A method for optimizing anti-cracking reinforcement configuration for high concrete face slab dam face slab

Abstract

The application discloses a crack-resistant reinforcement configuration optimization method for high concrete face slab dam panels, S1: acquiring first data; S2: generating second data based on a geometric model of dam panels; S3: generating an indication signal based on the first data and the second data through a Pareto frontier solver; S4: generating a reinforcement network optimization instruction based on a selected working point on a Pareto frontier curve; and S5: adjusting an initial reinforcement topology network in response to the reinforcement network optimization instruction, and outputting a final reinforcement configuration scheme; the application can realize significant synergistic gain of design safety and economic benefits by deep quantization of structural risk through probability inference, construction of a double-target optimization framework of efficiency and robustness, generation of a Pareto frontier performance boundary, and output of a reinforcement scheme with higher safety under the same cost or lower cost under the same safety standard through an interactive decision tool.

Description

Technical Field

[0001] This application relates to the field of water conservancy technology, and in particular to an optimization method for crack-resistant reinforcement configuration of high concrete panel dam panels. Background Technology

[0002] Ensuring the structural safety and durability of large-scale water conservancy infrastructure projects throughout their long service life is a core issue of ongoing concern in the engineering community. With advancements in computational mechanics and sensing technologies, engineering design is evolving from traditional methods based on deterministic safety factors to a more refined, performance- and risk-assessment-based resilient design paradigm. Particularly in the design of complex structures such as high concrete-faced rockfill dams, how to scientifically quantify and proactively manage long-term risks arising from inherent uncertainties such as material properties and environmental loads during the forward-looking design phase has become a key technological development direction for improving the inherent safety level of engineering projects.

[0003] Currently, the reinforcement design methods used for high concrete panel dams still face several technical limitations in addressing the aforementioned challenges.

[0004] Limitations of deterministic assumptions in risk characterization: Existing design methods largely rely on deterministic mechanical models, with input loads typically derived from standard working conditions specified in codes or from a single expected value prediction of future settlement. This approach inherently ignores the fact that the rockfill supporting the panel exhibits spatial variability in material properties and random creep behavior. Therefore, for probabilistic risks such as localized panel voids or stress concentrations caused by uneven settlement, existing technologies lack effective quantitative characterization methods, making targeted prevention and control in the design phase difficult. This leaves room for improvement in the design scheme's ability to withstand unforeseen extreme events.

[0005] The singularity of design objectives and the lack of trade-offs: Traditional optimization design objective functions typically focus on static indicators, such as minimizing overall structural flexibility or material usage—that is, maximizing material efficiency—while meeting strength constraints. However, a statically optimal structure may exhibit highly unstable performance when faced with uncertain disturbances. Existing technologies fail to incorporate structural robustness—the ability to maintain stable performance under uncertain inputs—as a quantifiable and independent design objective, equally important as efficiency, into the optimization framework. This prevents designers from scientifically and quantitatively weighing and choosing between the two mutually constraining core requirements of economy and safety within a clear decision space. Summary of the Invention

[0006] The main objective of this application is to provide an optimization method for crack-resistant reinforcement configuration of high concrete panel dam panels, in order to solve the problems of the limitations of deterministic assumptions in risk characterization and the lack of a single design objective and trade-offs in the prior art.

[0007] To achieve the above objectives, this application provides the following technical solution: An optimization method for crack-resistant reinforcement configuration of high concrete panel dam panels includes the following specific steps: S1: Obtain the first data characterizing the uncertainty of creep settlement of the rockfill below the dam. The first data is a probability field, which includes the expected value and variance of creep settlement. S2: Based on the geometric model of the dam panel, generate second data representing the optimal force transmission path inside the panel. The second data is the initial reinforcement topology network. S3: Based on the first and second data, the data is processed by the structural robustness efficiency Pareto front solver to generate an indicator signal that characterizes the trade-off between material efficiency and structural robustness of the reinforced topology network. The indicator signal is the Pareto front curve. S4: Generate reinforcement network optimization instructions based on the operating point selected on the Pareto front curve; S5: In response to the reinforcement network optimization command, adjust the initial reinforcement topology network to output the final reinforcement configuration scheme.

[0008] Furthermore, the first data in S1 is based on the on-site settlement monitoring data and material creep test data of the dam. Through a Bayesian inference process, the expected settlement value and settlement variance are calculated for each discrete unit of the rockfill. The first set of data is analyzed and processed, and a pre-set material creep model is loaded as the prior distribution. The parameters of the material creep model are derived from indoor experiments, and the model reads real-time or historical data from settlement monitoring instruments deployed during construction as observational evidence. The Markov chain Monte Carlo algorithm is used to update the prior distribution posteriorly, outputting a three-dimensional probability field, where each voxel corresponds to a physical region of the rockfill and is assigned an expected settlement value. and settlement variance The two attributes together constitute the first data.

