database containing a plurality of sets of test data based on the numerical simulation results of the finite element model of the angle steel connector verified by the push-out test; 6. The physical information neural network-based shear strength prediction method of an angle connection according to any one of claims 1-5, characterized in that, a physical constraint module, which is used for embedding the physical constraint condition of the shear capacity of the angle steel connector based on the elastic foundation beam theory into the loss function of the data-driven neural network model DNN; ； In the formula, denotes the target value, is the neural network prediction value of the first i sample, n is the total number of samples, v i denotes the physical formula prediction value; V is the shear capacity of the angle steel, expressed as , f c is the compressive strength of the concrete, L is the length of the angle steel, K v is a parameter related to the cross-sectional geometric characteristics, K c is a coefficient related to the elastic modulus of the concrete.

7. The physical information neural network-based shear strength prediction method of an angle steel connector according to claim 6, wherein, The physical term weight factor and the model learning rate are adjusted to ensure the balance between the model prediction accuracy and the physical consistency, respectively: the physical term weight factor a model construction module, which is used for training the neural network embedded with the physical constraint condition by using the database, adjusting and selecting a physical term weight factor and a model learning rate, to construct a physical information neural network PINN shear capacity prediction model; and is 10-15, preferably ​ 15; and the model learning rate ​ is not greater than 0.01, preferably ​ = 0.

005. 8.A physical information neural network-based angle steel connector shear strength prediction system, characterized in that, ​ ​ ​ ​ A model prediction module is configured to predict the shear capacity of the angle steel connector by using the trained physical information neural network (PINN) shear capacity prediction model.

9. An electronic device, comprising: The method comprises the steps of: a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to execute the instructions to implement the method for predicting the shear strength of an angle steel connector based on a physical information neural network as claimed in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, When the instructions in the storage medium are executed by the processor of the electronic device, the electronic device is enabled to perform the method for predicting the shear strength of an angle steel connector based on a physical information neural network as claimed in any one of claims 1 to 7.

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