Arch dam shape multi-objective intelligent design and optimization method based on machine learning

Abstract

The invention belongs to the technical field of arch dam shape design and artificial intelligence, and discloses an arch dam shape multi-target intelligent design and optimization method based on machine learning. Comprising the following steps: step 1, collecting and sorting arch dam body type design data of a domestic arch dam body type; step 2, performing data cleaning on the collected arch dam shape design data, performing correlation analysis based on the arch dam shape design data, and performing feature dimension reduction by using principal component analysis to complete feature engineering of the arch dam shape design data; and 3, calling the machine learning model for design optimization, inputting to-be-designed input parameters, performing intelligent design and optimization of arch dam shape design by using the machine learning model, and outputting an arch dam arch crown beam curve equation and a horizontal arch ring linear equation. According to the method, multi-target intelligent design and optimization of arch dam shape design are realized, and the efficiency of arch dam shape design is effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of arch dam shape design and artificial intelligence technology, and more specifically, to a multi-objective intelligent design and optimization method for an arch dam shape based on machine learning. Background Art

[0002] As a key structure in water conservancy and hydropower projects, the design of arch dams directly affects the project's safety, economy, and construction difficulty. Traditional arch dam design relies mainly on engineers' experience and a large amount of manual calculations. Although this method can meet project requirements, it has the following problems:

[0003] Arch dam design involves complex hydraulics, geotechnical mechanics, and structural mechanics calculations, making it difficult to systematically pass on the accumulated experience of senior engineers.

[0004] Traditional arch dam shape design usually requires a large amount of parameter adjustment and optimization calculation, involving complex processes such as nonlinear optimization and trial calculation adjustment. The design efficiency is low, it is difficult to adapt to the needs of rapid construction of modern projects, and the level of intelligence is low:

[0005] Traditional methods mainly rely on engineers' experience and analogy for optimization and adjustment. They lack the support of sufficient data and find it difficult to quickly identify the best design solution among many influencing factors, resulting in limited optimization capabilities.

[0006] In view of this, the present invention proposes a multi-objective intelligent design and optimization method for arch dam shape based on machine learning to solve the above problems. Summary of the Invention

[0007] In order to overcome the above-mentioned defects of the prior art and to achieve the above-mentioned objectives, the present invention provides the following technical solution: a multi-objective intelligent design and optimization method for arch dam shape based on machine learning, comprising the following steps:

[0008] Step 1: Collect and organize arch dam shape design data of domestic arch dam shapes, wherein the arch dam shape design data includes: the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the center angle, the dam top arc length, the dam height, and the foundation surface parameters;

[0009] Step 2: Clean the collected arch dam shape design data, conduct correlation analysis based on the arch dam shape design data, and use principal component analysis to perform feature dimensionality reduction to complete feature engineering of the arch dam shape design data, that is, to obtain input parameters and output parameters of the machine learning model. The input parameters are the processed arch dam shape design data, and the output parameters are the arch dam shape design results. The arch dam shape design results include the arch dam crown beam curve equation and the horizontal arch ring line equation.

[0010] Step 3: Call the machine learning model for design optimization and input the input parameters to be designed. Use the machine learning model to perform intelligent design and optimization of the arch dam body design, and output the arch crown beam curve equation and horizontal arch ring line equation.

[0011] Furthermore, the step of collecting and collating arch dam shape design data of domestic arch dam shapes includes:

[0012] Step 101: Collecting the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the central angle, the arc length of the dam top, the dam height, and the foundation surface parameters as arch dam body design data, wherein the foundation surface parameters include the valley cross-section shape and the physical and mechanical parameters of the dam foundation rock mass, and the physical and mechanical parameters of the dam foundation rock mass include the uniaxial saturated compressive strength of the rock mass, the rock mass structure, the degree of rock mass weathering, the deformation model, and the shear parameter;

[0013] Step 102: vectors are used to represent the text of the physical and mechanical parameters of the dam foundation rock mass. Floating-point numbers are used to represent key parameters of the physical and mechanical parameters of the dam foundation rock mass, and one-hot vectors are used to represent key categories.

