Dam body type intelligent design method and simulation system based on hybrid optimization algorithm

Abstract

The invention relates to the technical field of water conservancy and hydropower engineering design, and discloses a dam body type intelligent design method and simulation system based on a hybrid optimization algorithm, and the method comprises the steps: obtaining dam design parameters; dam body type parameter individuals are generated based on a hybrid optimization algorithm; calling a pre-trained deep neural network agent model to replace finite element calculation, and quickly predicting performance indexes of the individual, including maximum principal stress and an anti-sliding stability coefficient; calculating a fitness value after punishment according to the predicted performance index; and the hybrid optimization algorithm performs iterative updating according to the penalty fitness value until a termination condition is met, and outputs an optimal scheme. The invention further provides a simulation system which comprises a hybrid optimization module, a DNN simulation prediction module and a cooperative control module, and the cooperative control module is used for achieving real-time closed loop of optimization and simulation. According to the method, the technical problems of time consumption in simulation and low optimization efficiency in traditional design are solved, and the design efficiency and the scheme quality are effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of water conservancy and hydropower engineering design, in particular to a dam shape intelligent design method and simulation system based on a hybrid optimization algorithm. BACKGROUND

[0002] The shape design of high dams such as concrete gravity dams is a complex multi-objective optimization problem involving safety, economy, and construction feasibility. In the traditional design process, designers propose an initial shape scheme based on design specifications and engineering experience, and use numerical calculation methods such as finite element method to analyze the stress distribution and anti-sliding stability of the dam under static and dynamic loads. Although finite element numerical calculation can provide accurate structure response prediction, the calculation process involves massive grid division and nonlinear iterative solution, which is time-consuming and requires high computational resources.

[0003] With the development of intelligent optimization technology, heuristic algorithms such as genetic algorithm and particle swarm algorithm have been applied to dam shape optimization design. These algorithms need to search for the optimal solution through a large number of iterations, and in each iteration process, a numerical calculation model needs to be called to evaluate the performance of the generated individual scheme. When the population size of the optimization algorithm is large or the number of iterations is large, frequent calling of high-time-consuming finite element calculation model will lead to exponential growth of total calculation time, making the design cycle too long to meet the timeliness requirements of engineering practice. In order to control the time cost, existing technologies have to reduce the number of iterations or simplify the calculation model, but this will lead to insufficient optimization depth and difficulty in obtaining the truly global optimal scheme.

[0004] In addition, existing optimization design methods mostly use a single optimization strategy. Global search algorithms can explore a wide solution space, but have slow local convergence speed and limited accuracy. Traditional gradient-based algorithms have fast convergence speed, but are easily affected by initial values and fall into local optimal solutions. Simply relying on one of these algorithms cannot balance the breadth and accuracy of the search. At the same time, there are many uncertain factors such as geological parameters and material properties in dam engineering, and traditional deterministic optimization design cannot effectively evaluate the impact of these parameter fluctuations on structural safety. However, if Monte Carlo simulation or other methods are used for uncertainty analysis, a large amount of calculation will be required, which is difficult to achieve under the design framework based on traditional finite element calculation. SUMMARY

[0005] To overcome the deficiencies of the prior art, the present application provides a dam shape intelligent design method and simulation system based on a hybrid optimization algorithm, which solves the technical problem that simulation accuracy and optimization efficiency cannot be balanced in traditional dam shape optimization design.

[0006] To achieve the above object, the application is implemented by the following technical solutions: a dam shape intelligent design method and simulation system based on a hybrid optimization algorithm.

[0007] The first aspect of the application provides a dam shape intelligent design method based on a hybrid optimization algorithm.

[0008] The design method comprises the following steps:

[0009] First, the optimization variable search range of the dam shape parameters, the design constraint limit value and the load parameters are obtained.

[0010] In the optimization process, a group of current dam shape parameter individuals are generated based on the hybrid optimization algorithm.

[0011] Subsequently, the system calls a pre-trained deep neural network agent model, takes the dam shape parameter individuals as input, and predicts and outputs the predicted performance indicators corresponding to the individuals by the deep neural network agent model, wherein the predicted performance indicators at least include the maximum principal stress and the anti-slide stability coefficient.

[0012] The system calculates the penalty fitness value corresponding to the dam shape parameter individuals according to the predicted performance indicators. The hybrid optimization algorithm updates the algorithm state and generates a new generation of dam shape parameter individuals according to the penalty fitness value.

[0013] The above generation, prediction, calculation and update steps are repeatedly executed until a preset termination condition is met.

[0014] Finally, the dam shape parameter individuals that meet the termination condition are output as the optimal shape parameter scheme.

[0015] In one embodiment, the hybrid optimization algorithm adopts a hybrid strategy of genetic algorithm and gradient descent method. The hybrid strategy first performs global search by genetic algorithm to generate a Pareto optimal solution set; after the global search of the genetic algorithm is terminated, the individual with the minimum penalty fitness value in the Pareto optimal solution set is taken as the initial value, and local search is performed by gradient descent method.

[0016] In one embodiment, the calculation of the penalty fitness value F' includes calculating a multi-objective fitness function F and a constraint penalty term.

