Nuclear power plant room rapid evaluation method based on FFX algorithm and AEC

Abstract

The invention belongs to the technical field of mechanical calculation simulation, and particularly relates to a nuclear power plant house rapid evaluation method based on an FFX algorithm and AEC. According to the method, firstly, an initial input data set X1 is set to be the total usage amount of various materials, an initial input data set X2 is set to be the unit price and output parameters of various materials, then preprocessing operation of constructing an input and output matrix and removing abnormal data is carried out on the data, and then standardization processing is carried out on the data; and training the model and optimizing parameters by using an FFX algorithm and a path regularization learning technology, selecting an optimal primary function and generating a final symbol expression. And finally, flexibly selecting a model generated by taking mape and nrmse as minimization indexes by utilizing an adaptive error measurement adjustment mechanism. According to the method, the cost estimation model is efficiently and accurately constructed, the prediction performance of the model can be improved through an intelligent error measurement adjustment mechanism, and the purpose of optimizing a factory building cost estimation mode is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical calculation simulation, and in particular relates to a rapid valuation method for a nuclear power plant based on an FFX algorithm and AEC. Background Art

[0002] In the field of construction engineering, especially in the process of estimating the cost of plant buildings, there are many influencing factors. These factors include plant scale, amount of concrete, amount of steel bars, amount of steel structure and the price of these materials. Due to the complex relationship between variables, traditional linear regression models often have difficulty in effectively capturing the nonlinear relationship between them and the cost of plant buildings, resulting in low estimation accuracy.

[0003] With the widespread application of computer algorithms in various fields, they have also begun to be applied in factory cost estimation, including machine learning algorithms, optimization algorithms, symbolic regression algorithms, data mining and analysis, expert systems, etc. In the prior art, symbolic regression methods mainly include optimization methods based on genetic programming (GP) and neural networks. The GP method uses genetic operations (such as selection, crossover, and mutation) to generate symbolic models. Although it has strong global search capabilities, its computational complexity is high, the model complexity is difficult to control, and it is easy to cause overfitting. The neural network-based method captures complex nonlinear relationships through deep learning technology. However, its models are mostly black box in nature, lack intuitive mathematical expressions, and are difficult to provide good interpretability.

[0004] In contrast, the FFX (Fast Function Extraction) algorithm, as a symbolic regression method based on gradient optimization, can quickly process high-dimensional data while ensuring the generation of concise mathematical expressions. However, the FFX algorithm still faces some challenges in application, such as insufficient robustness of basis function selection in high-noise data and difficulty in dynamic adaptation under multiple error metrics, which limits its application in complex plant cost estimation.

[0005] Adaptive Error Correction (AEC) is a technology that dynamically adjusts error correction strategies to improve system performance and reliability. It can dynamically adjust error and correction strategies and automatically optimize error correction parameters according to the current state of the system and environmental changes. It also has the advantage of real-time performance, can respond and adjust quickly in real-time systems, ensure system stability and performance, and has strong resistance to noise and interference, and can maintain good performance under adverse conditions. Summary of the invention

[0006] In view of this, the purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for rapid estimation of nuclear power plants based on the FFX algorithm and combined with AEC. This method improves the above-mentioned deficiencies of the FFX algorithm by combining path regularization technology and adaptive error adjustment mechanism. The path regularization technology is used to dynamically adjust the regularization parameters in model training, which effectively improves the stability and robustness of the model. The AEC mechanism flexibly selects the error metric based on the data characteristics to ensure that the model can provide accurate predictions under different data distributions. Through the above improvements, the present invention is particularly suitable for plant cost estimation scenarios, and has significant advantages in model efficiency, accuracy and interpretability.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solution: a rapid valuation method for nuclear power plant based on FFX algorithm and AEC, comprising the following steps:

[0008] S1: Parameter setting: The total usage of various materials and their unit prices required for the construction of multiple sample factories are taken as input parameters, the total usage of various materials required for the construction of sample factories is defined as the initial input data set X1, the unit prices of various materials are defined as the initial input data set X2, and the total price of the sample factories is taken as the output parameter.

[0009] Preferably, the initial input data set X1 in step S1 includes the total amount of materials used, such as the amount of concrete, the amount of steel bars, the amount of steel structures, the amount of ordinary sleeves, the amount of anchor plates, and the amount of embedded parts, and the initial input data set X2 includes the unit prices of materials such as the unit price of concrete, the unit price of steel bars, the unit price of steel structures, the unit price of ordinary sleeves, the unit price of anchor plates, and the unit price of embedded parts.