[0014] Furthermore, the steps of performing data cleaning on the collected arch dam shape design data, conducting correlation analysis based on the arch dam shape design data, and performing feature dimensionality reduction using principal component analysis to complete feature engineering of the arch dam shape design data include:

[0015] Step 201: performing data feature processing on the arch dam shape design data processed in step 102;

[0016] Step 202: Perform correlation analysis on the data features of the arch dam shape design data, measure the correlation between high-dimensional features using the Pearson correlation coefficient, clean features with excessively high correlation, perform feature dimensionality reduction using principal component analysis, refine complex redundant features into key features as input parameters, i.e., processed arch dam shape design data, and use the upstream curve equation of the arch dam crown beam and the horizontal arch ring linear equation as output parameters, thus completing the feature engineering of the arch dam shape design data.

[0017] Furthermore, the steps of building, training, testing and evaluating the machine learning model include:

[0018] Step 301: Before the machine learning model has partition design capabilities, it is necessary to construct a corresponding training dataset and test dataset for the parallel machine learning model for model training and testing. The training dataset and test dataset are constructed using feature expressions of input parameters and output parameters.

[0019] Step 302: Build a machine learning model, which includes an artificial neural network model, a bagging algorithm, and a random forest, and optimize the machine learning model using an intelligent design optimization algorithm;

[0020] Step 303: Based on the constructed training data set, test data set and machine learning model, model training and testing are performed. If the design accuracy meets the requirements, it can be used for design;

[0021] Step 304: When training and validating the machine learning model, k-fold cross validation is used, and the root mean square error (MSE) is used as the error metric for accuracy evaluation.

[0022] Furthermore, in step 302,

[0023] An intelligent design optimization algorithm is constructed using ensemble learning technology, combining the advantages of multiple algorithms to obtain more accurate curve equations for the upstream surface of the crown beam and the linear equations for the horizontal arch ring in the arch dam body design.

[0024] At the same time, the hyperparameters of the constructed machine learning model are tuned based on the intelligent design optimization algorithm to obtain an optimized design algorithm.

[0025] Furthermore, the intelligent design optimization algorithm includes a genetic algorithm.

[0026] Furthermore, in step 302, the step of building a machine learning model includes:

[0027] Step 3021: Using an artificial neural network as the basic component of a machine learning model, a multi-layer structure is constructed, including an input layer, a hidden layer, and an output layer. The input layer receives the processed arch dam shape design data, the hidden layer uses the connection weights between neurons to perform nonlinear transformation and feature extraction on the data, and the output layer outputs the predicted arch dam shape design result.

[0028] Step 3022: Adjust the number of hidden layers, the number of neurons, and the connection weights. The artificial neural network model can continuously optimize the learning and prediction capabilities of the arch dam shape design data, and use the Bagging algorithm to enhance the stability and generalization capabilities of the machine learning model.

[0029] Furthermore, in step 3022,

[0030] The Bagging algorithm samples the original training and test datasets multiple times with replacement to generate multiple sub-datasets. A base model is trained for each sub-dataset.

[0031] In the prediction stage, the prediction results of each base model are integrated, usually using voting method or averaging method to obtain the final prediction result;

[0032] Moreover, each decision tree in the random forest is trained on the generated sub-dataset based on the Bagging algorithm, and when constructing the decision tree, for each node split, a part of the features is randomly selected to find the best split point instead of considering all features.

[0033] Furthermore, the steps of calling the design optimization machine learning model, inputting the input parameters to be designed, using the machine learning model to perform intelligent design and optimization of the arch dam body design, and outputting the arch crown beam curve equation and the horizontal arch ring line equation of the arch dam include:

[0034] The input parameters to be designed are input into the trained machine learning model, and the machine learning model outputs the predicted arch crown beam curve equation and horizontal arch ring line equation.