[0017] The multi-objective fitness function F is used to cooperatively process the concrete volume, stress and stability targets. After the multi-objective fitness function F is normalized on the concrete volume v, the maximum principal stress σ max and the anti-slide stability coefficient k, weighted summation is performed. Its form can be:

[0018]

[0019] wherein v0 is the reference concrete volume, [σ] is the maximum principal stress limit, [K] is the anti-slide stability coefficient limit, w1, w2, w3 are the corresponding weight coefficients.

[0020] The penalized fitness value F' is obtained by adding the multi-objective fitness function F and each constraint penalty term:

[0021] F' = F + P K + P σ + P H ;

[0022] wherein P K is the anti-slide stability constraint penalty term, P σ is the stress constraint penalty term, and P H is the dam crest elevation constraint penalty term.

[0023] Each penalty function can be defined as follows:

[0024]

[0025] wherein C K , C σ , C H are preset penalty coefficients.

[0026] In one embodiment, after obtaining the optimal body shape parameter scheme, the method can further include an uncertainty analysis step. The uncertainty analysis step performs parameter sampling on the fluctuation range of the load parameter or the geological parameter to form an input data set for uncertainty analysis; then, the deep neural network proxy model is called in batches to obtain a distribution set of the predicted performance indicators corresponding to the input data set; and the coefficient of variation of the distribution set is calculated to evaluate the robustness of the optimal body shape parameter scheme.

[0027] The deep neural network proxy model can be generated through offline training. The training process can include:

[0028] Latin hypercube sampling is used to generate sample combinations of the input variables, including the optimization variables corresponding to the dam body shape parameters, the geological parameters and the load parameters;

[0029] Through finite element numerical calculation, the true structure response indicators corresponding to the sample combinations are obtained;

[0030] and, a sample data set is constructed using the sample combinations of the input variables and the true structure response indicators, and the model is trained with the mean square error as the loss function.

[0031] The dam size parameter individual is defined by a set of optimization variables, including: dam height, upstream dam slope ratio, downstream dam slope ratio, and dam crest width.

[0032] The second aspect of the present application provides a dam size intelligent design simulation system based on a hybrid optimization algorithm.

[0033] The simulation system comprises:

[0034] a hybrid optimization module, a DNN simulation prediction module, and a collaborative control module.

[0035] The simulation system realizes a real-time collaborative closed-loop working mechanism of the hybrid optimization module and the DNN simulation prediction module.

[0036] The hybrid optimization module is configured to generate a set of current dam size parameter individuals based on a hybrid optimization algorithm, and update the hybrid optimization algorithm to generate a new generation of dam size parameter individuals according to a post-penalty fitness value.

[0037] The DNN simulation prediction module solidifies a pre-trained deep neural network proxy model, and is configured to receive the dam size parameter individuals and predict and output corresponding predicted performance indicators, the predicted performance indicators at least including maximum principal stress and anti-sliding stability coefficient.

[0038] The collaborative control module is electrically connected to the hybrid optimization module and the DNN simulation prediction module, and is configured to:

[0039] transfer the dam size parameter individuals from the hybrid optimization module to the DNN simulation prediction module;

[0040] transfer the predicted performance indicators from the DNN simulation prediction module back to the hybrid optimization module;

[0041] and determine whether the hybrid optimization algorithm meets a preset termination condition.

[0042] In the system, the hybrid optimization module is further configured to calculate the post-penalty fitness value according to the predicted performance indicators.

[0043] The present application provides a dam size intelligent design method and simulation system based on a hybrid optimization algorithm. The following beneficial effects are provided:

[0044] 1、The application replaces the traditional high-precision finite element numerical calculation in the optimization iteration step by adopting a pre-trained deep neural network proxy model. The DNN proxy model can quickly predict the structure response index, realize the real-time closed loop of the optimization algorithm and simulation analysis, solve the technical bottleneck of long simulation time in the traditional design process, leading to low iteration efficiency, and effectively shorten the design cycle.

[0045] 2、The hybrid optimization module adopted in the application combines the global search ability of the genetic algorithm and the local fine search ability of the gradient descent method. The hybrid strategy first explores in a wide solution space through the genetic algorithm to avoid falling into a local optimal solution, and then uses the gradient descent method to finely adjust the high-quality solution to improve the quality of the optimization search, so that the final dam body parameter scheme has better comprehensive performance.

[0046] 3、The application utilizes the efficient prediction ability of the deep neural network proxy model to further introduce an uncertainty quantification and robustness analysis process after obtaining the optimal body parameter scheme. By sampling key uncertain factors such as geological parameters and batch prediction, the application can quantitatively evaluate the performance stability of the design scheme under parameter fluctuation, ensuring that the final output scheme meets the optimization target while having the reliability required by engineering practice. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The genetic algorithm and gradient descent method hybrid optimization algorithm flowchart of the application;

[0048] Figure 2 The DNN proxy model construction and collaboration flowchart of the application. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the application will be described in detail below with reference to the drawings in the specification of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of protection of the application.

[0050] In order to better understand the application, the above content will be described in detail below in combination with specific embodiments.

[0051] Please refer to the drawings Figure 1 - the drawings Figure 2 The embodiment of the application provides a dam body intelligent design method and simulation system based on a hybrid optimization algorithm.

[0052] The simulation system can run on a computer device, which includes a processor and a memory. The memory stores computer-executable instructions, and the processor executes the executable instructions to implement the method of the present invention.

