Space-time process simulation of concrete sulfate erosion concentration based on NAS-PINN-GPR algorithm

Abstract

The invention discloses space-time process simulation of concrete sulfate erosion concentration based on an NAS-PINN-GPR algorithm. The space-time process simulation comprises the following steps: determining a control equation of a sulfate erosion process and collecting sample data; optimizing the PINN structure by using a neural architecture search (NAS) technology; setting a loss function of the PINN according to the control equation, the sample set, the boundary condition and the initial value condition; according to the loss function, training the optimized PINN structure based on the sample set, and simulating the time-space process of the concrete sulfate erosion concentration by using the trained PINN structure to obtain sulfate ion concentration point prediction; the trained PINN structure generates sufficient prediction data as training data of a Gaussian process regression (GPR) algorithm, and a trained GPR model is utilized to simulate and predict an uncertainty probability interval of the concrete sulfate erosion concentration. According to the method, the PINN algorithm and the GPR algorithm are combined, reliable interval estimation is provided on the basis of obtaining high-precision sulfate ion concentration point estimation, and the prediction capability of the model is improved.

Description

Technical Field

[0001] The present invention relates to the intersection of spatiotemporal process simulation of concrete sulfate attack concentration and artificial intelligence technology, and in particular to spatiotemporal process simulation of concrete sulfate attack concentration based on neural architecture search (NAS) technology, physical information neural network (PINN) algorithm or Gaussian process regression (GPR) algorithm. Background Art

[0002] Concrete is a material with a heterogeneous, multi-scale structure composed of cement, coarse aggregate and fine aggregate. Among the chemical corrosions that affect the durability of concrete, sulfate corrosion is the most widespread and an important factor that reduces the durability of concrete. Soil, saline-alkali land, groundwater, seawater and other environments contain a large amount of sulfate. In the sulfate exposure environment, sulfate ions penetrate into the concrete and a series of chemical reactions occur, causing the strength and stability of concrete to decrease, resulting in the destruction of concrete durability. Using numerical methods to study the spatiotemporal process of concrete sulfate corrosion concentration can predict the degree of concrete sulfate corrosion, determine its potential repair and continued use, thereby avoiding frequent repairs and replacements that will bring huge economic losses, and help engineers more accurately assess the health of the structure, take preventive and repair measures, and ensure the safety of the structure throughout its service life. At present, most of the research on the sulfate ion corrosion process of concrete at home and abroad adopts traditional numerical methods such as the finite element method, which usually faces problems such as complex research process, large model calculation and strong data dependence. With the rapid development of artificial intelligence technology, the use of artificial intelligence technology to study the sulfate attack process of concrete should be further explored. Physical information neural network (PINN) is an application method of scientific machines in the traditional numerical field, especially for solving partial differential equations (PDE). PINN uses physical laws such as PDE as constraints and embeds them into the training process of neural networks, so that the model output not only conforms to the training data, but also satisfies the physical laws, enhancing the interpretability of the model. The advantage of using the PINN method to solve the control equation for the spatiotemporal process simulation of concrete sulfate attack concentration is that it makes full use of physical information and has low data dependence, which effectively avoids the disadvantage of traditional regression simulation algorithms that require a large amount of data to train the model. Compared with traditional numerical methods, PINN is slightly inferior in the accuracy of solving control equations. Neural architecture search (NAS) technology is a technology for automatically designing neural network architectures, which improves PINN performance by searching for the optimal architecture. Existing studies usually cannot provide the possible distribution of sulfate attack concentrations and cannot cope with the uncertainty of the actual situation. In the present invention, the Gaussian process regression (GPR) algorithm provides uncertainty probability interval prediction of sulfate attack concentration. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a spatiotemporal process simulation of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm. The NAS-PINN-GPR model retains the characteristics of simple PINN processing control equation process and low data dependence, and improves the performance of PINN through NAS technology. The trained PINN can generate a large amount of data for GPR model training as an approximate solution to the control equation. The GPR model provides uncertainty probability interval prediction of sulfate attack concentration based on PINN simulation. The simulation of concrete sulfate attack concentration in the present invention includes both point prediction of erosion duration and spatial position and uncertainty probability interval estimation.