[0009] Furthermore, the second data in S2 is based on the finite element model of the dam panel and is generated through iterative calculation using a topology optimization algorithm with the goal of minimizing structural flexibility. By receiving the geometric model and material properties of the dam panel and setting an initial, uniform material pseudo-density field, the SIMP topology optimization algorithm is used for iteration under the condition of only considering the expected settlement load: finite element analysis is performed on the current pseudo-density field to calculate the sensitivity of each element and update the pseudo-density field accordingly until convergence; thresholding is performed on the pseudo-density field, and the extracted high-density region connectivity map constitutes the initial reinforcement topology network.

[0010] Furthermore, the three-dimensional probability field calculates the expected value and variance of settlement through Bayesian inference; it also includes calculating the fourth-order statistical moment of the settlement probability distribution in the three-dimensional probability field, namely the settlement kurtosis factor. The initial reinforcement topology network includes a baseline efficiency network generated based on the expected settlement value and through a topology optimization algorithm aimed at minimizing structural flexibility. Based on the settlement variance and settlement kurtosis factor in the three-dimensional probability field, an adaptive enhancement process is applied to the baseline efficiency network to adjust the baseline efficiency network.

[0011] Furthermore, the Pareto front solver in S3 generates the Pareto front curve by simultaneously optimizing two conflicting objective functions through a multi-objective optimization algorithm: First objective function: Minimize the expected settlement value. The total material consumption of the reinforced topology network is as follows; The second objective function is to minimize the conditional risk value of the reinforced topology network under a three-dimensional probability field, specifically the maximum principal stress.

[0012] Furthermore, the second objective function is constrained to minimize the conditional risk value of the maximum principal stress of the reinforced topology: The calculation of the maximum principal stress of the conditional risk value includes the following steps: Based on the probabilistic settlement scenario set, which is a data set containing multiple deterministic settlement displacement fields, finite element analysis is performed on each scenario to obtain the maximum principal stress set of the scenario. Based on the preset risk quantile level, the stress risk value of the stress set is calculated; Filter out all stress values ​​in the stress set that are not less than the stress risk value, and calculate the arithmetic mean of the stress values; The multi-objective optimization algorithm is a non-dominated sorting genetic algorithm, whose selection mechanism is based on Pareto rank and crowding distance.

[0013] Furthermore, the reinforcement network optimization instructions in S4 are generated as follows: The Pareto front curve is displayed on the visualization interface, and the user selects the operating point, which corresponds to a specific combination of material efficiency and structural robustness. Based on the operating point, reinforcement network optimization instructions containing target topology and member size parameters are generated.

[0014] Furthermore, the adjustment process in S5 in response to the reinforcement network optimization command is as follows: The topology and member dimensions of the final reinforcement configuration scheme are adjusted in conjunction with the position of the working point on the Pareto front curve; as the working point moves towards the high robustness region, the redundant connections of the reinforcement network increase and the member dimensions increase.

[0015] Furthermore, the specific control steps for the reinforcement network optimization command are as follows: The location information of the working point contained in the reinforcement network optimization command directly determines the characteristics of the final reinforcement configuration scheme. If a high-efficiency, low-robust working point located on the Pareto front curve is selected, the reinforcement network optimization command will drive the generation of a lightweight network with sparse members, direct paths, and truss-like structure. Conversely, if a low-efficiency, high-robust working point is selected, the reinforcement network optimization command will drive the generation of a redundant network with dense members, complex connections, and ribbed structure. The continuous movement of the working point on the Pareto front curve will cause a smooth and global change in the topology and dimensional parameters of the final reinforcement configuration scheme.

[0016] Furthermore, the steps for generating reinforcement network optimization instructions are as follows: Based on the two nearest Pareto optimal solutions on both sides of the working point, a hybrid reinforcement scheme is generated in real time through a dynamic interpolation generator; The interpolation process performed by the dynamic interpolation generator is a topology-size hybrid weighted interpolation algorithm; The topology-size hybrid weighted interpolation algorithm specifically includes: The topological existence of the interpolation scheme is determined by performing a logical union operation on the pseudo-density fields of two neighboring solutions. For all elements with known topology, the pseudo-density value of the interpolation scheme is determined by linearly weighting the pseudo-density values ​​of two neighboring solutions.