[0053] The simulation system includes a parameter input module for receiving and storing basic data for the dam design. This basic data includes, but is not limited to, geological parameters, load parameters, and design constraint limits. The parameter input module also defines the search range for optimization variables, including the dam height H. dam The upstream dam slope ratio m1, the downstream dam slope ratio m2, and the dam crest width B.

[0054] The hybrid optimization module is electrically connected to the parameter input module. It is used to perform iterative optimization of the dam's shape parameters. Internally, the module implements a hybrid strategy combining genetic algorithms and gradient descent, and performs global search and local fine-tuning of the optimization variables based on a custom multi-objective fitness function F and a constraint-based quantitative penalty mechanism F′.

[0055] The DNN simulation prediction module is electrically connected to the hybrid optimization module. The DNN simulation prediction module embeds a pre-trained deep neural network surrogate model. This deep neural network surrogate model receives the current body shape parameters from the hybrid optimization module and quickly predicts the corresponding structural response indices, which include at least the maximum principal stress σ. max And the anti-skid stability coefficient K.

[0056] The collaborative control module is electrically connected to the parameter input module, the hybrid optimization module, and the DNN simulation prediction module. As the system's control center, the collaborative control module is responsible for coordinating the data and control flows of optimization and simulation, and managing the start and stop of the iteration process, data transmission, and convergence determination.

[0057] The results output module is electrically connected to the collaborative control module and the hybrid optimization module. After optimization convergence, the results output module extracts and presents the final optimal body shape parameter scheme and its corresponding performance indicators. The results output module can also be used to output the results of uncertainty quantification analysis.

[0058] This invention provides an intelligent design method for dam shape based on a hybrid optimization algorithm. The design method can be executed by the system and includes the following steps:

[0059] S101. Initialization and Parameter Input. The system receives the input engineering geological parameters, load parameters, design constraint limits, and the search range of optimization variables, and completes the initialization.

[0060] S102, Hybrid Optimization Iteration Start. Initialize the genetic algorithm population and generate the first generation of individuals with dam body shape parameters.

[0061] S103, calling DNN agent model for real-time simulation. The body shape parameter individual generated in the current iteration is input, the trained DNN simulation prediction module is called, the predicted performance index corresponding to the body shape parameter individual is calculated and output, and the index at least includes the maximum principal stress σ max and the anti-slide stability coefficient K.

[0062] S104, multi-objective fitness and constraint penalty calculation. The predicted performance index output in step S103 is obtained, combined with data such as concrete volume V, the penalty fitness value F' is calculated according to the preset self-defined multi-objective fitness function and constraint quantitative penalty mechanism.

[0063] S105, optimization algorithm iteration and parameter update. Based on the F' value calculated in step S104, the iteration operation of genetic algorithm is executed, or the gradient descent method is switched to for local fine search, to generate a new generation of body shape parameter individual.

[0064] S106, convergence and termination judgment. Check whether the preset termination condition is met. The termination condition can include reaching the maximum number of iterations, or the penalty fitness value F' converges. If the termination condition is not met, the process returns to step S103; if it is met, step S107 is entered.

[0065] S107, uncertainty quantification and robustness analysis. For the optimal scheme output in step S106, the uncertainty analysis process is activated. The variation coefficient cv of the key safety index is calculated according to the preset quantification formula by parameter sampling and batch calling DNN simulation prediction module, to evaluate the robustness of the scheme.

[0066] S108, output optimal scheme. The final determined optimal body shape parameter scheme, corresponding performance index and robustness analysis result of step S107 are output or archived.

[0067] Before performing the mixed optimization iteration of step S102, the system needs to determine the calculation basis of the mixed optimization module according to the data obtained in step S101. This includes defining the basic input parameters and optimization variables.

[0068] The basic input parameters are known conditions for evaluating the pros and cons of the dam body shape scheme, which are provided to the mixed optimization module by the parameter input module. These parameters specifically include:

[0069] Geological parameters: data representing the mechanical properties of dam foundation and dam shoulder rock mass, at least including rock foundation friction angle φ, rock foundation cohesion c and rock foundation elastic modulus E r .

[0070] Load parameters: define the main external load working conditions that the dam bears during operation, at least including design flood level H w and design earthquake acceleration α.

[0071] Design constraint limits: Thresholds used as the basis for the constraint penalty mechanism in the subsequent step S104. These limits are derived from relevant design specifications, including at least: the limit of the anti-sliding stability coefficient [K], the limit of the maximum allowable principal stress of the dam material [σ], and the minimum dam crest elevation H crest,min .

[0072] Optimization variables are the target parameters that the hybrid optimization module needs to search and determine, which collectively define the geometry of the dam. The optimization variables take values within a pre-set search space, including specifically:

[0073] Dam height H dam : The vertical height of the dam from the dam foundation to the dam crest.

[0074] Upstream dam slope ratio m1: Defined as the slope of the upstream dam surface, expressed as 1:m1. In the optimization calculation, m1 is a continuously changing value.

[0075] Downstream dam slope ratio m2: Defined as the slope of the downstream dam surface, expressed as 1:m2. In the optimization calculation, m2 is a continuously changing value.

[0076] Dam crest width B: The width of the dam crest.

[0077] The hybrid optimization module performs the optimization process, that is, in the multi-dimensional solution space composed of H dam , m1, m2, and B, it searches for a set of optimal variable combinations that can minimize the value of F' according to the fitness function F of step S104.