[0010] S2: Data preprocessing:

[0011] A. Construct input and output matrices: Multiply the initial input data set X1 and the initial input data set X2 of multiple sample factories to obtain the total price input matrix X of each material, and the total cost of the sample factory is the output matrix Y.

[0012] B. Data cleaning: Processing missing values ​​and outliers: Use the column data of the total price input matrix X as the horizontal coordinate and the corresponding cost in the output matrix Y as the vertical coordinate. Determine the data whose scale is not proportional to the cost as outliers and delete the corresponding sample data in the total price input matrix X and the output matrix Y.

[0013] Preferably, the initial input data set X1 in step S2 is a two-dimensional matrix with a size of N*n, which represents the total amount of each material used in each sample plant; the initial input data set X2 is a two-dimensional matrix with a size of N*n, which represents the unit price of each material in each sample plant, where N is the total number of sample plants and n is the total number of features.

[0014] Preferably, the total price input matrix X in step S2 is a two-dimensional matrix with a size of N*n, which represents the total price of each material cost of each sample factory building; the output matrix Y is a two-dimensional matrix with a size of N*1, which represents the total construction cost of each sample factory building, where N is the total number of sample factories and n is the total number of features.

[0015] Preferably, in step S2, based on actual experience, the construction cost is proportional to the scale of the plant, the column data of the total price input matrix X is used as the horizontal coordinate to represent the total price of each column of materials in each sample plant, and the output matrix Y is used as the vertical coordinate to represent the total construction cost of each sample plant, and a curve graph is drawn. When the total price of each column of materials in the sample plant is not proportional to the total construction cost corresponding to the sample plant, the group of data is deleted.

[0016] S3: Data standardization: Define each material required for the construction of the sample plant as a feature, adjust the mean of each feature to 0, and the standard deviation to 1. The standardization formula for each feature is (1): In the formula, z is the standardized eigenvalue, x is the original eigenvalue, μ is the mean of the feature, and σ is the standard deviation of the feature.

[0017] The calculation formula of the mean μ in formula (1) is as follows (2):

[0018] In formula (2), N is the total number of sample plants, x i is the characteristic value of the i-th sample plant.

[0019] The standard deviation σ in formula (1) is calculated as follows (3):

[0020] In formula (3), N is the total number of sample plants, x i is the characteristic value of the i-th sample plant, and μ is the mean.

[0021] The standardized eigenvalue Z in formula (1) i The calculation formula is as follows (4):

[0022] Z in formula (4) i is the standardized characteristic value of the i-th sample plant.

[0023] S4: Use the FFX algorithm and path regularization learning technology to train the model and optimize the parameters:

[0024] A. Feature screening: According to the importance of features, the first 2*sqrt(n) feature sets U1 and the first n / 2 feature sets U2 are screened out, where n is the total number of features.

[0025] B. Define univariate basis functions: Generate univariate basis functions for each feature in feature sets U1 and U2, forming function sets F1 and F2 respectively.

[0026] C. Generate bivariate basis functions: cross-multiply the univariate basis functions in function set F1 to obtain bivariate basis function set F3, merge function set F2 and function set F3 to form the final function set F.

[0027] D. Combine regularized learning technology to train the model: use cross-validation method, select 11_ratio and alpha as regularization parameters, use mape and nrmse as minimization indicators respectively, adopt elastic net regression algorithm, generate models Hm and Hn respectively, train the total price input matrix X and output matrix Y, and return the values ​​of the two indicators, the mean absolute percentage error mape and the normalized root mean square error nrmse, as well as the corresponding coefficient matrix coeff and basis function mapping dictionary mapping.

[0028] The calculation formula of mape is formula (5):

[0029]

[0030] where yi is the actual observation value of the ith is the i-th predicted value, and n is the total number of samples.

[0031] The calculation formula of nrmse is formula (6):

[0032]

[0033] Where ymax is the maximum actual value and ymin is the minimum actual value.

[0034] The loss function of elastic net regression is formula (7):

[0035]

[0036] Where: n is the total number of samples, y i is the actual observation value of the ith is the i-th predicted value, w j is the jth regression coefficient of the model, λ 1 is the weight coefficient of the L1 regularization term (Lasso). 2 is the weight coefficient of the L2 regularization term (Ridge),

[0037] p is the total number of features.

[0038] E. Select the optimal basis function and generate the final symbolic expression: Evaluate the complexity and fitting error of each candidate expression and select the best expression.

