Concrete durability prediction method based on Bayesian neural network

Abstract

The invention discloses a Bayesian neural network-based concrete durability prediction method, which is characterized in that durability prediction is carried out by designing a multilayer Bayesian neural network model and combining data such as a concrete mix proportion, external environment conditions and material attributes. The Bayesian neural network updates the weight and bias through random sampling, and can quantify the uncertainty of prediction and provide a prediction confidence interval. The method comprises the specific steps of data preprocessing, network training, sampling, calculating and outputting a mean value and a standard deviation, optimizing model parameters through a gradient descent method, and finally evaluating model prediction performance. According to the method, the uncertainty in concrete durability prediction can be effectively quantified, more scientific and accurate decision support is provided for building engineers, and the cost and time of experimental testing are reduced.

Description

Technical Field

[0001] The invention specifically relates to performance prediction and design of engineering materials, in particular to a concrete durability prediction method based on Bayesian neural network. Background Art

[0002] As a basic material widely used in modern construction projects, the durability of concrete is directly related to the service life and safety of buildings. The durability of concrete is affected by many factors, such as mix ratio, external environment, temperature and humidity, salt concentration, etc. Traditional concrete durability prediction methods mostly rely on laboratory tests and empirical formulas, but these methods are not only time-consuming and labor-intensive, but also difficult to consider complex external environmental factors, and cannot accurately quantify the uncertainty in the prediction.

[0003] With the rapid development of machine learning and artificial intelligence technology, Bayesian neural network (BNN) has become an effective prediction tool because it can handle data uncertainty and capture complex nonlinear relationships. Bayesian neural network can flexibly adapt to different data distributions by sampling and updating model weights and biases, providing more accurate and reliable prediction results. In addition, Bayesian neural network can quantify the confidence of prediction results, providing engineers with more intuitive decision support.

[0004] However, the application of Bayesian neural networks also faces some challenges. First, the calculation process of Bayesian neural networks is relatively complicated, especially when processing large-scale data, which requires large computing resources. Secondly, the high-quality data required for concrete durability prediction is relatively scarce, and the data under different environmental conditions are unevenly distributed, which may affect the training effect of the model. Therefore, how to efficiently process and utilize existing data and explore the potential relationships between data has become the key to research in this field. Summary of the invention

[0005] Purpose of the invention: In view of the above technical problems, the present invention proposes a method for predicting the durability of concrete by introducing a Bayesian neural network, combining the material composition, environmental factors and historical data of concrete, designing a reasonable network structure, optimizing the training process of the Bayesian neural network, and solving the shortcomings of traditional prediction methods. This method can effectively quantify the uncertainty in the prediction of concrete durability, and provide more scientific and accurate decision support for construction engineers, reducing the cost and time of experimental testing.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0007] A concrete durability prediction method based on Bayesian neural network includes the following steps:

[0008] Step 1: Obtain the original experimental data of the concrete and perform data preprocessing;

[0009] Step 2: Use the preprocessed data to determine the input features of the Bayesian neural network, construct a Bayesian neural network model with multiple hidden layers, model the weights and biases of the Bayesian neural network model using a normal distribution, and perform initialization to provide a prior distribution for subsequent training;

[0010] Step 3: Utilize the training set part in the original data to optimize the Bayesian neural network model, estimate the posterior distribution of the weights and biases through variational inference, minimize the error using a loss function, and optimize the parameters in combination with gradient descent, enabling the Bayesian neural network model obtained in Step 2 to learn the relationship between concrete durability and input features;

[0011] Step 4: Use the trained Bayesian neural network model to predict the test set, calculate the mean of the output as the final prediction value, and estimate the uncertainty through the standard deviation of the posterior distribution to quantify the reliability of the prediction result;

[0012] Step 5: Calculate the evaluation metrics of the Bayesian neural network model, including calculating the mean squared error MSE, root mean squared error RMSE, and coefficient of determination R 2 index, and optimize the model parameters. If the following three conditions are simultaneously met, it is determined that the fitting effect is qualified.

[0013] Condition 1: The value of the root mean squared error RMSE is between 0 and 1:

[0014] Condition 2: The value of the root mean squared error RMSE is between 0 and 1;

[0015] Condition 3: The coefficient of determination R 2 The value is between 0.89 and 0.91:

[0016] If the above three conditions cannot be simultaneously met, adjust the model parameters to improve the accuracy and reliability of concrete durability prediction; the model parameters include the learning rate, the number of hidden layers, and the regularization term;

[0017] Step 6: Perform a complete concrete durability prediction based on the optimized final Bayesian neural network model and provide a confidence interval.

