Steel slag asphalt interface adhesion work prediction method based on physical neural network

Abstract

The invention proposes a steel slag asphalt interface adhesion work prediction method based on a physical neural network, and relates to the technical field of deep learning, and the method comprises the steps: obtaining chemical component parameters and environmental impact factors of a steel slag asphalt mixture interface sample; creating an original neural network prediction model based on a diffusion item, a reaction source item, a multi-mechanism dissipation item and a state variable corresponding to spatial-temporal evolution of the adhesion work; inputting the chemical component parameters and the environmental impact factors into an original neural network prediction model, and generating interface adhesion work prediction parameters in combination with physical constraint terms; training the original neural network prediction model by using the interface adhesion work prediction parameters and a gradient descent algorithm to obtain a target neural network prediction model; the physical constraint items comprise data loss, PDE residual error loss, state equation loss and boundary condition loss; and inputting the chemical component parameters and the environmental impact factors of a to-be-tested material into the target neural network prediction model to obtain target prediction parameters.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and in particular to a method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks. Background Technology

[0002] As a green building material, steel slag asphalt mixtures help reduce solid waste from the metallurgical industry and improve the skid resistance and durability of road surfaces. However, in actual use, under the long-term effects of traffic loads and environmental factors, delamination and loosening between the asphalt film and steel slag aggregate are prone to occur, seriously affecting the integrity and service life of the pavement structure. The interface between steel slag and asphalt is the weakest link in the mixture system, and the strength of its interfacial adhesion directly affects the overall stability and damage resistance of the mixture. Therefore, accurate prediction and scientific evaluation of the steel slag-asphalt interfacial adhesion performance is a key technical aspect for optimizing material design, preventing early damage, and ensuring the long-term service performance of pavements, and has significant research value and engineering application significance.

[0003] Currently, the assessment of the adhesion work at the steel slag-asphalt interface mainly relies on empirical formulas based on specific conditions or direct laboratory measurements. These methods are not only costly and time-consuming, but also suffer from limited prediction accuracy due to simplification assumptions and experimental errors, making it difficult to comprehensively reflect the real interface behavior under multi-field coupling. Although some studies have attempted to use data-driven neural networks for prediction, such models are usually pure "black box" models with insufficient extrapolation and generalization capabilities. They are unable to accurately characterize the physical mechanisms of the coupled effects of multiple factors such as the complex chemical composition of steel slag and time-varying temperature, thus limiting the prediction accuracy of adhesion performance. Summary of the Invention

[0004] In view of this, the present invention proposes a method for predicting the adhesion work of steel slag asphalt interface based on physical neural network.

[0005] The technical solution of this invention is implemented as follows: The first aspect of this invention provides a method for predicting the adhesion work of steel slag asphalt interfaces based on physical neural networks, comprising: Chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples were obtained; the chemical composition parameters included various oxide parameters, and the environmental impact factors included load cycle number, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to material property evolution. A primitive neural network prediction model is created based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work. The chemical composition parameters and the environmental impact factors are input into the original neural network prediction model, and the interface adhesion work prediction parameters are generated by combining the physical constraint terms. The original neural network prediction model is trained using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model. The physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss. The chemical composition parameters and environmental impact factors of the material to be tested are input into the target neural network prediction model to obtain the target prediction parameters.

[0006] Based on the above technical solutions, preferably, the acquisition of chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples includes: For the first type of oxide with a mass percentage greater than the first threshold, the corresponding first oxide parameters are obtained by normal distribution simulation. For the second type of oxide with a mass percentage not greater than the first threshold, the corresponding second oxide parameters are obtained by gamma distribution simulation. The chemical composition parameters are obtained by normalizing the first oxide parameter and the second oxide parameter.

[0007] Based on the above technical solutions, preferably, the acquisition of chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples includes: The number of load cycles was obtained by simulation using a log-normal distribution, the stress amplitude was obtained by simulation using a Weibull distribution, the temperature field was obtained by superimposing random noise with a sine function, and the moisture content was obtained by a Beta distribution. The temporal parameters in the spatiotemporal parameters are obtained using an exponential distribution model, and the spatial parameters are obtained based on the crack propagation theory of fracture mechanics.

[0008] Based on the above technical solutions, preferably, the original neural network prediction model includes a main prediction network and an auxiliary state network; The physical equations corresponding to the master prediction network include a first mapping relationship between the interface adhesion work and the diffusion term, the reaction source term, the multi-mechanism dissipation term, and the evolution time. The physical equations corresponding to the auxiliary state network include a second mapping relationship between the state variables and evolution time; wherein, the state variables include interface coverage and crack density; the evolution of the interface coverage characterizes the dynamic balance between reaction generation and environmental decay, and the change in crack density characterizes the dynamic balance between crack propagation and product arrest.