[0004] Technical solution: The present invention provides a method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm, the method comprising the following steps:

[0005] Step 1, determining the control equation of the concrete sulfate attack process, collecting the sulfate ion concentrations of the target concrete area at the preset sample coordinate positions under the preset attack durations, and forming a sample set;

[0006] Step 2, use NAS technology to optimize the PINN network structure and obtain the improved PINN structure;

[0007] Step 3, according to the control reaction equation of the concrete sulfate attack process, the sample set, the boundary conditions and the initial value conditions, the loss function of the PINN improved structure is set; according to the loss function, based on the sample set, with the erosion time and the sample coordinate position as input, and the corresponding sulfate ion concentration as output, the PINN improved structure is trained to obtain a trained model, that is, a sulfate ion concentration analysis model;

[0008] Step 4, applying a sulfate ion concentration analysis model according to each preset target erosion time and each target coordinate position in the target concrete area, to obtain the sulfate ion concentration corresponding to each target coordinate position in the target concrete area; wherein the number of target coordinate positions is greater than the number of sample coordinate positions;

[0009] Step 5, taking each preset target erosion time and the target coordinate position in the target concrete area as input, and taking the sulfate ion concentration at the target coordinate position in the target concrete area corresponding to each target erosion time as output, the GPR model is trained, and the trained GPR model is used to obtain the interval range of the sulfate ion concentration at the target coordinate position in the target concrete area corresponding to the target erosion time.

[0010] Furthermore, in step 1, the diffusion-reaction equation of sulfate corrosion on concrete is used as the control equation of the concrete sulfate corrosion process. The diffusion process of sulfate in concrete can be described by Fick's second law:

[0011]

[0012] Wherein, C=C(x, y, z, t) is the sulfate ion concentration, x, y, z are the spatial coordinates of the corresponding coordinate system in the target concrete area, t is the erosion time, D is the diffusion coefficient, In the process of sulfate attacking concrete, sulfate reacts chemically with the chemical components in concrete to form dissolved products. These reactions cause the sulfate ion concentration to be consumed, which can be described by chemical reaction kinetics:

[0013]

[0014] Where η is the sulfate ion concentration consumed by the chemical reaction, and k is the chemical reaction rate constant. Therefore, the diffusion-reaction equation of sulfate corrosion on concrete can be written as:

[0015]

[0016] The above equation is used as the control equation for simulating the sulfate corrosion process on concrete. At the same time, the boundary conditions and initial value conditions of the diffusion reaction equation should be determined according to the specific situation. Where z contains the coordinates of space and time, and u is the solution to the equation, The operator describes the initial value or boundary condition, Ω is the region where the equation is located, is the region boundary.

[0017] Furthermore, in step 2, a PINN is pre-built using a feedforward neural network, including an input layer, a hidden layer, and an output layer. The PINN model space is constructed by setting hidden layers with different numbers of nodes in the neural network and activation functions between different layers. The NAS technology is used to optimize the number of hidden layers, the number of nodes, and the activation function with a random sampling test model optimization strategy and a model evaluation criterion of minimizing the mean square error (MSE) of model prediction. The PINN that best solves the control equation is determined in the constructed PINN model space to obtain an improved PINN structure.

[0018] Furthermore, the loss term of sulfate ion concentration range restriction is added to the loss function in step 3, which is the value range loss, used to reduce the prediction of abnormal values. Therefore, the loss terms of the loss function of PINN in step 3 are physical constraint losses, namely control equation loss, boundary condition loss, initial value condition loss, data fitting loss and value range loss. The loss function can be written as:

[0019] loss = λ physics l physics +λ data l data +λ boundary l boundary +λ init l init +λ value l value where λ physics , ..., λ value is the weight of each loss item, l physics is the control equation loss, l data is the data loss, l boundary is the boundary condition loss, l init is the initial condition loss, l value is the value range loss; due to the different magnitudes and importance of different loss terms, appropriate weight setting can balance the influence of each loss term, so that the model can find the best balance between fitting data and satisfying physical constraints, which can help PINN's loss function value to be further reduced and accelerate convergence. In the present invention, λ is generally physics With λ data The weight of boundary and λ init The weight of is reduced, which helps to maintain the structure of the diffusion reaction equation and make full use of the existing data.