[0018] Technical effect: By introducing a Bayesian neural network to predict the durability of concrete, combining the material composition of concrete, environmental factors, and historical data, the present invention can not only provide an accurate prediction of concrete durability but also provide information on the uncertainty of the prediction results for engineers, thus guiding the selection of concrete formulations and the design of construction plans more scientifically and reliably in practical engineering applications. Additionally, in the prediction of concrete durability, the evaluation and optimization of the model are crucial steps to ensure the prediction accuracy and generalization ability. The present invention evaluates the model performance through the mean square error, root mean square error, and coefficient of determination, and decides whether to further adjust the model and how to optimize the hyperparameters accordingly, thereby ensuring that the prediction performance of the model is excellent and stable enough.

[0019] In an alternative embodiment, step 1 specifically includes the following sub-steps:

[0020] Step 11: Collect data on concrete mix proportions, including the proportions of cement, fly ash, mineral admixtures, water, and aggregate raw materials;

[0021] Step 12: Obtain data on the environmental impact factors of concrete, including external environmental parameters such as temperature, humidity, and chloride ion concentration;

[0022] Step 13: Perform data preprocessing, including removing outliers, filling in missing values, and standardizing the data. The standardization method is as follows:

[0023]

[0024] where: μ is the mean of the feature, and σ is the standard deviation of the feature.

[0025] Technical effect: In the prediction of concrete durability, the quality and integrity of the data directly determine the accuracy and generalization ability of the model. Steps 11 to 13 ensure the accuracy, representativeness, and consistency of the input data through comprehensive data collection, environmental factor acquisition, and data preprocessing, providing a solid foundation for the training of the Bayesian neural network.

[0026] In an alternative embodiment, step 2 specifically includes the following sub-steps:

[0027] Step 21: Design a multi-layer Bayesian neural network model, including an input layer, multiple hidden layers, and an output layer; where:

[0028] Input layer: Receive data on concrete material mix proportions and environmental factor characteristics;

[0029] Multiple hidden layers: Adopt a fully connected neural network, and the number of neurons in each layer is set according to the task complexity;

[0030] Output layer: used to predict the durability of concrete, including chloride ion diffusion coefficient and sulfate attack resistance;

[0031] Step 22: Model the weights and biases of the multi-layer Bayesian neural network model designed in Step 21 using a normal distribution. The prior distribution of the weights is:

[0032] ω i ~N(μ,σ 2 )

[0033] where ω i represents the weight of the i-th layer, and N(μ,σ 2 ) is a Gaussian distribution with a mean of 0 and a variance of σ 2 ;

[0034] Step 23: Approximately calculate the posterior distribution of the weights using the variational inference method, and construct a variational distribution to approximate the true posterior distribution;

[0035] Step 24: During the forward propagation calculation of the model, randomly sample the weights w and biases b each time, and calculate the activation values of the hidden layer:

[0036] h (l) =f(W (l) h (l-1) +b (l) )

[0037] where h (l) represents the output of the l-th layer, W (l) and b (l) are the weights and biases of this layer, and f() is the activation function;

[0038] Step 25: Use the Monte Carlo sampling method to randomly sample from the weight distribution. Randomly sample from the weight distribution each time during training to simulate the uncertainty of the weights, and construct a Bayesian neural network model that can quantify uncertainty.

[0039] Technical effect: In the task of predicting the durability of concrete, traditional neural network models usually ignore the uncertainty of data and model parameters, resulting in the lack of robustness and credibility of the prediction results. Steps 21 to 25 achieve the uncertainty modeling of the durability prediction of concrete by constructing a multi-layer Bayesian neural network, combining the variational inference and Monte Carlo sampling methods, making the prediction results more reliable and providing a confidence interval for auxiliary decision-making.