[0017] The beneficial effects of this invention are: This invention introduces a Bayesian inference framework to systematically integrate prior knowledge based on physical models with objective observation data from the field. By calculating higher-order statistical moments that include expectation, variance, and even kurtosis, it not only quantifies the general risk of settlement fluctuations but also transforms the prediction from a single point to a probability field characterization, providing unprecedented and comprehensive input for subsequent robust design. This invention reconstructs the design problem into a multi-objective optimization problem and proposes using the maximum principal stress of conditional risk value as the core indicator for measuring structural robustness. It directly focuses on stress performance under the most unfavorable scenario, which can more effectively suppress extreme risks compared to traditional indirect indicators. By solving this multi-objective problem, what is generated is not a single optimal solution, but a Pareto front curve that represents all the optimal trade-offs between material efficiency and structural robustness. The Pareto front curve concretizes the abstract design philosophy conflict into a clear and quantifiable performance boundary, revealing the highest efficiency achievable at a specific risk level or the maximum robustness obtainable under a specific cost constraint. This elevates the design process from single-point optimization to a strategic level of global exploration of the entire feasible design space. This invention ultimately transforms complex optimization results into an intuitive and interactive engineering decision-making tool through a visualized Pareto front curve and a dynamic interpolation generator. It allows for the free selection of the most suitable operating point on the performance boundary based on the project's specific safety level and budget constraints, and can respond in real time to generate a precisely corresponding, engineered final reinforcement configuration. This significantly enhances the flexibility and scientific rigor of the design, ensuring that the final output is a verified optimal solution under its specific risk appetite. Compared to traditional methods, the design scheme produced by this invention can significantly improve structural safety under extreme conditions with a more reasonable topological layout at the same material cost; or, while achieving the same safety standards, it can effectively control engineering costs by avoiding unnecessary material redundancy, ultimately realizing a deep synergy and quantifiable significant improvement in structural safety and economic benefits. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the steps of the method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to this application; Figure 2 A schematic diagram illustrating the calculation steps for the maximum principal stress of the conditional risk value of this application. Figure 3 This is a schematic diagram illustrating the specific control steps of the reinforcement network optimization instruction in this application. Figure 4 This is a flowchart illustrating the steps involved in generating the reinforcement network optimization instructions for this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0020] like Figures 1 to 4 As shown, this embodiment provides an example of a method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels. This embodiment includes the following specific steps: S1: Obtain the first data characterizing the uncertainty of creep settlement of the rockfill below the dam. The first data is a probability field, which includes the expected value and variance of creep settlement. The first data in S1 is based on the on-site settlement monitoring data and material creep test data of the dam. Through a Bayesian inference process, the expected settlement value and settlement variance are calculated for each discrete unit of the rockfill. The first set of data is analyzed and processed, and a pre-set material creep model is loaded as the prior distribution. The parameters of the material creep model are derived from indoor experiments, and the model reads real-time or historical data from settlement monitoring instruments deployed during construction as observational evidence. The Markov chain Monte Carlo algorithm is used to update the prior distribution posteriorly, outputting a three-dimensional probability field, where each voxel corresponds to a physical region of the rockfill and is assigned an expected settlement value. and settlement variance The two attributes together constitute the first data; This transforms the description of risk from qualitative to quantitative. By integrating prior knowledge with subsequent verification evidence, it is possible to dynamically and more accurately characterize the uncertainty of future settlement, providing high-fidelity input for subsequent robust design. This achieves the quantification of design risk and forms the basis for realizing synergistic gain effects.