[0035] The technical effects and advantages of the multi-objective intelligent design and optimization method of arch dam shape based on machine learning in the present invention are as follows:

[0036] 1. This invention enables intelligent design and multi-objective optimization of arch dam shape design. The optimization includes key arch dam design parameters and the optimization of the upstream curve equation of the crown beam. This optimization objective is to adjust the upstream curve equation of the crown beam to better meet engineering requirements. A suitable upstream curve shape helps improve the stress distribution of the arch dam and enhance its stability.

[0037] 2. By optimizing the characteristic parameters of the horizontal arch ring linear equation, the present invention can make the shape of the horizontal arch ring more reasonable. The reasonable horizontal arch ring linear shape can better transmit the load on the dam body, improve the overall bearing capacity and safety of the arch dam, and achieve intelligent and precise design through a series of technical means; greatly improve the design efficiency and enhance the intelligent level of arch dam design in my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flowchart of a multi-objective intelligent design and optimization method for arch dam shape based on machine learning of the present invention;

[0039] Figure 2 It is a schematic diagram of the process of the present invention;

[0040] Figure 3 For the present invention Figure 2 An enlarged schematic diagram of the second part;

[0041] Figure 4 For the present invention Figure 2 An enlarged schematic diagram of the third part. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0043] Example 1

[0044] See also Figure 1 、 Figure 2 、 Figure 3 as well as Figure 4 As shown, the multi-objective intelligent design and optimization method of arch dam shape based on machine learning described in this embodiment includes the following steps:

[0045] Step 1: Collect and organize arch dam shape design data of domestic arch dam shapes, wherein the arch dam shape design data includes: the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the center angle, the dam top arc length, the dam height, and the foundation surface parameters;

[0046] Step 2: Clean the collected arch dam shape design data, conduct correlation analysis based on the arch dam shape design data (such as the upstream surface curve equation, the arch ring linear equation, etc.), and use principal component analysis (PCA) to reduce the feature dimension and complete the feature engineering of the arch dam shape design data, that is, obtain the input parameters and output parameters of the machine learning model. The input parameters are the processed arch dam shape design data, and the output parameters are the arch dam shape design results. The arch dam shape design results include the arch dam crown beam curve equation and the horizontal arch ring linear equation.

[0047] Step 3: Call the machine learning model for design optimization and input the input parameters to be designed. Use the machine learning model to perform intelligent design and optimization of the arch dam body design, and output the arch crown beam curve equation and horizontal arch ring line equation.

[0048] Furthermore, the step of collecting and collating arch dam shape design data of domestic arch dam shapes includes:

[0049] Step 101: Collecting the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the central angle, the arc length of the dam top, the dam height, and the foundation surface parameters as arch dam body design data, wherein the foundation surface parameters include the valley cross-section shape and the physical and mechanical parameters of the dam foundation rock mass, and the physical and mechanical parameters of the dam foundation rock mass include the uniaxial saturated compressive strength of the rock mass, the rock mass structure, the degree of rock mass weathering, the deformation model, and the shear (fracture) resistance parameters;

[0050] Step 102: vectors are used to represent the text of the physical and mechanical parameters of the dam foundation rock mass. Floating-point numbers are used to represent key parameters of the physical and mechanical parameters of the dam foundation rock mass, and one-hot vectors are used to represent key categories.

[0051] Furthermore, the steps of performing data cleaning on the collected arch dam shape design data, carrying out correlation analysis based on data features (such as upstream surface curve equation, arch ring line equation, etc.) in the arch dam shape design data, and performing feature dimensionality reduction using principal component analysis (PCA) to complete feature engineering of the arch dam shape design data include:

[0052] Step 201: performing data feature processing on the arch dam shape design data processed in step 102;

[0053] Step 202: performing correlation analysis on the data features of the arch dam shape design data, obtaining the correlation between high-dimensional features using metrics such as the Pearson correlation coefficient, cleaning features with excessively high correlation, and performing principal component analysis (PCA) to reduce feature dimensionality. Complex and redundant features are refined into key features as input parameters, i.e., the processed arch dam shape design data. The upstream curve equation of the arch crown beam and the horizontal arch ring linear equation are used as output parameters, thus completing the feature engineering of the arch dam shape design data.

