Vegetation concrete porosity prediction method

Abstract

The invention discloses a vegetation concrete porosity prediction method. The method comprises the following steps: acquiring parameters of concrete; constructing a GA-BP neural network model, dividing the parameter data set of the concrete into a training set and a test set, and performing normalization processing; in the model training stage, concrete parameters serve as input variables, the porosity serves as output variables, and a GA-BP neural network model is trained through the training set; obtaining an optimal weight value and an optimal threshold value by optimizing the weight value and the threshold value in the GA-BP neural network model; and performing porosity prediction on the data in the test set based on the optimized BP neural network model to obtain a predicted value of the porosity. According to the vegetation concrete porosity prediction method provided by the invention, the concrete porosity can be effectively predicted, the time is saved, and the accuracy is high.

Description

Technical Field

[0001] The invention relates to the field of porosity testing, in particular to a porosity prediction method for vegetation concrete. Background Art

[0002] As a new type of material that combines the characteristics of concrete and vegetation, vegetated concrete has certain environmental protection and beautification functions. According to its structural characteristics, it can be considered that the apparent volume of vegetated concrete per unit volume is composed of tightly packed aggregates. That is, the cementitious material slurry is evenly wrapped on the surface of the aggregate, and the aggregates are bonded together by the cementitious material, eventually forming a connected three-dimensional spatial pore structure. The unit volume of vegetated concrete is composed of the volume of cementitious material slurry, the volume of coarse aggregate and the target pore volume. The mix design method is as follows: first, select the material according to the design requirements and test its basic properties; then, determine the amount of coarse aggregate in the unit volume of concrete; then, determine the volume of cementitious material slurry according to the tightly packed porosity of coarse aggregate and the designed porosity; finally, determine the water-cement ratio according to the molding process requirements, so as to calculate the amount of cement and mixing water per unit volume.

[0003] In vegetated concrete, appropriate porosity is conducive to water penetration, gas exchange, plant root growth, etc., thus affecting its ecological function and structural strength. Common porosity test methods include physical measurements such as drainage method, slicing method, and CT scanning method. For example, in the drainage method, the specimen is soaked in water to saturate, and the volume of the specimen v0 is measured. The specimen is placed in the basket of a hydrostatic balance, and water is soaked above the upper surface of the specimen. When no bubbles appear, the weight of the specimen in water is weighed. k2 , then take out the specimen and put it back into the curing room. After 24 hours, weigh the weight of the specimen in air. k1 The porosity of concrete is calculated according to the formula Where P w is the density of water. These methods are not only complicated and time-consuming, but also have limited sample quantity.

[0004] Liu Kexin et al. proposed a neural network concrete porosity prediction method based on wolf pack algorithm optimization. Although the wolf pack algorithm has a strong global search capability, it is easy to fall into the local optimal solution when the objective function is very complex, thus affecting the final effect of the neural network. Jin Nanguo et al. proposed a concrete porosity prediction BP network model. The predicted value is not much different from the measured value and is very close. However, it is easy to fall into the local optimum and is sensitive to the initial weight. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting the porosity of vegetation concrete. The method can effectively predict the porosity of concrete, which not only saves time but also has high accuracy; it provides the possibility for intelligent design of concrete porosity and will greatly improve the efficiency of porosity concrete preparation.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A method for predicting porosity of vegetated concrete includes the following steps:

[0008] Step 1: Get the parameters of concrete;

[0009] Step 2: Construct a GA-BP neural network model, divide the concrete parameter data set into a training set and a test set, and normalize them;

[0010] Step 3: In the model training phase, the parameters of concrete are used as input variables, the porosity is used as the output variable, and the GA-BP neural network model is trained using the training set; the optimal weights and thresholds are obtained by optimizing the weights and thresholds in the GA-BP neural network model;

[0011] Step 4: Predict the porosity of the data in the test set based on the optimized BP neural network model to obtain the predicted value of the porosity.

[0012] It also includes step 5: evaluation based on the training set and the test set to evaluate the accuracy and performance of the GA-BP neural network model in predicting the porosity of concrete, as well as the degree of fit of the GA-BP neural network model.

[0013] In step 1, the parameters of concrete include: water, cement, water-cement ratio, coarse aggregate and compressive strength.