[0020] Furthermore, in step 3, the prediction error is reduced by adjusting the neural network parameters by the gradient descent method according to the loss function through iterative training, and the iterative training is terminated when the loss function value is stable or before the loss function value diverges. By actively selecting a specific number of training rounds of PINN, a model with better performance can be determined, which is also a means to prevent model overfitting. For the GPR model, if there are too few training samples, the prediction performance of the GPR model will be reduced, while the sulfate ion concentration analysis model can output sufficient training data for GPR training, which effectively improves the prediction ability of the GPR model.

[0021] Further, in step 5, each preset target erosion time, each target coordinate position in the target concrete area, and the corresponding target erosion time and sulfate ion concentration at the target coordinate position obtained by the sulfate ion concentration analysis model are combined into training data. In particular, each training data contains 5 items of information, time coordinate t, spatial coordinates x, y, z, sulfate ion concentration, i.e., approximate solution u of the control equation. The GPR model is trained with the target erosion time and target coordinate position as input and the corresponding approximate solution as output. In the process of multiple model training, the Bayesian parameter optimization method, which is a common method for hyperparameter tuning of machine learning models, is used to further improve the GPR performance.

[0022] Furthermore, the simulation and prediction capabilities of the model are evaluated on an independent test set using evaluation indicators to determine whether the model meets expectations. In step 2, NAS technology can optimize the network structure to improve model performance. In step 3, adjusting the weights of each loss item in the loss function can also further optimize the model performance. Therefore, if the simulation result does not meet expectations, return to step 2 and use NAS technology to optimize PINN again or return to step 3 to redesign the weights of each loss function to improve model performance. Then, perform simulation again according to the subsequent steps to further improve the simulation effect. If the simulation error is small, the model of the present invention is built.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] 1. The present invention simulates the spatiotemporal process of sulfate attack concentration of concrete by introducing the PINN algorithm, fully extracts the physical information of the control equation of the sulfate attack process of concrete, reduces the dependence of the model on data, and can simulate the concentration change process of sulfate attack concrete with only a small amount of data;

[0025] 2. The present invention improves the simulation accuracy of the PINN model and the quality of the GPR model training data by combining the NAS technology with the PINN algorithm, thereby improving the simulation results of the PINN algorithm and the GPR algorithm at the same time, making the simulation prediction of the present invention more accurate;

[0026] 3. The present invention utilizes the PINN algorithm to embed various physical information into the neural network loss function, and reduces the abnormal values ​​of the model simulation by designing and adding the range constraint of the concrete sulfate attack concentration;

[0027] 4. Compared with the existing spatiotemporal process simulation technology of concrete sulfate attack concentration, the present invention generates a large amount of data for GPR model training by utilizing the characteristics of PINN to fully utilize the physical information of the control equation and fit the solution of the control equation with a small amount of data, thereby effectively solving the problem of insufficient training samples for the GPR model. The present invention provides a reliable interval range estimation based on obtaining the point estimation of sulfate ion concentration at the corresponding corrosion time and spatial position in the concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the present invention;

[0029] Figure 2 It is a flowchart of NAS technology implementation;

[0030] Figure 3 The bar graph of the loss function values ​​of the PINN model structure and other parts of the model space determined by the NAS technology;

[0031] Figure 4 Schematic diagram of the PINN model structure determined for NAS technology;

[0032] Figure 5 A trend diagram of the training loss function when the weights of the loss function are adjusted and when the loss function is not adjusted;

[0033] Figure 6 The time-space process effect diagram of sulfate ion concentration analysis model simulating the concentration of sulfate attack on concrete;

[0034] Figure 7 Uncertainty probability interval diagram for the GPR model predicting the concentration of concrete sulfate attack;

[0035] Figure 8 This is an overview of the various evaluation indicators of the PINN model and the GPR model on the test set. DETAILED DESCRIPTION

[0036] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is clearly and completely described below in conjunction with specific embodiments and drawings. It is obvious that the described embodiments are only partial embodiments of the present invention, not all embodiments.