[0039] Preferably, the function sets F1 and F2 generated in step S4 include univariate basis functions such as X, X^2, X^3, sqrt(X), log(X), max(X, 0), min(X, 0), etc.

[0040] Preferably, in the regularization learning technique in step S4, the regularization parameter selection 11_ratio is set to 0.95, and the regularization parameter alpha generates 666 logarithmically uniformly distributed alpha values using the np.logspace function, where the minimum value of the logarithm is 1e-10 and the maximum value of the logarithm is 100.

[0041] Preferably, when training the model in step S4, search for different alpha values from large to small, and add an early stopping strategy. When the change in the training index is less than 0.001 for two consecutive times, stop training in advance.

[0042] S5: Adaptive error metric adjustment mechanism: According to the statistical characteristics of the standard deviation σ and the mean μ calculated in step (S3), determine its distribution type, and then determine the parameters k1 and k2 in the adaptive error metric strategy. When the standard deviation σ < 0.8, set k1 = 1.1 and k2 = 1.21 to adapt to the characteristics of the central tendency of the dataset. When the standard deviation σ ≥ 0.8, set k1 = 1.2 and k2 = 1.44 to enhance the robustness of the model.

[0043] S6: Model selection: According to the values of the mean absolute percentage error mape and the normalized root mean square error nrmse returned in step (S3), determine the selected model:

[0044] When mape < 0.05, use the model Hm generated with mape as the minimization index.

[0045] When 0.05 ≤ mape < 0.1, if nrmse < mape, use the model Hn generated with nrmse as the minimization index. If nrmse ≥ mape, use the model Hm generated with mape as the minimization index.

[0046] When 0.1 ≤ mape < 0.2, if nrmse < k1 * mape, use the model Hn generated with nrmse as the minimization index. If nrmse ≥ k1 * mape, use the model Hm generated with mape as the minimization index.

[0047] When 0.2 ≤ mape < 0.3, if nrmse < k2 * mape, use the model Hn generated with nrmse as the minimization index. If nrmse ≥ k2 * mape, use the model Hm generated with mape as the minimization index.

[0048] When mape ≥ 0.3, nrmse is directly used as the model Hn generated by minimizing the index.

[0049] Obviously, the number of feature sets U1 screened according to feature importance in step S4, the number of feature sets U2, the number of univariate basis functions generated in feature sets U1 and U2 and the univariate basis functions, the minimization index in the regularization learning technology, and the numerical values ​​of the regularization parameters are all selected according to actual conditions; the standard deviation σ, parameters k1 and k2 in step S5 are all selected according to actual conditions; the value ranges of mape and nrmse in step S6 are all selected according to actual conditions.

[0050] The beneficial effects of the present invention are: 1. High efficiency and speed: The FFX algorithm combined with path regularization learning technology can generate a symbolic model in a relatively short time, which is suitable for large-scale plant cost estimation. 2. Adaptive error measurement: Dynamically optimize the use of NRMS and MAPE based on the data characteristics of the true value to ensure that the model can select the optimal error measurement method under different characteristics. 3. High transparency and interpretability: Generate concise mathematical expressions to facilitate engineering application and interpretation, and improve model transparency and operability. 4. Strong scalability: The algorithm can handle large-scale input variables and automatically screen out the most influential features to enhance model scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is the algorithm flow chart of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the structure of the present invention.

[0053] like Figure 1 As shown in the flowchart in, a rapid valuation method for a nuclear power plant based on the FFX algorithm and AEC includes the following steps:

[0054] S1: Parameter setting: The total usage of various materials and their unit prices required for the construction of multiple sample factories are taken as input parameters, the total usage of various materials required for the construction of sample factories is defined as the initial input data set X1, the unit prices of various materials are defined as the initial input data set X2, and the total price of the sample factories is taken as the output parameter.

[0055] The initial input data set X1 in step S1 includes the total amount of materials used, such as the amount of concrete, the amount of steel bars, the amount of steel structures, the amount of ordinary sleeves, the amount of anchor plates, and the amount of embedded parts. The initial input data set X2 includes the unit prices of materials such as the unit price of concrete, the unit price of steel bars, the unit price of steel structures, the unit price of ordinary sleeves, the unit price of anchor plates, and the unit price of embedded parts.

