Neural network based response surface design method for high durability concrete

Abstract

The application discloses a high-durability concrete response surface design method based on a neural network. The application establishes a high-durability concrete response surface prediction model based on a neural network based on real marine service environment influencing factors and building material raw material composition characteristics, realizes prediction on key index parameters of concrete durability, iteratively optimizes the response surface model through an error function, and determines influencing factors of each input variable on the key index parameters of concrete durability through sensitivity analysis, so as to guide optimization design of high-durability concrete under real marine service environment.

Description

Technical Field

[0001] This invention belongs to the field of high-durability concrete design technology, and relates to a response surface design method for high-durability concrete based on neural networks. Background Technology

[0002] With the development of the marine economy, the construction of marine engineering projects such as ports and wharves has placed new demands on the design of building materials and the performance matching of concrete structures. In the marine service environment, concrete structures are affected by various environmental factors such as seawater erosion, salt spray, radiation, and wave erosion, and will face extremely high risks of fatigue failure. Therefore, conducting high-durability concrete optimization design targeting the key influencing factors of concrete service life is crucial to improving the service stability and service life of concrete in marine environments.

[0003] Current design methods for high-durability concrete in marine service environments can guide the design and preparation of high-durability concrete to some extent, but they still have some shortcomings: On the one hand, existing high-durability concrete design methods mainly consider the influence of corrosive ions on concrete durability, and have not carried out design research on multiple influencing factors of concrete service life under real service environments; on the other hand, traditional response surface methodology usually uses Box-Behnken, quadratic regression, and other methods, which are usually less accurate for complex nonlinear relationships and cannot achieve accurate multi-objective output under multivariable conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a high-durability concrete response surface design method based on neural networks, which realizes high-durability optimization design and durability prediction of concrete based on considering multiple environmental influencing factors in the real marine service environment and the characteristics of building material raw materials.

[0005] The technical solution for achieving the objective of this invention is as follows:

[0006] The neural network-based high-durability concrete response surface design method includes the following steps:

[0007] S1. Determine the environmental factors under real marine service conditions;

[0008] S2. Determine the composition parameters of concrete raw materials;

[0009] S3. Select concrete durability evaluation indicators under real marine service environment;

[0010] S4. Establish concrete durability experiments in real marine service environments using response surface methodology, and obtain concrete durability evaluation indicators under environmental factors and concrete raw material composition parameters under different real marine service environments.

[0011] S5. Establish a response surface prediction model based on a feedforward neural network between concrete durability evaluation index and environmental factors and raw material composition parameters under real service conditions; the feedforward neural network includes an input layer, a hidden layer and an output layer; the environmental factors and concrete raw material composition parameters under real marine service conditions are input variables, and the concrete durability evaluation index is the output variable.

[0012] S6. Divide the response surface experimental data into a test set and a validation set, use mean squared error (MSE) to evaluate the prediction results of the response surface prediction model, and iteratively optimize the prediction model.

[0013] S7. Calculate the influence factors of each input variable in the response surface prediction model through sensitivity analysis to determine the key influencing factors of concrete durability.

[0014] Furthermore, in S1, the environmental factors in the real marine service environment include, but are not limited to, concrete exposure time t (years), annual average temperature T (°C), and chloride ion concentration in seawater (g / L) in the real marine service environment.

[0015] Furthermore, in S2, the composition parameters of the concrete raw materials include, but are not limited to, ordinary Portland cement, water, different types of mineral admixtures (such as fly ash, mineral powder, silica fume, etc.), admixtures (such as water-reducing agents), aggregate content, and concrete water-cement ratio.

[0016] Furthermore, in S3, the concrete durability evaluation indicators under real marine service environment include, but are not limited to, the chloride ion concentration (%) on the concrete surface, the average chloride ion concentration (%) of the concrete cover, and the chloride ion concentration (%) on the steel reinforcement surface.

[0017] Furthermore, in S5, the hidden layers are typically 1 to 3 layers, determined based on the number of input variables and the complexity of the model; the hidden layer includes h neurons, used to extract features from the input data; for each neuron j in the hidden layer, a weighted sum is calculated using equation (1):

[0018]

[0019] Where, x i For input variables, w ij x i Input variable x i The weights of hidden neuron j, b j For the bias of neurons, Z j The weighted sum of the j-th neuron;

[0020] The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value a of the neuron is calculated by equation (2). j :

[0021]

[0022] Furthermore, in S5, the weighted sum of the outputs is calculated using formula (3), and an activation function is applied to obtain the output variable y:

[0023]

[0024] Among them, w j is the weight of the output layer, and b is the bias of the output layer.

[0025] Furthermore, in S6, the number of iterations is between 100 and 1000.