[0078] In executing step S104, the hybrid optimization module needs a quantitative standard to evaluate the overall performance of each individual geometry parameter individual generated in step S103.

[0079] To achieve this purpose, the present application constructs a self-defined multi-objective fitness function F. The multi-objective fitness function F is used to cooperatively handle the three mutually restrictive objectives of minimizing concrete volume, optimizing stress distribution, and meeting the anti-sliding stability standard.

[0080] The fitness function F adopts the form of weighted summation. In order to enable different physical quantities of the same scale to be compared and weighted, the function first normalizes each objective. The fitness function F is defined as follows:

[0081]

[0082] Wherein, F is the fitness function value of the current body parameter individual. The fitness function value is the direct basis for the mixed optimization module to evaluate the individual. The smaller the F value is, the better the comprehensive performance of the scheme is. v is the concrete quantity corresponding to the current body parameter individual. The fitness function value can be calculated by the mixed optimization module according to the current optimization variable through the standard geometric formula; v0 is a reference concrete quantity, for example, the quantity of the initial trial scheme input in step S101. v0 is used to normalize the quantity v, so that it becomes a dimensionless ratio; σ max is the maximum principal stress of the dam body corresponding to the current body parameter individual, which is predicted and output by the DNN simulation prediction module in step S103; [σ] is the maximum principal stress limit value allowed by the design specification, which is set in step S101. The maximum principal stress limit value is used to normalize the stress σ max ; k is the anti-sliding stability coefficient corresponding to the current body parameter individual, which is predicted and output by the DNN simulation prediction module in step S103; [K] is the minimum anti-sliding stability coefficient limit value required by the design specification, which is set in step S101; w1, w2, and w3 are weight coefficients corresponding to the above three normalized targets, respectively.

[0083] The weight coefficients w1, w2, and w3 are all non-negative values, and satisfy the constraint condition w1+w2+w3=1.

[0084] These weight coefficients w1, w2, and w3 can be dynamically set by the user according to the actual engineering requirements in step S101, so as to adjust the priority of different targets. For example, in the working condition with high safety requirement, a higher safety weight and a lower economic weight can be set, so as to guide the mixed optimization module to preferentially search for a solution that meets the high safety standard in step S105. Conversely, the weight of w1 can be appropriately increased.

[0085] The value of the fitness function F calculated by the mixed optimization module will serve as the basis for calculating the final penalty fitness value F' in step S104.

[0086] After the mixed optimization module calculates the fitness function F in step S104, the body parameter individual that violates the constraint needs to be punished to ensure that the optimization process finally converges to a feasible solution.

[0087] To achieve this purpose, the present application establishes a constraint quantitative punishment mechanism. The core of the constraint quantitative punishment mechanism is to quantify the degree of constraint violation as a penalty term, which is added to the fitness function F, so as to obtain a penalty fitness value F'. The mixed optimization module will use the penalty fitness value F' as the final basis for evaluating the individual in step S105.

[0088] The calculation of the penalty fitness value F' is as follows:

[0089] F' = F + P K + P σ + P H ;

[0090] where F' is the fitness value after penalty. The fitness value after penalty is the final evaluation value used for comparison and selection in the optimization algorithm. The smaller the F', the better the scheme. F is the multi-objective fitness value without constraint penalty; P K is the anti-slide stability constraint penalty term; P σ is the stress constraint penalty term; P H is the dam crest elevation constraint penalty term.

[0091] When an individual of a size parameter does not violate any constraint, P K , P σ and P H are all 0, and F' = F. When the individual violates any constraint, the corresponding penalty term will be greater than 0, resulting in an increase in the F' value.

[0092] The specific definitions of the penalty functions are as follows:

[0093] Anti-slide stability constraint penalty term P K This penalty term is used to handle the case of K < [K]. Its calculation formula is as follows:

[0094]

[0095] where C K is a preset penalty coefficient, for example, C K = 10. This formula ensures that when the scheme satisfies the anti-slide stability constraint, the penalty is 0; when the scheme does not satisfy the constraint, the smaller the stability coefficient K, the larger the value of P K , and the stronger the penalty.

[0096] Stress penalty P σ This penalty term is used to handle the case of . Its calculation formula is as follows:

[0097]

[0098] where C σ is a preset penalty coefficient, for example, C σ = 5. When the scheme satisfies the stress constraint, the penalty is 0; when the scheme does not satisfy the constraint, the larger the maximum principal stress σ max , the larger the value of P σ .

[0099] Dam crest elevation penalty P H This penalty term is used to handle the case of H 顶<H 顶min The formula is as follows:

[0100]

[0101] Wherein, C H is a preset penalty coefficient, for example, C H = 8. When the scheme satisfies the elevation constraint, the penalty is 0; when the scheme does not satisfy, the value of P 顶 is greater, the lower the elevation H H is.

[0102] The hybrid optimization module calculates F' so that the individual that violates the constraint has a lower survival probability in the genetic algorithm selection operation of step S105 due to its higher F' value, or is guided back to the feasible region in the gradient descent of the gradient descent method, thereby ensuring that the optimization search process converges to an excellent scheme that satisfies all the constraints.

[0103] In step S105, the hybrid strategy adopted by the hybrid optimization module first performs a genetic algorithm for global search. This stage aims to explore a wide range of parameter space to identify multiple potential high-quality solution regions, avoiding falling into local optimum due to improper initial value selection.

