Method for predicting diffusion of chloride ions in concrete under freeze-thaw action based on pinn
By using the PINN-based method, combining freeze-thaw depth and equivalent freeze-thaw cycle number, a chloride ion diffusion prediction model was constructed and Fick's second law was introduced. This solved the problem of non-uniform chloride ion diffusion under freeze-thaw cycles, and improved the prediction accuracy and generalization ability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI'AN UNIVERSITY OF ARCHITECTURE AND TECHNOLOGY
- Filing Date
- 2026-03-04
- Publication Date
- 2026-06-19
AI Technical Summary
Existing models fail to adequately account for the uneven effect of freeze-thaw cycles on chloride ion diffusion in concrete, and the physical mechanisms are unclear, resulting in inaccurate predictions and insufficient generalization ability.
A chloride ion diffusion prediction model was constructed using a PINN-based approach, combining freeze-thaw depth and equivalent freeze-thaw cycle number. Fick's second law was introduced as a physical constraint, and the model parameters were trained using a deep neural network to comprehensively consider the influence of multiple factors.
It improves the accuracy of chloride ion diffusion prediction and the model's generalization ability in new scenarios, and can more realistically simulate the uneven diffusion behavior of chloride ions under freeze-thaw action.
Smart Images
Figure CN122245492A_ABST
Abstract
Description
Technical Field
[0001] This application relates to a method for predicting chloride ion diffusion in concrete, and more particularly to a method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN. Background Technology
[0002] Chloride ion attack and freeze-thaw cycles are the main factors causing steel corrosion in concrete, severely affecting the durability of reinforced concrete structures. In practical engineering, these two factors often work together and exacerbate each other. Chloride ion attack reduces the freeze-thaw resistance of concrete, while freeze-thaw cycles promote the propagation of microcracks within the concrete, thereby accelerating chloride ion intrusion. This coupled effect accelerates the damage to concrete structures and shortens their service life. Therefore, studying the diffusion behavior of chloride ions under freeze-thaw cycles is of great significance for accurately assessing the service life of concrete structures.
[0003] Traditional methods are primarily based on Fick's law, modified according to experimental parameters such as water-cement ratio, concrete strength, and environmental conditions, to quantify the distribution of chloride ions in concrete. While these methods provide a useful reference for understanding the chloride ion diffusion coefficient, they still have certain limitations. Most studies tend to focus on the influence of a single factor on the chloride ion diffusion coefficient, failing to fully consider the complex synergistic effects between multiple factors. Furthermore, traditional Fick's law models typically treat the chloride ion diffusion coefficient as a constant, while in reality, freeze-thaw damage causes significant inhomogeneities in the internal structure of concrete (such as microcrack distribution and porosity changes), resulting in a spatially non-uniform distribution of the diffusion coefficient.
[0004] In recent years, machine learning-based chloride ion diffusion prediction models have gradually become a research hotspot, demonstrating significant advantages in handling nonlinear problems. These models accurately simulate the complex nonlinear relationships between input and output variables by utilizing multilayer structures and nonlinear activation functions. For example, a neural network model is used to predict the time-varying law of chloride ion transport coefficients. This model simultaneously considers various environmental and material factors, aiming to more accurately predict chloride ion diffusion in different concrete structures. However, existing research mainly focuses on chloride ion diffusion in undamaged concrete, with relatively little discussion on concrete subjected to freeze-thaw damage. Furthermore, current machine learning-based methods are mostly data-driven models, with prediction results highly dependent on the quality and coverage of training data. The models themselves often fail to consider the physical mechanisms behind chloride ion diffusion, which to some extent limits the accuracy of prediction results and the model's generalization ability. Summary of the Invention
[0005] The present invention aims to at least partially solve one of the technical problems in the related art.
[0006] Therefore, the first objective of this invention is to propose a method for predicting chloride ion diffusion in concrete under freeze-thaw cycles based on PINN, in order to solve the problems of unclear physical mechanisms in existing models and the failure to consider the uneven distribution of chloride ions caused by freeze-thaw cycles.
