A large prestressed continuous beam aqueduct optimization design method based on genetic algorithm

Abstract

The genetic algorithm-based large prestressed continuous beam aqueduct optimization design method of the application comprises the following steps: constructing multi-dimensional design variables and generating a high-fidelity training data set; adopting hybrid coding chromosome to represent design individuals, executing geometric interference self-healing logic and engineering modulus normalization; constructing a full working condition matrix, converting concrete shrinkage, concrete creep and prestress long-term loss into response correction amounts respectively and establishing a constraint judgment library; training an agent model as a transient evaluation engine; adopting an adaptive genetic algorithm for global optimization, maintaining a Pareto non-inferior solution set; screening the optimal scheme for high-fidelity review and selective incremental learning. The application realizes millisecond-level reasoning through an AI agent model, solves the bottleneck of frequent calling of finite element calculation in traditional methods, ensures the constructability of the scheme through self-healing logic and modulus normalization, guarantees the whole life cycle performance through full working condition time-varying effect evaluation, and forms a closed-loop evolution through active learning and high-fidelity review, thereby improving the optimization efficiency and search depth on the premise of ensuring safety and compliance.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower engineering and transportation bridge engineering design, specifically to an optimization design method for large prestressed continuous beam aqueducts based on genetic algorithms. Background Technology

[0002] Large-scale prestressed continuous beam aqueducts, as core water conveyance structures in inter-basin water transfer projects, bear the heavy responsibility of maintaining the longitudinal slope balance of the water transfer route and ensuring the continuity of water conveyance. With the continuous expansion of water transfer scale, aqueduct structures are evolving towards ultra-large spans, high self-weight, and heavy loads. Because aqueducts must bear the enormous dynamic weight of water during their service life, and as hydraulic structures, they have almost stringent requirements for seepage prevention and crack resistance, their design process involves a deep intersection of multiple disciplines such as mechanics, hydraulics, and materials science, making it extremely complex.

[0003] However, existing aqueduct design and optimization methods reveal the following core technical bottlenecks when facing increasingly complex engineering requirements: The design space of aqueducts exhibits extremely high dimensional coupling characteristics. There is a deep nonlinear interweaving relationship between the geometric parameters of the cross-section (such as beam height, web slope, and bottom plate thickness) and the parameters of the prestressing system (such as steel strand linear coordinates, tension force values, and anchorage layout). Current designs largely rely on manual experience for a limited number of scheme comparisons, making it difficult to achieve optimal global performance in a massive design space, often resulting in suboptimal local solutions. Aqueducts undergo drastic changes in operating conditions throughout their entire life cycle. Existing calculation models are mostly limited to single operating conditions after bridge completion, failing to fully quantify the time-varying stress characteristics during the construction tensioning stage, the empty channel maintenance stage, the stage of drastic water level fluctuations, and under extreme environmental temperature differences. This "static design" ignores the redistribution of internal forces caused by concrete shrinkage and creep and long-term prestress loss, easily leading to the risk of structural cracking or insufficient safety margin at specific stages. Key design parameters such as prestressed steel strands, anchorage specifications, and rebar diameter are all discrete variables in actual engineering. Traditional optimization algorithms, for the sake of computational simplicity, often process the data in a "continuous" manner, then simply round the result back to the discrete space. This approach undermines the rigor of mechanical equilibrium, resulting in significant discrepancies between the optimized theoretical solution and actual construction, making the calculation results difficult to directly apply to construction drawing preparation. Existing optimization criteria often overemphasize the economic efficiency of material usage, lacking a comprehensive consideration of multiple objectives such as construction difficulty, long-term crack resistance reserves, and life-cycle maintenance costs. This directly leads to many theoretically "optimal solutions" experiencing soaring costs in actual construction due to excessive reinforcement and difficulties in formwork erection, or resulting in huge maintenance costs due to insufficient durability.

[0004] In summary, in order to meet the requirements of modern water diversion projects for high-performance and long-life structures, it is urgent to develop an intelligent, data-driven design method that can automatically handle mixed variables, dynamically cover all working condition constraints, and achieve multi-objective balance and collaborative optimization. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides an optimization design method for large-scale prestressed continuous beam aqueducts based on genetic algorithms. The purpose of this method is to achieve millisecond-level instantaneous reasoning through an AI agent model, ensure the constructability of the scheme by constructing self-healing logic and modular normalization, guarantee the performance throughout the entire life cycle through evaluation of time-varying effects under all working conditions, and improve optimization efficiency and search depth by forming a closed-loop evolution through active learning and high-fidelity verification, while ensuring structural safety and engineering compliance.