[0104] The specific implementation steps of the genetic algorithm global search are as follows:

[0105] S1051, population initialization. The hybrid optimization module randomly generates an initial population within the optimization variable search space defined in step S101. The initial population contains multiple individuals, for example, 50 to 100. Each individual is a potential dam body design scheme encoded by a set of optimization variables.

[0106] S1052, iterative operation. The system takes a preset number of generations as a loop, and in each generation, the following operations are performed in turn to drive the population to evolve in a better direction:

[0107] Selection operation: this operation selects individuals according to the penalty fitness value F' calculated in step S104. The smaller the F' value of an individual, the better its overall performance, and the higher the probability of being selected to produce the next generation. A specific implementation is to use roulette method. For the specific implementation of roulette method, it belongs to the known technology in the art, and will not be described here.

[0108] Cross operation: the selected individuals will be paired and their partial codes will be exchanged according to a preset crossover probability. This simulates gene recombination in biological inheritance, aiming to generate new individuals containing the excellent features of the parents. A specific implementation is to use single-point crossover, that is, a crossover point is randomly selected in the individual's code string, and the parts after the crossover point of the two parents are exchanged.

[0109] Mutation operation: To maintain the diversity of the population and prevent the algorithm from converging too early, each individual in the population will be randomly mutated with a small preset mutation probability. A specific implementation is to randomly select an optimization variable in the individual's code and replace its value with another random value within the search range of the optimization variable.

[0110] S1053, Pareto optimal solution set screening. After the preset number of iterations is completed, the global search stage of the genetic algorithm is terminated. At this time, the hybrid optimization module will sort all individuals in the final generation population according to their F' values. The module will screen a batch of individuals with the smallest F' values, for example, the top 10% of individuals, to form a Pareto optimal solution set.

[0111] The Pareto optimal solution set represents a series of design schemes with excellent performance and different characteristics found by the global search stage of the genetic algorithm. Among them, the individual with the smallest F' value, i.e., the optimal solution of the current stage, will be used as the initial value for the next step of local fine search by the gradient descent method.

[0112] After the global search of the genetic algorithm is completed, the hybrid optimization module continues to step S105 and enters the local fine search stage of the gradient descent method. The local fine search stage aims to finely tune the high-quality solutions found by the genetic algorithm to make up for the lack of local search accuracy of the genetic algorithm, so as to obtain a better final scheme.

[0113] The specific implementation steps of the local fine search of the gradient descent method are as follows:

[0114] S1054, setting initial value. The hybrid optimization module takes the optimization variable corresponding to the individual with the smallest F' value in the Pareto optimal solution set screened by the optimal solution set as the initial search point of the gradient descent method algorithm.

[0115] S1055, parameter iteration update. The module performs iterative fine tuning on key optimization variables that affect the safety of the structure and the engineering investment, such as the upstream dam slope ratio m1, the downstream dam slope ratio m2, and the dam height H dam . In each iteration, the update of the parameters is performed according to the gradient descent rule as follows:

[0116]

[0117] where x represents an optimization variable being optimized, such as m1, m2, or H dam . t is the iteration number of the gradient descent method stage; x t is the value of the optimization variable x at the tth iteration; x t+1is the updated value of the variable x at the t+1th iteration; η is a preset learning rate, which is a positive value, used to control the step size of each iteration update; is the gradient of the post-adaptive fitness function F' at the point x t with respect to the variable x. The gradient reflects the rate and direction of the change of F' value with respect to the variable x.

[0118] The specific calculation of the gradient can use numerical methods, such as finite difference method. The specific implementation of the gradient calculation belongs to the prior art and is not described here.

[0119] S1056, convergence judgment and output. After updating the parameters at each iteration, the hybrid optimization module will re-call steps S103 and S104 to calculate the new F' value, and judge whether the convergence and termination conditions of step S106 are met. In the gradient descent phase, a specific termination condition is that when the absolute value of the gradient is less than a preset minimum threshold, the algorithm is considered to have converged to a local optimal solution.

[0120] When the termination condition is met, the gradient descent local fine search is completed. At this time, the hybrid optimization module outputs the final body shape parameter after fine tuning as the optimal solution of the entire optimization process, and waits to enter step S107.

[0121] The DNN simulation prediction module can perform fast prediction in steps S103 and S107, provided that the deep neural network model built in the DNN simulation prediction module has been fully trained offline. The present application completes offline training by constructing a high-quality, high-coverage sample data set, the specific steps are as follows:

[0122] S201, determine the input and output variables. To establish the mapping relationship between the dam shape, material, load parameters and structural response, determine the input and output variables of the DNN model.

[0123] Input variables: 7 dimensions in total, including 3 geometric parameters, 2 material parameters, and 2 load parameters.

[0124] Output variables: 3 dimensions in total, are the key structural response indicators concerned in the optimization process, including the maximum principal stress σ max , the anti-slide stability coefficient K and the dam crest displacement u 顶 .

[0125] S202, generating input variable sample combinations. To ensure that the sample points are uniformly distributed and representative in the multi-dimensional input space, a Latin hypercube sampling method is used to generate 5000 to 10000 input variable combinations within the value ranges of the 7 input variables defined in S201. The sample set also needs to include uncertainty samples that impose random perturbations on the geological or material parameters. For example, within a range of 20% fluctuation above and below the reference value of the rock foundation elastic modulus E r or within a range of 3° fluctuation above and below the reference value of the rock foundation friction angle φ, the corresponding input variable combinations are generated.