[0009] Based on the above technical solutions, preferably, the creation of the original neural network prediction model based on the spatiotemporal evolution of adhesion work, including the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables, comprises: By using the second mapping relationship to restrict the state variables in the first mapping relationship, the original neural network prediction model is obtained.

[0010] Based on the above technical solutions, preferably, the step of inputting the chemical composition parameters and the environmental impact factors into the original neural network prediction model, and combining them with physical constraint terms to generate interface adhesion work prediction parameters, includes: The weight of each constraint term in the physical constraint term is determined based on the current physical context; The corresponding constraint terms are weighted based on the aforementioned weights to obtain the total constraint terms. The original neural network prediction model is optimized using the total constraint term, and the chemical composition parameters and the environmental impact factors are input into the optimized original neural network prediction model to generate interface adhesion work prediction parameters.

[0011] Based on the above technical solutions, preferably, the step of training the original neural network prediction model using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model includes: During training, the weight of the data loss is gradually reduced, while the weight of the PDE residual loss and the state equation loss are increased until the loss function of the original neural network prediction model is less than the second threshold, thus obtaining the target neural network prediction model.

[0012] More preferably, a second aspect of the present invention provides a system for predicting the adhesion work of steel slag asphalt interface based on a physical neural network, comprising: a parameter acquisition module, a model creation module, a model training module, and a parameter prediction module; wherein, The parameter acquisition module is configured to acquire the chemical composition parameters and environmental impact factors of the steel slag asphalt mixture interface sample; the chemical composition parameters include various oxide parameters, and the environmental impact factors include the number of load cycles, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to the evolution of material properties; The model creation module is configured to create an original neural network prediction model based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work. The model training module is configured to input the chemical composition parameters and the environmental impact factors into the original neural network prediction model, and generate interface adhesion work prediction parameters by combining physical constraint terms; the original neural network prediction model is trained using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model; the physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss. The parameter prediction module is configured to input the chemical composition parameters and environmental impact factors of the material to be tested into the target neural network prediction model to obtain the target prediction parameters.

[0013] More preferably, a third aspect of the present invention provides an electronic device, including a processor and a memory; the memory has a computer program stored thereon, wherein the computer program, when executed by the processor, implements the method for predicting the adhesion work of steel slag asphalt interface based on a physical neural network as described in the first aspect.

[0014] More preferably, in a fourth aspect of the present invention, a non-transitory computer storage medium is provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the method for predicting the adhesion work of steel slag asphalt interface based on a physical neural network as described in the first aspect.

[0015] The method for predicting the adhesion work of steel slag-asphalt interface based on physical neural networks of the present invention has the following advantages over the prior art: 1. By incorporating various chemical composition parameters and environmental influencing factors, a mapping relationship from microscopic composition to macroscopic performance is constructed, characterizing the synergistic effect mechanism of multiple factors on adhesion work and enhancing the generalization ability of the prediction model. Based on this, data loss, PDE residual loss, equation of state loss, and boundary condition loss are introduced to ensure that the model output conforms to fundamental physical laws such as thermodynamics and mechanics. Temperature field, water content, and spatiotemporal parameters are used as inputs, combined with diffusion terms, reaction source terms, and multi-mechanism dissipation terms, to construct a spatiotemporal evolution prediction framework that adapts to the deterioration process of material properties over time, improving long-term prediction accuracy.

[0016] 2. The main prediction network constructs a first mapping relationship between interface adhesion work and diffusion, reaction source, multi-mechanism dissipation, and evolution time through physical equations, decomposing the spatiotemporal evolution of adhesion work into quantifiable physical processes. The auxiliary state network establishes a second mapping relationship between state variables and evolution time through physical equations, explicitly linking the microstructure evolution to adhesion work prediction. The physical equations constrain the range of state variables in the main network, ensuring that adhesion work prediction conforms to physical laws.

[0017] 3. Spatiotemporal parameters are generated based on the physical laws governing the evolution of material properties to simulate changes in time and space scales during actual service. Time series modeling can simulate the time interval characteristics of actual observation and data acquisition, while spatial coordinate modeling can simulate the basic physical relationship between crack propagation and stress intensity factor and crack length, as well as the propagation path deviation caused by material inhomogeneity and external environmental fluctuations, ensuring the reliability of the prediction model. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating the method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks provided in an embodiment of the present invention. Figure 2 A schematic diagram illustrating the principle of generating physical constraint terms provided in an embodiment of the present invention; Figure 3 A scatter plot of the output of the neural network prediction model provided in this embodiment of the invention; Figure 4 A comparison chart of the error distribution between the PINN model and the data-driven model provided in this embodiment of the invention; Figure 5 A schematic diagram of the structure of the steel slag asphalt interface adhesion work prediction system based on physical neural network provided in an embodiment of the present invention. Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] In some embodiments, such as Figure 1 As shown, Figure 1 This is a flowchart illustrating the method for predicting the adhesion work of steel slag asphalt interface based on a physical neural network, as provided in an embodiment of the present invention. The method for predicting the adhesion work of steel slag asphalt interface based on a physical neural network provided by the present invention includes: S110, obtain the chemical composition parameters and environmental impact factors of the interface sample of steel slag asphalt mixture; the chemical composition parameters include various oxide parameters, and the environmental impact factors include the number of load cycles, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to the evolution of material properties.