[0040] In an optional embodiment, Step 3 specifically includes the following sub-steps:

[0041] Step 31: Calculate the loss. Use the mean square error as the data fitting loss to measure the error between the predicted value of the Bayesian neural network model and the actual durability value. The mean square error is defined as:

[0042]

[0043] where: m is the number of samples; is the predicted value of the i-th sample, representing the concrete durability index output by the neural network; y true,i is the true durability value of the i-th sample;

[0044] The total form of the loss function is:

[0045] L = L data + λL reg

[0046] where, L data is the mean squared error, and L reg is the regularization loss;

[0047] Step 32: Perform posterior update. Through posterior update, the distribution of weights is continuously adjusted. The application formula of Bayes' theorem is as follows:

[0048]

[0049] where:

[0050] P(W∣D) is the posterior distribution; P(D∣W) is the likelihood function; P(W) is the prior distribution; P(D) is the marginal likelihood of the data;

[0051] Step 32: Update the neural network parameters using the stochastic gradient descent method. Its gradient update formula is:

[0052]

[0053] where:

[0054] η is the learning rate, which controls the step size of each parameter update,

[0055] and are the gradients of the loss function with respect to the weights and biases, respectively;

[0056] Step 33: Iteratively update the weights until the loss function converges, meets the pre-set error threshold, or reaches the maximum number of training epochs to obtain the optimal Bayesian neural network prediction model.

[0057] Technical effect: During the training process of the Bayesian neural network, loss calculation, posterior update, and gradient optimization are the core steps. Steps 31 to 33 evaluate the model prediction error through the mean squared error, perform weight update using Bayesian inference, and use stochastic gradient descent for optimization, thereby ensuring the stability, convergence, and prediction credibility of the model.

[0058] In an alternative embodiment, step 4 specifically includes the following sub-steps:

[0059] Step 41: Use the Bayesian neural network model trained in step S3 to perform forward propagation calculation to obtain the predicted value of concrete durability;

[0060] Step 42: Conduct multiple random samplings, calculate the mean μ and standard deviation σ of the predicted values, and construct a confidence interval;

[0061] Step 43: Provide a confidence interval for the durability prediction result according to the prediction uncertainty. The confidence interval is calculated as follows:

[0062]

[0063] indicating a 95% confidence level, the prediction result is The standard deviation is

[0064] Technical effect: In a Bayesian neural network, the prediction not only needs to calculate a definite output value, but also should provide a measure of uncertainty so that engineers can evaluate the credibility of the prediction when making decisions. Steps 41 to 43 ensure the accuracy and reliability of the concrete durability prediction result through forward propagation calculation, random sampling to estimate the mean and standard deviation, and confidence interval construction.

[0065] In an alternative embodiment, the mean squared error MSE, root mean squared error RMSE, and coefficient of determination R 2 in step 5 are calculated as follows:

[0066] Mean squared error MSE: Used to calculate the difference between the predicted value and the true value.

[0067]

[0068] Root mean squared error RMSE: The square root of MSE, used to provide a scale of the error.

[0069]

[0070] Coefficient of determination R 2 value: Measures the degree of fit of the Bayesian neural network model to the data.

[0071] where y true represents the true durability value of the sample. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a composition diagram of the overall idea of the present invention;

[0073] Figure 2Comparison graph of true values and predicted values for the training set: It shows the comparison between the true values and the model-predicted values in the training set, and marks the confidence interval of the prediction results to help users understand the fitting effect of the model;

[0074] Figure 3 Comparison graph of true values and predicted values for this test set: It shows the comparison between the true values and the model-predicted values in the test set to help evaluate the generalization ability of the model;

[0075] Figure 4 Scatter plot for this training set: It shows the scatter distribution between the true values and the predicted values in the training set and is used to analyze the fitting effect of the model;

[0076] Figure 5 Scatter plot for this test set: It shows the scatter distribution between the true values and the predicted values in the test set and is used to evaluate the performance of the model on unknown data;

[0077] Figure 6 Predicted values and confidence intervals for this test set. Specific implementation manners

[0078] To make the objectives, technical solutions and advantages of this application clearer, the following describes this application clearly and completely in combination with specific embodiments and the attached drawings. Obviously, the described embodiments are partial embodiments of the present invention, not all embodiments.

[0079] In any machine learning model, the design and initialization of the network are crucial for the final performance of the model. For Bayesian neural networks, reasonable structure design and weight initialization not only help accelerate training, but also improve the accuracy of prediction and uncertainty measurement.

[0080] The first step is the design and initialization of the network structure. The main work is to initialize the network structure and parameters as well as the setting of the optimization objective.