[0007] The second objective of this invention is to provide a device for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN.
[0008] The third objective of this invention is to provide a computer device.
[0009] A fourth objective of this invention is to provide a non-transitory computer-readable storage medium.
[0010] To achieve the above objectives, a first aspect of the present invention proposes a method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, comprising: S1: Collect measured data samples from concrete freeze-thaw experiments and screen the set of characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient. The set of characteristic parameters includes the number of freeze-thaw cycles. S2: Convert the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; S3: Preprocess the measured data samples and divide them into training set and test set; S4: Based on the positive proportional relationship between the chloride ion diffusion coefficient in concrete and the freeze-thaw depth and the equivalent number of freeze-thaw cycles, a formula for the chloride ion diffusion coefficient considering uneven freeze-thaw damage is established. S5: Based on the chloride ion diffusion coefficient relationship, a chloride ion diffusion prediction model based on PINN is constructed. The model is based on a deep neural network, with the input being the feature parameters of the training set, and the output including the predicted chloride ion concentration and the chloride ion diffusion coefficient. During the training process, Fick's second law is introduced as a physical constraint, and the total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. S6: Input the test set into the trained prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
[0011] In one embodiment of the present invention, S1 includes: Feature parameters are selected based on the Pearson correlation coefficient, and redundant parameters with high correlation are removed to construct a reasonable feature dataset. The calculation formula is as follows:
[0012] in, The correlation coefficient between the two parameters. and There are two random parameters. and It is the average of the two parameters.
[0013] In one embodiment of the present invention, S2 includes: The formula for calculating the equivalent number of freeze-thaw cycles is:
[0014] in, It is the equivalent number of freeze-thaw cycles. This refers to the actual number of freeze-thaw cycles in the experiment. This is a correction factor, which takes different values depending on the freeze-thaw environment; when the specimen is completely submerged in water for freeze-thaw cycles... Take 1; when the specimen is placed in air for freeze-thaw cycles, Take 0.7; the specimen was only partially immersed in water, and the degree of freeze-thaw damage was between that of full immersion and air freeze-thaw. Take 0.6; the specimen is subjected to freeze-thaw cycles in a high-humidity water vapor environment. Take 0.4.
[0015] In one embodiment of the present invention, S3 includes: Preprocessing included mean imputation of missing values, standardization of feature parameters, and random partitioning of the data into 80% training set and 20% test set.
[0016] In one embodiment of the present invention, S4 includes: The chloride ion diffusion coefficient is expressed as a function of freeze-thaw depth and equivalent number of freeze-thaw cycles, with the following relationship:
[0017] in, It takes freeze-thaw depth into account and equivalent freeze-thaw cycles The chloride ion diffusion coefficient after that, This represents the initial chloride ion diffusion coefficient without considering freeze-thaw damage. , , These are parameters to be determined. and These represent the influence of freeze-thaw depth and equivalent freeze-thaw cycle number on the diffusion coefficient, respectively. This represents the baseline value that affects the diffusion coefficient, and is used to accurately describe the deviation of the diffusion coefficient caused by other factors in reality.
[0018] In one embodiment of the present invention, S5 includes: The differential equation for Fick's second law is as follows:
[0019] in, It is the chloride ion concentration. It is the chloride ion diffusion coefficient. This represents the rate of change of concentration over time. The second spatial derivative represents the concentration.
[0020] In one embodiment of the present invention, S5 includes: The total loss function used in the PINN model includes a data error term and a physical information error term, and the calculation model is as follows: Data loss items are
[0021] in, Due to data error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples; The physical information error term is:
[0022] in, For physical information error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples, The predicted chloride ion diffusion coefficient; The total loss function is:
[0023] in, The total loss error, and These are the weights for controlling data error and physical information error, respectively, which are optimized through cross-validation.