[0006] To achieve the above objectives, the specific solution of the present invention is as follows:

[0007] A method for optimizing the design of large-scale prestressed continuous beam aqueducts based on genetic algorithms includes the following steps:

[0008] S1: Decompose the design parameters into geometric feature vectors, prestress feature vectors, material property vectors, and construction stage label vectors, which together constitute multi-dimensional input design variables; use experimental design methods to generate N sets of sample points in the design space, with the sampling optimization objective being to minimize the correlation between samples; use the finite element analysis interface to batch calculate the mechanical response of the N sets of sample points under key working conditions throughout the entire life cycle, forming an initial high-fidelity training dataset.

[0009] S2: A hybrid coding chromosome directly corresponding to the multidimensional input design variables in step S1 is used to represent a design individual. The hybrid coding chromosome is differentiated according to the variable type. In the decoding stage, the geometric interference self-healing logic is executed in real time: the minimum distance from the prestressed duct to the concrete surface is calculated. If the minimum distance is less than the minimum protective layer thickness, the coordinates are adjusted along the normal gradient of that point until the protective layer thickness requirement is met. Engineering modulus normalization is performed on all design parameters to make their values ​​conform to the standard modulus of construction and manufacturing, and a normalized design parameter vector is output.

[0010] S3: Based on the standardized design parameter vector output in step S2, construct a full-condition matrix covering the construction and operation stages; respectively, convert concrete shrinkage into initial strain, concrete creep into elastic modulus reduction, and long-term prestress loss into effective prestress reduction, and obtain shrinkage response correction, creep response correction, and prestress loss response correction through corresponding condition reanalysis; superimpose the shrinkage response correction, creep response correction, and prestress loss response correction into the initial response of each condition according to the linear superposition principle to obtain the full-condition response considering time-varying effects; establish a comprehensive constraint judgment library with crack resistance criteria, deflection limit, and bearing capacity margin as objectives, as the output label of the surrogate model;

[0011] S4: Train the surrogate model based on the high-fidelity training dataset generated in step S3, and establish a high-precision nonlinear mapping relationship from the multidimensional design variables in step S1 to the mechanical response vector; the mechanical response vector includes at least stress, deformation and crack width indices; adopt the mean square error loss function, and combine L2 regularization and early stopping strategy to optimize the model's generalization ability; integrate the trained model into the instantaneous evaluation engine in the genetic algorithm;

[0012] S5: Adaptive genetic algorithm is used for global optimization, and crossover rate and mutation rate are dynamically adjusted according to population diversity; Pareto non-dominated solution set is maintained and updated to address the dual objective conflict of minimizing structural self-weight and maximizing stress safety reserve; fitness evaluation is completed by using the instantaneous evaluation engine in step S4 to replace finite element calculation.

[0013] S6: From the Pareto non-dominated solution set obtained in step S5, select the comprehensive optimal solution based on the TOPSIS multi-criteria decision method; perform a high-fidelity finite element verification on the comprehensive optimal solution and calculate the prediction error of the surrogate model; if the prediction error of the surrogate model meets the preset engineering tolerance, output the corresponding multidimensional design variables as the final optimization result; otherwise, feed the comprehensive optimal solution as a new sample back to step S1 for incremental model learning.

[0014] Furthermore, the experimental design method described in step S1 is optimal Latin hypercube sampling. The formula for generating N sets of sample points within the design space using optimal Latin hypercube sampling is as follows:

[0015] ,

[0016] In the formula, D0 is the initial sample set generated by optimal Latin hypercube sampling; x i Let be the multidimensional design variable vector corresponding to the i-th sample point; N is the number of samples; L and U are the lower and upper bound vectors of the design variables, respectively;

[0017] The formula for minimizing the correlation between samples is as follows:

[0018] ,

[0019] In the formula, x i and x j Let be the multidimensional design variable vectors corresponding to the i-th and j-th sample points.