[0081] First, in the design of the input layer, according to the durability prediction problem of concrete materials, we selected multiple features obtained from an Excel table as inputs. Specifically, we used the following feature data:

[0082] OPC (kg / m 2 ): Quantity of ordinary Portland cement; FA (kg / m 3 ): Quantity of fly ash; GGBS (kg / m 3 ): Quantity of ground granulated blast-furnace slag; SF (kg / m 3 ): Quantity of silica fume; Superplasticiser (kg / m 3 ): Quantity of water reducer; Water (kg / m 3):Water consumption; Fine agg(kg / m 3 ):Fine aggregate consumption; Coarse agg(kg / m 3 ):Coarse aggregate consumption; w / b (water - binder ratio): water - binder ratio; Exposure time(t / a): Exposure time; Annual mean temperature(T / ℃): Annual mean temperature; [Cl - ] in seawater(g / L): Chloride ion concentration in seawater.

[0083] These input features determine the chloride ion diffusion coefficient and durability of concrete, so they are fully considered in the input layer of the network. Each feature is standardized so that all input data is within the same dimension range, thus ensuring smooth gradient update during training.

[0084] In the design of the network, the Bayesian neural network adopts a multi - layer structure, including three hidden layers. Through this multi - layer design, the network can capture the complex non - linear relationship between the input data and the output target. The number of nodes in each layer is reasonably set to avoid overfitting and underfitting. For example, the number of nodes in the first layer and the third layer are set to 64 and 128 respectively, while the middle layer selects 64 nodes.

[0085] The initialization of weights and biases is carried out through a Gaussian distribution with a mean of 0 and a standard deviation of 0.1. This can ensure that the weights are not too large in the initial stage of training, thus avoiding problems such as gradient explosion or gradient vanishing. Each time of sampling, the weights and biases are sampled from a Gaussian distribution to maintain the randomness of the model.

[0086] W l ~N(0,0.1 2 )b l ~N(0,0.1 2 )

[0087] Among them, W l represents the weight matrix of the l - th layer, and b l represents the bias of the l - th layer. In this way, the initialized weights and biases have a good variance, which can effectively avoid problems such as gradient explosion or gradient vanishing in the initial stage of training.

[0088] Secondly, in the process of designing the optimization objective, the Bayesian neural network not only has to deal with the training problems of traditional neural networks, but also needs to handle the uncertainty of weights. To introduce this uncertainty into the model, we adopt the method of Bayesian inference, sampling each weight instead of directly updating the weights as in traditional neural networks. This method enables the network to automatically adjust the posterior distribution of weights and biases according to Bayesian inference when facing different input data.

[0089] The second step is forward propagation and sampling. In a Bayesian neural network, forward propagation is not only the process of computing the input data through the network in a traditional neural network, but also involves how to introduce the uncertainty of the model through the sampling mechanism. This process is one of the core features of a Bayesian neural network, which can handle the randomness and uncertainty in the data, thereby improving the performance of the model in complex tasks. In the application of concrete durability prediction, the design of the forward propagation and sampling process enables the model to effectively combine the diversity of concrete and the influence of different environmental conditions, providing accurate predictions with uncertainty quantification.

[0090] First, for the forward propagation process, in a Bayesian neural network, the computational process of forward propagation is not much different from that of a traditional neural network. However, due to the randomness of the model, we introduce sampling on the weights and biases of each layer. Whenever the input data passes through the network, it first performs a weighted sum through the weights of the input layer, and then, after being processed by the activation function, calculates the activation values of each layer, and finally obtains the output of the network. This process not only reflects how the neural network extracts features from the data but also how to perform inference in uncertainty through sampling.

[0091] Taking the prediction of concrete durability as an example, assume that the input data includes variables such as the cement mix ratio of concrete, the amount of fly ash used, and the chloride ion concentration. These input information are passed through the neural network layer by layer, and finally the predicted concrete durability value is output. In this process, the calculation of each layer performs a weighted sum and introduces non-linear factors through the activation function to help the network learn the complex relationship between the input and output.