[0026] Furthermore, in S6, the mean square error L is calculated using formula (4):

[0027]

[0028] Where m is the number of samples, y k The values ​​represent the true values ​​of key durability indicators for concrete in real marine service environments. These are the predicted values ​​from the response surface prediction model based on a feedforward neural network.

[0029] Furthermore, in S6, the weights and biases are updated using the backpropagation algorithm to minimize the loss function:

[0030]

[0031] Where σ is the learning efficiency, which is usually set between 0.001 and 0.1.

[0032] Furthermore, in S7, the influence factors of each input variable in the response surface prediction model are calculated through sensitivity analysis to determine the key influencing factors of concrete durability, specifically:

[0033] (1) Using test set X test As a benchmark, the baseline predicted values ​​corresponding to the test set were calculated by the high-durability concrete response surface prediction model based on a feedforward neural network.

[0034] (2) For each input variable X i Create data copy X temp Add a perturbation δ to the variable to perturb the input variable:

[0035] X temp (:,i)=X temp (:,i)+δ (6)

[0036] (3) Based on the perturbed input variables, the predicted values ​​after perturbation are calculated using a high-durability concrete response surface model based on a feedforward neural network.

[0037] (4) Calculate the baseline prediction value Compared with the predicted value after the disturbance The differences yielded the influence factor (Importance(X)) of each input variable. i ):

[0038]

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] Based on the environmental influencing factors of real marine service environment and the composition characteristics of building materials, this invention establishes a response surface prediction model for high-durability concrete based on neural networks. This model predicts key durability parameters of concrete, iterates and optimizes the response surface model through an error function, and determines the influence factors of each input variable on key durability parameters of concrete through sensitivity analysis. This guides the optimized design of high-durability concrete under real marine service environment. Attached Figure Description

[0041] Figure 1 Visualization results of the durability response surface model of concrete structures;

[0042] Figure 2 This is a distribution chart showing the predicted and actual values ​​of key indicators for concrete durability. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0044] Example 1

[0045] The neural network-based high-durability concrete response surface design method includes the following steps:

[0046] S1. Determine the environmental factors under real marine service conditions, including: concrete exposure time t (years), annual average temperature T (°C), and chloride ion concentration in seawater (g / L) under real marine service conditions.

[0047] S2. Determine the composition parameters of concrete raw materials, including: ordinary Portland cement dosage (kg / m³) 3 ), fly ash usage (kg / m³) 3 Mineral powder dosage (kg / m³) 3 ), Silica fume usage (kg / m³) 3 ), Water-reducing agent dosage (kg / m³) 3 Water consumption (kg / m³)3 Fine aggregate dosage (kg / m³) 3 Coarse aggregate dosage (kg / m³) 3 ), water-to-binder ratio.

[0048] S3. The concentration (%) of chloride ions on the surface of concrete under real marine conditions was selected as the evaluation index of concrete durability under real marine service conditions.

[0049] S4. Response surface methodology was used to establish concrete durability experiments in real marine service environments to obtain concrete durability evaluation indicators under different environmental factors and concrete raw material composition parameters in real marine service environments.

[0050] S5. Establish a response surface prediction model based on a feedforward neural network between concrete durability evaluation index and environmental factors and raw material composition parameters under real service conditions; the feedforward neural network includes an input layer, a hidden layer and an output layer; the environmental factors and concrete raw material composition parameters under real marine service conditions are input variables, and the concrete durability evaluation index is the output variable.

[0051] The hidden layer consists of one layer and contains 10 neurons, used to extract features from the input data. For each neuron j in the hidden layer, a weighted sum is calculated using equation (1):

[0052]

[0053] Where, x i For input variables, w ij x i Input variable x i The weights of hidden neuron j, b j For the bias of neurons, Z j The weighted sum of the j-th neuron;

[0054] The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value a of the neuron is calculated by equation (2). j :

[0055]

[0056] The output variable y is obtained by calculating the weighted sum of the outputs using formula (3) and applying the activation function:

[0057]

[0058] Among them, w j is the weight of the output layer, and b is the bias of the output layer.

[0059] S6. Divide the response surface experimental data into a test set and a validation set. Use mean squared error (MSE) to evaluate the prediction results of the response surface prediction model. Iterate and optimize the prediction model 1000 times.

[0060] The mean square error L is calculated using formula (4):

[0061]

[0062] Where m is the number of samples, y k The values ​​represent the true values ​​of key durability indicators for concrete in real marine service environments. These are the predicted values ​​from the response surface prediction model based on a feedforward neural network.

[0063] The weights and biases are updated using the backpropagation algorithm to minimize the loss function:

[0064]

[0065] Where σ is the learning efficiency, which is 0.01.