[0022] The chemical composition of the interface sample of steel slag asphalt mixture mainly consists of various oxides, such as... , , , , , For a large number of components, specific component parameters can be based on extensive chemical composition analysis data of steel slag, ensuring that the generated data is consistent with the actual material composition range. Environmental impact factors can be obtained based on the actual stress characteristics of road materials, using statistical models that conform to the fatigue life distribution law.

[0023] In some embodiments, obtaining the chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples includes: For the first type of oxide with a mass percentage greater than the first threshold, the corresponding first oxide parameters are obtained by normal distribution simulation. For the second type of oxide with a mass percentage not greater than the first threshold, the corresponding second oxide parameters are obtained by gamma distribution simulation. The parameters of the first oxide and the second oxide are normalized to obtain the chemical composition parameters.

[0024] In this embodiment, a normal distribution is used to simulate the main oxide components to reflect normal fluctuations during the production process; a gamma distribution is used for trace components to better describe the skewed distribution of trace elements in actual production. See Table 1 for details:

[0025] Table 1. Oxide composition and corresponding distribution model To ensure the physical validity of the data, the sum of all oxide components was strictly constrained to between 85% and 100%, and a scaling factor was used to normalize the sum, thereby maintaining the relative proportions between the components. Furthermore, based on metallurgical principles, the key parameter of steel slag basicity was derived, defined as... By adjusting parameters, the peak value of the steel slag alkalinity distribution is made to fall within the range of 1.8-2.5, ensuring that the generated data corresponds to the optimal hydraulic activity state of the steel slag.

[0026] In some embodiments, obtaining the chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples includes: The number of load cycles was obtained by simulation using a log-normal distribution, the stress amplitude was obtained by simulation using a Weibull distribution, the temperature field was obtained by superimposing a sine function with random noise, and the moisture content was obtained by a Beta distribution. The time parameters in the spatiotemporal parameters are obtained using an exponential distribution model, and the spatial parameters are obtained based on the crack propagation theory of fracture mechanics.

[0027] In this embodiment, a log-normal distribution is used for the number of load cycles of the vehicle to accurately reflect the right-skewed characteristics of the material fatigue data. The log-normal distribution can accurately describe the common right-skewed characteristics of fatigue data. Its parameter settings refer to the fatigue test data of typical road materials, and the values ​​are set as follows: The median number of cycles is approximately 8103, and the 90th percentile is approximately 100000. The stress amplitude is calculated using a Weibull distribution for statistical description of material strength. Its shape and dimensional parameters are determined through actual load spectrum analysis. Scale parameters The generated stress amplitude ranges from 0.1 to 0.8 MPa, accurately matching the actual stress level of asphalt pavement base materials. The generation of environmental parameters considers the temporal variation characteristics and coupling effects of actual environmental factors. For example, the temperature field simulation uses a model of sinusoidal functions superimposed with random noise; the sinusoidal function simulates seasonal temperature variations, while the random noise reflects the impact of weather fluctuations. It should be noted that during the generation of environmental impact factors, corresponding physical constraints are added between each feature to ensure that the generated dataset conforms to actual variation patterns. For instance, parameter settings are based on meteorological statistics from typical temperate climate zones to ensure that the amplitude and period of temperature changes are consistent with reality. The specific function is:

[0028] ; Among them, an amplitude of 20°C simulates seasonal temperature differences, a baseline temperature of 20°C corresponds to the annual average temperature, and a noise standard deviation of 5°C reflects weather fluctuations. These parameters are determined based on climate statistics data from most parts of China.

[0029] The formation of moisture content takes into account its physical relationship with temperature. A Beta distribution is used to describe the basic statistical properties of moisture content, while a temperature coupling factor is introduced to simulate the effect of temperature on moisture evaporation and condensation. Under high-temperature conditions, enhanced moisture evaporation leads to a decrease in content, while under low-temperature conditions, the tendency for moisture condensation increases. This physical mechanism is achieved through a temperature-dependent scaling factor. The specific function is:

[0030] ; in, Based on the basic moisture content, the temperature coupling coefficient reveals the physical mechanism of enhanced condensation at -20℃ (coefficient of 1) and strong evaporation at 60℃ (coefficient of 0.25), truly reflecting the influence of temperature on moisture migration.