[0020] Furthermore, the correction formula for adjusting the coordinates along the normal gradient in step S2 is as follows:

[0021] ,

[0022] In the formula, P d The coordinates of the center point of the prestressed duct; The adaptive step size; n is the normal unit vector; These are the corrected coordinates;

[0023] All design parameters are normalized using engineering modules to ensure their values ​​conform to the standard modules for construction and manufacturing. The formula is as follows:

[0024] ,

[0025] In the formula, 1 represents the normalized design parameters; x represents the original design parameters, including section height h, base plate thickness t, and transverse spacing of prestressed tendons, in millimeters (mm); M represents the standard engineering module.

[0026] Furthermore, the creep response correction amount mentioned in step S3 is obtained by the equivalent secant modulus reduction method, and the calculation formula of the equivalent secant modulus is as follows:

[0027] ,

[0028] In the formula, The nominal modulus of elasticity of concrete at 28 days of age; is the concrete creep coefficient, which is the ratio of creep deformation to initial elastic deformation at time t under sustained load. Let be the equivalent secant modulus of concrete at any time t.

[0029] Furthermore, the surrogate model described in step S4 is at least one of a deep neural network, a radial basis function network, or a gradient boosting tree model.

[0030] Furthermore, the formula for dynamically adjusting the crossover rate and mutation rate based on population diversity in step S5 is as follows:

[0031] ,

[0032] In the formula, P c P m These represent the dynamically adjusted crossover rate and mutation rate, respectively. , These are the initial probabilities; The threshold for maximum similarity among populations; This is the adjustment coefficient.

[0033] Furthermore, the formula for the prediction error of the surrogate model in step S6 is as follows:

[0034]

[0035] In the formula, For the surrogate model prediction error; The predicted value is from the proxy model; These are values ​​calculated using the finite element method.

[0036] Advantages of the present invention

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) This invention constructs an AI proxy model in step S4 as an instantaneous evaluation engine in the genetic algorithm, establishing a high-precision nonlinear mapping relationship from the multidimensional design variables in step S1 to the mechanical response vector, realizing millisecond-level instantaneous reasoning from design variables to mechanical response, and completely solving the bottleneck of traditional genetic algorithms that require frequent calls to time-consuming finite element calculations. While maintaining accuracy, the time consumption of a single scheme evaluation is greatly reduced, making it possible to conduct large-scale in-depth exploration of the design space and increase the scale of the population.

[0039] (2) In step S2, the present invention executes the geometric interference self-healing logic in real time during the decoding stage, automatically detects and corrects the interference problem between the prestressed duct and the concrete protective layer, and transforms illegal individuals into legal solutions, which greatly reduces the loss of the algorithm in the invalid search space. At the same time, step S2 performs engineering modulus normalization processing on all design parameters to ensure that the optimized output parameters directly conform to the construction modulus and industry standards, and realizes a deep connection between design and construction.

[0040] (3) In step S3, this invention constructs a full-condition matrix covering the construction and operation stages, and equates concrete shrinkage, concrete creep, and long-term prestress loss to time-varying correction coefficients. Based on the time-varying correction coefficients, the corresponding response correction amount is calculated, and the response correction amount is linearly superimposed on the initial response of each condition. The comprehensive constraint judgment library established in step S3, which aims at crack resistance criteria, deflection limits, and bearing capacity margins, ensures that the crack resistance, deflection, and bearing capacity reserves of the aqueduct structure can be rigorously and reliably evaluated throughout its entire life cycle.

[0041] (4) In step S6, the present invention uses the TOPSIS multi-criteria decision-making method to screen the comprehensive optimal solution and performs a high-fidelity finite element verification to calculate the prediction error of the surrogate model and set strict engineering tolerances to ensure the reliability of the optimization results. When the error meets the engineering tolerance, the final design variables are output. Otherwise, the comprehensive optimal solution is fed back to step S1 as a new sample for incremental model learning, realizing the self-improvement and closed-loop evolution of the surrogate model accuracy. Attached Figure Description

[0042] Figure 1 This is a flowchart of the optimization design method for large prestressed continuous beam aqueducts based on genetic algorithms according to the present invention.

[0043] Figure 2 This is a cross-sectional view of the aqueduct at mid-span of the present invention; where 1 represents a large prestressed continuous beam aqueduct. Detailed Implementation

[0044] The following explanation and description are provided in conjunction with the accompanying drawings and specific embodiments. It should be noted that these specific embodiments are not intended to limit the scope of the invention.