[0014] In the step 2, the constructed GA-BP neural network model includes: an input layer, a hidden layer, and an output layer; and transfer functions f and F are provided between the input layer and the hidden layer and between the hidden layer and the output layer; the hidden layer adopts the tansig transfer function, which can map the input to the interval [-1,1]; the output layer adopts the purelin transfer function, does not perform any nonlinear transformation on the output, and directly outputs the predicted value of the network.

[0015] In step 3, the genetic algorithm GA uses a roulette method to select individuals in the population, uses a single-point crossover operator to generate two new individuals, uses an adaptive mutation operator to generate new individuals, and then optimizes the weights and thresholds of the BP neural network model to obtain initial optimal weights and thresholds; the initial optimal weights and thresholds are then brought into the BP neural network model for error calculation, and the weights and thresholds are updated until the requirements of the model are met.

[0016] In step 3, the genetic algorithm GA specifically includes the following process steps:

[0017] Step 2.1, determine the network parameters;

[0018] Step 2.2, population initialization: Encode the network parameters to form the initial solution of the population, and use real number encoding for the individuals in the population.

[0019] Step 2.3, calculate fitness: a standard used to measure the quality of individuals in a population, and calculate the fitness of individuals in the generated initial population.

[0020] Step 2.4, selection operation: Select the roulette method as the selection operator, and the probability pi of individual i being selected is

[0021]

[0022] Where: fi is the fitness value of the individual, N is the number of individuals in the population, K is the coefficient, and Fi is the ranking of individual i.

[0023] Step 2.5, crossover operation and mutation: Perform crossover operation on different chromosomes to achieve gene exchange and generate new individuals; mutation operation is adopted to prevent falling into the local optimal solution; the calculation formula for the crossover operation of the kth and ith chromosomes at position j is:

[0024]

[0025] Where: b is a random number from 0 to 1, α kj represents the value of the kth individual in the parent generation at the jth gene locus, α ij represents the value of the jth gene locus of the i-th individual in the parent generation, represents the value of the kth individual in the offspring at the jth gene locus, Represents the value of the jth gene locus of the i-th individual in the offspring.

[0026] The calculation formula for single-point mutation of the jth gene of the i-th individual is:

[0027]

[0028] Where: α ij represents the value of the i-th individual at the j-th gene locus, represents the value of the i-th individual at the j-th gene locus after mutation, a max 、a min Gene a ij The upper and lower bounds of; r2 is a random number; F = (1-g / Gmax) 2 , g is the current iteration number, Gmax is the maximum evolution number; r is a random number in [0,1];.

[0029] Step 2.6: Update the new population and calculate its fitness, replacing individuals with low fitness with individuals with high fitness to form a new population; until the fitness is greater than the preset threshold, or the number of iterations reaches the preset number; finally, substitute the obtained optimal weights and thresholds into the BP neural network model for prediction.

[0030] In step 3, the BP neural network model includes hidden layer training, using the LM algorithm as the training algorithm, including the following steps:

[0031] First, set the initial weights and thresholds of the BP neural network model;

[0032] Then, the input value is input into the input layer of the BP neural network model, and after weighted summation and activation function processing of each layer, the output result of the BP neural network model is obtained;

[0033] Finally, the output results of the BP neural network model are compared with the actual result labels to obtain the error between the predicted results and the actual labels.

[0034] The LM algorithm is used as a training algorithm, and the output calculation formula of the hidden layer and the output layer is:

[0035] H i =f(∑W i x i + b);

[0036] Where f is the transfer function, W i is the weight of the neuron, x i is the input signal, b is the neuron bias, H i is the output signal.

[0037] In step 4, the performance of the predicted values ​​and the true values ​​is evaluated using the root mean square error (RMSE) and the coefficient of determination (R 2 ), the root mean square error (RMSE) is used to measure the prediction accuracy of the GA-BP neural network model on continuous data; the root mean square error (RMSE) measures the root mean square difference between the predicted value and the true value, indicating the average deviation between the predicted value and the true value; the formula is:

[0038]

[0039] In the formula: Y is the predicted value, X is the actual value, and N is the number of data groups;

[0040] Coefficient of determination (R 2 ) is used to measure the degree of fit of the GA-BP neural network model to the observed data; the coefficient of determination (R 2) indicates the proportion of the variance of the dependent variable that the GA-BP neural network model can explain, that is, the degree to which the GA-BP neural network model fits the data; its formula is:

[0041]

[0042] Where: Y is the predicted value, X is the actual value, Z is the average value, and n is the number of data groups.