[0054] Step 203: constructing a training data set and a test data set using the feature expressions of the input parameters and the output parameters;

[0055] It should be noted that the data features are normalized to obtain the input parameters for the arch dam shape design; the arch dam design data features are subjected to correlation analysis, and the correlation between high-dimensional features is obtained using metrics such as the Pearson correlation coefficient. Features with excessive correlation are cleaned, and principal component analysis (PCA) is performed to reduce the dimensionality of features. Complex redundant features are refined into key features as input, and the Pearson correlation coefficient is used to measure the correlation between design data features, which can clearly present the degree of association between high-dimensional features. When two or more features are highly correlated, it means that they may carry similar information. For example, some features that describe the geometry of an arch dam may be highly correlated due to mutual influence. By setting an appropriate correlation threshold, features with excessive correlation are cleaned out, and the model is prevented from learning duplicate information, thereby reducing the amount of calculation, preventing overfitting, and allowing the model to focus on key information;

[0056] PCA is a powerful linear transformation technology that can convert the original complex redundant features into a set of unrelated principal components. These principal components are linear combinations of the original features, sorted by variance contribution. In the data processing of arch dam shape design, PCA finds the main direction of change in the data by characteristic decomposition of the data covariance matrix. For example, the numerous original features describing the arch dam shape, geological conditions, etc. are converted into a few comprehensive principal components. Usually, the first few principal components can retain most of the variance information of the original data, that is, the key features. By selecting these principal components as model input, while retaining important information, the data dimension is greatly reduced, the efficiency of model training and prediction is improved, and the model can learn the relationship between the key factors and objectives in the arch dam shape design more concisely and efficiently. Finally, the arch dam crown beam curve equation and the horizontal arch ring linear parameters are output;

[0057] It should be noted that in the feature engineering of arch dam shape design data, it is necessary to: obtain parameter distribution patterns: collect existing arch dam shape design data, which includes images and design information texts, extract key features of drawings and text data of existing arch dam shape design data, count the arch dam crown beam cross-section and horizontal arch ring design drawings in the images, count the curve equations, horizontal arch ring linear equations and physical and mechanical parameters of the arch dam foundation rock mass in the text, and obtain the distribution patterns of different parameters. Among them, the key feature extraction of drawing data: for the arch dam crown beam cross-section and horizontal arch ring design drawings, use AutoCAD to directly measure and mark parameters such as the arch crown beam thickness and the horizontal arch ring thickness;

[0058] Extraction of key features of text data: Using natural language processing technology, for texts containing curve equations and horizontal arch ring linear equations, through grammatical and semantic analysis, the mathematical expressions and related parameters are identified and extracted. For texts containing the physical and mechanical parameters of the arch dam foundation rock mass, information extraction technology is used to extract key parameters such as the uniaxial saturated compressive strength of the rock mass, rock mass structure, and rock mass weathering degree from texts such as engineering reports and design documents. Statistical analysis is performed on the various extracted parameters, and statistical quantities such as the mean, median, and standard deviation of the parameters are calculated. For the parameters of the curve equation of the upstream surface of the arch crown beam, the mean and standard deviation of these parameters in different arch dams are calculated to understand their concentration trend and degree of dispersion. Frequency distribution histograms of the parameters are drawn to intuitively display the frequency of occurrence of the parameters in different value ranges, so as to clearly see the distribution of the parameters. For example, a frequency distribution histogram of the uniaxial saturated compressive strength of the dam foundation rock mass is drawn to observe the distribution characteristics of its strength values.