[0045] like Figure 1 and Figure 2 As shown in the figure, this specific embodiment provides an optimization design method for large-scale prestressed continuous beam aqueducts based on genetic algorithms, which includes the following steps:

[0046] S1: Feature Space Construction and High-Fidelity Sample Sampling

[0047] Decompose the design parameters into geometric feature vectors Prestressed eigenvectors Material property vector and construction phase tag vectors Together they constitute multidimensional input design variables. The experimental design method is used to generate N sets of sample points in the design space, and the sampling optimization objective is to minimize the correlation between samples.

[0048] The experimental design method employed is optimal Latin hypercube sampling to ensure the uniformity and representativeness of the samples within the design space. Optimal Latin hypercube sampling is achieved by minimizing the Euclidean distance between sample points and maximizing space filling. The formula for generating N sets of sample points within the design space using the optimal Latin hypercube sampling method is as follows:

[0049] ,

[0050] In the formula, D0 is the initial set of sampling points; x iLet N be the i-th sample point; N be the number of samples; L and U be the lower and upper bound vectors of the design variables, respectively.

[0051] The formula for minimizing the correlation between samples is as follows:

[0052] ,

[0053] In the formula, x i and x j Let be the multidimensional design variable vectors corresponding to the i-th and j-th sample points.

[0054] The mechanical response Y of the N sets of sample points under key working conditions throughout the entire life cycle is calculated in batches using the finite element analysis interface to form an initial high-fidelity training dataset.

[0055] ,

[0056] In the formula, D train X is the initial high-fidelity training dataset; i For the i-th sample point, a multidimensional input design variable;

[0057] Mechanical response vector Its formula is:

[0058] ,

[0059] In the formula, Y i The output response of the i-th finite element method is given; N is the total number of samples. This indicates a high-fidelity finite element solver.

[0060] S2: Hybrid coding and feature preprocessing

[0061] A hybrid encoded chromosome, directly corresponding to the multidimensional input design variables in step S1, is used to represent a design individual. The hybrid encoded chromosome is differentially encoded according to the variable type to adapt to the operation of the genetic algorithm.

[0062] ,

[0063] In the formula, C is a mixed coding chromosome, and c r It is a real number encoding, corresponding to continuous variables; c i It is an integer encoding, corresponding to discrete variables.

[0064] During the decoding phase, the geometric interference self-healing logic is executed in real time: the minimum distance d from the prestressed duct to the concrete surface is calculated, and if d < d min Then, adjust the coordinates along the normal gradient of that point until the minimum protective layer thickness requirement is met. Define the minimum distance constraint between the prestressed duct and the outer edge of the concrete as follows:

[0065] ,

[0066] In the formula, d min d is the minimum protective layer thickness; d(·) is the Euclidean distance function; P d P is the coordinate vector of the center point of the prestressed duct; S The coordinate vector of the nearest point on the outer surface of the concrete structure.

[0067] If d < d is detected min Then, coordinate correction is performed, and the correction formula for adjusting the coordinates along the normal gradient is:

[0068] ,

[0069] In the formula, P d The coordinates of the center point of the prestressed duct; For adaptive step size, It is the normal unit vector; These are the corrected coordinates.

[0070] The geometric interference self-healing logic uses an iterative gradient descent method to fine-tune the coordinates, ensuring that the smoothness requirements of the steel strand line are still met after adjustment.

[0071] All design parameters are normalized to conform to the standard modularity for construction and manufacturing.

[0072] ,

[0073] In the formula, x' is the normalized design parameter vector, x is the original design parameter, such as the section height h, the base plate thickness t, and the transverse spacing of the prestressed tendons, in millimeters (mm); M is the standard engineering module.

[0074] The standard engineering module is the smallest indivisible design unit determined by construction technology, formwork system, material specifications, and industry standards, and is expressed in millimeters (mm). x' represents the normalized design parameters, which constitute a discrete feasible solution space.

[0075] ,

[0076] In the formula, L and U are the upper and lower limits of the parameter; round(⋅) is the engineering rounding rule of the rounding function to minimize the cumulative error of the system.