[0043] The present invention provides a method for predicting the porosity of vegetation concrete, which has the following technical effects:

[0044] 1) The present invention optimizes the BP neural network through genetic algorithm, and can obtain a better network initial weight and threshold (bias), using individuals to represent the initial weight and threshold (bias) of the network, using the BP neural network test error as the objective function output, and calculating the fitness value of the individual. The optimal individual, that is, the optimal BP neural network initial weight and threshold (bias) is found through selection, crossover and mutation operations.

[0045] 2) Use the LM algorithm to calculate and adjust the weight of each connection and the bias of each neuron in the network to reduce the error between the predicted result and the actual label. The threshold (bias) and weight are updated according to the error gradient to make the predicted result close to the actual label.

[0046] 3) The advantage of step 1 is that by obtaining the parameter data of concrete, basic information is provided for the model, which can accurately reflect the composition and characteristics of concrete, provide comprehensive data support, and help the neural network better learn the relationship between parameters and porosity, thereby improving the prediction ability of the model and ensuring the accuracy of the prediction.

[0047] 4) The advantage of step 2 is that by dividing the data set, normalizing the data, flexibly constructing the neural network structure, and introducing genetic algorithm optimization, the training efficiency, accuracy, and generalization ability of the BP neural network model can be improved, ensuring that it performs better in the concrete porosity prediction task.

[0048] 5) The advantage of step 3 is that the genetic algorithm is used to globally optimize the parameters of the neural network, which not only improves the training efficiency, prediction accuracy and generalization ability of the model, but also enhances the robustness of the model to noise and uncertain data. At the same time, the genetic algorithm can also optimize the network structure and hyperparameters, reduce manual parameter adjustment work, and improve the flexibility and scalability of the entire model.

[0049] 6) The patent with application number "201510527431.8" "Method for establishing a property prediction model for high-aluminum bronze coating and method for optimizing a single property index of high-aluminum bronze coating" also uses a genetic algorithm to optimize the BP network model to improve the research efficiency of high-aluminum bronze coating. The hidden layer transfer function of this application is the tansig transfer function, and the transfer function of this file is an S-type activation function. First, the two transfer functions have different output ranges. The gradient of the S-type activation function approaches zero when the input is large or small, which will lead to the gradient vanishing problem, especially in deep neural networks, which may affect the training efficiency of the model. Compared with the S-type activation function, the tansig transfer function has a larger gradient near 0, so it usually has better gradient propagation performance during training.

[0050] 7) The patent application number "202310769210.6" "High-temperature alloy additive manufacturing process optimization prediction method based on small sample learning" also uses genetic algorithm to optimize the BP network model to improve efficiency. The learning function of this application is learngd (learning function based on gradient descent method), and the learning function of this file is learngdm (gradient descent momentum learning function). The learngdm learning function is suitable for the training process of deep learning and large-scale neural networks, which can accelerate convergence and avoid oscillation. The learngd learning function is a basic gradient descent method that only considers the current gradient to update the weight, which is suitable for situations with small data sets and limited computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0052] Figure 1 It is a flow chart of the present invention.

[0053] Figure 2 This is the schematic diagram of the GA-BP neural network model.

[0054] Figure 3 Schematic diagram of the GA-BP neural network model in Example 3.

[0055] Figure 4 Schematic diagram of a single node of the GA-BP neural network model.

[0056] Figure 5(a) Schematic diagram of the degree of fit between the training set and the test set (first group).

[0057] Figure 5(b) Schematic diagram of the degree of fit between the training set and the test set (second group).

[0058] Figure 6(a) is a schematic diagram showing the comparison between the predicted values ​​and the true values ​​in the training set and the test set (first group).

[0059] Figure 6(b) is a schematic diagram showing the comparison between the predicted values ​​and the true values ​​in the training set and the test set (the second group). DETAILED DESCRIPTION

[0060] Example 1

[0061] like Figure 1 ,A method for predicting porosity of vegetation concrete is proposed. The specific steps are as follows:

[0062] Step 1: Establish a GA-BP neural network structure based on concrete parameters and porosity, divide the data set into training set and test set, and normalize them.

[0063] The BP neural network model includes an input layer, a hidden layer, and an output layer.

[0064] The normalization formula is: x is the input value; min and x max are the minimum and maximum values ​​of the input values, respectively. is the normalized result of the input value. The normalized data is distributed between [0, 1].