[0037] The spatiotemporal simulation of the concentration of sulfate attack on concrete based on the NAS-PINN-GPR algorithm described in this embodiment is as follows: Figure 1 As shown, the following steps are included:

[0038] Step 1, determining the control equation of the concrete sulfate attack process, collecting the sulfate ion concentrations of the target concrete area at the preset sample coordinate positions under the preset attack durations, and forming a sample set;

[0039] Step 2, using a feedforward neural network to build a PINN, including an input layer, a hidden layer, and an output layer, constructing a PINN model space by setting different numbers of nodes in the hidden layer of the neural network and activation functions between different layers, using NAS technology with a model optimization strategy of random sampling test and a model evaluation criterion of minimum mean square error (MSE) of model prediction, optimizing the number of hidden layers, the number of nodes, and the activation function, determining the PINN that best solves the control equation in the constructed PINN model space, and obtaining an improved PINN structure;

[0040] Step 3, according to the control reaction equation of the concrete sulfate erosion process, the sample set, the boundary conditions and the initial value conditions, the loss function of the PINN improved structure is set; according to the loss function, based on the sample set, with the erosion time and the sample coordinate position as input, and the corresponding sulfate ion concentration as output, the PINN improved structure is trained. During the training process, the loss term of the sulfate ion concentration range limitation is also added to the loss function. According to the error value of each item in the loss function, the weight of each loss term is adjusted. After the training is completed, the trained model, that is, the sulfate ion concentration analysis model, is obtained;

[0041] Step 4, applying a sulfate ion concentration analysis model according to each preset target erosion time and each target coordinate position in the target concrete area, to obtain the sulfate ion concentration corresponding to each target coordinate position in the target concrete area; wherein the number of target coordinate positions is greater than the number of sample coordinate positions;

[0042] Step 5, taking each preset target erosion time and the target coordinate position in the target concrete area as input, and taking the sulfate ion concentration at the target coordinate position in the target concrete area corresponding to each target erosion time as output, the GPR model is trained. During the training process, the Bayesian parameter optimization method is used to perform multiple tuning processes on the GPR model, and the trained GPR model is used to obtain the interval range of the sulfate ion concentration at the target erosion time corresponding to the target coordinate position in the target concrete area. That is, the trained GPR model combined with the sulfate ion concentration analysis model can predict the uncertainty probability interval of the sulfate ion concentration at any concrete erosion time and target coordinate position.

[0043] Furthermore, in step 1, the diffusion-reaction equation of sulfate corrosion on concrete is used as the control equation of the sulfate corrosion process of concrete; the diffusion-reaction equation of sulfate corrosion on concrete is usually used to simulate the damage and corrosion of concrete in a sulfate corrosion environment. The diffusion process of sulfate in concrete can be described by Fick's second law:

[0044]

[0045] Where C = C (x, y, z, t) is the sulfate ion concentration in mol / m 3 , x, y, z are the spatial coordinates of the corresponding coordinate system in the target concrete area, the unit is m, t is the erosion time, the unit is s, and D is the diffusion coefficient, the unit is m 2 / s, In the process of sulfate attacking concrete, sulfate reacts chemically with chemical components in concrete, such as calcium hydrogen sulfide in cement, to form dissolved products. These reactions cause the consumption of sulfate ion concentration, which can be described by chemical reaction kinetics:

[0046]