[0021] The material creep model is constructed as follows: Model identification and determination: An internationally recognized theoretical model suitable for long-term performance prediction of large-volume concrete structures was selected as the basic framework. In a preferred embodiment of the present invention, the CEB-FIP-Model-Code-1990-(MC90) model is selected, and the MC90 model framework is used for reference in the future; the total strain of concrete after loading is decomposed into a linear superposition of multiple independent components, the internal logic of which is clear, and the parameters have clear physical meaning. Strain component decomposition: Based on the MC90 model framework, at any time... The total strain is calculated by summing the instantaneous elastic strain at time t, the creep strain caused by the continuous load, and the contraction strain caused by the humidity change. Creep strain is further subdivided into: a basic creep component that is independent of drying, and a drying creep component that is related to the humidity gradient inside and outside the component; The mathematical expression of the MC90 model framework is public, and its core is the creep compliance function, which describes the strain of the material as a function of unit stress increases over time. The core task of this specification is to accurately determine the key unknown parameters in this function through experiments. Experimental design and specimen preparation: To obtain the raw data required for calibrating the model parameters, a standard uniaxial constant load compression creep test was performed; Standards followed: The entire experimental process strictly followed the "Test Procedure for Hydraulic Concrete (SL / T-352-2020)" or equivalent international standards. In this embodiment, the international standard adopted is ASTM-C512 / C512M. Specimen specifications: Using the same concrete mix ratio as the actual dam panel pouring, at least two sets (at least three in each set) of standard prism specimens were prepared. In this embodiment, the parameters of the quasi-prism specimens were set to 150mm×150mm×550mm; one set was used for creep loading test, and the other set was used as an accompanying specimen to measure synchronous shrinkage. Curing conditions: All standard prism specimens were cured in a standard curing room (temperature 20±2°C, relative humidity ≥95%) until the predetermined loading age, which was set to 28 days or 90 days in this embodiment; Loading procedure: The specimens of the creep test group were moved into a constant temperature and humidity test environment. In this embodiment, the temperature was set to 20±1°C and the relative humidity to 60±5%, and a constant axial compressive stress was immediately applied through a high-precision hydraulic servo loading device; the axial compressive stress level was set to 40% of the compressive strength of the concrete at the loading age. At the moment of loading and at specific time points after loading (in this embodiment, 1, 2, 4, 8 hours; 1, 3, 7, 14, 28, 56, 90, 180, 365 days), high-precision strain gauges (with accuracy better than...) bonded to the surface of the specimen were used. Simultaneously record the total strain and the accompanying shrinkage strain of the loaded specimen; At each recording point, the pure experimental creep strain data point is obtained by subtracting the concurrent shrinkage strain measured on the specimen from the total strain measured on the loaded specimen, and then subtracting the instantaneous elastic strain generated at the moment of loading. Target parameter identification: Within the MC90 model framework, the core parameters that need to be calibrated using experimental data include: the final value of the basic creep coefficient, and the shape parameters describing the development process of drying creep over time. These together determine the shape of the theoretical creep curve. Calibration algorithm execution: The Levenberg-Marquardt nonlinear least squares algorithm is used to fit the obtained experimental creep strain data point sequence to identify the optimal target parameter value; Objective function definition: The optimization objective of the algorithm is to minimize the sum of squared residuals; the calculation logic of the sum of squared residuals is as follows: For each data acquisition time point, calculate the difference between the creep strain value predicted by the MC90 theoretical model (with undetermined parameters as variables) and the creep strain value measured experimentally; then square this difference for all time points; finally sum all the squared differences. Iterative optimization: The Levenberg-Marquardt nonlinear least squares algorithm starts with a set of initial parameter guesses and iteratively calculates the Jacobian matrix and gradient to continuously update the parameter values, driving the residual sum of squares to converge toward its minimum. The iteration terminates when the change in parameter values ​​or the change in the residual sum of squares between two consecutive iterations is less than a preset convergence tolerance. In this embodiment, the preset convergence tolerance is [value missing]. ; Output: The parameter values ​​obtained when the algorithm converges are the final output of the calibrated creep model parameter set of this procedure; Cross-validation: To ensure the generalization ability of the calibration model, a set of independent creep experimental data (not involved in the calibration process) is reserved as a validation set; the obtained set of parameters of the calibrated creep model is substituted into the MC90 model to calculate its predicted creep strain at the corresponding time points of the validation set; Error quantification and acceptance criteria: Calculate the root mean square error between the model's predicted values ​​and the actual values ​​on the validation set; Acceptance criteria: Set an upper limit for acceptable error in engineering; if the calculated root mean square error is less than 5% of the maximum measured creep strain in the validation set, the creep model is deemed to have passed validation and has sufficient prediction accuracy. Model integration: The validated MC90 creep model, which includes calibrated parameters, is compiled and integrated into the finite element analysis model of the overall dam structure used in step S1 of this invention, in the form of a user-defined material subroutine (in this embodiment, USERMAT in ANSYS software or UMAT / CREEP in ABAQUS software).