[0031] The spatiotemporal parameters are generated based on the physical laws governing the evolution of material properties, simulating changes in time and space scales during actual service. The time parameter is generated using an exponential distribution model to simulate the time interval characteristics of actual observations and data acquisition. The spatial parameter uses radial coordinates, generated based on crack propagation theory in fracture mechanics. The square root function of time is used to simulate the fundamental laws of crack propagation, a relationship derived from the basic physical relationship between stress intensity factor and crack length. Superimposed random noise simulates the propagation path deviation caused by material inhomogeneity and external environmental fluctuations. The radial coordinates are normalized to... Range refers to the relative position from the interior of the material to its surface. Strict physical constraints are imposed during the generation of spatiotemporal parameters to ensure the rationality of the evolutionary laws.

[0032] In addition, environmental impact factors may also include load frequency and pH value. The load frequency uses a discrete distribution model, selecting four typical values: 1Hz, 2Hz, 5Hz, and 10Hz. Weights are assigned based on actual traffic flow statistics to ensure the generated data covers different service scenarios. The pH value is generated using a truncated normal distribution, with the mean set in the neutral-to-alkaline range to reflect typical road service environments. The distribution range covers environmental conditions from weakly acidic to weakly alkaline, simulating the environmental effects of acid rain and de-icing salt use in different regions.

[0033] Simultaneously, based on the previously generated feature data, crack density and adhesion work are constructed. Crack density is constructed through a multi-factor cumulative model to quantify the evolution of interfacial damage; adhesion work is obtained by multiplying the initial adhesion work determined by the basicity of the steel slag by a series of degradation modulation factors of environmental and load effects, and is used to describe the decay of interfacial bonding capacity.

[0034] S120, based on the spatiotemporal evolution of adhesion work, a primitive neural network prediction model is created using diffusion terms, reaction source terms, multi-mechanism dissipation terms, and state variables.

[0035] The evolution of the adhesion work at the steel slag-asphalt interface is the result of the coupling effects of multiple physical fields, including diffusion, chemical reaction, fatigue damage, and environmental aging. Therefore, based on classical physicochemical principles such as thermodynamic conservation laws, diffusion theory, chemical kinetics, and damage mechanics, a coupled evolutionary equation system of "energy transfer-generation-dissipation" can be constructed to obtain the original neural network prediction model.

[0036] In some embodiments, the original neural network prediction model includes a main prediction network and an auxiliary state network; The physical equations corresponding to the master prediction network include the interface adhesion work and diffusion term, reaction source term, multi-mechanism dissipation term, and the first mapping relationship of evolution time; The physical equations corresponding to the auxiliary state network include a second mapping relationship between state variables and evolution time; among which, state variables include interface coverage and crack density; the evolution of interface coverage characterizes the dynamic balance between reaction generation and environmental decay, and the change in crack density characterizes the dynamic balance between crack propagation and product arrest.

[0037] The first mapping relationship can be described by the following partial differential equation: ; in, The work done by the interface adhesion is given by t, which is the evolution time. For the effective diffusion coefficient, For diffusion term, For the adhesive power source term, It is a multi-mechanism dissipation term.

[0038] The diffusion term is based on Fick's diffusion law, the reaction term is dominated by the chemical reaction between the alkaline active components in the steel slag and the acidic groups in the asphalt, and the dissipation term mainly comes from irreversible processes such as microcrack damage, fatigue damage and environmental aging.

[0039] Based on Fick's diffusion law (Fick's first law), energy flux and It is proportional to the gradient: ; In the formula, The diffusion coefficient is denoted as m² / s, and the negative sign indicates that the transport direction is opposite to the gradient direction.

[0040] Combining the continuity equation, the rate of accumulation of energy in space is equal to the negative of the flux divergence: ; Substituting Fick's first law and considering the axisymmetric characteristics of the interface, flux divergence... .

[0041] When the interface thickness is much smaller than the feature radius of the specimen, it can be approximated as: The final diffusion term is: .

[0042] In practical interface systems, the effective diffusion coefficient is affected by temperature, crack density, and interface coverage state: ; in, The diffusion pre-factor has a value of [value missing]. , For diffusion activation energy, take , The universal gas constant is taken as 8.314. This is absolute temperature, measured in Kelvin (K). and These are the transport resistance factors for crack defects and interface covering layers, respectively. Crack density, This refers to the interface coverage.