[0024] To achieve the above objectives, a second aspect of the present invention provides a device for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, comprising: Data acquisition and screening module: Collects measured data samples from concrete freeze-thaw experiments and screens the characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient; Equivalent conversion module: Converts the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; Preprocessing and partitioning module: preprocesses the measured data samples and partitions them into training and testing sets; Diffusion model construction module: Based on the proportional relationship between chloride ion diffusion coefficient in concrete and freeze-thaw depth and equivalent freeze-thaw cycle number, establish a chloride ion diffusion coefficient relationship considering uneven freeze-thaw damage; Model building and training module: Based on the chloride ion diffusion coefficient relationship, a chloride ion diffusion prediction model based on PINN is constructed. The model uses a deep neural network as its core, with the input being the feature parameters of the training set, and the output including the predicted chloride ion concentration and the chloride ion diffusion coefficient. During the training process, Fick's second law is introduced as a physical constraint, and the total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. Test and evaluation module: Input the test set into the prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
[0025] Compared with the prior art, the present invention has the following significant features: 1. Unlike traditional models that only consider the influence of a single factor on the chloride ion diffusion coefficient, this model comprehensively considers the influence of multiple factors, including the internal structural characteristics of concrete (such as porosity and water-cement ratio) and external environmental characteristics (freeze-thaw cycles and freeze-thaw temperatures).
[0026] 2. Considering the uneven freeze-thaw damage of concrete under freeze-thaw action, the distribution law of chloride ion diffusion coefficient with depth and equivalent freeze-thaw cycles was constructed, and this distribution law was substituted into the PINN-based network model to more realistically reflect the uneven diffusion behavior of chloride ions under freeze-thaw action.
[0027] 3. This model incorporates Fick's second law as a physical constraint into the loss function, ensuring that its predictions conform to the actual chloride ion diffusion patterns. Thanks to this introduced physical constraint, the model exhibits stronger generalization ability when facing new scenarios beyond the training data distribution, thereby improving the accuracy and reliability of its predictions.
[0028] To achieve the above objectives, a third aspect of this application provides a computer device comprising a processor and a memory; wherein the processor reads executable program code stored in the memory to run a program corresponding to the executable program code, for implementing a method for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN as described in the first aspect embodiment.
[0029] To achieve the above objectives, a fourth aspect of this application provides a non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements a method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, as described in the first aspect embodiment.
[0030] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of a method for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN, according to an embodiment of the present invention. Figure 2 This is an architecture diagram of a method for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the PINN model architecture according to an embodiment of the present invention; Figure 4 This is a structural diagram of a device for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN, according to an embodiment of the present invention. Figure 5 It is a computer device according to an embodiment of the present invention. Detailed Implementation
[0032] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0033] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0034] The following describes, with reference to the accompanying drawings, a method and apparatus for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN, according to an embodiment of the present invention.
[0035] Figure 1 This is a flowchart of a task-general visual model construction method based on self-supervised representation according to an embodiment of the present invention, such as... Figure 1 As shown, it includes: S1: Collect measured data samples from concrete freeze-thaw experiments and screen the set of characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient. The set of characteristic parameters includes the number of freeze-thaw cycles. S2: Convert the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; S3: Preprocess the measured data samples and divide them into training set and test set; S4: Based on the positive proportional relationship between the chloride ion diffusion coefficient in concrete and the freeze-thaw depth and the equivalent number of freeze-thaw cycles, a formula for the chloride ion diffusion coefficient considering uneven freeze-thaw damage is established. S5: Based on the chloride ion diffusion coefficient relationship, a chloride ion diffusion prediction model based on PINN is constructed. The model is based on a deep neural network, with the input being the feature parameters of the training set, and the output including the predicted chloride ion concentration and the chloride ion diffusion coefficient. During the training process, Fick's second law is introduced as a physical constraint, and the total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. S6: Input the test set into the trained prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
[0036] In one embodiment of the present invention, a method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN is provided, such as... Figure 2 As shown, it includes the following steps: Step 1: Collect sample data based on published research literature. Perform correlation analysis on the initially screened characteristic parameters that have a significant impact on chloride ion diffusion, and remove redundant parameters with high correlation to construct a reasonable dataset.