[0077] The specific method of hybrid encoding and feature preprocessing is as follows: continuous and discrete variables are uniformly encoded and embedded with engineering construction constraint rules; the encoded feature data is normalized; self-healing logic is introduced in the encoding process to automatically detect and correct design variables that violate construction requirements; the physical properties of discrete variables are preserved through hybrid variable encoding, thereby improving the accuracy of mechanical calculations.

[0078] The self-healing logic specifically includes: when it is detected that the position of the prestressed steel strand does not meet the minimum clear distance requirement of the concrete cover, the steel strand coordinates are automatically adjusted along the normal direction until all structural constraints are met.

[0079] S3: Constraint Labelling and Condition Response Mapping

[0080] Based on the normalized design parameter vector output in step S2 Construct a full-condition matrix covering both construction and operation phases:

[0081] .

[0082] The full-condition matrix includes at least the following conditions: pouring condition, prestressing tensioning condition, trenching condition, full trench operation condition, empty trench maintenance condition, temperature gradient condition, and long-term operation condition.

[0083] For each calculation case, the initial response without considering time-varying effects is first calculated. Then, the initial response is corrected based on the response correction caused by concrete shrinkage, concrete creep, and long-term prestress loss, to obtain the case response considering time-varying effects.

[0084] The concrete shrinkage response correction is achieved by equating concrete shrinkage to the initial strain of the concrete element. The shrinkage strain of the concrete at time t is expressed as:

[0085] ,

[0086] In the formula, Let T be the shrinkage strain of the concrete at time t; This refers to the final shrinkage strain of the concrete. This is the shrinkage development coefficient, used to characterize the degree to which concrete shrinkage develops over time.

[0087] In obtaining shrinkage strain Subsequently, this strain was applied as an equivalent initial strain to the concrete elements in the finite element model. Keeping the structural geometric parameters, boundary conditions, and external load conditions unchanged, the structural analysis was repeated for the k-th load case to obtain the response considering concrete shrinkage. The response after concrete shrinkage will be taken into account. With the initial response By subtracting the values, we obtain the correction amount for the response caused by concrete shrinkage:

[0088] ,

[0089] In the formula, This is the response correction amount caused by concrete shrinkage at time t for the k-th working condition.

[0090] The correction for the creep response caused by concrete creep is obtained through the equivalent secant modulus reduction method. Specifically, the equivalent secant modulus of the concrete at any time t is first calculated using the following formula:

[0091] ,

[0092] In the formula, The nominal modulus of elasticity of concrete at 28 days of age; is the concrete creep coefficient, which is the ratio of creep deformation to initial elastic deformation at time t under sustained load. The equivalent secant modulus of concrete is defined as the equivalent secant modulus of concrete at any time t. This equivalent secant modulus is used to characterize the comprehensive instantaneous stiffness of the material under continuous load history and is the core time-varying parameter for calculating the time-varying deformation of the structure and analyzing the redistribution of internal forces.

[0093] When calculating the creep correction, the elastic modulus of concrete in the structural analysis model is changed from... Replace with Recalculate the response under the k-th operating condition to obtain the response considering creep. The creep response correction is determined by the following formula:

[0094] .

[0095] The effective prestress of the prestressed steel strand at time t is expressed as:

[0096] ,

[0097] In the formula, The effective prestress at time t; To control the tension stress; Let t be the total prestress loss at time t.

[0098] The total prestress loss can be expressed as:

[0099]

[0100] In the formula, For the friction loss of the channel; For anchorage retraction loss; This refers to the elastic compression loss of concrete. This refers to the loss of prestress caused by concrete shrinkage. This refers to the loss of prestress caused by concrete creep; This refers to the prestress loss caused by the relaxation of the steel strands.

[0101] To obtain effective prestress Then, the prestressed steel strand tension stress in the finite element model was changed by... Replace with Keeping the structural geometry, boundary conditions, and external load conditions unchanged, the structural analysis is performed again for the k-th load case to obtain the response considering the long-term loss of prestress. .

[0102] The response after considering long-term prestress loss will be taken into account. With the initial response By subtraction, the response correction caused by long-term prestress loss is obtained:

[0103] ,

[0104] In the formula, This is the response correction amount caused by long-term prestress loss at time t for the k-th working condition. The initial response for the k-th load case without considering shrinkage, creep, and long-term prestress loss.