[0092] Specific calculation process:

[0093] Input layer to the first hidden layer: The input data X composed of the concrete mix ratio and environmental data (such as the amount of cement used, temperature, etc.) and the weight matrix W of the first layer l Perform a weighted sum and add the bias b1 to obtain the input z1 of the first hidden layer, and then calculate the activation value a1 through the activation function tanh:

[0094] z1 = XW l + b1

[0095] a1 = tanh(z1)

[0096] First hidden layer to the second hidden layer: Take the output a1 of the first hidden layer as the input. After passing through the weight matrix W2 and bias b2 of the second layer, obtain the input z2 of the second layer, and calculate the activation value a2 of the second layer through the activation function tanh:

[0097] z2 = a1W2 + b2

[0098] a2 = tanh(z2)

[0099] Second hidden layer to third hidden layer: Similarly, use the output a2 of the second hidden layer to calculate the activation value a3 of the third layer:

[0100] z3 = a2W3 + b3

[0101] a3 = tanh(z3)

[0102] Third hidden layer to output layer: Finally, the output a3 of the third hidden layer will be calculated through the weight matrix W4 and bias b4 of the output layer to obtain the predicted value of concrete durability

[0103] z4 = a3W4 + b4

[0104]

[0105] Through this series of calculations, the network gradually learns the relationship between the input features (such as concrete mix ratio) and the output target (such as durability prediction), and thus obtains the predicted value.

[0106] Then comes the part of sampling weights and biases. In traditional neural networks, the weights and biases are fixed, and the training process of the model is to minimize the loss function by adjusting the values of these weights and biases. In Bayesian neural networks, however, the weights and biases are not fixed values but are sampled from a probability distribution, which enables the model to reflect uncertainty during prediction.

[0107] Specifically, each weight W l and bias b l in the Bayesian neural network are sampled from a Gaussian distribution, representing our confidence in the network parameters. During each forward propagation, the network calculates based on the sampled weights and biases, thus generating different prediction results. This process makes each forward propagation produce different outputs, and this uncertainty can help the model better adapt to different data situations.

[0108] In this example, the weights and biases of each network layer in the concrete durability prediction problem follow the following Gaussian distribution:

[0109] W l ~N(0, σ 2 ) b l ~N(0, σ 2 )

[0110] This means that the weights and biases of each network layer are sampled from a normal distribution with a mean of 0 and a standard deviation of σ, ensuring that during each forward propagation, the changes in network parameters can introduce sufficient randomness, so that the predicted results of the network output have diversity.

[0111] In the application of concrete durability prediction, we do not fixedly use a set of weights and biases for prediction. Instead, by sampling different weights and biases from the Gaussian distribution each time, we simulate the changes of the model when dealing with different samples. For example, suppose we have a sample. The network will sample from the distribution of weights for this sample and perform a forward propagation to calculate the corresponding durability prediction value. For another sample, the network will obtain different prediction results based on different samplings. Through multiple samplings and forward propagations, the final predicted values will have certain distribution characteristics, thus enabling the quantification of prediction uncertainty.

[0112] This method is particularly suitable for engineering problems because in practical applications, the quality of data and environmental conditions often vary. By sampling and introducing uncertainty, Bayesian neural networks enable the model to flexibly handle various actual situations and provide more reliable and robust prediction results.

[0113] The forward propagation and sampling process of Bayesian neural networks in concrete durability prediction not only enable the model to learn the relationships between features based on training data but also provide the quantification of uncertainty during prediction. Through multiple samplings, the network can show potential fluctuations in different situations in the prediction results, which is particularly important for the practical application of concrete materials.

[0114] For example, when facing different environmental conditions (such as temperature and humidity changes), Bayesian neural networks can predict multiple possible values of concrete durability, rather than just a single value. This quantification of uncertainty can help engineers and decision-makers better understand the performance of materials under different conditions and make more scientific and accurate decisions.

[0115] In the practical application of concrete durability prediction, we hope that the network can give the confidence interval of the predicted value, such as the probability that the predicted durability value is within a certain range. This process is achieved through the forward propagation and sampling mechanism. The output of the model is not just a point estimate but a distribution, thus providing more reference information for the service life and durability of concrete materials.

[0116] In the third step, loss calculation and posterior update are carried out. In a Bayesian neural network, the choice of loss function directly affects the training effect of the model, especially in complex engineering applications such as concrete durability prediction. In this case, we use the mean squared error (MSE) as the loss function to measure the error between the model's predicted value and the actual durability value. The mean squared error is the most commonly used loss function in regression problems and is defined as follows:

[0117]

[0118] where:

[0119] m is the number of samples,

[0120] is the predicted value of the i-th sample, representing the concrete durability index output by the neural network,

[0121] y true,i is the true durability value of the i-th sample.