[0056] For example, the factory building has 11 basic parameters, including total concrete volume (m3), total steel bar volume (tons), common sleeves (pieces), anchor plates (pieces), anti-aircraft sleeves (pieces), embedded parts (tons), stainless steel coverings (tons), prestressed steel strands (tons), steel structures (including external water tanks) (tons), steel linings (including corbels and penetrations) (tons), and outer shell steel formwork (tons), as well as the unit price (yuan) of the material corresponding to each parameter, for a total of 22 input parameters. The initial input data set X1 is the total amount of these 11 materials used, and the initial input data set X2 is the unit price of these 11 materials.

[0057] Output parameter: Construction cost of the factory building (yuan), a total of 1 output parameter.

[0058] S2: Data preprocessing:

[0059] Construct input and output matrices: Multiply the initial input data set X1 and the initial input data set X2 of multiple sample factories to obtain the total price input matrix X of each material, and the total cost of the sample factory is the output matrix Y.

[0060] Taking 14 factories as an example, the initial input data set X1 is a 14*11 matrix, where 14 are rows, representing each factory, hereinafter referred to as the number of samples, and 11 are columns, representing the total amount of 11 materials used; and the initial input data set X2 is also a 14*11 matrix, where 14 rows represent each factory, and 11 columns represent the unit price of 11 materials; then multiply the corresponding elements of X1 and X2 to obtain the total price input matrix X, which is still a 14*11 matrix, where 14 rows represent each factory, and 11 columns represent the total price of various materials. The output matrix Y is a 14*1 matrix, where 14 rows represent each factory, and 1 column represents the total cost of the factory.

[0061] B. Data cleaning: Processing missing values ​​and outliers: Use the column data of the total price input matrix X as the horizontal coordinate and the corresponding cost in the output matrix Y as the vertical coordinate. Determine the data whose scale is not proportional to the cost as outliers and delete the corresponding sample data in the total price input matrix X and the output matrix Y.

[0062] The initial input data set X1 in step S2 is a two-dimensional matrix with a size of N*n, which represents the total amount of each material used in each sample plant; the initial input data set X2 is a two-dimensional matrix with a size of N*n, which represents the unit price of each material in each sample plant, where N is the total number of sample plants and n is the total number of features.

[0063] The total price input matrix X in step S2 is a two-dimensional matrix with a size of N*n, which represents the total price of each material cost of each sample factory building; the output matrix Y is a two-dimensional matrix with a size of N*1, which represents the total construction cost of each sample factory building, where N is the total number of sample factories and n is the total number of features.

[0064] In step S2, according to actual experience, the construction cost is proportional to the scale of the plant. The column data of the total price input matrix X is used as the horizontal coordinate to represent the total price of each column of materials in each sample plant, and the output matrix Y is used as the vertical coordinate to represent the total construction cost of each sample plant. A curve chart is drawn. When the total price of each column of materials in the sample plant is not proportional to the total construction cost corresponding to the sample plant, the group of data is deleted.

[0065] Suppose two sets of data are found to be abnormal. After data cleaning, the size of the input matrix X becomes 12*11, and the size of the output matrix Y becomes 12*1.

[0066] S3: Data standardization: Define each material required for the construction of the sample plant as a feature, adjust the mean of each feature to 0, and the standard deviation to 1. The standardization formula for each feature is (1): In the formula, z is the standardized eigenvalue, x is the original eigenvalue, μ is the mean of the feature, and σ is the standard deviation of the feature.

[0067] The calculation formula of the mean μ in formula (1) is as follows (2): In formula (2), N is the total number of sample plants, and xi is the characteristic value of the i-th sample plant.

[0068] The standard deviation σ in formula (1) is calculated as follows (3): In formula (3), N is the total number of sample plants, x i is the characteristic value of the i-th sample plant, and μ is the mean.

[0069] The standardized eigenvalue Z in formula (1) i The calculation formula is as follows (4): Z in formula (4) i is the standardized characteristic value of the i-th sample plant.

[0070] After data is standardized, it has the following advantages: 1. It can eliminate the impact of dimension: the value ranges of different features can be very different. After standardization, each feature can be compared more fairly under the same dimension. 2. Improve the convergence speed of the model: FFX is essentially an algorithm based on gradient descent. Standardized data can speed up the convergence speed and thus improve training efficiency. 3. The scale of the input and output matrices remains unchanged after standardization.

[0071] S4: Use the FFX algorithm and path regularization learning technology to train the model and optimize the parameters:

[0072] A. Feature screening: According to the importance of features, the first 2*sqrt(n) feature sets U1 and the first n / 2 feature sets U2 are screened out, where n is the total number of features.