[0022] S2: Based on the geometric model of the dam panel, generate second data representing the optimal force transmission path inside the panel. The second data is the initial reinforcement topology network. The second data in S2 is based on the finite element model of the dam panel and is generated iteratively through a topology optimization algorithm with the goal of minimizing structural flexibility. By receiving the geometric model and material properties of the dam panel, and setting an initial, uniform material pseudo-density field, the SIMP (Solid Isotropic Material Penalty) topology optimization algorithm is used iteratively, considering only the expected settlement load: finite element analysis is performed on the current pseudo-density field, the sensitivity of each element is calculated, and the pseudo-density field is updated accordingly until convergence; the pseudo-density field is thresholded, with the threshold value preferably ranging from [0.4, 0.6], and the extracted high-density region connectivity map constitutes the initial reinforcement topology network. Through topology optimization, the generated reinforcement network has the highest material utilization efficiency in a static sense, that is, the strongest load-bearing capacity is achieved with the least amount of material; this provides an optimal starting point for subsequent trade-offs between efficiency and robustness.

[0023] The three-dimensional probability field calculates the expected value and variance of settlement through Bayesian inference; it also includes calculating the fourth-order statistical moment of the settlement probability distribution in the three-dimensional probability field, namely the settlement kurtosis factor. The initial reinforcement topology network includes a baseline efficiency network generated based on the expected settlement value and through a topology optimization algorithm aimed at minimizing structural flexibility. Based on the settlement variance and settlement kurtosis factor in the three-dimensional probability field, the baseline efficiency network is adaptively enhanced to adjust the baseline efficiency network. The basic reinforcement is driven by the settlement variance, and additional extreme risk reinforcement is driven when the settlement kurtosis factor exceeds a first preset threshold; the first preset threshold is 0.7. In this embodiment, the key parameter symbols are defined as follows: The parameter symbols for the on-site settlement monitoring data are: Settlement time series data, after temperature correction, is periodically collected from multiple static leveling monitoring points or tension line displacement gauges located inside the dam's rockfill body; settlement time series data is an objective physical quantity that reflects the actual deformation behavior of the dam. The parameter symbols for material creep test data are: This refers to the stress-strain-time relationship data obtained from triaxial creep tests conducted on rockfill samples taken from different dam material areas under laboratory conditions, under various confining pressures and deviatoric stress levels; the stress-strain-time relationship data constitutes the basis for establishing prior knowledge of creep behavior; The parameter symbol for the expected settlement value is: Furthermore, the expected settlement value includes several unit expected settlement values, and the unit expected settlement value parameter symbol is... , where index tags The element number in the finite element discrete model of the rockfill; the physical meaning of the expected settlement value of the element is the settlement at the end of the design reference period. Mathematical expectation of the predicted settlement of Unit 1; The parameter sign of the settlement variance is: Furthermore, the settlement variance includes several element settlement variances, and the parameter sign of the element settlement variance is... , where index tags Let be the element number in the finite element discrete model of the rockfill; the physical meaning of the element settlement variance is, the th A measure of the uncertainty or fluctuation range of the predicted settlement in the unit number; The parameter sign of the settling kurtosis factor is: The settlement kurtosis factor includes several unit settlement kurtosis factors, and the parameter symbols of the unit settlement kurtosis factors are as follows: , where index tags Let be the element number in the finite element discrete model of the rockfill; the physical meaning of the element settlement kurtosis factor is, the th The sharpness and tail thickness of the predicted settlement probability distribution of cell number are key indicators characterizing the likelihood of extreme settlement events. Expected settlement of unit Unit settlement variance and unit settlement kurtosis factor The creep behavior of riprap is calculated through probabilistic inference; in this embodiment, it is based on an improved form of the Merchant model, which describes the creep behavior of riprap. The Merchant model first utilizes material creep test data. The prior probability distribution of Merchant model parameters is determined using the maximum likelihood estimation method. In this embodiment, it is assumed that the creep coefficient follows a log-normal distribution, and the on-site settlement monitoring data is used. As observational evidence, the Markov Chain Monte Carlo (MCMC) algorithm is used. In this embodiment, the Metropolis-Hastings algorithm is employed for each unit. The Merchant model parameters are sampled for posterior probability distribution. The calculation logic is as follows: For a unit The MCMC algorithm outputs a series of posterior sample sets. ,in, This represents the sample size, with a value greater than 10000. Expected settlement of unit The calculation method is as follows: calculate the arithmetic mean of the posterior sample set; Unit settlement variance The calculation method is as follows: calculate the sample variance of the posterior sample set; Unit Settlement Kurtosis Factor The calculation method originates from the definition of the fourth-order central moment in statistics: calculate the deviation of each sample point from the expected value, then calculate the fourth power of the deviation, calculate the arithmetic mean of the fourth power of the deviations of all samples, and divide the arithmetic mean by the unit settlement variance. The square of; The parameter sign of the normalized variance risk indicator is: is a dimensionless parameter with a range of [0,1]; it characterizes the unit The relative level of general fluctuation risk within the entire dam body; The calculation logic is as follows: Normalized variance risk indicator value The calculations are derived from the max-min normalization method; using the current unit settlement variance Subtract the variance of settlement of all units Find the minimum value among them, and then divide the resulting difference by the variance of settlement of all units. The difference between the maximum and minimum values ​​in the range; The parameter symbol for the normalized kurtosis risk indicator is: is a dimensionless parameter with a range of [0,1]; it characterizes the unit The relative level of extreme outlier risk throughout the dam body; The calculation logic is as follows: The maximum-minimum normalization method is used; the current unit's settlement kurtosis factor is used. Subtract all unit settlement kurtosis factors The minimum value in the range is then calculated, and the resulting difference is divided by the settlement kurtosis factor of all units. The difference between the maximum and minimum values ​​in the range; The parameter symbol for the pseudo-density of a unit material is: , where index tags is the element number in the finite element discrete model of the concrete panel; is a dimensionless design variable that takes values ​​in the interval [0,1] and is used in the topology optimization process. The indicated unit should be filled with reinforced concrete. This indicates that the unit should be empty, meaning no reinforcement is required; The calculation steps for the final reinforcement scheme are as follows: Loading on-site settlement monitoring data and material creep test data , and finite element geometric models of the dam's rockfill and concrete panels; Perform MCMC sampling: For each element in the finite element discretization model of the rockfill mass The MCMC algorithm is executed to generate a posterior sample set of settlement. Calculate statistical moments: Based on the posterior sample set, calculate the expected settlement value for each unit. Unit settlement variance and unit settlement kurtosis factor ; Risk normalization: Traverse all elements and determine the element settlement variance. and unit settlement kurtosis factor The maximum and minimum values ​​are used to calculate the normalized variance risk indicator for each unit. and normalized kurtosis risk indicator ; Final output: will contain The three-dimensional data field with three components is used as the final output; Start the topology optimization algorithm: The optimization problem is defined as follows: To determine the pseudo-density of the element material of all elements in the finite element geometric model of the concrete panel. Initialize to 0.5; set the optimization objective as minimizing the total structural flexibility, and the constraint condition as the total material volume not exceeding a preset upper limit. In this embodiment, the preset upper limit is set to 3%. Apply desired load: Set the desired settlement value of the element It is applied as a displacement load to the bottom surface of the panel; Iterative optimization: Execute the SIMP topology optimization algorithm to iteratively update the pseudo-density of the element material for each element. until convergence; Final output: The converged pseudo-density field This serves as the baseline efficiency network output.