[0105] Specifically, concrete shrinkage, concrete creep, and long-term prestress loss are each represented as equivalent response corrections, which are then superimposed onto the responses of each load case according to the principle of linear superposition. For the k-th load case, its corrected response at time t is expressed as:

[0106] ,

[0107] In the formula, This is the corrected response for the k-th operating condition at time t; The initial response of the kth working condition is without considering shrinkage, creep and long-term prestress loss; This is the correction amount for the response caused by concrete shrinkage; This is the correction amount for the response caused by concrete creep; This is the response correction amount caused by long-term prestress loss.

[0108] Therefore, the concrete elastic modulus reduction formula is used to generate the creep response correction, while the linear superposition method is used to superimpose the creep response correction along with the response corrections for concrete shrinkage, long-term prestress loss, etc., into the initial response of each working condition, thereby obtaining the full working condition response considering time-varying effects.

[0109] A comprehensive constraint judgment library with crack resistance criteria, deflection limits, and bearing capacity margin as objectives is established and used as the output label for the surrogate model;

[0110] The performance indicators of the structure under key working conditions throughout its entire life cycle are defined as the output labels of the surrogate model; the time-varying effects such as long-term prestress loss and concrete shrinkage and creep are quantified into response correction quantities and integrated into the constraint decision logic.

[0111] S4: AI Agent Model Training and Instantaneous Evaluation

[0112] Based on the high-fidelity training dataset generated in step S3 Train the surrogate model to establish a high-precision nonlinear mapping relationship from the multidimensional design variable X in step S1 to the mechanical response vector Y. The surrogate model is one or a combination of deep neural networks, radial basis function networks, or XGBoost ensemble learning models. It can be an MLP, XGBoost, or a hybrid model of both. The optimal hyperparameters are determined by cross-validation.

[0113] The mechanical response vector includes at least the indices of stress, deformation, and crack width.

[0114] The training process uses the mean squared error loss function and combines L2 regularization and early stopping strategy to optimize the model's generalization ability and prevent overfitting;

[0115] The trained model is integrated into the instantaneous evaluation engine of the genetic algorithm, enabling millisecond-level prediction of the mechanical performance of a single scheme. In subsequent optimization searches, this surrogate model is used to replace finite element software for millisecond-level performance prediction and constraint violation evaluation.

[0116] S5: Heuristic Search and Global Optimization

[0117] An adaptive genetic algorithm is used for global optimization, and the crossover rate and mutation rate are dynamically adjusted according to population diversity. The formulas for dynamically adjusting the crossover rate and mutation rate according to population diversity are as follows:

[0118] ,

[0119] In the formula, P c P m The crossover rate and mutation rate are shown separately after dynamic adjustment. , These are the initial probabilities; The threshold for maximum similarity among populations; This is the adjustment coefficient.

[0120] To address the conflict between the dual objectives of minimizing structural self-weight and maximizing stress safety reserve, we maintain and update the Pareto non-dominated solution set.

[0121] The fitness assessment is completed by replacing the finite element calculation with the instantaneous evaluation engine in step S4.

[0122] Based on the AI ​​agent model trained in step S4, a heuristic global search is performed using a genetic algorithm. The population is iteratively evolved through selection, crossover, and mutation operations, and the fitness value is quickly calculated using the agent model to guide the search direction.

[0123] The genetic algorithm employs adaptive crossover and mutation rates, and its population size and number of generations can be increased by more than an order of magnitude compared to traditional finite element-driven methods.

[0124] S6: Intelligent Decision-Making and High-Fidelity Verification

[0125] From the Pareto non-dominated solution set obtained in step S5, the comprehensive optimal solution is selected based on the TOPSIS multi-criteria decision-making method.

[0126] A high-fidelity finite element analysis was performed on the optimal solution to calculate the prediction error of the surrogate model. The formula for the prediction error of the surrogate model is as follows:

[0127]

[0128] In the formula, For the surrogate model prediction error; The predicted value of the surrogate model is the mechanical response vector trained in step S4. These are values ​​calculated using the finite element method.

[0129] If the prediction error of the surrogate model meets the preset engineering tolerance, the corresponding multidimensional design variables are output as the final optimization result; otherwise, the comprehensive optimal solution is fed back as a new sample to step S1 for incremental model learning.