[0122] In the application of concrete durability prediction, the input data for each sample includes the raw material mix of concrete (such as cement, fly ash, chloride ion concentration, etc.) and environmental conditions (such as temperature, humidity, etc.). The task of the model is to predict the durability of concrete based on this input data. By calculating the prediction error of each sample, squaring it, and finally taking the average, the total mean squared error is obtained. This loss value provides an important basis for optimizing the model.

[0123] Specific application: Suppose we have a training set containing 100 concrete samples. The input for each sample includes concrete mix and environmental information, and the true durability values are from experimental measurements. There may be differences between the preliminary prediction results of the model and the actual measured values. By calculating the mean squared error, the model can quantify this difference and use it as a basis for optimization during the training process. Each time during training, the calculation of the loss function helps the model evaluate its performance and guides the network to adjust its parameters.

[0124] Posterior update

[0125] One of the core advantages of a Bayesian neural network is that it can dynamically adjust the weights and biases of the network through posterior update, enabling the model to better fit the complexity and uncertainty in the data. In a traditional neural network, the training process only adjusts the fixed weights by minimizing the loss function, while in a Bayesian neural network, each network weight and bias not only has a fixed value but also an uncertainty range (standard deviation). The Bayesian neural network continuously adjusts the distribution of these weights through posterior update to make more accurate predictions for the diversity and changes in the data.

[0126] Application of Bayes' Theorem: Bayes' Theorem is the basis for posterior update, which calculates the posterior distribution by combining prior knowledge and observed data. The formula for Bayes' Theorem is:

[0127]

[0128] Where:

[0129] P(W∣D) is the posterior distribution, representing the distribution of network parameter W given data D.

[0130] P(D∣W) is the likelihood function, representing the probability of observing data D given parameter W.

[0131] P(W) is the prior distribution, representing the distribution of network parameter W without observed data.

[0132] P(D) is the marginal likelihood of the data.

[0133] Through Bayes' Theorem, we can update the posterior distribution of network weights, so that in each sampling and training process, the prediction results of the network can reflect the uncertainty of the weights. During the training process, the network will continuously update the mean and standard deviation of the weights according to the input data, so as to achieve more accurate prediction.

[0134] Specific Application: In the prediction of concrete durability, we will perform forward propagation based on each sample in the training set (including the mix ratio of concrete and environmental factors) to calculate the predicted durability value of the concrete sample. Each time during training, the network updates the values of each weight and bias from the posterior distribution of the weights by sampling. Through multiple trainings and forward propagations, the network gradually optimizes its prediction results, making the predicted durability value closer to the actual value. In addition, the Bayesian neural network will also adjust the standard deviation of the weights to handle the uncertainty and noise in the data, so that the model has stronger robustness.

[0135] Gradient Descent and Posterior Distribution Optimization

[0136] When training a Bayesian neural network, the gradient descent method is the main method for optimizing the loss function. After each calculation of the loss function, the network calculates the gradients of the loss function with respect to the weights and biases, and then passes these gradient information back to the network through the backpropagation algorithm to update the weights and biases.

[0137] The Bayesian neural network not only updates the mean of the weights, but also updates the standard deviation of the weights in order to handle the uncertainty in the input data. The specific parameter update formula is:

[0138]

[0139] Where:

[0140] η is the learning rate, which controls the step size of each parameter update.

[0141] and are the gradients of the loss function with respect to the weights and biases, respectively.

[0142] During the training process, the network continuously updates the mean and standard deviation of the weights to ensure that when dealing with concrete durability prediction, the model can make more accurate predictions based on the characteristics of the input data and can also evaluate the uncertainty of the prediction results.

[0143] Specific application: For the problem of concrete durability prediction, the update process of the weights and biases ensures that the network can make accurate predictions under complex engineering conditions. As the training progresses, the network gradually adjusts the mean and standard deviation of the weights to better adapt to different concrete mix ratios and environmental conditions. In each optimization step, the Bayesian neural network not only improves the accuracy of the model but also reduces the uncertainty of the prediction results, enabling more reliable durability predictions in practical applications.