[0047] Where ηη is the sulfate ion concentration consumed by the chemical reaction, in mol / m 3 , k is the chemical reaction rate constant, therefore, the diffusion-reaction equation of sulfate corrosion on concrete can be written as:

[0048]

[0049] The above equation is used as the control equation for simulating the sulfate corrosion process on concrete. At the same time, the boundary conditions and initial value conditions of the diffusion reaction equation should be determined according to the specific situation. Where z contains the coordinates of space and time, and u is the solution to the equation, The operator describes the initial value or boundary condition, Ω is the region where the equation is located, This embodiment takes a cubic concrete block of one cubic meter as the object, and the corresponding boundary condition is the constant concentration of sulfate ions on the six surfaces, which is specifically written as:

[0050] C(0,y,z,t)=C0,y,z∈[0,L],t∈[0,T],

[0051] C(x, 0, z, t) = C0, x, z∈[0, L], t∈[0, T],

[0052] C(x,y,0,t)=C0,x,y∈[0,L],t∈[0,T],

[0053] C(L,y,z,t)=C0,y,z∈[0,L],t∈[0,T],

[0054] C(x, L, z, t) = C0, x, z∈[0, L], t∈[0, T],

[0055] C(x,y,L,t)=C0,x,y∈[0,L],t∈[0,T].

[0056] Where C0 = 75.5 mol / m 3 , is a constant concentration; L = 1m, is the side length of the cube; T = 7 years, is the longest simulated erosion time; the initial conditions are:

[0057] C(x,y,z,0)=0,x,y,z∈[0,L].

[0058] The ion permeability in the diffusion reaction equation is D = 2.6 × 10 -9 m 2 / s, the sulfate ion reaction rate constant is k = 2.125 × 10-7 This embodiment uses the finite element method simulation data of the sulfate attack process under the above conditions as a reference, and the data is divided into a training set and a test set. The training set contains 2000 data and the test set contains 500 data.

[0059] Further, in step 2, a feedforward neural network is used to build a PINN, and a PINN model space is constructed by setting hidden layers with different numbers of nodes in the neural network and activation functions between different layers. In this embodiment, the model space includes a neural network with 2, 3, and 4 hidden layers, and the number of nodes in the hidden layer has four possible choices of 16, 32, 64, and 128. The activation functions between different layers include Tanh function, ReLU function, and Sigmoid function, and their expressions are as follows:

[0060] ReLU(x)=max(0,x). Multiple trials NAS technology includes multiple model optimization strategies, among which the random sampling test strategy is a non-systematic search method. By randomly selecting an architecture in a predefined search space for evaluation, this method has excellent performance in many cases and is a commonly used search strategy in NAS technology. In order to construct a PINN model with the most accurate simulation effect, the minimum loss function of the PINN model for solving the control equation is used as the model evaluation criterion. Therefore, this embodiment uses the model optimization strategy of random sampling test and the model evaluation criterion of minimizing the model prediction mean square error (MSE) to determine the PINN that best solves the control equation in the constructed PINN model space. Figure 3 The bar graph of the loss function values ​​of the PINN model structure and other structures in the model space determined by the NAS technology optimization. The horizontal axis in the figure is shaped like abcde, which represents the number of neurons in each layer of the network. For example, 4128128161 means that the input layer has 4 nodes, the three hidden layers have 128, 128 and 16 nodes respectively, and the output layer has one node. In this embodiment, 4128128161 is the optimal PINN structure, and the activation function between each layer is the Tanh function. Figure 4 A schematic diagram of the structure is shown. Figure 3 The paper also compares PINNs with some other structures in the model space. Their performance is slightly inferior to the PINN structure determined by NAS technology in terms of loss function optimization or computational cost.