[0066] S7. Calculate the influencing factors of each input variable in the response surface prediction model through sensitivity analysis to determine the key influencing factors of concrete durability, specifically:

[0067] (1) Using test set X test As a benchmark, the baseline predicted values ​​corresponding to the test set were calculated by the high-durability concrete response surface prediction model based on a feedforward neural network.

[0068] (2) For each input variable X i Create data copy X temp Add a perturbation δ to the variable to perturb the input variable, and set δ to 10% of the standard deviation:

[0069] X temp (:,i)=X temp (:,i)+10%×std(X temp (:,i)) (6)

[0070] (3) Based on the perturbed input variables, the predicted values ​​after perturbation are calculated using a high-durability concrete response surface model based on a feedforward neural network.

[0071] (4) Calculate the baseline prediction value Compared with the predicted value after the disturbance The differences yielded the influence factor (Importance(X)) of each input variable. i ):

[0072]

[0073] Specifically, in this embodiment, a response surface methodology is used to establish a concrete durability experiment in a real marine service environment. The experiment tests evaluation indices for concrete durability under different environmental factors and raw material compositions. A total of 12 input variables are included, such as: ordinary Portland cement content (kg / m³). 3 ), fly ash usage (kg / m³) 3 Mineral powder dosage (kg / m³) 3 ), Silica fume usage (kg / m³) 3 ), Water-reducing agent dosage (kg / m³) 3 Water consumption (kg / m³) 3 Fine aggregate dosage (kg / m³) 3 Coarse aggregate dosage (kg / m³) 3 The parameters include water-cement ratio, exposure time (a), annual average temperature (°C), and chloride ion concentration in seawater (g / L). The output variable is the chloride ion concentration (%) on the concrete surface.

[0074] A concrete durability prediction model based on a feedforward neural network is constructed under real marine service environment, and the corresponding relationship between multiple input factors and output factors is established.

[0075] Based on the concrete durability response surface prediction model in real marine service environment, 75% of the data in the response surface experiment was extracted as the training set and 25% of the data was used as the validation set. The mean square error function was used to evaluate the model prediction results and the concrete durability response surface prediction model was iteratively optimized.

[0076] Sensitivity analysis is used to calculate the degree of influence of each input variable on the model output, determine the magnitude of the influence of each input variable on the durability of concrete under real marine service environment, and guide the multi-objective optimization design of high-durability concrete under real marine service environment.

[0077] In this embodiment, Matlab software is used to construct a response surface model for high-durability concrete based on a feedforward neural network, iteratively optimize the prediction model for key durability indicators, and calculate the influencing factors of input variables. This yields the key influencing factors affecting the parameters of key durability indicators of concrete under real marine service environments, thereby guiding the multi-objective optimization design of high-durability concrete.

[0078] Taking the response surface methodology design and the actual marine environmental factors in a certain region as an example, the amount of ordinary Portland cement used is...

[0079] (kg / m 3 ), fly ash usage (kg / m³) 3 Mineral powder dosage (kg / m³) 3 ), Silica fume usage (kg / m³)3 ), Water-reducing agent dosage (kg / m³) 3 Water consumption (kg / m³) 3 Fine aggregate dosage (kg / m³) 3 Coarse aggregate dosage (kg / m³) 3 Twelve parameters were used as input variables: water-cement ratio, exposure time (a), annual average temperature (°C), and chloride ion concentration in seawater (g / L). The chloride ion concentration on the concrete surface (%) was used as one output variable. Some response surface experimental data are shown in Table 1.

[0080] Table 1

[0081]

[0082] This study utilizes Matlab software to construct a response surface model for high-durability concrete based on a feedforward neural network, iteratively optimize a prediction model for key durability parameters of concrete, and conduct sensitivity analysis on the influencing factors of input variables. Matlab is a scientific computing and numerical analysis software that provides an integrated development environment encompassing numerical computation, data visualization, programming, and algorithm development. It is widely used in engineering design, numerical simulation, and other fields, and will not be elaborated upon further here.

[0083] Table 2

[0084]

[0085]