[0024] S3: Based on the first and second data, the data is processed by the structural robustness efficiency Pareto front solver to generate an indicator signal that characterizes the trade-off between material efficiency and structural robustness of the reinforced topology network. The indicator signal is the Pareto front curve. The Pareto front solver in S3 generates the Pareto front curve by simultaneously optimizing two conflicting objective functions through a multi-objective optimization algorithm: First objective function: Minimize the expected settlement value. The total material consumption of the reinforced topology network is as follows; The second objective function is to minimize the maximum principal stress of the conditional risk value of the reinforced topology network under a three-dimensional probability field. The second objective function is constrained to minimize the conditional risk value of the maximum principal stress of the reinforced topology: The calculation of the maximum principal stress of the conditional risk value includes the following steps: Based on the probabilistic settlement scenario set, which is a data set containing multiple deterministic settlement displacement fields, finite element analysis is performed on each scenario to obtain the maximum principal stress set of the scenario. Based on the preset risk quantile level, the stress risk value of the stress set is calculated; Filter out all stress values ​​in the stress set that are not less than the stress risk value, and calculate the arithmetic mean of these values; The multi-objective optimization algorithm is a non-dominated sorting genetic algorithm, whose selection mechanism is based on Pareto rank and crowding distance; The risk quantile level is determined based on the design safety level standard for high concrete-faced dams; In this embodiment, the key parameters involved in the Pareto front solver during operation are defined as follows: The parameter symbols for the probabilistic settlement scenario set are: It is a dataset containing multiple deterministic settlement displacement fields, that is... Among them, index tags From 1 to , The total number of scenarios is set to an integer greater than 1000 to ensure statistical convergence. In this embodiment, it is set to... Each scenario is a probabilistic set of settlement scenarios. These are all three-dimensional vector fields, which define the displacement values ​​of all nodes at the bottom of the panel under possible settlement modes.

[0025] The parameter symbols for individual design schemes are: , where index tags Individual IDs in the multi-objective genetic algorithm population; individual design schemes. It is a vector whose dimension is equal to the total number of elements in the panel finite element model. Each element in the vector represents the pseudo-density of the material of the corresponding element. The value ranges from [0,1]; individual design scheme The reinforcement topology network scheme is fully defined; The parameter sign of the objective function value of material volume is It is a scalar value, and its physical meaning is an individual design scheme. The total volume of the corresponding reinforced concrete material; The calculation logic is as follows: material volume objective function value The calculation originates from the weighted summation of the discrete element volumes; the calculation method is as follows: traverse all elements in the panel finite element model, and sum the volume of each element with the corresponding material pseudo-density. Multiply them, and then sum the products of all units. The parameter symbol for the maximum principal stress in the scenario is: , is a scalar value, and its physical meaning is: when an individual design scheme is adopted. When designing a reinforced topology network, under a single probabilistic settlement scenario... The maximum tensile principal stress value that appears inside the entire panel structure under the action; The parameter sign of the risk quantile level is is a dimensionless parameter, taking values ​​within the interval (0,1), and is expressed as a smaller value in this embodiment. Its physical meaning is the acceptable probability threshold for the occurrence of extremely high stress events, that is, it defines the few most unfavorable scenarios.

[0026] The symbol for the stress risk value parameter is: , is a scalar value, and its physical meaning is for an individual design scheme. At a given risk quantile level Under the given conditions, the risk value of the maximum principal stress distribution is determined.

[0027] The symbol for the parameter of the maximum principal stress in conditional risk value is: , is a scalar value, and its physical meaning is that, for an individual design scheme When the stress risk value exceeds the value of stress. The most unfavorable risk quantile level In the proportional settlement scenario, the conditional mathematical expectation of the maximum principal stress, i.e., the average value; The calculation logic is as follows: This value is derived from the conditional value definition in risk management; the calculation method is: after calculating the stress risk value... Then, all stresses in the stress set that are greater than or equal to the stress risk value are selected. The stress values ​​constitute the tail risk subset; the arithmetic mean of all stress values ​​in the tail risk subset is the maximum principal stress of the conditional risk value. The Pareto front solver employs an improved non-dominated sorting genetic algorithm to perform multi-objective optimization, and its computational flow is as follows: Pareto front solver loading scenario probabilistic settlement scenario set Panel finite element model and preset risk quantile level ; Randomly generated containing (in this embodiment,) Individual design scheme initial population ; For the current population Each individual design scheme Perform the following calculations: Calculate the objective function value of material volume ; Traversing the probabilistic set of settlement scenarios All of them Each scenario Perform a finite element analysis to obtain the maximum principal stress in the scenario. ; Based on the obtained Maximum principal stress in each scenario Calculate individual design schemes Conditional risk value of maximum principal stress This value is the value of the second objective function; Based on the two objective function values ​​of all individuals For the entire population Perform a fast non-dominated sort to divide the population into multiple Pareto levels. ; For each individual within a Pareto level, calculate its crowding distance to maintain solution diversity; Using a binary tournament selection method, based on Pareto rank and crowding distance, from the population Select superior individuals to form a group of size The mating pool; Simulated binary crossover and polynomial mutation operations are performed on individuals in the mating pool to generate a number of individuals of size 1. offspring population ; parental population With offspring population Merge into a size of temporary population ; right Perform the non-dominated sorting and crowding calculation again; from In the process, individuals are selected sequentially according to Pareto level from highest to lowest, and within the same level, from largest to smallest crowding distance, until the desired outcome is achieved. The best individuals constitute the next generation of the species. ; Determine the current algebra In this embodiment, whether the preset maximum number of algebras has been reached is determined. If the target is not reached, iterate again; if the target is reached, terminate the loop. The final generation population In the middle, all individual design schemes with a Pareto level of 1 The set of values ​​is output as the final Pareto front curve; the data file contains the topology definition of an optimal design scheme and its corresponding material volume, conditional risk value, and maximum principal stress for each line. .