[0073] B. Define univariate basis functions: Generate univariate basis functions for each feature in feature sets U1 and U2, forming function sets F1 and F2 respectively. The selection strategy of basis functions can be customized. This example selects 6 univariate basis functions, including X, X^2, sqrt(X), log(X), max(X, 0), and min(X, 0).

[0074] C. Generate bivariate basis functions: cross-multiply the univariate basis functions in function set F1 to obtain bivariate basis function set F3, merge function set F2 and function set F3 to form the final function set F.

[0075] D. Combine regularized learning technology to train the model: use cross-validation method, select 11_ratio and alpha as regularization parameters, use mape and nrmse as minimization indicators respectively, adopt elastic net regression algorithm, generate models Hm and Hn respectively, train the total price input matrix X and output matrix Y, and return the values ​​of the two indicators, the mean absolute percentage error mape and the normalized root mean square error nrmse, as well as the corresponding coefficient matrix coeff and basis function mapping dictionary mapping.

[0076] The calculation formula of mape is formula (5):

[0077]

[0078] where yi is the actual observation value of the ith is the i-th predicted value, and n is the total number of samples.

[0079] The calculation formula of nrmse is formula (6):

[0080]

[0081] Where ymax is the maximum actual value and ymin is the minimum actual value.

[0082] The loss function of elastic net regression is formula (7):

[0083]

[0084] Where: n is the total number of samples, y i is the actual observation value of the ith is the i-th predicted value, w j is the jth regression coefficient of the model, λ 1 is the weight coefficient of the L1 regularization term (Lasso). 2 is the weight coefficient of the L2 regularization term (Ridge),

[0085] p is the total number of features.

[0086] In the regularized learning technique, the regularization parameter 11_ratio is set to 0.95, and the regularization parameter alpha uses the np.logspace function to generate 666 logarithmically uniformly distributed alpha values, where the minimum value of the logarithm is 1e-10 and the maximum value of the logarithm is 100.

[0087] Search for different alpha values ​​from large to small, add an early stopping strategy, and stop training early when the change in the index for two consecutive training runs is less than 0.001.

[0088] Obviously, the number of feature sets U1 selected according to feature importance, the number of feature sets U2, the number of univariate basis functions generated in feature sets U1 and U2 and the univariate basis functions, the minimization index in the regularization learning technology, and the numerical values ​​of the regularization parameters in this part are all selected according to actual conditions.

[0089] E. Select the optimal basis function and generate the final symbolic expression: Evaluate the complexity and fitting error of each candidate expression and select the best expression.

[0090] S5: Adaptive error metric adjustment mechanism: According to the statistical characteristics of the standard deviation σ and mean μ calculated in step (S3), determine their distribution type, and then determine the parameters k1 and k2 in the adaptive error metric strategy. When the standard deviation σ<0.8, set k1=1.1 and k2=1.21 to adapt to the characteristics of the trend in the data set. When the standard deviation σ≥0.8, set k1=1.2 and k2=1.44 to enhance the robustness of the model.

[0091] Obviously, the values ​​of σ, k1, and k2 can be selected and determined according to actual conditions.

[0092] S6: Model selection: Determine the selected model based on the values ​​of the mean absolute percentage error mape and the normalized root mean square error nrmse returned in step (S3):

[0093] When mape<0.05, the model Hm generated by using mape as the minimization index is

[0094] When \(0.05\leq mape < 0.1\), if \(nrmse < mape\), then the model \(H_n\) generated with \(nrmse\) as the minimization metric is adopted; if \(nrmse\geq mape\), then the model \(H_m\) generated with \(mape\) as the minimization metric is adopted.

[0095] When \(0.1\leq mape < 0.2\), if \(nrmse < k1*mape\), then the model \(H_n\) generated with \(nrmse\) as the minimization metric is adopted; if \(nrmse\geq k1*mape\), then the model \(H_m\) generated with \(mape\) as the minimization metric is adopted.

[0096] When \(0.2\leq mape < 0.3\), if \(nrmse < k2*mape\), then the model \(H_n\) generated with \(nrmse\) as the minimization metric is adopted; if \(nrmse\geq k2*mape\), then the model \(H_m\) generated with \(mape\) as the minimization metric is adopted.

[0097] When \(mape\geq 0.3\), then directly adopt the model \(H_n\) generated with \(nrmse\) as the minimization metric.

[0098] Obviously, regarding the setting of the threshold range in this part, it can be selected and determined according to the actual situation.