[0126] S203, performing finite element numerical calculation. A general finite element numerical calculation framework is used to perform high-precision simulation calculation on each input variable combination generated in S202. The finite element numerical calculation framework is based on the elastoplastic theory and takes into account the constitutive model of concrete and the contact effect between the dam body and the foundation. By performing calculation on each input variable combination through the finite element numerical calculation framework, the accurate solution of the corresponding output variable is obtained. The construction and implementation of the finite element numerical calculation framework belong to the known technology in the art, and will not be described here.

[0127] S204, constructing sample data set. Each input variable combination generated in S202 is one-to-one corresponding to the accurate solution of the output variable calculated in S203, and finally forms a complete data set containing 5000 to 10000 samples. Each sample in the complete data set is composed of a 7-dimensional input vector and a 3-dimensional output vector, which will serve as the basis for subsequent DNN proxy model training and verification.

[0128] After obtaining the sample data set generated in S204, the present application constructs and trains the DNN proxy model, which is solidified in the DNN simulation prediction module for subsequent online prediction.

[0129] The construction and training process of the DNN proxy model is as follows:

[0130] S205, defining model structure. The DNN proxy model constructed by the present application includes an input layer, multiple hidden layers and an output layer.

[0131] Input layer: 7 neurons are set, the number of which is one-to-one corresponding to the 7-dimensional input variable defined in S201.

[0132] Hidden layer: 3 layers can be set, each of which can contain 64 to 128 neurons. Nonlinear activation functions are used between the hidden layers, and a specific embodiment is to use the rectified linear unit function.

[0133] Output layer: 3 neurons are set, the number of which is one-to-one corresponding to the 3-dimensional output variable defined in S201.

[0134] S206, model training.

[0135] Dataset division: Before training, the sample dataset generated in S204 is divided according to a preset ratio. The training set is used to adjust the weights and biases within the model, and the validation set is used to evaluate the generalization ability of the model on unseen data and prevent overfitting.

[0136] Loss function definition: To quantify the deviation between the predicted value of the DNN model and the true value calculated by the finite element method, the mean square error is used as the loss function. The calculation is as follows:

[0137]

[0138] where N is the number of samples; y i is the true output value of the i-th sample calculated by the finite element method; is the predicted value of the DNN model for the input of the i-th sample.

[0139] Optimization and convergence: The Adam optimizer is used to train the model, and the learning rate is set to minimize the MSE loss function. For the specific implementation of the Adam optimizer, it is a well-known technology in the art, and will not be described here. The training process is performed through multiple iterations until the MSE value on the validation set meets the preset convergence criteria, at which point the prediction error of the model is considered to have met the requirements, and the training process is terminated.

[0140] After training is completed, the DNN surrogate model has the ability to quickly predict the 3D output response based on the input 7D parameters, which can be called online by steps S103 and S107.

[0141] After confirming the optimal body shape scheme in step S106, the system can continue to perform step S107. Step S107 aims to evaluate the performance stability of the final design scheme when facing inherent uncertainties in geological, material and other parameters. This function utilizes the efficient prediction capability of the trained DNN surrogate model.

[0142] The steps of implementing the uncertainty quantification and transfer method are as follows:

[0143] S207, uncertainty parameter sampling. For key parameters that have discrete characteristics in actual engineering, such as rock foundation elastic modulus E r or rock foundation friction angle φ, a set of random samples is generated within the fluctuation range. A specific implementation is to use Latin hypercube sampling to generate a set of parameter samples within an interval of 20% above and below the mean value of E r or within an interval of 3° above and below the mean value of φ. These samples are combined with the determined optimal body shape parameters and other fixed parameters to form an input dataset for uncertainty analysis.

[0144] S208, batch prediction and response distribution acquisition. The input data set generated in S207 is batch input into the trained DNN agent model of the DNN simulation prediction module. The model quickly predicts each group of input samples to obtain a corresponding output index distribution set.

[0145] S209, robustness quantitative evaluation. To quantitatively evaluate the dispersion degree of the output index distribution obtained in S208, the coefficient of variation CV is calculated. The calculation of the coefficient of variation is as follows:

[0146]

[0147] Wherein, CV is the coefficient of variation, a dimensionless relative standard deviation, the smaller the value, the smaller the volatility of the output index, and the stronger the robustness of the scheme; X represents an output index, for example, or K; Var(X) is the variance of the output index distribution set obtained in S208; E[X] is the mean of the output index distribution set obtained in S208. max

[0148] By setting an acceptable coefficient of variation threshold, the robustness of the design scheme can be quantitatively judged. If the calculated CV value meets the current requirement, it indicates that the design scheme can still maintain sufficient safety margin under parameter fluctuation, and the scheme is reliable. The result will be finally output as part of step S108.

[0149] The core of the dam body intelligent design system provided by the application is the efficient collaborative working mechanism between the hybrid optimization module and the DNN simulation prediction module.

[0150] In the traditional body design process, the coupling efficiency of optimization iteration and simulation analysis is low. The reason is that each iteration of the optimization algorithm needs to evaluate the structure and performance of the current generated body scheme, and the traditional evaluation method relies on finite element numerical calculation. A single high-precision finite element analysis takes 3 to 72 hours, which makes the optimization algorithm unable to iterate a sufficient number of times within a reasonable time, thereby seriously restricting the efficiency and effectiveness of the optimization design.