[0043] The alkaline active components (CaO, MgO) in steel slag react with the acidic groups in asphalt to produce cementing products such as asphaltates and hydrated calcium silicate, which enhance the interfacial bonding strength. Essentially, this injects energy into the interfacial system, increasing the interfacial adhesion work. The rate of increase is significant. The core of the adhesion work source term is the quantification of the chemical reaction rate. An equation is constructed based on two main theories: Arrhenius chemical kinetics and the steel slag activity characterization theory. Its expression is:

[0044] ; in, Let be the reaction rate constant, which characterizes the maximum reaction rate under ideal conditions. The activation energy of the reaction is taken as... , This represents the initial basicity of the steel slag.

[0045] Interface coverage The evolution of [the process] is a dynamic equilibrium between reaction formation and environmental degradation. The reaction products [cause / effect]... Rising temperature, water erosion Reduced. Based on reaction kinetics and decay kinetics, The rate of change over time is the difference between the generation rate and the decay rate. It is governed by the following equation:

[0046] ; in, For the coverage formation rate constant, Both are learnable parameters to cover the degradation rate constant. This equation describes the dynamic equilibrium process of interfacial active sites being covered by reaction products.

[0047] Crack density The change represents a dynamic balance between crack propagation and crack arrest by reaction products. Fatigue dissipation drives crack propagation, while reaction products fill the crack, enhance interfacial strength, and inhibit crack propagation. The evolution equation is:

[0048] ; in, For fatigue dissipation components, This is the crack initiation coefficient. denoted as the self-healing coefficient, and all are learnable parameters. This equation reflects the competitive mechanism between fatigue damage-driven crack propagation and interfacial reactions promoting self-healing.

[0049] Based on the above, add boundary conditions and initial conditions. In the computational domain... Internally, based on physical symmetry and flux continuity, the boundary conditions are set as follows: centrosymmetric conditions. External boundary flux conditions: .

[0050] Initial conditions were determined experimentally, including initial adhesion work. Initial interface coverage and initial crack density .

[0051] In some embodiments, a primitive neural network prediction model is created based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work, including: By using the second mapping relationship to restrict the state variables in the first mapping relationship, the original neural network prediction model is obtained.

[0052] In this embodiment, the main prediction network adopts a deep feedforward neural network structure, containing four hidden layers, each with 128 neurons, and uses the hyperbolic tangent (Tanh) activation function to ensure the smoothness and differentiability of the output. The output layer has one neuron and directly predicts the value of the interface adhesion work W. The auxiliary state network takes into account the interface coverage. With crack density Due to physical constraints, a shallow network structure (2-layer MLP, 64 neurons) is adopted. The output is constrained to the [0,1] interval by the Sigmoid function to conform to the physical definition of interface coverage; the crack density is guaranteed to be non-negative by the Softplus function, which conforms to the physical meaning.

[0053] Both the main prediction network and the auxiliary state network use evolution time as an independent variable, describing the dynamic changes of state variables and adhesion work through differential equations or difference equations. Furthermore, the auxiliary state network updates state variables in real time; for example, an increase in crack density reduces the effective contact area at the interface, thereby weakening the adhesion work. This is then fed back to the main prediction network through physical constraints, forming a closed loop of "state evolution → performance prediction → state re-evolution," accurately simulating the dynamic evolution process of material properties.

[0054] S130: Input chemical composition parameters and environmental impact factors into the original neural network prediction model, and generate interface adhesion work prediction parameters by combining physical constraint terms; use the interface adhesion work prediction parameters and gradient descent algorithm to train the original neural network prediction model to obtain the target neural network prediction model; physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss.

[0055] Please see Figure 2 , Figure 2 This is a schematic diagram illustrating the principle of generating physical constraint terms according to an embodiment of the present invention. The input layer receives external input data; the hidden layer consists of multiple neurons that transform data through weights and biases, with the output of each layer serving as the input to the next layer; the output layer produces the final prediction result. Each loss term is multiplied by a weight coefficient to balance its contribution to the total loss. The model calculates the gradient of the loss function with respect to the neural network parameters using the backpropagation algorithm. An optimization algorithm updates the weights and biases of the neural network based on the gradient information to minimize the total loss function. The training process continues until the loss function value falls below a preset threshold, at which point the model is considered to have converged, and training ends.

[0056] In some embodiments, chemical composition parameters and environmental impact factors are input into the original neural network prediction model, and physical constraint terms are combined to generate interfacial adhesion work prediction parameters, including: The weights of each constraint term in the physical constraint terms are determined based on the current physical context. The corresponding constraint terms are weighted according to their weights to obtain the total constraint terms. The original neural network prediction model is optimized using the total constraint term, and the chemical composition parameters and environmental impact factors are input into the optimized original neural network prediction model to generate interface adhesion work prediction parameters.

[0057] In this embodiment, the total constraint term can be expressed as: ; The weighting coefficients of each constraint term can be determined through physical guidance and numerical experiments, such as... (Data constraints) (PDE residual constraints) (State equation constraints) (Boundary condition constraints) ensure that all losses are of similar magnitude in the early stages of training.