[0059] It should be noted that the construction of the training dataset and the test dataset: parametric generation of multi-source heterogeneous datasets: based on the statistical distribution law of parameters, the parametric adjustment technology is adopted. According to the distribution law of different parameters obtained before, the parameters that have a greater impact on the arch dam body design are selected as the adjustment objects. Within the set parameter adjustment range, different parameters are quickly generated through proportional scaling and random perturbation methods, and the geometric and physical mechanical parameters are augmented and expanded to construct multi-source heterogeneous training datasets and test datasets.

[0060] Furthermore, the steps of building, training, testing and evaluating the designed and optimized machine learning model include:

[0061] Step 301: constructing a training dataset and a test dataset using the feature expressions of the input parameters and the output parameters;

[0062] Step 302: Build a machine learning model, which includes an artificial neural network model, a bagging algorithm, and a random forest, and optimize the machine learning model using an intelligent design optimization algorithm;

[0063] Step 303: Based on the constructed training data set, test data set and machine learning model, model training and testing are performed. If the design accuracy meets the requirements, it can be used for design;

[0064] Step 304: k-fold cross validation is used during machine learning model training and validation, and root mean square error (MSE) is used as the error metric for accuracy evaluation.

[0065] It should be noted that k-fold cross-validation is used during model training and verification to solve the problem of insufficient precision of intelligent design due to small data volume, and the root mean square error (MSE) is used as the error metric for precision evaluation; the machine learning model includes machine learning model algorithms based on multiple regression, artificial neural network (ANN), random forest, XGBoost, etc., and an intelligent design optimization algorithm is constructed by adopting ensemble learning technology, combining the advantages of multiple algorithms to obtain more accurate curve equations of the upstream surface of the crown beam and the linear equation of the horizontal arch ring in the arch dam body design. At the same time, the hyperparameters of the constructed machine learning model are tuned based on optimization algorithms such as genetic algorithms to obtain an optimized design algorithm; a machine learning model is built, and the model composition includes an artificial neural network model, a bagging algorithm, and a random forest; based on the constructed data set and the machine learning model, the model is trained and tested, and it can be used for design if the design precision meets the requirements.

[0066] Furthermore, in step 302,

[0067] An intelligent design optimization algorithm is constructed using ensemble learning technology, combining the advantages of multiple algorithms to obtain more accurate curve equations for the upstream surface of the crown beam and the linear equations for the horizontal arch ring in the arch dam body design.

[0068] At the same time, the hyperparameters of the constructed machine learning model are tuned based on the intelligent design optimization algorithm to obtain an optimized design algorithm.

[0069] Furthermore, the intelligent design optimization algorithm includes a genetic algorithm.

[0070] Furthermore, in step 302, the step of building a machine learning model includes:

[0071] Step 3021: Using an artificial neural network as the basic component of a machine learning model, a multi-layer structure is constructed, including an input layer, a hidden layer, and an output layer. The input layer receives the processed arch dam shape design data, the hidden layer uses the connection weights between neurons to perform nonlinear transformation and feature extraction on the data, and the output layer outputs the predicted arch dam shape design result.

[0072] It should be noted that the artificial neural network model is used as the basic component of the machine learning model. The artificial neural network model has powerful nonlinear mapping capabilities and can learn complex data patterns and relationships. In arch dam shape design, it can capture the complex nonlinear relationship between design parameters (such as the curve equation parameters of the upstream surface of the crown beam, dam height, valley cross-section shape, etc.) and the target results (crown beam curve equation and horizontal arch ring linear equation). By constructing a multi-layer structure consisting of input layer, hidden layer and output layer, the input layer receives the processed arch dam shape design data, the hidden layer uses the connection weights between neurons to perform nonlinear transformation and feature extraction on the data, and the output layer outputs the predicted arch dam shape design results. By adjusting the number of hidden layers, the number of neurons and the connection weights, the artificial neural network model can continuously optimize the learning and prediction capabilities of arch dam shape design data.

[0073] Step 3022: Adjust the number of hidden layers, the number of neurons, and the connection weights. The artificial neural network model can continuously optimize the learning and prediction capabilities of the arch dam shape design data, and use the Bagging algorithm to enhance the stability and generalization capabilities of the machine learning model.