[0065] Step 2: Genetic Algorithm (GA) uses roulette wheel method to select individuals in the population, uses single-point crossover operator to generate two new individuals, uses adaptive mutation operator to generate new individuals, and then optimizes the weights and thresholds (biases) of BP neural network model to obtain the initial optimal weights and thresholds, which are brought into BP neural network model for error calculation, and weights and thresholds are updated until they meet the requirements of BP neural network model;

[0066] Step 3: Use the BP neural network model optimized by genetic algorithm to predict the porosity of the data in the test set and obtain the predicted value of the porosity.

[0067] Step 4: Based on the training set and the test set, the accuracy and performance of the GA-BP neural network model in predicting the porosity of concrete and the degree of fit of the GA-BP neural network model are evaluated.

[0068] The evaluation method uses the root mean square error (RMSE) and the coefficient of determination (R 2 ), the root mean square error (RMSE) is an indicator used to measure the prediction accuracy of the prediction model on continuous data. It measures the root mean square difference between the predicted value and the true value, indicating the average degree of deviation between the predicted value and the true value. Its formula is:

[0069]

[0070] Where: Y is the predicted value, X is the actual value, and N is the number of data groups.

[0071] Coefficient of determination (R 2 ) is a common indicator to measure the degree of fit of the model to the observed data. It indicates the proportion of the variance of the dependent variable that the model can explain, that is, the degree to which the model fits the data. Its formula is:

[0072]

[0073] Where: Y is the predicted value, X is the actual value, Z is the average value, and n is the number of data groups.

[0074] Step 5: Data prediction: randomly select training sets and test sets for prediction, predict concrete porosity, and evaluate the accuracy and fit.

[0075] Example 2

[0076] like Figure 2 ,A method for predicting porosity of vegetated concrete is proposed. The key is to introduce genetic algorithm to calculate individual fitness values ​​of the initial population, and to judge whether the output error meets the termination condition according to the individual fitness value calculation.

[0077] The calculation of individual fitness value includes the fitness function of genetic algorithm, the calculation of selection function of genetic algorithm, crossover operation and mutation operation. This GA-BP neural network model selects the initial population as 30, the crossover probability as 0.6, and the mutation probability as 0.1. Specifically, it includes:

[0078] Step 1: Determine the network parameters: training times 1000, target error 0.000001, learning rate 0.001.

[0079] Step 2: Population initialization: Encode the network parameters to form the initial solution of the population, and use real number encoding for the individuals in the population.

[0080] Step 3: Calculate fitness: This is a standard used to measure the quality of individuals in a population. Calculate the fitness of individuals in the generated initial population.

[0081] Step 4: Selection operation: Select the roulette method as the selection operator. The probability pi of individual i being selected is

[0082]

[0083] Where: fi is the fitness value of the individual, N is the number of individuals in the population, K is the coefficient, and Fi is the ranking of individual i.

[0084] Step 5: Crossover and mutation: Crossover and exchange operations are performed between different chromosomes to achieve gene exchange and generate new individuals. In order to avoid falling into the local optimal solution, mutation operations are adopted. The calculation formula for the crossover operation of the kth and ith chromosomes at position j is:

[0085]

[0086] Where: α kj represents the value of the kth individual in the parent generation at the jth gene locus, α ij It represents the value of the jth gene locus of the i-th individual in the parent generation. represents the value of the kth individual in the offspring at the jth gene locus, It represents the value of the jth gene locus of the i-th individual in the offspring, and b is a random number between 0 and 1.

[0087] The calculation formula for single-point mutation of the jth gene of the i-th individual is:

[0088]

[0089] Where: α ij represents the value of the i-th individual at the j-th gene locus, Represents the value of the i-th individual at the j-th gene locus after mutation, F = (1-g / Gmax) 2 , g is the current iteration number, Gmax is the maximum evolution number; a max 、a min Gene a ij The upper and lower bounds of ; r is a random number in [0,1]; r2 is a random number.

[0090] Step 6: Update the new population and calculate the fitness. Replace the individuals with high fitness with individuals with low fitness to form a new population. This continues until the fitness is greater than the preset threshold (bias), or the number of iterations reaches the preset number. Genetic Algorithms The optimal weights and thresholds (bias) obtained by (GA) are substituted into the BP neural network model for prediction. Genetics algorithm (GA) can optimize the calculation results through continuous iteration, making them infinitely close to the global optimal solution.