[0151] The collaborative working mechanism of the application solves the above technical bottleneck. During the optimization iteration process of step S105, when the hybrid optimization module generates a new set of body parameters, the collaborative control module inputs the set of body parameters and calls the DNN simulation prediction module in real time.

[0152] After receiving the input, the DNN simulation prediction module performs a forward propagation calculation of the trained model, and outputs the predicted performance index corresponding to the body parameters in a very short time. The prediction result is immediately fed back to the hybrid optimization module.​

[0153] After the performance index returned by the DNN simulation prediction module is obtained, the hybrid optimization module can immediately execute step S104 to calculate the post-punishment fitness value F' of the current individual. The post-punishment fitness value F' is immediately used for selection, crossover and mutation operations of the genetic algorithm, or gradient calculation and parameter updating of the gradient descent method, so as to complete a complete optimization iteration.

[0154] The real-time closed loop of optimization and simulation enables the hybrid optimization module to quickly and accurately evaluate the performance of thousands or even tens of thousands of individual scheme in one complete run. Each iteration of the optimization algorithm can obtain immediate simulation feedback, thereby ensuring the continuity and efficiency of the optimization search. Through the cooperative mechanism, the design optimization period originally taking 15 to 30 days is shortened to 1 to 2 days, thereby solving the technical problem that the simulation accuracy and optimization efficiency cannot be considered in the prior art.

[0155] To further illustrate the specific embodiments of the present application, a concrete gravity dam with a planned dam height in the range of 80 to 120 meters in a certain river basin will be taken as an example to illustrate the technical solutions of the present application.

[0156] First, step S101 is executed to set the engineering input parameters.

[0157] Geological parameters: the design value of the rock foundation friction angle φ is 35°, and a fluctuation range of ±3° is considered; the design value of the rock foundation cohesion c is 1.5 MPa, and a fluctuation range of ±0.2 MPa is considered; the design value of the rock foundation elastic modulus E r is 25 GPa, and a fluctuation range of ±2 GPa is considered.

[0158] Load parameters: the design flood level H w is 180 m, and the checking flood level is 182 m; the design earthquake acceleration a is 0.2g.

[0159] Design constraint limits: the anti-sliding stability coefficient limit [K] is not less than 1.15; the maximum principal stress limit [σ] is not greater than 5 MPa; and the minimum dam crest elevation H 顶min is not less than 183 m.

[0160] Optimization variable search range: the dam height H dam is searched between 80 m and 120 m; the upstream dam slope ratio m1 is searched between 1:0.6 and 1:0.9; the downstream dam slope ratio m2 is searched between 1:0.8 and 1:1.1; and the dam crest width B is searched between 8 m and 12 m.

[0161] Multi-objective fitness function weights: According to the high safety requirements of the project, the weights are set as w1=0.3, w2=0.4, and w3=0.3.

[0162] Next, the system performs a hybrid optimization process. In this example, the initial trial scheme has a concrete volume V0of about 1.2 million m 3 .

[0163] Genetic algorithm global search phase: The population size is set to 80 individuals, and 40 generations of iteration are performed. After 40 generations of evolution, a Pareto optimal scheme selected by the genetic algorithm is: H dam = 105 m, m1=1:0.75, m2=1:0.95, and B=10 m. The hybrid optimization module calculates the concrete volume of the optimal scheme as 1.08 million m 3 . At the same time, the system calls the DNN surrogate model to predict the maximum principal stress of the optimal scheme as 4.8 MPa, and the anti-slide stability coefficient as 1.20. According to the following calculation, the fitness function value F is:

[0164]

[0165] Gradient descent method local fine search phase: Taking the above genetic algorithm optimal solution as the initial value, the learning rate η is set to 0.03 and 20 iterations are performed. In the iteration, the system calculates the gradient of F' with respect to m1, m2, etc. After fine-tuning, the final optimization scheme is obtained: H dam = 105 m, m1=1:0.78, m2=1:0.92, and B=10 m. The final optimization scheme corresponds to a concrete volume of 1.06 million m 3 , with a predicted maximum principal stress of 4.5 MPa and an anti-slide stability coefficient of 1.22. At this time, the penalized fitness value F' is calculated as:

[0166]

[0167] The penalized fitness F' value is reduced by about 5.3% compared to the optimal solution in the genetic algorithm phase, indicating that the comprehensive performance of the scheme has been further improved.

[0168] Before or in parallel with the optimization execution, the system needs to complete the construction and training of the DNN surrogate model:

[0169] Sample data set generation: A general finite element calculation framework is used to generate 5000 samples. In this example, a single finite element calculation takes about 2 hours on average, and through distributed parallel computing, the total sample generation takes about 417 hours.

[0170] DNN agent model training: a model structure with 7 input neurons, 128 neuron hidden layers, 96 neuron hidden layers, 64 neuron hidden layers, and 3 output neurons is adopted. After about 1000 iterations of training, the MSE of the model on the validation set reaches 8.5X10 -5 The prediction error of the maximum principal stress σ max is 2.8%, and the prediction error of the anti-sliding stability coefficient K is 2.1%, which meets the accuracy requirements.