[0144] The last step is model evaluation and optimization

[0145] After completing the network training, the next step is to evaluate the performance of the model and perform necessary optimizations. This includes using the test set data for prediction and using appropriate evaluation metrics to measure the performance of the model. For the application of this patent, common evaluation metrics include the mean squared error MSE, root mean squared error RMSE, and R 2 etc.

[0146] After completing the training, we use the test set to evaluate the model. By comparing the prediction results of the model with the real data, we calculate metrics such as the mean squared error MSE, root mean squared error RMSE, and R 2 etc. to evaluate the accuracy of the model.

[0147] Mean squared error (MSE): Used to calculate the difference between the predicted value and the real value;

[0148]

[0149] Root mean squared error (RMSE): The square root of MSE, used to provide a scale of the error;

[0150]

[0151] R 2 value: Measures the goodness of fit of the model to the data, and the closer it is to 1, the better the fit;

[0152]

[0153] After obtaining these evaluation metrics, we optimize and adjust the model. If the following three conditions are met simultaneously, it is determined that the fitting effect meets the standard.

[0154] Condition 1: The value of the root mean square error RMSE is between 0 and 1:

[0155] Condition 2: The value of the root mean square error RMSE is between 0 and 1;

[0156] Condition 3: The coefficient of determination R 2 is between 0.89 and 0.91:

[0157] If the above three conditions cannot be met simultaneously, the parameters are adjusted by increasing the learning rate, increasing the number of hidden layers, and adding a regularization term to improve the accuracy and reliability of concrete durability prediction.

[0158] Through the above process, the Bayesian neural network can effectively handle the concrete durability prediction task. The specific application of each step in practice can fully demonstrate the advantages of this method, especially its ability to quantify uncertainty and handle complex data relationships. The corresponding evaluation metrics of the training set and test set are shown in Table 1:

[0159] MSE RMSE <![CDATA[R 2 > Test set 0.4736 0.6882 0.9034

[0160] Table 1

[0161] System Implementation and Application

[0162] System Architecture

[0163] The system architecture of the present invention includes a data acquisition module, a data preprocessing module, a Bayesian neural network module, a prediction module, and a result display module. The system can collect the material properties and environmental data of concrete in real time. After preprocessing, it is input into the Bayesian neural network model for durability prediction, and the prediction results are displayed to the user through a graphical interface.

[0164] System Application

[0165] This system can be widely applied in fields such as construction engineering and infrastructure construction. Engineers can adjust the concrete formula and construction plan according to the prediction results provided by the system, thereby improving the durability of concrete, reducing maintenance costs, and extending the service life of the structure.

Claims

1. A concrete durability prediction method based on Bayesian neural network, characterized in that, It includes the following steps: Step 1: Obtain the original experimental data of the concrete and perform data preprocessing; Step 2: Use the preprocessed data to determine the input features of the Bayesian neural network, construct a Bayesian neural network model with multiple hidden layers, model the weights and biases of the Bayesian neural network model using a normal distribution, and perform initialization to provide a prior distribution for subsequent training; Step 3: Utilize the training set part in the original data to optimize the Bayesian neural network model, estimate the posterior distribution of the weights and biases through variational inference, minimize the error using a loss function, and combine gradient descent to optimize the parameters, enabling the Bayesian neural network model obtained in Step 2 to learn the relationship between concrete durability and input features; Step 4: Use the trained Bayesian neural network model to predict the test set, calculate the mean of the output as the final prediction value, and estimate the uncertainty through the standard deviation of the posterior distribution to quantify the reliability of the prediction result; Step 5: Calculate the evaluation metrics of the Bayesian neural network model, including calculating the mean squared error MSE, root mean squared error RMSE, and coefficient of determination R 2 index. If the following three conditions are met simultaneously, it is determined that the fitting effect meets the standard Condition 1: The value of the root mean square error RMSE is between 0 and 1; Condition 2: The value of the root mean square error RMSE is between 0 and 1; Condition 3: The coefficient of determination R 2 is between 0.89 and 0.91; If the above three conditions cannot be satisfied simultaneously, adjust the model parameters to improve the accuracy and reliability of concrete durability prediction; the model parameters include the learning rate, the number of hidden layers, and the regularization term; Step 6: Perform complete concrete durability prediction based on the optimized final Bayesian neural network model and provide a confidence interval.