[0058] The data loss term supervises the deviation between the network's predictions and experimental observations. By minimizing the data loss, the network can better fit the actual observed data. ; The PDE residual loss forces the adhesion work control equation to be satisfied, ensuring that the model's predictions are physically consistent. ; State equation loss ensures that the evolution of auxiliary variables conforms to physical laws: ; Boundary condition loss applies spatial boundary constraints to ensure that the model meets the corresponding physical requirements at the boundaries: ; , , The number of samples for each constraint term is calculated.

[0059] In some embodiments, the original neural network prediction model is trained using interface adhesion work prediction parameters and a gradient descent algorithm to obtain a target neural network prediction model, including: During training, the weight of data loss is gradually reduced while the PDE residual loss and state equation loss are increased until the loss function of the original neural network prediction model is less than the second threshold, thus obtaining the target neural network prediction model.

[0060] To ensure the numerical stability and convergence efficiency of model training, all input features and target variables were Z-score standardized before training to eliminate the dimensional differences between different physical quantities.

[0061] ; in, The mean, The standard deviation is denoted as σ. Standardization effectively accelerates training convergence and improves numerical stability.

[0062] In an alternative embodiment, please refer to Figure 3 , Figure 3This is a scatter plot of the output of the neural network prediction model provided in this embodiment of the invention. The constructed dataset is randomly divided into training, validation, and test sets in a 6:2:2 ratio to ensure the consistency and statistical independence of the data distribution in each set. The Adam adaptive optimization algorithm is used for optimization, and the learning rate is dynamically adjusted based on the performance of the validation set to improve training efficiency. Furthermore, to avoid gradient explosion and improve training stability, the model imposes an upper bound constraint on the gradient norm (gradient clipping) and introduces an early stopping mechanism. Training is terminated when the validation loss no longer decreases after several iterations, thereby effectively suppressing overfitting. In addition, a dual-batch training strategy and a progressive weight adjustment mechanism are employed. In each iteration, 1024 data points are sampled simultaneously for data loss calculation, and 256 physical placement points are used for PDE residual and state equation residual calculation to balance the contributions of data fitting and physical constraints. In the early stages of training, the model focuses more on data-driven terms, improving its fitting ability by learning the main changing features in the experimental samples. As training progresses, the weights of the PDE residuals and the state equation loss are gradually increased, guiding the model to converge to a physical solution that satisfies the partial differential equation constraints. This data-first, physics-driven, and progressive strategy helps improve the trainability of the model and the physical reliability of the final solution in high-dimensional, multi-physics coupled problems.

[0063] S140, input the chemical composition parameters and environmental impact factors of the material to be tested into the target neural network prediction model to obtain the target prediction parameters.

[0064] Here, the material to be tested can be sampled and analyzed to determine its chemical composition parameters and environmental impact factors. The measured chemical composition parameters and environmental impact factors are then input into the target neural network prediction model to obtain the target prediction parameter, i.e., the interfacial adhesion work.

[0065] In an alternative embodiment, prediction accuracy can be evaluated using mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²). The specific formulas are as follows:

[0066] ; in, , , Let represent the true value, the predicted value, and the mean of the true values ​​of the i-th sample, respectively. Characterizes the number of samples.

[0067] In an alternative embodiment, please refer to Figure 4 , Figure 4This is a comparison chart of the error distribution of the PINN model and the data-driven model provided in this embodiment of the invention. Taking the PINN (Physical Information Neural Network) model and the data-driven model as examples, the adhesion work of the steel slag asphalt interface is predicted respectively. On the validation set and the test set, the PINN model shows a certain degree of improvement in the median and mean indices, indicating that the PINN model has better generalization ability and adaptability when facing new data. That is, on a wider range of data, the PINN model can better combine physical information, thus showing better performance. The specific error distribution parameters of the two models are shown in Table 1:

[0068] Table 1. Error distribution parameters of the PINN model and the data-driven model In some embodiments, please refer to Figure 5 , Figure 5 This is a schematic diagram of the structure of the steel slag-asphalt interface adhesion work prediction system based on a physical neural network provided in an embodiment of the present invention. The present invention provides a steel slag-asphalt interface adhesion work prediction system 500 based on a physical neural network, comprising: a parameter acquisition module 510, a model creation module 520, a model training module 530, and a parameter prediction module 540; wherein,

[0069] The parameter acquisition module 510 is configured to acquire the chemical composition parameters and environmental impact factors of the interface sample of steel slag asphalt mixture; the chemical composition parameters include various oxide parameters, and the environmental impact factors include the number of load cycles, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to the evolution of material properties; The model creation module 520 is configured to create an original neural network prediction model based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work. The model training module 530 is configured to input the chemical composition parameters and the environmental impact factors into the original neural network prediction model, and generate interface adhesion work prediction parameters by combining physical constraint terms; the original neural network prediction model is trained using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model; the physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss. The parameter prediction module 540 is configured to input the chemical composition parameters and environmental impact factors of the material to be tested into the target neural network prediction model to obtain the target prediction parameters.