[0091] Example 3

[0092] like Figure 3 , Figure 4As shown, the GA-BP neural network model includes an input layer, a hidden layer and an output layer, and the BP neural network model includes an input layer, a hidden layer and an output layer. The number of neurons in the input layer of the BP neural network model is set to 5, the number of hidden layers is 1, and the output layer contains 1 neuron. The number of neurons in the hidden function selected in this model is 8. The error back propagation algorithm Levenberg-Marquardt is selected as the training algorithm, and learngd (learning function based on gradient descent method) is selected as the learning function. Transfer functions are set between the input layer and the hidden layer and between the hidden layer and the output layer. The transfer functions are f and F respectively. Using the error back propagation algorithm Levenberg-Marquardt as the training algorithm, the output of the hidden layer and the output layer is calculated as: H i =f(ΣW i x i +b); where f is the transfer function, Wi is the weight of the neuron, xi is the input signal, b is the neuron bias, H i is the output signal.

[0093] As can be seen from Figures 5(a), 5(b), 6(a), and 6(b), a porosity prediction method for vegetated concrete has effectively solved the problem of low computational efficiency based on traditional methods, improved computational efficiency, and achieved high accuracy. In this model, a total of 105 experimental data from scholars were selected. A BP neural network model based on genetic algorithm was constructed, and the data set was divided into a training set and a test set, including 74 training sets and 31 test sets, and the data was normalized. The genetic algorithm was used to optimize the weights and thresholds (biases) of the BP neural network model, and the parameters were encoded to form the initial solution of the population. The roulette method was selected as the selection operator to select individuals in the population, and the crossover operator was used to generate new individuals. The mutation operator was used to generate new individuals, and the BP model based on the genetic neural network was obtained to obtain the predicted value of the porosity. The number of neurons in the input layer is set to 5, the number of hidden layers is 1, and the output layer contains 1 neuron. The empirical formula for the number of neurons in the hidden layer is: Where m is the number of input layer nodes, n is the number of output layer nodes, and t is a constant between 0 and 10.

[0094] The number of neurons selected in the BP neural network model is 8. The topology of the three-layer network of 5-8-1 is obtained, the initial population is 30, the number of iterations is 150, the crossover probability is 0.6, and the mutation probability is 0.1. The network parameters are determined as follows: the number of training times is 1000, the target error is 0.000001, and the learning rate is 0.001.

[0095] Figure 5(a) and Figure 5(b) show the degree of fit of the training set and the test set, where R is the coefficient for evaluating the correlation between the predicted value and the test value of the GA-BP neural network model. The closer the R value is to 1, the better the predictive ability of the network model.

[0096] Figure 6(a) and Figure 6(b) show the comparison of the root mean square error of the training set and the validation set with the prediction results. The smaller the RMSE value, the closer the actual value is to the predicted value.

[0097] It can be seen from Figure 5(a), Figure 5(b) and Figure 6(a), Figure 6(b) that the predicted output values ​​generated by the BP neural network model after optimization by the genetic algorithm GA are consistent with the measured values, and the optimized BP neural network model has a higher prediction accuracy.

Claims

1. A method for predicting porosity of vegetated concrete, characterized in that: The following steps are involved: Step 1: Get the parameters of concrete; Step 2: Construct a GA-BP neural network model, divide the concrete parameter data set into a training set and a test set, and normalize them; Step 3: In the model training phase, the parameters of concrete are used as input variables, the porosity is used as the output variable, and the GA-BP neural network model is trained using the training set; the optimal weights and thresholds are obtained by optimizing the weights and thresholds in the GA-BP neural network model; Step 4: Predict the porosity of the data in the test set based on the optimized BP neural network model to obtain the predicted value of the porosity.

2. The porosity prediction method of vegetation concrete according to claim 1, characterized in that: It also includes step 5: evaluation based on the training set and the test set to evaluate the accuracy and performance of the GA-BP neural network model in predicting the porosity of concrete, as well as the degree of fit of the GA-BP neural network model.

3. The porosity prediction method of vegetation concrete according to claim 1, characterized in that: In step 1, the parameters of concrete include: water, cement, water-cement ratio, coarse aggregate and compressive strength.