[0028] S4: Generate reinforcement network optimization instructions based on the operating point selected on the Pareto front curve; The reinforcement network optimization command in S4 is generated as follows: The Pareto front curve is displayed on the visualization interface, and the user-selected operating point is received. The operating point corresponds to a specific combination of material efficiency and structural robustness. Based on the operating point, reinforcement network optimization instructions containing target topology and member size parameters are generated. The Pareto front curve (i.e., the initial reinforced topology network scheme and its corresponding efficiency and robustness values) is plotted as a two-dimensional curve. The user selects an operating point on the Pareto front curve through an interactive interface. Then, all geometric and topological information of the initial reinforced topology network scheme corresponding to the operating point is extracted, including node coordinates, member connection relationships, and cross-sectional areas of each member. The geometric and topological information is encoded into structured data objects as reinforcement network optimization instructions. This process focuses on transforming abstract decision logic (in this embodiment, the decision logic is the selection of the operating point) into specific instruction signals that can be executed by downstream modules. The abstract design trade-off process is visualized into interactive and decision-making engineering steps; it provides designers with intuitive tools to make scientific final design choices based on the specific risk tolerance and budget constraints of the project, ensuring the engineering practicality of the method.

[0029] S5: In response to the reinforcement network optimization command, adjust the initial reinforcement topology network to output the final reinforcement configuration scheme; The adjustment process in S5 in response to reinforcement network optimization commands is as follows: The topology and member dimensions of the final reinforcement configuration scheme are adjusted in conjunction with the position of the working point on the Pareto front curve; as the working point moves towards the high robustness region, the redundant connections of the reinforcement network increase and the member dimensions increase. The specific control steps for reinforcement network optimization commands are as follows: The location information of the working point contained in the reinforcement network optimization command directly determines the characteristics of the final reinforcement configuration scheme. If a high-efficiency, low-robust working point located on the Pareto front curve is selected, the reinforcement network optimization command will drive the generation of a lightweight network with sparse members, direct paths, and truss-like structure. Conversely, if a low-efficiency, high-robust working point is selected, the reinforcement network optimization command will drive the generation of a redundant network with dense members, complex connections, and ribbed structure. The continuous movement of the working point on the Pareto front curve will cause a smooth and global change in the topology and dimensional parameters of the final reinforcement configuration scheme. Robust strategies under abnormal conditions: In S1, if the settlement variance of the calculated three-dimensional probability field exceeds a preset threshold due to missing monitoring data, wherein the preset threshold value range is... The specific value is This will trigger a degradation strategy: automatically disable the region on the Pareto front curve where the risk-adjusted efficiency is below a certain safety baseline, and prompt the user that the current design is based on high-uncertainty inputs, recommending the selection of a more robust final reinforcement configuration; ensuring that the output is inherently safe even when the input data quality deteriorates; The control and regulation concept is clearly explained, revealing how the user's single decision input, set as the operating point, simultaneously and nonlinearly drives multiple core attributes (topology, density, size) of the final reinforcement configuration scheme to adaptively change through the Pareto front curve translator. The global control and regulation response ensures that the output final reinforcement configuration scheme is the optimal solution under its specific risk preference, which cannot be achieved by any single optimization scheme.

[0030] When the user-selected operating point is not located on an existing discrete solution on the Pareto front curve, the steps for generating reinforcement network optimization instructions are as follows: Based on the two nearest Pareto optimal solutions on both sides of the working point, a hybrid reinforcement scheme is generated in real time through a dynamic interpolation generator; The interpolation process performed by the dynamic interpolation generator is a topology-size hybrid weighted interpolation algorithm; The topology-size hybrid weighted interpolation algorithm specifically includes: The topological existence of the interpolation scheme is determined by performing a logical union operation on the pseudo-density fields of two neighboring solutions. For all elements with known topology, the pseudo-density value of the interpolation scheme is determined by linearly weighting the pseudo-density values ​​of two neighboring solutions. In this embodiment, the initial reinforcement topology is adjusted; the key parameters involved are defined as follows: The parameter notation of the Pareto optimal solution set is: It is a structured dataset, and each record in a structured dataset... (in Each solution index number contains three parts: individual design scheme. This involves defining a pseudo-density vector to understand the topology, and corresponding two performance metrics: the material volume objective function value. Conditional risk value and maximum principal stress .