[0171] After obtaining the final optimization scheme, uncertainty analysis and scheme verification are performed:

[0172] Uncertainty analysis: 100 groups of Latin hypercube sampling are performed on the elastic modulus E r and the rock foundation friction angle φ. The samples are input into the trained DNN model for batch prediction, and the mean value of the maximum principal stress σ max is 4.5MPa, and the coefficient of variation cv is 3.2%; the mean value of the anti-sliding stability coefficient K is 1.22, and the coefficient of variation cv is 2.5%. The cv values of the two key indicators are both less than 5%, indicating that the design scheme has good robustness.

[0173] Final verification of the scheme: to ensure the reliability of the final result, the final scheme output by the hybrid optimization algorithm is re-input into the general finite element calculation framework for high-precision checking calculation. The calculation results are: σ max = 4.6MPa, K = 1.21. The calculated concrete volume is 1.06 million m 3 , which is reduced by 11.7% compared with the initial trial scheme. All indicators meet the design constraints, verifying the effectiveness and accuracy of the method proposed in the present invention.

Claims

1. A dam shape intelligent design method based on a hybrid optimization algorithm, characterized in that, The method comprises the following steps: S1, obtaining an optimization variable search range of a dam body parameter, a design constraint limit value and a load parameter; S2, generating a group of current dam body parameter individuals based on a hybrid optimization algorithm; S3, calling a pre-trained deep neural network proxy model, inputting the dam body parameter individuals, predicting and outputting predicted performance indicators corresponding to the dam body parameter individuals, the predicted performance indicators at least including a maximum principal stress and a sliding stability coefficient; S4, calculating a post-punishment fitness value corresponding to the dam body parameter individuals according to the predicted performance indicators; S5, updating the hybrid optimization algorithm according to the post-punishment fitness value to generate a new generation of dam body parameter individuals; S6, repeatedly executing steps S2 to S5 until a preset termination condition is met; S7, outputting the dam body parameter individuals when the termination condition is met as an optimal body parameter scheme.

2. The method according to claim 1, wherein, The hybrid optimization algorithm comprises: firstly performing a genetic algorithm for global search to generate a Pareto optimal solution set; and after the global search of the genetic algorithm is terminated, the individual with the minimum post-punishment fitness value in the Pareto optimal solution set is an initial value, and a gradient descent method is performed for local search.

3. The method according to claim 1, wherein, The post-punishment fitness value in the S4 step comprises: firstly, calculating a multi-objective fitness function according to the predicted performance indicators and the calculated concrete volume; then, calculating a constraint punishment item according to whether the predicted performance indicators meet the design constraint limit value; finally, adding the multi-objective fitness function and the constraint punishment item to obtain the post-punishment fitness value.

4. The method according to claim 3, wherein, The multi-objective fitness function comprises: after normalization processing of the concrete volume, the maximum principal stress and the sliding stability coefficient, weighted summation is performed.

5. The method according to claim 1, wherein, The intelligent dam body design method further comprises the following steps after step S6: S8, for the optimal body parameter scheme, parameter sampling is performed in a fluctuation range of the load parameter or the geological parameter to form an input data set for uncertainty analysis; S9, batch calling the deep neural network proxy model to obtain a distribution set of predicted performance indicators corresponding to the input data set; S10, calculating a variation coefficient of the distribution set to evaluate the robustness of the optimal body parameter scheme.

6. The method according to claim 5, wherein, The deep neural network proxy model is generated based on offline training of a sample data set; input variables of the sample data set comprise optimization variables corresponding to dam body parameters, and the geological parameters and the load parameters.

7. The method according to claim 6, wherein, The offline training of the deep neural network proxy model comprises: generating a sample combination of the input variables by Latin hypercube sampling; obtaining real structure response indicators corresponding to the sample combination through finite element numerical calculation; and the sample combination of the input variables and the real structure response indicators construct the sample data set, and model training is performed with mean square error as a loss function.

8. The dam type intelligent design method based on hybrid optimization algorithm according to claim 1, characterized in that, The dam body parameter individual is defined by a group of optimization variables, and the optimization variables comprise dam height, upstream dam slope ratio, downstream dam slope ratio and dam crest width.

9. The dam type intelligent design method based on hybrid optimization algorithm according to claim 1, characterized in that, In the S3 step, the deep neural network agent model is called to replace the finite element numerical calculation to obtain the predicted performance index.

10. A simulation system for the dam type intelligent design method based on the hybrid optimization algorithm according to any one of claims 1-9, characterized in that, The method comprises the following steps: a hybrid optimization module, configured to generate a group of current dam shape parameter individuals based on a hybrid optimization algorithm, and update the hybrid optimization algorithm to generate a new generation of dam shape parameter individuals according to a penalized fitness value; a DNN simulation prediction module, configured to solidify a pre-trained deep neural network agent model, and configured to receive the dam shape parameter individuals and predict and output corresponding predicted performance indexes, wherein the predicted performance indexes at least include a maximum principal stress and a sliding resistance stability coefficient; a cooperative control module, electrically connected to the hybrid optimization module and the DNN simulation prediction module, and configured to: transfer the dam shape parameter individuals from the hybrid optimization module to the DNN simulation prediction module; return the predicted performance indexes from the DNN simulation prediction module to the hybrid optimization module; and determine whether the hybrid optimization algorithm meets a preset termination condition; wherein the hybrid optimization module is further configured to calculate the penalized fitness value according to the predicted performance indexes.

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