[0099] Using the adaptive error metric has the following advantages: 1. Dynamic adaptability: The cost estimation of nuclear power plants involves various non-linear relationships and complex variables. The adaptive error metric can be adjusted in real time according to the data distribution, enabling the model to adopt the most suitable error metric in different data characteristics. This strategy improves the sensitivity and adaptability of the model to data, thereby enhancing the prediction accuracy. 2. Improving model robustness: By dynamically adjusting the error metric, the model can maintain a stable performance when facing different input features and data noise. Especially when the standard deviation of the data is large, such as in the case of outliers or increased uncertainty, the adaptive adjustment mechanism can enhance the robustness of the model and avoid performance degradation caused by data anomalies. 3. Optimizing model selection: Dynamically select the optimal model as the prediction basis according to the error metrics in different ranges (such as MAPE and NRMSE). This selection logic is clear and practical, making the model design more flexible, capable of implementing the best error assessment for specific problems and data characteristics, and thus improving the estimation accuracy. 4. Improving computational efficiency: The adaptive error metric adjustment can reduce unnecessary computational burdens during the training and prediction processes. By dynamically selecting the error metric in real time, the types of errors that the model needs to evaluate can be reduced, thereby achieving more efficient calculations and faster response times.

[0100] Regarding the application of this algorithm, a model can be trained for each subclass of the plant, and the storage method of the final model is as follows:

[0101] The total price input matrix X' is the matrix after calculating material parameters*material prices and filtering outliers;

[0102] Final output variable Y': total cost of factory building;

[0103] The coefficient matrix coeff corresponding to the selected model: the coefficient of each item in the regression function;

[0104] The basis function mapping matrix mapping corresponding to the selected model: stores the mapping relationship of the basis functions.

[0105] When the model needs to be called: first calculate the material parameters * material price, then get the final function set F' after feature expansion through the mapping dictionary, and then calculate the final predicted cost through the linear combination of F' and the coefficient matrix coeff.

[0106] In addition, the definitions of terms used in this application are as follows:

[0107] 1. Symbolic Regression: A regression method that aims to fit the relationship between input variables and output variables by generating symbolic expressions (such as mathematical formulas). Unlike traditional regression, its goal is to find an optimal function structure and parameter values.

[0108] 2. Genetic Algorithm (GA): An optimization algorithm based on the principles of natural selection and genetics. It simulates the biological evolution process through operations such as selection, crossover and mutation, and is used to generate candidate solutions and find the optimal solution.

[0109] 3. Neural Network (NN): A computational model that simulates the behavior of biological neural networks. It processes data through a multi-layer structure (such as input layer, hidden layer, output layer). It is good at capturing nonlinear relationships, but lacks interpretability.

[0110] 4. FFX algorithm (Fast Function Extraction): A symbolic regression method based on gradient optimization that can quickly extract concise mathematical expressions from data. The FFX algorithm balances the complexity and fitting accuracy of the model through techniques such as path regularization.

[0111] 5. Elastic Net Regression: A regularization method for linear regression that combines the advantages of L1 (Lasso) and L2 (Ridge) regularization to effectively deal with high-dimensional feature selection and multicollinearity problems. The elastic net controls the complexity of the model by adjusting two regularization parameters.

[0112] 6. Path Regularization: A regularization technique that generates a series of model paths by gradually adjusting the regularization parameters (such as the ratio of L1 and L2 regularization parameters) to balance model complexity and fitting ability.

[0113] 7. Basis Function: A single or multivariable function generated by the input variables, used to construct complex symbolic regression models. For example, common basis functions include linear functions, polynomial functions, logarithmic functions, square root functions, etc.

[0114] 8. Regularization Parameter: It is used to control the weight of the regularization term in model training. Common parameters include L1 regularization coefficient (controlling sparsity) and L2 regularization coefficient (controlling smoothness).

[0115] 9. Root Mean Square Error (RMSE): An indicator for evaluating model prediction error, which represents the square root of the sum of squares of the deviations between the predicted value and the true value. The smaller the value, the better the model fitting effect.

[0116] 10. Normalized Root Mean Square Error (NRMSE): It is a normalized version of the root mean square error (RMSE). By dividing the RMSE by the range or mean of the predicted values, it makes it suitable for data of different scales and provides a measure of relative error.

[0117] 11. Mean Absolute Percentage Error (MAPE): A normalized error metric used to represent the average relative error between the predicted value and the true value, suitable for processing data with different dimensions.