[0130] like If the result is positive, the final design drawings and parameters will be output; otherwise, the sample will be fed back as new data to step S1 for incremental model learning, forming a self-improving intelligent closed loop.

[0131] The error tolerance for the high-fidelity verification is set to be less than or equal to 5% for the relative error between the predicted response and the finite element calculation result. .

[0132] From the set of non-dominated solutions obtained through optimization, a recommended design scheme that meets the engineering weights is selected based on a multi-criteria decision-making method. A high-fidelity finite element analysis is performed on the final recommended scheme to verify the prediction accuracy of the surrogate model. If the error meets the engineering tolerance, a complete set of design parameters is output to complete the closed-loop design process.

[0133] In summary, this invention deeply integrates active sampling technology, geometric interference self-healing logic, full-lifecycle time-varying response mapping, and a high-performance AI proxy model to construct an intelligent full-lifecycle optimization design system for large prestressed continuous beam aqueducts. While ensuring structural design safety and engineering compliance, it improves both optimization efficiency and search depth.

[0134] As described above, multi-objective optimization of the aqueduct structure can be achieved through optimal Latin hypercube sampling, surrogate model construction, and genetic algorithm solution. In a specific application, taking a large prestressed continuous beam aqueduct 1 as the object, an initial sample library is established using the optimal Latin hypercube sampling method, and multi-objective optimization is performed by combining the surrogate model and genetic algorithm. The parameters used in the specific implementation are shown in Table 1: (The parameters shown in Table 1 are only used to illustrate the implementation method of the present invention and are not intended to limit the scope of protection of the present invention.)

[0135] Table 1

[0136]

[0137] Under the above parameters, an initial sample library is first formed using N=240 optimal Latin hypercube samples. After finite element analysis, a surrogate model is trained, and then an adaptive genetic algorithm with a population size of 120 and 200 generations is used for multi-objective optimization. Since the fitness evaluation of candidate solutions in the genetic algorithm iteration is mainly completed by the surrogate model, the total computation time can be significantly reduced compared to the traditional finite element driven method that directly calls the finite element solver for each candidate solution.

[0138] For long-term operating conditions, concrete creep is handled by reducing the equivalent secant modulus. For example, taking Ec28 = 3.50 × 10^4 MPa and creep coefficient φ(t) = 1.80, then Ec(t) = Ec28 / [1 + φ(t)] = 1.25 × 10^4 MPa. After replacing the concrete elastic modulus in the finite element model with Ec(t), the response is recalculated, and the resulting creep response correction is linearly superimposed with corrections for shrinkage, long-term prestress loss, etc., into the initial operating condition response.

[0139] The optimization process was run once with the parameters shown in Table 1. The comparison of key parameters before and after optimization and the results are shown in Table 2.

[0140] Table 2:

[0141]

[0142] A high-fidelity finite element method (FEM) verification is performed on the final scheme. If the overall relative error between the surrogate model prediction and the finite element calculation is no more than 5% in terms of stress, deflection, and crack width responses, the geometric dimensions, prestress parameters, and material parameters of the scheme are output as the final optimized design result. If the error exceeds 5%, the scheme is added to the sample library and the surrogate model is retrained.