[0037] Step 2: Using a theoretical model, the number of freeze-thaw cycles collected under different experimental conditions is unified into an equivalent number of freeze-thaw cycles.
[0038] Step 3: Preprocess the original sample data. First, impute missing values in the data to ensure data integrity; then, normalize the feature parameters to eliminate scale differences; finally, divide the processed data into a training set for model training and a test set for model evaluation.
[0039] Step 4: Based on the proportional relationship between the chloride ion diffusion coefficient in concrete, the freeze-thaw depth, and the equivalent number of freeze-thaw cycles, consider the impact of uneven freeze-thaw damage on the chloride ion diffusion coefficient. The chloride ion diffusion coefficient is expressed as a function of the freeze-thaw depth and the equivalent number of freeze-thaw cycles, with the following formula:
[0040] in, It takes freeze-thaw depth into account ( ) and equivalent freeze-thaw cycles ( The chloride ion diffusion coefficient after ( ) This represents the initial chloride ion diffusion coefficient without considering freeze-thaw damage. , , These are parameters to be determined. and These represent the influence of freeze-thaw depth and equivalent freeze-thaw cycle number on the diffusion coefficient, respectively. It is a benchmark value that affects the diffusion coefficient, and can more accurately describe the deviation of the diffusion coefficient that may be caused by experimental conditions, material properties or other factors in reality.
[0041] Step 5: Construct a PINN-based model for predicting chloride ion diffusion behavior under freeze-thaw cycles. This model uses a deep neural network as its core architecture, such as... Figure 3 As shown, the specific training process is as follows: First, the feature parameters of the training set obtained in step 3 are used as the network input. The output includes two parts: one is the predicted value of chloride ion concentration in concrete, and the other is the undetermined parameter in the function defined in step 4. , , Furthermore, the chloride ion diffusion coefficient at different freeze-thaw depths is quantified based on this functional relationship. During training, to ensure consistency between the model and physical laws, the differential equation corresponding to Fick's second law is introduced as a physical constraint. Model training is performed using the backpropagation algorithm, with iterative optimization to minimize the overall loss function. The overall loss function consists of two terms: a data error term, measuring the difference between the model output and the actual measured value; and a physical information error term, used to measure whether the model output satisfies Fick's second law.
[0042] Fick's second law is expressed as follows:
[0043] in, It is the chloride ion concentration. It is the chloride ion diffusion coefficient. This represents the rate of change of concentration over time. The second spatial derivative represents the concentration.
[0044] Step 6: Input the test set constructed in Step 3 into the PINN prediction model trained in Step 5, and output the predicted value of the chloride ion diffusion coefficient. The accuracy of the proposed method is evaluated by comparing it with the experimental value.
[0045] In this embodiment, step 1 involves constructing a dataset containing 624 sets of data based on published research literature. Each set records different key parameters and their corresponding chloride ion diffusion coefficients. The initial selection of parameters in the dataset includes two main categories: concrete intrinsic property parameters and environmental effect parameters, totaling 18 parameters: concrete strength, porosity, water-cement ratio, water-binder ratio, water usage, cement usage, fly ash content, silica fume content, fine aggregate content, coarse aggregate content, slag content, number of freeze-thaw cycles, highest and lowest temperatures experienced by the concrete during freeze-thaw cycles, initial chloride ion concentration, initial chloride ion diffusion coefficient, diffusion time, and diffusion depth. It is important to note that if there is a high correlation between parameters during dataset construction, it may lead to model estimation distortion, making it difficult to accurately assess the impact of each parameter on chloride ion diffusion. To avoid this problem, the Pearson correlation coefficient is used for testing; when the correlation coefficient between any two parameters is greater than 0.7, the most representative parameter is selected and retained based on the actual needs of the research objective. After the above screening process, the final dataset contains 12 key parameters, namely: concrete strength, porosity, water-cement ratio, fly ash content, silica fume content, number of freeze-thaw cycles, maximum and minimum temperatures of concrete during freeze-thaw cycles, initial chloride ion concentration, initial chloride ion diffusion coefficient, diffusion time, and diffusion depth.