[0118] 12. Adaptive Error Adjustment Mechanism: A mechanism that dynamically adjusts the error measurement method based on data distribution characteristics (such as standard deviation) to improve the prediction accuracy and robustness of the model.

[0119] 13. Basis Function Mapping Dictionary: A structure that stores the mapping relationship between basis functions and original features, used to quickly locate the feature combinations and their coefficients used by the model during the prediction phase.

[0120] 14. Early Stopping: A strategy to prevent model overfitting. During the training process, when the model performance no longer improves significantly after several consecutive rounds, training is stopped to save computing resources.

[0121] 15. Normalization: A data preprocessing method that adjusts the mean and standard deviation of features so that they are distributed within a standard range, which helps improve the training speed and stability of the model.

[0122] 16. High-Noise Data: refers to data that contains a large amount of random errors or irrelevant information, which usually has an adverse effect on the model's fitting ability.

[0123] 17. Robustness: The ability of a model to maintain stable performance when facing abnormal or noisy data is an important indicator to measure the practicality of the model.

[0124] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A rapid valuation method for nuclear power plants based on FFX algorithm and AEC, characterized by: The following steps are involved: S1: Parameter setting: The total usage of various materials and their unit prices required for the construction of multiple sample plants are taken as input parameters, the total usage of various materials required for the construction of sample plants is defined as the initial input data set X1, the unit prices of various materials are defined as the initial input data set X2, and the total price of the sample plants is taken as the output parameter; S2: Data preprocessing: A. Construct input and output matrices: Multiply the initial input data set X1 and the initial input data set X2 of multiple sample plants to obtain the total price input matrix X of each material, and the total cost of the sample plant is the output matrix Y; B. Data cleaning: Processing missing values ​​and outliers: Using the column-wise data of the total price input matrix X as the horizontal coordinate and the corresponding cost in the output matrix Y as the vertical coordinate, the data whose scale and cost are not proportional are determined as outliers, and the corresponding sample data in the total price input matrix X and the output matrix Y are deleted; S3: Data standardization: Define each material required for the construction of the sample plant as a feature, adjust the mean of each feature to 0, and the standard deviation to 1. The standardization formula for each feature is (1): In the formula, z is the standardized eigenvalue, x is the original eigenvalue, μ is the mean of the feature, and σ is the standard deviation of the feature; The calculation formula of the mean μ in formula (1) is as follows (2): In formula (2), N is the total number of sample plants, x i is the characteristic value of the i-th sample plant, The standard deviation σ in formula (1) is calculated as follows (3): In formula (3), N is the total number of sample plants, x i is the characteristic value of the i-th sample plant, μ is the mean, The standardized eigenvalue Z in formula (1) i The calculation formula is as follows (4): Z in formula (4) i is the standardized characteristic value of the i-th sample plant; S4: Use the FFX algorithm and path regularization learning technology to train the model and optimize the parameters: A. Feature screening: According to the importance of features, select the first 2*sqrt(n) feature sets U1 and the first n / 2 feature sets U2, where n is the total number of features; B. Define univariate basis functions: Generate univariate basis functions for each feature in feature sets U1 and U2, forming function sets F1 and F2 respectively; C. Generate bivariate basis functions: cross-multiply the univariate basis functions in function set F1 to obtain bivariate basis function set F3, and merge function set F2 and function set F3 to form the final function set F; D. Combine regularized learning technology to train the model: Use cross-validation, select l1_ratio and alpha as regularization parameters, use mape and nrmse as minimization indicators, and generate models H respectively. m and H n , train the total price input matrix X and output matrix Y, select the optimal basis function and generate the final symbolic expression, and the optimal basis function returns the values ​​of the two indicators, the mean absolute percentage error mape and the normalized root mean square error nrmse, as well as the corresponding coefficient matrix coeff and basis function mapping dictionary mapping; E. Select the optimal basis function and generate the final symbolic expression: evaluate the complexity and fitting error of each candidate expression and select the best expression; S5: Adaptive error metric adjustment mechanism: According to the statistical characteristics of the standard deviation σ and mean μ calculated in step (S3), its distribution type is determined, and then the parameters k1 and k2 in the adaptive error metric strategy are determined. When the standard deviation σ<0.8, k1=1.1 and k2=1.21 are set to adapt to the characteristics of the trend in the data set. When the standard deviation σ ≥ 0.8, k1 = 1.2 and k2 = 1.44 are set to enhance the robustness of the model; S6: Model selection: Determine the selected model based on the values ​​of the mean absolute percentage error mape and the normalized root mean square error nrmse returned in step (S4): When mape<0.05, the model H generated by using mape as the minimization index m , When 0.05 ≤ mape < 0.1, if nrmse < mape, then the model H generated using nrmse as the minimization metric is adopted n , if nrmse ≥ mape, then the model H generated using mape as the minimization metric is adopted m , When 0.1 ≤ mape < 0.2, if nrmse < k1 * mape, then the model H generated with nrmse as the minimization metric is adopted n , if nrmse ≥ k1 * nape, then the model H generated with mape as the minimization metric is adopted m , When \(0.2\leq mape \lt 0.3\), if \(nrmse \lt k2*mape\), then the model \(H\) is generated using \(nrmse\) as the minimization metric n , if \(nrmse\geq k2*mape\), then the model \(H\) is generated using \(mape\) as the minimization metric m , When mape ≥ 0.3, nrmse is directly used as the minimization index to generate the model H n .