[0061] Furthermore, the loss term of the sulfate ion concentration range restriction added to the loss function in step 3 is the value range loss; therefore, the loss terms of the loss function of the PINN model are physical constraint loss, boundary condition loss, initial value condition loss, data fitting loss and value range loss. The loss function can be written as:

[0062] loss = λ physicsl physics +λ data l data +λ boundary l boundary +λ init l init +λ value l value where λ physics , ..., λ value is the weight of each loss item, l physics is the physical constraint loss, i.e., the control equation loss, l data is the data loss, l boundary is the boundary condition loss, l init is the initial condition loss, l value The loss is the value range. Due to the different magnitudes and importance of different loss terms, appropriate weights can balance the impact of each loss term, so that the model can find the best balance between fitting data and satisfying physical constraints, which can help the PINN model's loss function value to be further reduced and accelerate convergence. In this invention, λ is generally used. physics With λ data The weight of boundary and λ init The weight of is reduced, which helps to maintain the structure of the diffusion reaction equation and make full use of the existing data. In this embodiment, the above idea is adopted to adjust the weights of each loss term in the loss function to generate a new loss function. The weights are as follows:

[0063] λ physics =10,λ data =λ value =1,λ boundary =λ init =0.1.

[0064] Compared with the PINN model trained and optimized for the original loss function, the weighted loss function can make the sum of the loss items of the PINN model smaller and achieve better prediction results. Figure 5 As shown, the sum of the loss terms of the three loss functions in the later stage of training is tested respectively: physics +l data +l boundary +l init +l value , the three loss functions are: original loss function, weighted loss function 1 and weighted loss function 2, and their loss function weight settings are:

[0065] λ physics =1,λ data =λ value =1,λ boundary =λ init =1.

[0066] λ physics =10,λ data =λ value =1,λ boundary =λ init =0.1.

[0067] λ physics =20,λ data =λ value =1,λ boundary =λ init =0.01.

[0068] Figure 5 It shows that the sum of the loss terms achieved by weighted loss function 1 in the later stage of training is significantly better than the original loss function and weighted loss function 2. It can be seen that adjusting the weight hyperparameters of the loss function is of great help to improve the performance of the P1NN model. In this embodiment, the outlier loss term penalizes the abnormal numerical simulation of the internal concentration of concrete greater than C0 and less than 0. Specifically, if the predicted value is less than 0 or greater than C0, the prediction of the deviation range is added to l by 10 times the deviation value. value In the item, this does not violate the physical constraints and prevents simulation anomalies. After determining the loss function, the model is trained for 20,000 rounds in this example. In each round of training, 1,000 points are sampled in the internal spatiotemporal domain, and 100 points are sampled on each boundary spatiotemporal domain, for a total of 600 points. Ten points are randomly selected from the training data set for training the PINN model.

[0069] Further, in step 3, the neural network model generally adjusts the network parameters by the gradient descent method according to the loss function through iterative training to reduce the prediction error. In the PINN model, the iterative training should be terminated when the loss function value is stable or before the loss function value diverges. By actively selecting a PINN model with a specific number of training rounds, it is possible to determine a model with better performance and also a means to prevent the model from overfitting. For the GPR model, if there are too few training samples, the prediction performance of the GPR model will be reduced, and the sulfate ion concentration analysis model can output sufficient training data for GPR model training, which effectively improves the prediction ability of the GPR model; in this embodiment, 4000 spatiotemporal coordinate points are randomly generated inside the cubic concrete block and input into the sulfate ion concentration analysis model. The sulfate ion concentration analysis model outputs the approximate solution of the control equation, namely the sulfate ion concentration, and the erosion time, spatial coordinates and corresponding sulfate ion concentration are combined into 4000 data as the training data of the GPR. Figure 6 The simulation results of the sulfate ion concentration analysis model are presented. Since the approximate solution u(x, y, z, t) is a function of the erosion time and spatial coordinates, Figure 6 The simulation results are shown in two cross-sectional diagrams. Figure 6(a) is a cross-sectional view of the spatial coordinates x and y at a fixed z=0.5m and t=3.5 years. Figure 6 (b) is a cross-sectional diagram with fixed y=z=0.25m regarding the erosion time coordinate t and the spatial coordinate x. The two cross-sectional diagrams show the process of sulfate erosion from the concrete surface to the inside.