[0086] A high-durability concrete response surface model based on a feedforward neural network was used, employing the root mean square error (MSE) as the error function for iterative optimization. Sensitivity analysis was used to calculate the influence factors of each input variable. The model was set with 1 hidden layer, 10 neurons, a maximum of 1000 iterations, and a learning rate of 0.01. The root mean square error (RMSE) was calculated to be 0.17869 for 75% of the training set and 25% of the validation set. The distribution of predicted and true values ​​is shown below. Figure 2As shown in Table 2, the influencing factors of each input variable were obtained. Table 2 shows that, on the one hand, the influencing factors of different input variables exhibit positive and negative differences, indicating a positive or negative correlation between different variables and the output variable. Taking the amount of ordinary Portland cement and exposure time as examples, the influencing factor of ordinary Portland cement amount is negative, indicating that increasing the amount of ordinary Portland cement is beneficial to reducing the chloride ion concentration on the concrete surface, thus promoting the durability of the concrete structure. Conversely, the positive correlation between exposure time and surface chloride ion concentration indicates that extending the exposure time will have an adverse effect on the durability of the concrete structure. On the other hand, the absolute values ​​of the influencing factors of different input variables differ, indicating that different input variables have different degrees of influence on the durability of concrete structures under real marine service environments. Taking the amount of water-reducing agent and annual average temperature as examples, the absolute value of the influencing factor of water-reducing agent amount is 0.0022229, which is less than the absolute value of the influence shadow of annual average temperature (0.011104), indicating that compared to the amount of water-reducing agent, the annual average temperature in the service environment of the concrete structure has a more significant impact on the durability of the concrete structure.

Claims

1. A neural network-based response surface methodology for high-durability concrete, characterized in that, Includes the following steps: S1. Determine the environmental factors under real marine service conditions; S2. Determine the composition parameters of concrete raw materials; S3. Select concrete durability evaluation indicators under real marine service environment; S4. Establish concrete durability experiments in real marine service environments using response surface methodology, and obtain concrete durability evaluation indicators under environmental factors and concrete raw material composition parameters under different real marine service environments. S5. Establish a response surface prediction model based on a feedforward neural network between concrete durability evaluation index and environmental factors and raw material composition parameters under real service conditions; the feedforward neural network includes an input layer, a hidden layer and an output layer; the environmental factors and concrete raw material composition parameters under real marine service conditions are input variables, and the concrete durability evaluation index is the output variable. S6. Divide the response surface experimental data into a test set and a validation set, use mean square error to evaluate the prediction results of the response surface prediction model, and iteratively optimize the prediction model. S7. Calculate the influencing factors of each input variable in the response surface prediction model through sensitivity analysis to determine the key influencing factors of concrete durability, specifically: (1) Using the test set As a benchmark, the baseline predicted values ​​corresponding to the test set were calculated by the high-durability concrete response surface prediction model based on a feedforward neural network. ; (2) For each input variable Create a data copy Add a perturbation δ to the variable to perturb the input variable: （6） (3) Based on the perturbed input variables, the predicted values ​​after perturbation are calculated using a high-durability concrete response surface model based on a feedforward neural network. ; (4) Calculate the baseline prediction value Compared with the predicted value after the disturbance The differences yielded the influence factors of each input variable. : （7）。 2. The high-durability concrete response surface design method according to claim 1, characterized in that, In S1, the environmental factors in the real marine service environment are selected from one or more of the following: concrete exposure time, annual average temperature, and chloride ion concentration in seawater under the real marine service environment.

3. The high-durability concrete response surface design method according to claim 1, characterized in that, In S2, the composition parameters of the concrete raw materials are selected from one or more of the following: ordinary Portland cement, water, fly ash, mineral powder, silica fume, water-reducing agent, aggregate content, and water-cement ratio.

4. The high-durability concrete response surface design method according to claim 1, characterized in that, In S3, the concrete durability evaluation index under real marine service environment is selected from one of the following: chloride ion concentration on the concrete surface, average chloride ion concentration in the concrete cover, and chloride ion concentration on the steel reinforcement surface.

5. The high-durability concrete response surface design method according to claim 1, characterized in that, In S5, there are 1 to 3 hidden layers; each hidden layer contains h neurons; for each neuron j in the hidden layer, a weighted sum is calculated using equation (1): （1） in, For input variables, Input variables The weights of hidden neuron j For the bias of neurons, The weighted sum of the j-th neuron; The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value of the neuron is calculated by equation (2). : （2）。 6. The high-durability concrete response surface design method according to claim 1, characterized in that, In S5, the weighted sum of the outputs is calculated using formula (3), and the activation function is applied to obtain the output variables. : （3） in, For the weights of the output layer, This is the bias for the output layer.

7. The high-durability concrete response surface design method according to claim 1, characterized in that, In S6, the number of iterations is between 100 and 1000.

8. The high-durability concrete response surface design method according to claim 1, characterized in that, In S6, the mean square error is calculated using formula (4). : （4） in, For the sample size, The values ​​represent the true values ​​of key durability indicators for concrete in real marine service environments. These are the predicted values ​​from the response surface prediction model based on a feedforward neural network.

9. The high-durability concrete response surface design method according to claim 1, characterized in that, In S6, the weights and biases are updated using the backpropagation algorithm to minimize the loss function: （5） in, For optimal learning efficiency, it is typically set between 0.001 and 0.1.

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