[0074] It should be noted that the Bagging algorithm is used to enhance the stability and generalization ability of the model. It is based on the bootstrap sampling method and samples the original training data set and test data set multiple times with replacement to generate multiple different sub-data sets. For each sub-data set, a base model is trained separately (the base model here can be an artificial neural network model or a decision tree in a random forest). In the prediction stage, the prediction results of each base model are combined, and the voting method (for classification problems) or the averaging method (for regression problems) is usually used to obtain the final prediction result. In this way, the Bagging algorithm can effectively reduce the variance of a single model, reduce the risk of overfitting, and improve the overall stability and generalization performance of the model, so that the machine learning model can show relatively stable prediction capabilities when facing different arch dam body design data.

[0075] Random Forest: A random forest is an ensemble model composed of multiple decision trees and plays a key role in this ensemble learning architecture. Each decision tree is trained on a subset of datasets generated by the bagging algorithm. During the tree construction process, for each node split, a subset of features is randomly selected to find the optimal split point, rather than considering all features. This randomization creates a degree of independence between different decision trees, further enhancing the model's generalization capabilities.

[0076] Furthermore, in step 3022,

[0077] The Bagging algorithm samples the original training and test datasets multiple times with replacement to generate multiple sub-datasets. A base model is trained for each sub-dataset.

[0078] In the prediction stage, the prediction results of each base model are integrated, usually using voting method or averaging method to obtain the final prediction result;

[0079] Moreover, each decision tree in the random forest is trained on the generated sub-dataset based on the Bagging algorithm, and when constructing the decision tree, for each node split, a part of the features is randomly selected to find the best split point instead of considering all features.

[0080] It should be noted that random forests, by integrating the predictions of multiple decision trees, can more accurately capture complex patterns and relationships in data. In arch dam shape design, random forests can process high-dimensional design data and uncover potential connections between different design parameters, providing rich information for predicting arch dam shape. They complement artificial neural network models and bagging algorithms to enhance the performance of machine learning models. In this machine learning model, the artificial neural network model, bagging algorithm, and random forest collaborate. The bagging algorithm provides diverse training data for the artificial neural network model and random forest, reducing model variance. The artificial neural network model leverages its nonlinear learning capabilities to handle complex design data relationships. The random forest, by integrating multiple decision trees, enhances the model's generalization and ability to handle high-dimensional data. Ultimately, the predictions from these multiple models are fused to produce a more accurate and reliable prediction for arch dam shape design. Based on the constructed dataset and machine learning model, the model is trained and tested. Once the design meets the required accuracy, it can be used for design.

[0081] Furthermore, the step of inputting the input parameters to be designed, performing intelligent design and optimization of the arch dam shape design using a machine learning model, and outputting the arch dam crown beam curve equation and the horizontal arch ring line equation includes:

[0082] Input the input parameters to be designed into the trained machine learning model, and the machine learning model outputs the predicted arch crown beam curve equation and horizontal arch ring line equation;

[0083] It should be noted that the reference Figure 3 In arch dam design, y cu (z) is the mathematical expression of the upstream surface of the crown beam. Generally, the equation of the upstream surface is set as a cubic curve of the z coordinate, that is, y cu (z) = a0 + a1z + a2z 2 +a3z 3 , where y cu (z) is a function with elevation z as the independent variable, which is used to quantitatively describe the geometric profile of the upstream surface of the crown beam. a0, a1, a2, and a3 are the parameters of the upstream curved surface of the crown beam.