2. The concrete durability prediction method based on a Bayesian neural network according to claim 1, wherein Step 1 specifically includes the following sub-steps: Step 11: Collect concrete mix proportion data, including the proportions of cement, fly ash, mineral admixtures, water, and aggregate raw materials; Step 12: Obtain the environmental impact factor data of the concrete, including external environmental parameters such as temperature, humidity, and chloride ion concentration; Step 13: Perform data preprocessing, including removing outliers, filling missing values, and standardizing the data. The standardization method is as follows: where: μ is the mean of the feature, and σ is the standard deviation of the feature.

3. The concrete durability prediction method based on a Bayesian neural network according to claim 1, characterized in that Step 2 specifically includes the following sub-steps: Step 21: Design a multi-layer Bayesian neural network model, including an input layer, multiple hidden layers, and an output layer; where: Input layer: Receive concrete material mix proportion and environmental factor feature data; Multiple hidden layers: Adopt a fully connected neural network, and the number of neurons in each layer is set according to the task complexity; Output layer: Used to predict concrete durability, including chloride ion diffusion coefficient and sulfate resistance performance; Step 22: Model the weights and biases of the multi-layer Bayesian neural network model designed in Step 21 using a normal distribution. The prior distribution of the weights is: ω i ~N(μ,σ 2 ) Among them, ω i represents the weight of the i-th layer, and N(μ, σ 2 ) is a Gaussian distribution with a mean of 0 and a variance of σ 2 ; Step 23: Use the variational inference method to approximately calculate the posterior distribution of the weights, and construct a variational distribution to approximate the true posterior distribution; Step 24: During the forward propagation calculation of the model, randomly sample the weights w and biases b each time and calculate the activation values of the hidden layers: h (l) = f(W (l) h (l-1) + b (l) ) where h (l) represents the output of the l-th layer, W (l) and b (l) are the weights and biases of this layer, and f() is the activation function; Step 25: Adopt the Monte Carlo sampling method to randomly sample from the weight distribution. Randomly sample from the weight distribution each time during training to simulate the uncertainty of the weights and construct a Bayesian neural network model that can quantify uncertainty.

4. The concrete durability prediction method based on a Bayesian neural network according to claim 1, wherein Step 3 specifically includes the following sub-steps: Step 31: Calculate the loss. The mean squared error is used as the data fitting loss to measure the error between the predicted value of the Bayesian neural network model and the actual durability value. The mean squared error is defined as: Where: m is the number of samples; is the predicted value of the i-th sample, representing the concrete durability index output by the neural network; y true,i is the true durability value of the i-th sample; The total form of the loss function is: L = L data + λL reg Among them, L data is the mean squared error, and L reg is the regularization loss; Step 32: Perform posterior update. Through posterior update, the distribution of weights is continuously adjusted. The application formula of Bayes' theorem is as follows: Where: P(W∣D) is the posterior distribution; P(D∣W) is the likelihood function; P(W) is the prior distribution; P(D) is the marginal likelihood of the data; Step 32: Update the neural network parameters using the stochastic gradient descent method. Its gradient update formula is: Where: η is the learning rate, which controls the step size of each parameter update. and are the gradients of the loss function with respect to the weights and biases, respectively; Step 33: Iteratively update the weights until the loss function converges, meets the pre-set error threshold or reaches the maximum number of training epochs to obtain the best Bayesian neural network prediction model.

5. The concrete durability prediction method based on a Bayesian neural network according to claim 1, wherein Step 4 specifically includes the following sub-steps: Step 41: Use the Bayesian neural network model trained in Step S3 to perform forward propagation calculation to obtain the predicted value of concrete durability. Step 42: Perform multiple random samplings, calculate the mean μ and standard deviation σ of the predicted values and construct a confidence interval. Step 43: Provide the confidence interval of the durability prediction result according to the prediction uncertainty. The confidence interval is calculated as follows: Indicating a 95% confidence level, the predicted result is The standard deviation is 6. The method for predicting the durability of concrete based on a Bayesian neural network according to claim 1, wherein In step 5, the mean square error MSE, root mean square error RMSE, and coefficient of determination R 2 , and their calculation formulas are as follows: Mean Squared Error MSE: Used to calculate the difference between the predicted value and the true value. Root Mean Squared Error RMSE: The square root of MSE, used to provide the scale of the error. Coefficient of determination R 2 Value: Measures the degree of fit of the Bayesian neural network model to the data Among them, y true represents the true durability value of the sample.

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