[0046] The formula for calculating the Pearson correlation coefficient is as follows:
[0047] in, The correlation coefficient between the two parameters. and There are two random parameters. and It is the average of the two parameters.
[0048] Furthermore, in step 2, based on the relative dynamic elastic modulus of concrete, the number of freeze-thaw cycles collected in step 1 from different freeze-thaw environmental conditions is uniformly converted into the equivalent number of freeze-thaw cycles under standard test conditions, thereby achieving a unified quantification and cross-environmental comparison of the degree of freeze-thaw damage to concrete. The formula for calculating the equivalent number of freeze-thaw cycles is as follows:
[0049] in, It is the equivalent number of freeze-thaw cycles. This refers to the actual number of freeze-thaw cycles in the experiment. This is a correction factor, with different values depending on the freeze-thaw environment, to compensate for damage differences caused by factors such as freezing method, humidity, and degree of specimen immersion. When the specimen is fully submerged in water for freeze-thaw cycles... Take 1; when the specimen is placed in air for freeze-thaw cycles, Take 0.7; the specimen was only partially immersed in water, and the degree of freeze-thaw damage was between that of full immersion and air freeze-thaw. Take 0.6; the specimen is subjected to freeze-thaw cycles in a high-humidity water vapor environment. Take 0.4.
[0050] Further, step 3 involves data preprocessing, specifically as follows: First, for missing values in the original data, mean imputation is used to fill in the corresponding data columns. This method is simple to operate, computationally efficient, and does not introduce significant computational complexity. Then, Z-score normalization is applied to scale the feature parameters to eliminate the influence of differences in scale between different features, ensuring that each feature has a balanced contribution during model training, thereby avoiding features with larger scales dominating model training. Finally, the cleaned data is randomly sampled, dividing the total sample into a training set and a test set, with the training set accounting for 80% of the total sample and the test set accounting for 20%, to evaluate the model's generalization performance on unseen data.
[0051] The formula for Z-score standardization is:
[0052] in, These are the standardized feature parameter values. These are the original values of the feature parameters. and These are the mean and standard deviation of the corresponding feature parameters, respectively.
[0053] Furthermore, in step 4, based on the proportional relationship between the chloride ion diffusion coefficient in concrete, the freeze-thaw depth, and the equivalent number of freeze-thaw cycles, the influence of uneven freeze-thaw damage on the chloride ion diffusion coefficient is considered. The chloride ion diffusion coefficient is expressed as a function of the freeze-thaw depth and the equivalent number of freeze-thaw cycles, with the following relationship:
[0054] in, It takes freeze-thaw depth into account ( ) and equivalent freeze-thaw cycles ( The chloride ion diffusion coefficient after ( ) This represents the initial diffusion coefficient without considering freeze-thaw damage. , , These are parameters to be determined. and These represent the influence of freeze-thaw depth and equivalent freeze-thaw cycle number on the diffusion coefficient, respectively. It is a benchmark value that affects the diffusion coefficient, and can more accurately describe the deviation of the diffusion coefficient that may be caused by experimental conditions, material properties or other factors in reality.
[0055] Furthermore, in step 5, based on the training set constructed in step 3, a deep neural network model architecture is used to train the chloride ion diffusion prediction model, such as... Figure 2 As shown. The input layer of this model consists of the 12 feature parameters finally determined in step 1. The hidden layer consists of 7 fully connected layers, each containing 50 neurons, and uses the Tanh activation function to introduce non-linearity, enabling the model to learn complex features. Its output layer includes the predicted chloride ion concentration and the undetermined parameters involved in the relationship in step 4. , , The chloride ion diffusion coefficient was further calculated based on this relationship. To ensure consistency between the model and physical laws, the differential equation corresponding to Fick's second law was introduced as a physical constraint into the loss function, thereby ensuring that the model's predictions conform to the actual diffusion process. Training employed a backpropagation algorithm, iteratively adjusting network weights to minimize the overall loss function. This loss function consists of two parts: first, the error between the model's predicted chloride ion concentration and the actual measured concentration, i.e., the data error term; second, the physical information error term obtained by substituting the model's output chloride ion concentration and diffusion coefficient into Fick's second law, used to measure whether the model's output satisfies Fick's second law.