4. The porosity prediction method of vegetation concrete according to claim 1, characterized in that: In the step 2, the constructed GA-BP neural network model includes: an input layer, a hidden layer, and an output layer; and transfer functions f and F are provided between the input layer and the hidden layer and between the hidden layer and the output layer; the hidden layer adopts the tansig transfer function, which can map the input to the interval [-1,1]; the output layer adopts the purelin transfer function, which directly outputs the predicted value of the network.

5. The porosity prediction method of vegetation concrete according to claim 1, characterized in that: In step 3, the genetic algorithm GA uses a roulette method to select individuals in the population, uses a single-point crossover operator to generate two new individuals, uses an adaptive mutation operator to generate new individuals, and then optimizes the weights and thresholds of the BP neural network model to obtain initial optimal weights and thresholds; the initial optimal weights and thresholds are then brought into the BP neural network model for error calculation, and the weights and thresholds are updated until the requirements of the model are met.

6. The method for predicting porosity of vegetation concrete according to claim 5, characterized in that: In step 3, the genetic algorithm GA specifically includes the following process steps: Step 2.1, determine the network parameters; Step 2.2, population initialization: Encode the network parameters to form the initial solution of the population, and use real number encoding for the individuals in the population; Step 2.3, calculate fitness: a standard used to measure the quality of individuals in a population, and calculate the fitness of individuals in the generated initial population; Step 2.4, selection operation: Select the roulette method as the selection operator, and the probability pi of individual i being selected is In the formula: fi is the fitness value of the individual, N is the number of individuals in the population, K is the coefficient, and Fi is the ranking of individual i; Step 2.5, crossover operation and mutation: crossover operation is performed between different chromosomes to achieve gene exchange and produce new individuals; In order to avoid falling into the local optimal solution, mutation operation is adopted; the calculation formula for the crossover operation of the kth and ith chromosomes at position j is: Where: b is a random number from 0 to 1, α kj represents the value of the kth individual in the parent generation at the jth gene locus, α ij represents the value of the jth gene locus of the i-th individual in the parent generation, represents the value of the kth individual in the offspring at the jth gene locus, Represents the value of the jth gene locus of the i-th individual in the offspring; The calculation formula for single-point mutation of the jth gene of the i-th individual is: Where: α ij represents the value of the i-th individual at the j-th gene locus, represents the value of the i-th individual at the j-th gene locus after mutation, a max 、a min Gene a ij The upper and lower bounds of; r2 is a random number; F = (1-g / Gmax) 2 , g is the current iteration number, Gmax is the maximum evolution number; r is a random number in [0,1]; Step 2.6: Update the new population and calculate its fitness, replacing individuals with low fitness with individuals with high fitness to form a new population; Until the fitness is greater than the preset threshold, or the number of iterations reaches the preset number; finally, the optimal weight and threshold are substituted into the BP neural network model for prediction.

7. The method for predicting porosity of vegetation concrete according to claim 6, characterized in that: In step 3, the BP neural network model includes hidden layer training, using the LM algorithm as the training algorithm, including the following steps: First, set the initial weights and thresholds of the BP neural network model; Then, the input value is input into the input layer of the BP neural network model, and after weighted summation and activation function processing of each layer, the output result of the BP neural network model is obtained; Finally, the output of the BP neural network model is compared with the actual result label to obtain the error between the predicted result and the actual label; The LM algorithm is used as a training algorithm, and the output calculation formula of the hidden layer and the output layer is: H i =f(∑W i x i +b); Where f is the transfer function, W i is the weight of the neuron, x i is the input signal, b is the neuron bias, H i is the output signal.

8. The porosity prediction method of vegetation concrete according to claim 1, characterized in that: In step 4, the performance of the predicted value and the true value is evaluated using the root mean square error RMSE and the coefficient of determination R 2 , the root mean square error RMSE is used to measure the prediction accuracy of the GA-BP neural network model on continuous data; the root mean square error RMSE is used to measure the root mean square difference between the predicted value and the true value, indicating the average deviation between the predicted value and the true value; the formula is: In the formula: Y is the predicted value, X is the actual value, and N is the number of data groups; Coefficient of determination R 2 Used to measure the degree of fit of the GA-BP neural network model to the observed data; the determination coefficient R 2 It indicates the proportion of the variance of the dependent variable that the GA-BP neural network model can explain, that is, the degree to which the GA-BP neural network model fits the data; The formula is: Where: Y is the predicted value, X is the actual value, Z is the average value, and n is the number of data groups.

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