Claims

1. A method for optimizing the design of large-scale prestressed continuous beam aqueducts based on genetic algorithms, characterized in that, Includes the following steps: S1: Taking a large prestressed continuous beam aqueduct as the optimization object, the design parameters are decomposed into geometric feature vectors, prestress feature vectors, material property vectors, and construction stage label vectors, which together constitute multi-dimensional input design variables. An experimental design method is used to generate N sets of sample points in the design space, and the sampling optimization objective is to minimize the correlation between samples. The mechanical response of the N sets of sample points under key working conditions throughout the entire life cycle is calculated in batches through the finite element analysis interface to form an initial high-fidelity training dataset. S2: A design individual is represented by a hybrid coding chromosome that directly corresponds to the multidimensional input design variables in step S1. The hybrid coding chromosome is differentially encoded according to the variable type. In the decoding phase, the geometric interference self-healing logic is executed in real time: the minimum distance from the prestressed duct to the concrete surface is calculated. If the minimum distance is less than the minimum protective layer thickness, the coordinates are adjusted along the normal gradient of that point until the protective layer thickness requirement is met. All design parameters are normalized to conform to the standard modulus of construction and manufacturing, and a standardized design parameter vector is output. S3: Based on the standardized design parameter vector output in step S2, construct a full-condition matrix covering the construction and operation stages; respectively, convert concrete shrinkage into initial strain, concrete creep into elastic modulus reduction, and long-term prestress loss into effective prestress reduction, and obtain shrinkage response correction, creep response correction, and prestress loss response correction through corresponding condition reanalysis; superimpose the shrinkage response correction, creep response correction, and prestress loss response correction into the initial response of each condition according to the linear superposition principle to obtain the full-condition response considering time-varying effects; establish a comprehensive constraint judgment library with crack resistance criteria, deflection limit, and bearing capacity margin as objectives, as the output label of the surrogate model; S4: Train the proxy model based on the high-fidelity training dataset generated in step S3, and establish a high-precision nonlinear mapping relationship from the multidimensional design variables in step S1 to the mechanical response vector. The mechanical response vector includes at least stress, deformation, and crack width indices; the mean square error loss function is used, and L2 regularization and early stopping strategy are combined to optimize the model's generalization ability; the trained model is integrated into the instantaneous evaluation engine in the genetic algorithm; S5: Adaptive genetic algorithm is used for global optimization, and crossover rate and mutation rate are dynamically adjusted according to population diversity; Pareto non-dominated solution set is maintained and updated to address the dual objective conflict of minimizing structural self-weight and maximizing stress safety reserve; fitness evaluation is completed by using the instantaneous evaluation engine in step S4 to replace finite element calculation. S6: From the Pareto non-dominated solution set obtained in step S5, the comprehensive optimal solution is selected based on the TOPSIS multi-criteria decision-making method; a high-fidelity finite element verification is performed on the comprehensive optimal solution, and the prediction error of the surrogate model is calculated. If the prediction error of the surrogate model meets the preset engineering tolerance, the corresponding multidimensional design variables are output as the final optimization result. Otherwise, the optimal solution is fed back as a new sample to step S1 for incremental model learning.

2. The method according to claim 1, characterized in that, The experimental design method described in step S1 is optimal Latin hypercube sampling. The formula for generating N sets of sample points within the design space using optimal Latin hypercube sampling is as follows: ， In the formula, D0 is the initial set of sampling points; x i Let N be the i-th sample point; N be the number of samples; L and U be the lower and upper bound vectors of the design variables, respectively. The formula for minimizing the correlation between samples is as follows: ， In the formula, x i and x j Let be the multidimensional design variable vectors corresponding to the i-th and j-th sample points.

3. The method according to claim 1, characterized in that, The correction formula for adjusting the coordinates along the normal gradient in step S2 is as follows: ， In the formula, P d The coordinates of the center point of the prestressed duct; The adaptive step size; n is the normal unit vector; These are the corrected coordinates; All design parameters are normalized using engineering modules to ensure their values ​​conform to the standard modules for construction and manufacturing. The formula is as follows: ， In the formula, 1 represents the normalized design parameters; x represents the original design parameters, including section height h, base plate thickness t, and transverse spacing of prestressed tendons, in millimeters (mm); M represents the standard engineering module.

4. The method according to claim 1, characterized in that, The creep response correction amount mentioned in step S3 is obtained by the equivalent secant modulus reduction method. The calculation formula of the equivalent secant modulus is as follows: ， In the formula, The nominal modulus of elasticity of concrete at 28 days of age; is the concrete creep coefficient, which is the ratio of creep deformation to initial elastic deformation at time t under sustained load. Let be the equivalent secant modulus of concrete at any time t.

5. The method according to claim 1, characterized in that, The surrogate model mentioned in step S4 is at least one of a deep neural network, a radial basis function network, or a gradient boosting tree model.

6. The method according to claim 1, characterized in that, The formula for dynamically adjusting the crossover rate and mutation rate based on population diversity in step S5 is as follows: ， In the formula, P c P m These represent the dynamically adjusted crossover rate and mutation rate, respectively. , These are the initial probabilities; The threshold for maximum similarity among populations; This is the adjustment coefficient.

7. The method according to claim 1, characterized in that, The formula for the prediction error of the surrogate model in step S6 is as follows: ， In the formula, For the surrogate model prediction error; The predicted value is from the proxy model; These are values ​​calculated using the finite element method.

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