[0056] The data error term measures the difference between the network's predicted output and the actual observed data, with the aim of enabling the network to fit the data as closely as possible. This part of the loss function is set as follows:
[0057] in, Due to data error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples.
[0058] Fick's second law is expressed as follows:
[0059] in, It is the chloride ion concentration. It is the chloride ion diffusion coefficient. This represents the rate of change of concentration over time. The second spatial derivative represents the concentration.
[0060] The physical information error term is used to measure whether the model's predictions satisfy Fick's second law. The root mean square error calculated by substituting the predicted chloride ion concentration and diffusion coefficient into the differential equation of Fick's second law constitutes this part of the loss function.
[0061] in, For physical information error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples, This represents the predicted chloride ion diffusion coefficient.
[0062] The final total loss function is:
[0063] in, The total loss error, and These are the weights for controlling data error and physical information error, respectively. Cross-validation was used to... 1 and 2. Optimization is carried out to achieve the best balance between data fitting accuracy and consistency with physical laws.
[0064] Further, in step 6, the accuracy of the trained prediction model is evaluated based on the test set constructed in step 3. This is achieved by calculating various regression evaluation metrics, including mean squared error (MSE), root mean square error (RMSE), and coefficient of determination (R²), to quantitatively analyze the model's performance. This evaluation process helps identify whether the model exhibits overfitting or underfitting. The results show that the proposed method demonstrates high prediction accuracy.
[0065] To achieve the above embodiments, such as Figure 4 As shown, this embodiment also provides a prediction device 10 for chloride ion diffusion in concrete under freeze-thaw action based on PINN. The device 10 includes a data acquisition and screening module 101, an equivalent conversion module 102, a preprocessing and partitioning module 103, a diffusion model construction module 104, a model construction and training module 105, and a testing and evaluation module 106.
[0066] Data acquisition and screening module 101: collects measured data samples from concrete freeze-thaw experiments and screens the set of characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient, the set of characteristic parameters including the number of freeze-thaw cycles; Equivalent conversion module 102: Converts the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; Preprocessing and partitioning module 103: preprocesses the measured data samples and partitions them into training set and test set; Diffusion Model Construction Module 104: Based on the proportional relationship between the chloride ion diffusion coefficient in concrete and the freeze-thaw depth and equivalent freeze-thaw cycle number, establish a chloride ion diffusion coefficient relationship considering uneven freeze-thaw damage; Model building and training module 105: Based on the chloride ion diffusion coefficient relationship, a chloride ion diffusion prediction model based on PINN is constructed. The model is based on a deep neural network, with the input being the feature parameters of the training set, and the output including the predicted chloride ion concentration and the chloride ion diffusion coefficient. During the training process, Fick's second law is introduced as a physical constraint, and the total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. Test and evaluation module 106: Input the test set into the prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
[0067] Furthermore, the aforementioned data acquisition and filtering module 101 is also used for: Feature parameters are selected based on the Pearson correlation coefficient, and redundant parameters with high correlation are removed to construct a reasonable feature dataset. The calculation formula is as follows:
[0068] in, The correlation coefficient between the two parameters. and There are two random parameters. and It is the average of the two parameters.