[0084] T c (z) is the mathematical expression of the thickness equation of the crown beam. Generally, the thickness of the crown beam is also the cubic curve of the z coordinate, that is, T c (z) = b0 + b1z + b2z 2 +b3z 3 , where T c (z) is a function of height z, b0, b1, b2, b3 are parameters of the crown beam thickness equation;

[0085] Then, the surface equation y of the downstream side of the crown beam is cd The mathematical expression of (z) is: cd (z) = y cu (z)+T c (z), where y cu (z), T c (z) are the upstream curved surface of the crown beam and the thickness of the crown beam respectively;

[0086] In arch dam design, the arch axis of the arch dam is generally a curve, but it can also be a quadratic curve such as a parabola, ellipse, or hyperbola. These different curve forms can be comprehensively described by a quadratic equation, that is, x 2 =ay 2 +by, a and b are the parameters that determine this quadratic equation, x represents the horizontal distance from a point on the cross section of the arch dam to the centerline of the arch axis, and y represents the vertical distance from the point to the bottom of the arch dam (i.e., elevation). Special note: when a>0, the quadratic equation is a hyperbola; when a<0, the quadratic equation is an ellipse. For an ellipse, there is a definition of the radius of curvature, that is, the radius of curvature R is expressed as: In the formula, the coefficients a and b in the arch axis equation are predicted by machine learning, and the curvature radius R can be calculated based on the predicted a and b. For example, for y = a + bx, it is necessary to determine this straight line, that is, it is necessary to determine a and b, and this straight line can be expressed in space. The same is true in arch dam design, where a 0、 a 1、 a 2、 a 3、 b 0、 b1, b 2、 b3 is the surface equation of the upstream of the crown beam y cu (z) and the parameters (coefficients) of the crown beam thickness equation Tc(z). When determining these two cubic functions, these related parameters need to be determined. In the present invention, these related parameters are all predicted by machine learning.

[0087] In the embodiment, the present application can realize intelligent design and multi-objective optimization of the arch dam body design, and the optimization content includes the key design parameters of the arch dam and the optimization of the upstream curve equation of the arch crown beam: taking the upstream curve equation of the arch crown beam as the optimization target, the purpose is to make the shape of the upstream surface of the arch dam more in line with engineering requirements by adjusting its characteristic parameters. The appropriate upstream curve shape helps to improve the force distribution of the arch dam and enhance the stability of the arch dam; by optimizing the characteristic parameters of the horizontal arch ring line equation, the shape of the horizontal arch ring can be made more reasonable, and the reasonable horizontal arch ring line can better transfer the load on the dam body, improve the overall bearing capacity and safety of the arch dam, and achieve intelligent and precise design through a series of technical means; greatly improve the design efficiency and improve the level of intelligence of my country's arch dam design.

[0088] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0089] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only one type. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0090] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed by the present invention, which should be covered by the scope of protection of the present invention.

[0091] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-objective intelligent design and optimization method for arch dam shape based on machine learning, characterized in that: The following steps are involved: Step 1: Collect and organize arch dam shape design data of domestic arch dam shapes, wherein the arch dam shape design data includes: the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the center angle, the dam top arc length, the dam height, and the foundation surface parameters; Step 2: Clean the collected arch dam shape design data, conduct correlation analysis based on the arch dam shape design data, and use principal component analysis to perform feature dimensionality reduction to complete feature engineering of the arch dam shape design data, that is, to obtain input parameters and output parameters of the machine learning model. The input parameters are the processed arch dam shape design data, and the output parameters are the arch dam shape design results. The arch dam shape design results include the arch dam crown beam curve equation and the horizontal arch ring line equation. Step 3: Call the machine learning model for design optimization and input the input parameters to be designed. Use the machine learning model to perform intelligent design and optimization of the arch dam body design, and output the arch crown beam curve equation and horizontal arch ring line equation.

2. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 1 is characterized in that: The step of collecting and collating arch dam shape design data of domestic arch dam shapes includes: Step 101: Collecting the curve equation of the upstream surface of the crown beam, the thickness equation, the top thickness of the crown, the bottom thickness, the linear equation of the horizontal arch ring, the central angle, the arc length of the dam top, the dam height, and the foundation surface parameters as arch dam body design data, wherein the foundation surface parameters include the valley cross-section shape and the physical and mechanical parameters of the dam foundation rock mass, and the physical and mechanical parameters of the dam foundation rock mass include the uniaxial saturated compressive strength of the rock mass, the rock mass structure, the degree of rock mass weathering, the deformation model, and the shear parameter; Step 102: vectors are used to represent the text of the physical and mechanical parameters of the dam foundation rock mass. Floating-point numbers are used to represent key parameters of the physical and mechanical parameters of the dam foundation rock mass, and one-hot vectors are used to represent key categories.

3. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 2 is characterized in that: The steps of performing data cleaning on the collected arch dam shape design data, conducting correlation analysis based on the arch dam shape design data, and performing feature dimensionality reduction using principal component analysis to complete feature engineering of the arch dam shape design data include: Step 201: performing data feature processing on the arch dam shape design data processed in step 102; Step 202: Perform correlation analysis on the data features of the arch dam shape design data, measure the correlation between high-dimensional features using the Pearson correlation coefficient, clean features with excessively high correlation, perform feature dimensionality reduction using principal component analysis, refine complex redundant features into key features as input parameters, i.e., processed arch dam shape design data, and use the arch dam crown beam curve equation and the horizontal arch ring line equation as output parameters, thus completing the feature engineering of the arch dam shape design data.

4. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 3 is characterized in that: The steps of building, training, testing, and evaluating the machine learning model include: Step 301: constructing a training dataset and a test dataset using the feature expressions of the input parameters and the output parameters; Step 302: Build a machine learning model, which includes an artificial neural network model, a bagging algorithm, and a random forest, and optimize the machine learning model using an intelligent design optimization algorithm; Step 303: Based on the constructed training data set, test data set and machine learning model, model training and testing are performed. If the design accuracy meets the requirements, it can be used for design; Step 304: When training and validating the machine learning model, k-fold cross validation is used, and the root mean square error (MSE) is used as the error metric for accuracy evaluation.

5. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 4 is characterized in that: In step 302, An intelligent design optimization algorithm is constructed using ensemble learning technology, combining the advantages of multiple algorithms to obtain more accurate arch crown beam curve equations and horizontal arch ring linear equations in arch dam body design; At the same time, the hyperparameters of the constructed machine learning model are tuned based on the intelligent design optimization algorithm to obtain an optimized design algorithm.

6. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 5 is characterized in that: The intelligent design optimization algorithm includes a genetic algorithm.

7. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 4 is characterized in that: In step 302, the steps of building a machine learning model include: Step 3021: Using an artificial neural network as the basic component of a machine learning model, a multi-layer structure is constructed, including an input layer, a hidden layer, and an output layer. The input layer receives the processed arch dam shape design data, the hidden layer uses the connection weights between neurons to perform nonlinear transformation and feature extraction on the data, and the output layer outputs the predicted arch dam shape design result. Step 3022: Adjust the number of hidden layers, the number of neurons, and the connection weights. The artificial neural network model continuously optimizes the learning and prediction capabilities of the arch dam shape design data, and uses the Bagging algorithm to enhance the stability and generalization capabilities of the machine learning model.

8. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 7 is characterized in that: In step 3022, The Bagging algorithm samples the original training and test datasets multiple times with replacement to generate multiple sub-datasets. A base model is trained for each sub-dataset. In the prediction stage, the prediction results of each base model are integrated and the voting method or averaging method is used to obtain the final prediction result; Moreover, each decision tree in the random forest is trained on the generated sub-dataset based on the Bagging algorithm, and when constructing the decision tree, for each node split, a part of the features is randomly selected to find the best split point.

9. The multi-objective intelligent design and optimization method for arch dam shape based on machine learning according to claim 8 is characterized in that: The steps of inputting the input parameters to be designed, performing intelligent design and optimization of the arch dam body design using a machine learning model, and outputting the arch dam crown beam curve equation and the horizontal arch ring line equation include: The input parameters to be designed are input into the trained machine learning model, and the machine learning model outputs the predicted arch crown beam curve equation and horizontal arch ring line equation.

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