[0070] Furthermore, in step 5, the data structure of the GPR model training data includes the erosion time, spatial coordinates and approximate solutions of the control equations output by the sulfate ion concentration analysis model. In particular, each piece of data contains five pieces of information: erosion time coordinate t, spatial coordinates x, y, z, and approximate solution u. The GPR model uses erosion time and spatial coordinates as inputs and the corresponding approximate solutions as outputs for model training. During multiple training sessions, the Bayesian parameter optimization method, a common method for hyperparameter tuning of machine learning models, is used to further improve the GPR performance. Figure 7 The uncertainty probability interval estimation diagram is generated for the trained GPR model on a total of 200 test data on part of the test set data. In fact, in this embodiment, for the concrete sulfate corrosion situation of any spatiotemporal coordinate point that needs to be investigated, it is only necessary to input the corrosion time and coordinate position into the sulfate ion concentration analysis model to obtain a point estimate of the sulfate ion concentration, and to input the corrosion time and coordinate position into the trained GPR model to obtain an interval estimate.

[0071] Furthermore, the simulation and prediction capabilities of the model are evaluated using mean square error (MSE), root mean square error (RMSE) and determination coefficient (R2) on an independent test set to determine whether the model meets expectations or needs further adjustment. In the present invention, the NAS technology in step 2 can optimize the PINN structure to improve model performance, and adjusting the weights of each loss term of the loss function in step 3 can also further optimize the model performance. Therefore, for models that need to be adjusted, you can return to step 2 and follow the methods of steps 2 to 5 again, or return to step 3 and follow the methods of steps 3 to 5 again to build the model to further improve the simulation effect. Figure 8 It is an overview of various evaluation indicators of PINN and GPR on the test set. Combining the indicators, it can be seen that the NAS-PINN-GPR algorithm of the present invention simultaneously obtains high-precision point simulation and reliable interval range estimation, realizes the spatiotemporal process simulation of concrete sulfate attack concentration, and reflects the feasibility and superiority of the present invention.

[0072] The invention provides a spatiotemporal process simulation of concrete sulfate attack concentration based on a NAS-PINN-GPR algorithm, a new method for simulating the spatiotemporal process of concrete sulfate attack concentration, and improves the overall simulation effectiveness of the NAS-PINN-GPR algorithm through NAS technology and loss function weight hyperparameter tuning. The method is a physical information and data dual-driven method, which makes full use of various known information to make simulation predictions on the simulation process, and organically combines the PINN and GPR models to avoid the problem that the GPR model cannot make more accurate predictions when the data volume is insufficient, and adds the uncertainty probability interval estimation function of the GPR model, thereby improving the simulation ability of the invention, thereby realizing effective simulation of the spatiotemporal process of sulfate ion concentration in the concrete sulfate attack process.

Claims

1. A method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm, characterized in that: The method comprises the following steps: Step 1, determining the control equation of the concrete sulfate attack process, collecting the sulfate ion concentrations of the target concrete area at the preset sample coordinate positions under the preset attack durations, and forming a sample set; Step 2, use NAS technology to optimize the PINN network structure and obtain the improved PINN structure; Step 3, according to the control reaction equation of the concrete sulfate attack process, the sample set, the boundary conditions and the initial value conditions, the loss function of the PINN improved structure is set; according to the loss function, based on the sample set, with the erosion time and the sample coordinate position as input, and the corresponding sulfate ion concentration as output, the PINN improved structure is trained to obtain a trained model, that is, a sulfate ion concentration analysis model; Step 4, applying a sulfate ion concentration analysis model according to each preset target erosion time and each target coordinate position in the target concrete area, to obtain the sulfate ion concentration corresponding to each target coordinate position in the target concrete area; wherein the number of target coordinate positions is greater than the number of sample coordinate positions; Step 5, taking each preset target erosion time and the target coordinate position in the target concrete area as input, and taking the sulfate ion concentration at the target coordinate position in the target concrete area corresponding to each target erosion time as output, the GPR model is trained, and the trained GPR model is used to obtain the interval range of the sulfate ion concentration at the target coordinate position in the target concrete area corresponding to the target erosion time.

2. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 1, characterized in that: In step 1, the diffusion-reaction equation of sulfate corrosion on concrete is used as the control equation of the concrete sulfate corrosion process. The diffusion process of sulfate in concrete can be described by Fick's second law: Among them, C = C (x, y, z, t) is the sulfate ion concentration, x, y, z are the spatial coordinates of the target concrete area in the corresponding coordinate system, t is the erosion time, D is the diffusion coefficient, In the process of sulfate attacking concrete, sulfate reacts chemically with the chemical components in concrete to form dissolved products. These reactions cause the sulfate ion concentration to be consumed, which can be described by chemical reaction kinetics: Where η is the sulfate ion concentration consumed by the chemical reaction, and k is the chemical reaction rate constant. Therefore, the diffusion-reaction equation of sulfate corrosion on concrete, that is, the control equation of concrete sulfate corrosion process can be written as: And the boundary conditions and initial conditions Where z contains the coordinates of space and erosion duration, and u is the solution of the control equation. The operator describes the initial value or boundary condition, Ω is the region where the control equation is located, is the region boundary.

3. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 2, characterized in that: In step 2, a feedforward neural network is used to build a PINN in advance, including an input layer, a hidden layer, and an output layer. The PINN model space is constructed by setting hidden layers with different numbers of nodes in the neural network and activation functions between different layers. NAS technology is used to optimize the number of hidden layers, the number of nodes, and the activation function with a random sampling test model optimization strategy and a model evaluation criterion with the minimum mean square error of model prediction to obtain an improved PINN structure.

4. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 3, characterized in that: The improved PINN structure includes an input layer, three hidden layers and an output layer. The number of nodes in the input layer is 4, the number of nodes in the three hidden layers is 128, 128 and 16 respectively, and the number of nodes in the output layer is 1; the 4 nodes in the input layer are respectively connected to the nodes in the first hidden layer, the nodes in the first hidden layer are respectively connected to the nodes in the second hidden layer, the nodes in the second hidden layer are respectively connected to the nodes in the third hidden layer, and the nodes in the third hidden layer are all connected to 1 node in the output layer.

5. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 4, characterized in that: In step 3, the loss function also adds a loss term for the sulfate ion concentration range limit, which is the value range loss; therefore, the loss terms of the PINN loss function in step 3 are physical constraint loss, boundary condition loss, initial value condition loss, data fitting loss and value range loss. The loss function can be written as: loss=λ physics l physics +λ data l data +λ boundary l boundary +λ init l init +λ value l value where λ physics ,…,λ value is the weight of each loss item, l physics is the physical constraint loss, l data is data loss, l boundary is the boundary condition loss, l init is the initial value condition loss, l value is the value range loss; during the training process, the weights of each loss item are adjusted, and λ physics With λ data The weight of boundary and λ init The weight of is reduced.

6. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 5, characterized in that: In step 3, the PINN parameters are adjusted by the gradient descent method through iterative training according to the loss function to reduce the prediction error. The iterative training is terminated when the loss function value is stable or before the loss function value diverges to obtain the trained model.

7. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 6, characterized in that: Use evaluation indicators on an independent test set to evaluate the simulation and prediction capabilities of the model to determine whether the model meets expectations; if the simulation results do not meet expectations, return to step 2 and re-use NAS technology to optimize PINN or return to step 3 to redesign the weights of the loss function to improve model performance, and then simulate according to subsequent steps to improve the simulation effect; if expectations have been met, the construction of the model of the present invention is completed.

8. The method for simulating the spatiotemporal process of concrete sulfate attack concentration based on the NAS-PINN-GPR algorithm according to claim 7, characterized in that: The evaluation indicators used on the independent test set are mean square error (MSE), root mean square error (RMSE) and determination coefficient (R2).

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