[0069] Furthermore, the aforementioned equivalent conversion module 102 is also used for: The formula for calculating the equivalent number of freeze-thaw cycles is:
[0070] in, It is the equivalent number of freeze-thaw cycles. This refers to the actual number of freeze-thaw cycles in the experiment. This is a correction factor, which takes different values depending on the freeze-thaw environment; when the specimen is completely submerged in water for freeze-thaw cycles... Take 1; when the specimen is placed in air for freeze-thaw cycles, Take 0.7; the specimen was only partially immersed in water, and the degree of freeze-thaw damage was between that of full immersion and air freeze-thaw. Take 0.6; the specimen is subjected to freeze-thaw cycles in a high-humidity water vapor environment. Take 0.4.
[0071] Furthermore, the aforementioned preprocessing and partitioning module 103 is also used for: Preprocessing included mean imputation of missing values, standardization of feature parameters, and random partitioning of the data into 80% training set and 20% test set.
[0072] Furthermore, the diffusion model construction module 104 described above is also used for: The chloride ion diffusion coefficient is expressed as a function of freeze-thaw depth and equivalent number of freeze-thaw cycles, with the following relationship:
[0073] in, It takes freeze-thaw depth into account and equivalent freeze-thaw cycles The chloride ion diffusion coefficient after that, This represents the initial chloride ion diffusion coefficient without considering freeze-thaw damage. , , These are parameters to be determined. and These represent the influence of freeze-thaw depth and equivalent freeze-thaw cycle number on the diffusion coefficient, respectively. This represents the baseline value that affects the diffusion coefficient, and is used to accurately describe the deviation of the diffusion coefficient caused by other factors in reality.
[0074] Furthermore, the aforementioned model building and training module 105 is also used for: The differential equation for Fick's second law is as follows:
[0075] in, It is the chloride ion concentration. It is the chloride ion diffusion coefficient. This represents the rate of change of concentration over time. The second spatial derivative represents the concentration.
[0076] Furthermore, the aforementioned model building and training module 105 is also used for: The total loss function used in the PINN model includes a data error term and a physical information error term, and the calculation model is as follows: Data loss items are
[0077] in, Due to data error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples; The physical information error term is:
[0078] in, For physical information error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples, The predicted chloride ion diffusion coefficient; The total loss function is:
[0079] in, The total loss error, and These are the weights for controlling data error and physical information error, respectively, which are optimized through cross-validation.
[0080] This invention discloses a PINN-based device for predicting chloride ion diffusion in concrete under freeze-thaw conditions. By introducing multiple factors and physical constraints, this invention more realistically simulates the uneven diffusion behavior of chloride ions under freeze-thaw conditions, thereby improving the accuracy of prediction results and the generalization ability of the model.
[0081] To implement the methods of the above embodiments, the present invention also provides a computer device, such as... Figure 5 As shown, the computer device 600 includes a memory 601 and a processor 602; wherein, the processor 602 reads executable program code stored in the memory 601 to run a program corresponding to the executable program code, so as to implement the various steps of the method described above.
[0082] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method described in the foregoing embodiments.
[0083] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0084] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.
Claims
1. A method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, characterized in that, include: S1: Collect measured data samples from concrete freeze-thaw experiments and screen the set of characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient. The set of characteristic parameters includes the number of freeze-thaw cycles. S2: Convert the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; S3: Preprocess the measured data samples and divide them into training set and test set; S4: Based on the positive proportional relationship between the chloride ion diffusion coefficient in concrete and the freeze-thaw depth and the equivalent number of freeze-thaw cycles, a formula for the chloride ion diffusion coefficient considering uneven freeze-thaw damage is established. S5: Based on the chloride ion diffusion coefficient relationship, construct a chloride ion diffusion prediction model based on PINN. The model uses a deep neural network as its core, takes training set feature parameters as input, and outputs predicted chloride ion concentration and chloride ion diffusion coefficient. Fick's second law is introduced as a physical constraint during training. The total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. S6: Input the test set into the trained prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
2. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, S1 includes: Feature parameters are selected based on the Pearson correlation coefficient, and redundant parameters with high correlation are removed to construct a reasonable feature dataset. The calculation formula is as follows: in, The correlation coefficient between the two parameters. and There are two random parameters. and It is the average of the two parameters.
3. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, S2 includes: The formula for calculating the equivalent number of freeze-thaw cycles is: in, It is the equivalent number of freeze-thaw cycles. This refers to the actual number of freeze-thaw cycles in the experiment. This is a correction factor, which takes different values depending on the freeze-thaw environment; when the specimen is completely submerged in water for freeze-thaw cycles... Take 1; when the specimen is placed in air for freeze-thaw cycles, Take 0.7; the specimen was only partially immersed in water, and the degree of freeze-thaw damage was between that of full immersion and air freeze-thaw. Take 0.6; the specimen is subjected to freeze-thaw cycles in a high-humidity water vapor environment. Take 0.
4.
4. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, The S3 includes: Preprocessing included mean imputation of missing values, standardization of feature parameters, and random partitioning of the data into 80% training set and 20% test set.
5. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, The S4 includes: The chloride ion diffusion coefficient is expressed as a function of freeze-thaw depth and equivalent number of freeze-thaw cycles, with the following relationship: in, It takes freeze-thaw depth into account and equivalent freeze-thaw cycles The chloride ion diffusion coefficient after that, This represents the initial chloride ion diffusion coefficient without considering freeze-thaw damage. , , These are parameters to be determined. and These represent the influence of freeze-thaw depth and equivalent freeze-thaw cycle number on the diffusion coefficient, respectively. This represents the baseline value that affects the diffusion coefficient, and is used to accurately describe the deviation of the diffusion coefficient caused by other factors in reality.
6. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, The S5 includes: The differential equation for Fick's second law is as follows: in, It is the chloride ion concentration. It is the chloride ion diffusion coefficient. This represents the rate of change of concentration over time. The second spatial derivative represents the concentration.
7. The method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN according to claim 1, characterized in that, The S5 includes: The total loss function used in the PINN model includes a data error term and a physical information error term, and the calculation model is as follows: Data loss items are in, Due to data error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples; Physical information error term is in, For physical information error, For the predicted chloride ion concentration, This represents the actual chloride ion concentration. The total number of samples, The predicted chloride ion diffusion coefficient; The total loss function is: in, The total loss error, and These are the weights for controlling data error and physical information error, respectively, which are optimized through cross-validation.
8. A device for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, characterized in that, include: Data acquisition and screening module: Collects measured data samples from concrete freeze-thaw experiments and screens the set of characteristic parameters that have the most significant impact on the chloride ion diffusion coefficient. The set of characteristic parameters includes the number of freeze-thaw cycles. Equivalent conversion module: Converts the number of freeze-thaw cycles under different freeze-thaw test conditions into the equivalent number of freeze-thaw cycles under standard test conditions; Preprocessing and partitioning module: preprocesses the measured data samples and partitions them into training and testing sets; Diffusion model construction module: Based on the proportional relationship between chloride ion diffusion coefficient in concrete and freeze-thaw depth and equivalent freeze-thaw cycle number, establish a chloride ion diffusion coefficient relationship considering uneven freeze-thaw damage; Model building and training module: Based on the chloride ion diffusion coefficient relationship, a chloride ion diffusion prediction model based on PINN is constructed. The model uses a deep neural network as its core, takes training set feature parameters as input, and outputs predicted chloride ion concentration and chloride ion diffusion coefficient. Fick's second law is introduced as a physical constraint during training. The total loss function consists of a data error term and a physical information error term. The model parameters are optimized through the backpropagation algorithm. Test and evaluation module: Input the test set into the prediction model to obtain the predicted value of the chloride ion diffusion coefficient, and compare it with the experimental value to evaluate the accuracy of the model.
9. A computer device, characterized in that, Including processor and memory; The processor reads the executable program code stored in the memory to run a program corresponding to the executable program code, so as to implement the method for predicting chloride ion diffusion in concrete under freeze-thaw action based on PINN as described in any one of claims 1-7.
10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a method for predicting chloride ion diffusion in concrete under freeze-thaw conditions based on PINN, as described in any one of claims 1-7.