2. According to claim 1, a rapid valuation method for nuclear power plant based on FFX algorithm and AEC is characterized by: The initial input data set X1 in step S1 includes the total amount of concrete, steel bar amount, steel structure amount, ordinary sleeve amount, anchor plate amount, and embedded parts used, and the initial input data set X2 includes the unit price of concrete, the unit price of steel bar, the unit price of steel structure, the unit price of ordinary sleeve, the unit price of anchor plate, and the unit price of embedded parts.

3. According to claim 1, a rapid valuation method for nuclear power plant based on FFX algorithm and AEC is characterized by: The initial input data set X1 in step S2 is a two-dimensional matrix with a size of N*n, which represents the total amount of each material used in each sample plant; the initial input data set X2 is a two-dimensional matrix with a size of N*n, which represents the unit price of each material in each sample plant, where N is the total number of sample plants and n is the total number of features.

4. According to claim 1, a rapid valuation method for nuclear power plant based on FFX algorithm and AEC is characterized by: The total price input matrix X in step S2 is a two-dimensional matrix with a size of N*n, which represents the total price of each material cost of each sample factory building; the output matrix Y is a two-dimensional matrix with a size of N*1, which represents the total construction cost of each sample factory building, where N is the total number of sample factories and n is the total number of features.

5. According to claim 1, a rapid valuation method for nuclear power plant based on FFX algorithm and AEC is characterized by: In step S2, according to actual experience, the construction cost is proportional to the scale of the plant. The column data of the total price input matrix X is used as the horizontal coordinate to represent the total price of each column of materials in each sample plant, and the output matrix Y is used as the vertical coordinate to represent the total construction cost of each sample plant. A curve chart is drawn. When the total price of each column of materials in the sample plant is not proportional to the total construction cost corresponding to the sample plant, the group of data is deleted.

6. The method for rapid valuation of nuclear power plant buildings based on FFX algorithm and AEC according to claim 1 is characterized by: The function sets F1 and F2 generated in step S4 include univariate basis functions X, X^2, X^3, sqrt(X), log(X), max(X, 0), and min(X, 0).

7. The method for rapid valuation of nuclear power plant buildings based on FFX algorithm and AEC according to claim 1 is characterized by: In the regularized learning technique in step S4, the regularization parameter l1_ratio is set to 0.95, and the regularization parameter alpha uses the np.logspace function to generate 666 logarithmically uniformly distributed alpha values, where the minimum logarithm value is 1e-10 and the maximum logarithm value is 100.

8. According to claim 1, a method for rapid valuation of nuclear power plant based on FFX algorithm and AEC., characterized in that: In step S4, when training the model, different alpha values ​​are searched from large to small, and an early stopping strategy is added. When the change in the training index is less than 0.001 for two consecutive times, the training is stopped early.

9. The method for rapid valuation of nuclear power plant buildings based on FFX algorithm and AEC according to claim 1 is characterized by: In step S5, error adjustment parameters k1 and k2 are dynamically set according to the statistical distribution characteristics of the sample data to enhance the robustness of the model.

10. The method for rapid valuation of nuclear power plant buildings based on FFX algorithm and AEC according to claim 1 is characterized by: In step S4, the number of feature sets U1 screened according to feature importance, the number of feature sets U2, the number of univariate basis functions generated in feature sets U1 and U2 and the univariate basis functions, the minimization index in the regularization learning technology, and the numerical values ​​of the regularization parameters are all selected based on actual conditions; the standard deviation σ, parameters k1 and k2 in step S5 are all selected based on actual conditions; the value ranges of mape and nrmse in step S6 are all selected based on actual conditions.

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