[0070] In some embodiments, the parameter acquisition module 510 is specifically configured as follows: For the first type of oxide with a mass percentage greater than the first threshold, the corresponding first oxide parameters are obtained by normal distribution simulation. For the second type of oxide with a mass percentage not greater than the first threshold, the corresponding second oxide parameters are obtained by gamma distribution simulation. The parameters of the first oxide and the second oxide are normalized to obtain the chemical composition parameters.

[0071] In some embodiments, the parameter acquisition module 510 is specifically configured as follows: The number of load cycles was obtained by simulation using a log-normal distribution, the stress amplitude was obtained by simulation using a Weibull distribution, the temperature field was obtained by superimposing a sine function with random noise, and the moisture content was obtained by a Beta distribution. The time parameters in the spatiotemporal parameters are obtained using an exponential distribution model, and the spatial parameters are obtained based on the crack propagation theory of fracture mechanics.

[0072] In some embodiments, the original neural network prediction model includes a main prediction network and an auxiliary state network; The physical equations corresponding to the master prediction network include the interface adhesion work and diffusion term, reaction source term, multi-mechanism dissipation term, and the first mapping relationship of evolution time; The physical equations corresponding to the auxiliary state network include a second mapping relationship between state variables and evolution time; among which, state variables include interface coverage and crack density; the evolution of interface coverage characterizes the dynamic balance between reaction generation and environmental decay, and the change in crack density characterizes the dynamic balance between crack propagation and product arrest.

[0073] In some embodiments, the model creation module 520 is specifically configured as follows: By using the second mapping relationship to restrict the state variables in the first mapping relationship, the original neural network prediction model is obtained.

[0074] In some embodiments, the model training module 530 is specifically configured as follows: The weights of each constraint term in the physical constraint terms are determined based on the current physical context. The corresponding constraint terms are weighted according to their weights to obtain the total constraint terms. The original neural network prediction model is optimized using the total constraint term, and the chemical composition parameters and environmental impact factors are input into the optimized original neural network prediction model to generate interface adhesion work prediction parameters.

[0075] In some embodiments, the model training module 530 is specifically configured as follows: During training, the weight of data loss is gradually reduced while the PDE residual loss and state equation loss are increased until the loss function of the original neural network prediction model is less than the second threshold, thus obtaining the target neural network prediction model.

[0076] It should be noted that the steel slag asphalt interface adhesion work prediction system based on physical neural network provided in this application embodiment and the steel slag asphalt interface adhesion work prediction method based on physical neural network provided in this application embodiment are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned steel slag asphalt interface adhesion work prediction method based on physical neural network, and the repeated parts will not be described again.

[0077] In some embodiments, please refer to Figure 6 , Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device 600 provided in this application includes a processor 610 and a memory 620; the memory 620 stores a computer program, wherein the computer program, when executed by the processor, implements the aforementioned method for predicting the adhesion work of steel slag and asphalt interfaces based on physical neural networks.

[0078] Specifically, processor 610 may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. Processor 610 may also include onboard memory for caching purposes. Processor 610 may be a single processing unit or multiple processing units for performing different actions of the method flow according to embodiments of this application.

[0079] Memory 620 may be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory 620 may include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, or propagation media. Specific examples of memory 620 include: magnetic storage devices such as magnetic tape or hard disk drives (HDDs); optical storage devices such as optical discs (CD-ROMs); and may also be random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0080] This application also provides a non-transitory computer-readable medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned method for predicting the adhesion work of steel slag-asphalt interface based on a physical neural network. This computer-readable medium may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into that device / apparatus / system. The aforementioned computer-readable medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0081] According to embodiments of this application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wired, optical fiber, radio frequency signals, etc., or any suitable combination thereof.

[0082] Those skilled in the art will understand that the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application. Therefore, the scope of this application should not be limited to the above embodiments, but should be defined not only by the appended claims, but also by their equivalents. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for predicting the adhesion work at the steel slag-asphalt interface based on a physical neural network, characterized in that, include: Chemical composition parameters and environmental impact factors of steel slag asphalt mixture interface samples were obtained; the chemical composition parameters included various oxide parameters, and the environmental impact factors included load cycle number, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to material property evolution. A primitive neural network prediction model is created based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work. The chemical composition parameters and the environmental impact factors are input into the original neural network prediction model, and the interface adhesion work prediction parameters are generated by combining the physical constraint terms. The original neural network prediction model is trained using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model. The physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss. The chemical composition parameters and environmental impact factors of the material to be tested are input into the target neural network prediction model to obtain the target prediction parameters.

2. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 1, characterized in that, The process of obtaining the chemical composition parameters and environmental impact factors of the steel slag asphalt mixture interface sample includes: For the first type of oxide with a mass percentage greater than the first threshold, the corresponding first oxide parameters are obtained by normal distribution simulation. For the second type of oxide with a mass percentage not greater than the first threshold, the corresponding second oxide parameters are obtained by gamma distribution simulation. The chemical composition parameters are obtained by normalizing the first oxide parameter and the second oxide parameter.

3. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 1, characterized in that, The process of obtaining the chemical composition parameters and environmental impact factors of the steel slag asphalt mixture interface sample includes: The number of load cycles was obtained by simulation using a log-normal distribution, the stress amplitude was obtained by simulation using a Weibull distribution, the temperature field was obtained by superimposing random noise with a sine function, and the moisture content was obtained by a Beta distribution. The temporal parameters in the spatiotemporal parameters are obtained using an exponential distribution model, and the spatial parameters are obtained based on the crack propagation theory of fracture mechanics.

4. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 1, characterized in that, The original neural network prediction model includes a main prediction network and an auxiliary state network; The physical equations corresponding to the master prediction network include a first mapping relationship between the interface adhesion work and the diffusion term, the reaction source term, the multi-mechanism dissipation term, and the evolution time. The physical equations corresponding to the auxiliary state network include a second mapping relationship between the state variables and evolution time; wherein, the state variables include interface coverage and crack density; the evolution of the interface coverage characterizes the dynamic balance between reaction generation and environmental decay, and the change in crack density characterizes the dynamic balance between crack propagation and product arrest.

5. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 4, characterized in that, The original neural network prediction model, based on the spatiotemporal evolution of adhesion work and corresponding diffusion, reaction source, multi-mechanism dissipation, and state variables, includes: By using the second mapping relationship to restrict the state variables in the first mapping relationship, the original neural network prediction model is obtained.

6. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 1, characterized in that, The step of inputting the chemical composition parameters and the environmental impact factors into the original neural network prediction model, and combining them with physical constraint terms to generate interface adhesion work prediction parameters, includes: The weight of each constraint term in the physical constraint term is determined based on the current physical context; The corresponding constraint terms are weighted based on the aforementioned weights to obtain the total constraint terms. The original neural network prediction model is optimized using the total constraint term, and the chemical composition parameters and the environmental impact factors are input into the optimized original neural network prediction model to generate interface adhesion work prediction parameters.

7. The method for predicting the adhesion work of steel slag asphalt interface based on physical neural networks as described in claim 6, characterized in that, The step of training the original neural network prediction model using the interface adhesion work prediction parameters and gradient descent algorithm to obtain the target neural network prediction model includes: During training, the weight of the data loss is gradually reduced, while the weight of the PDE residual loss and the state equation loss are increased until the loss function of the original neural network prediction model is less than the second threshold, thus obtaining the target neural network prediction model.

8. A system for predicting the adhesion work of steel slag asphalt interface based on physical neural networks, characterized in that, include: The system comprises a parameter acquisition module, a model creation module, a model training module, and a parameter prediction module; among which, The parameter acquisition module is configured to acquire the chemical composition parameters and environmental impact factors of the steel slag asphalt mixture interface sample; the chemical composition parameters include various oxide parameters, and the environmental impact factors include the number of load cycles, stress amplitude, temperature field, moisture content, and spatiotemporal parameters related to the evolution of material properties; The model creation module is configured to create an original neural network prediction model based on the diffusion term, reaction source term, multi-mechanism dissipation term, and state variables corresponding to the spatiotemporal evolution of adhesion work. The model training module is configured to input the chemical composition parameters and the environmental impact factors into the original neural network prediction model, and generate interface adhesion work prediction parameters by combining physical constraint terms; the original neural network prediction model is trained using the interface adhesion work prediction parameters and the gradient descent algorithm to obtain the target neural network prediction model; the physical constraint terms include data loss, PDE residual loss, state equation loss and boundary condition loss. The parameter prediction module is configured to input the chemical composition parameters and environmental impact factors of the material to be tested into the target neural network prediction model to obtain the target prediction parameters.

9. An electronic device comprising a processor and a memory; said memory having a storage for a computer program, wherein, When the computer program is executed by the processor, it implements the method for predicting the adhesion work of steel slag asphalt interface based on any one of claims 1 to 7.

10. A non-transitory computer storage medium, characterized in that, It stores a computer program, wherein the computer program, when executed by a processor, implements the method for predicting the adhesion work of steel slag asphalt interface based on any one of claims 1 to 7.

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