[0031] The parameter symbol for the user-selected workpoint is: , is a two-dimensional coordinate point, that is The physical meaning is the combination of material volume and structural robustness (characterized by the reciprocal of CVaR-Stress in this embodiment) that the designer specifies and expects to achieve through mouse clicks or numerical input on the visualization interface.

[0032] Real-time data is obtained by listening to user interaction events; the horizontal axis of the interface represents... The vertical axis represents The coordinates of the user's click location are captured as the user's selected work point. ; The parameter sign of the normalized performance coordinate is , is a dimensionless scalar value, ranging from [0,1]; it represents the relative position of the user-selected operating point on the Pareto front curve; The calculation logic is as follows: for the Pareto optimal solution set All solutions in the material volume objective function value Sort in ascending order; On the piecewise linear curve formed by the permuted solutions, find the distance from the user-selected working point. The point closest to the Euclidean distance is called the projection point. ; The calculation starts from the most efficient endpoint of the curve and proceeds along the curve path to the projection point. The arc length is denoted as ; Calculate the total arc length of the entire Pareto front curve, denoted as . ; Normalized performance coordinates The calculation method is as follows: the arc length is... Divide by total arc length ; The parameter symbols of the nearest Pareto solution include those of the left-hand side solution. and the right side solution ; respectively refer to the points located on the Pareto front curve, at the projection points. The two closest original Pareto optimal solutions on both sides; the solution on the left. The solution on the less robust side, and the solution on the right side. This is the solution on the more robust side; The parameter sign of the interpolation weighting factor is: , is a dimensionless parameter with a value range in the interval [0,1]; it is used to control the contribution of two neighboring Pareto solutions when generating a new scheme; The calculation logic is as follows: Obtain the projection point Left side solution and the right side solution The normalized performance coordinates of each solution are calculated by subtracting the coordinates of the left-hand side from the coordinates of the projection point. Then, the interval length is obtained by subtracting the coordinates of the left-hand side from the coordinates of the right-hand side. Dividing the aforementioned difference by the interval length yields the interpolation weight factor. ; The parameter symbols for interpolation-generated reinforcement schemes are: , is a pseudo-density vector with the same structure as the individual design scheme; it represents a brand-new reinforcement scheme dynamically generated based on user selection; The parameter symbols for the reinforcement network optimization command are: It is a structured data object; it includes a complete description of the final reinforcement scheme, specifically: the topology diagram of the member connection after geometric reconstruction and engineering processing, and a list of diameter or cross-sectional dimension parameters for each member; The specific steps for the final reinforcement configuration scheme are as follows: Loading the Pareto optimal solution set On a two-dimensional graphical user interface, the Pareto optimal solution set is displayed. All solutions are plotted as scatter plots to visualize the Pareto front curve. In the 3D window, the reinforcement 3D model of a certain endpoint of the curve (in this embodiment, the most efficient scheme is adopted) is displayed by default. When the user clicks or drags the mouse on the Pareto front plot, the screen coordinates of the current mouse pointer are captured and converted into performance coordinates to obtain the user-selected work point. ; Calculate the user-selected work point Normalized performance coordinates ; Logical judgment: Determine the projection point Is it consistent with the Pareto optimal solution set? It coincides with one of the original solutions in; If they overlap, then directly use the individual design schemes of the original solution. As a final solution; If they do not overlap, proceed to the next step; Determine the projection point Left side solution on both sides and the right side solution ; Calculate the interpolation weighting factor used to fuse the two solutions. ; Perform a hybrid weighted interpolation algorithm based on the left-hand solution. and the right side solution and interpolation weight factor Calculate and generate a completely new interpolation-based reinforcement scheme ; Post-processing of the pseudo-density vector: The image skeleton extraction algorithm is used to convert it into a rod centerline network; the geometric contours of the rods are extracted using the marching-cubes algorithm or a similar method, and the equivalent diameter of each rod is calculated; The processed member topology and dimensional information are encapsulated into standardized reinforcement network optimization instructions. In this embodiment, the file is set to JSON or XML format; Optimize the generated reinforcement network instructions The estimated performance metrics of the new solution are also sent back to the visualization interface. In response to the received reinforcement network optimization command The system also includes the performance indicators predicted by the new scheme, updates the reinforcement model in the 3D window in real time, and highlights the current working point and its detailed performance parameters on the interface. The entire process is executed in a high-frequency loop (more than 10 times per second in this embodiment) when the user drags the mouse, forming a smooth linkage effect.

[0033] The storage medium in this application embodiment stores program instructions capable of implementing all the above methods. These program instructions can be stored in the storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or terminal devices such as computers, servers, mobile phones, and tablets.

[0034] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0035] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units. The above are merely embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0036] The specific embodiments of the invention have been described in detail above, but they are only examples, and this application is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions to the invention are also within the scope of this application. Therefore, all equivalent changes, modifications, and improvements made without departing from the spirit and principles of this application should be covered within the scope of this application.

Claims

1. A method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels, characterized in that, The specific steps include the following: S1: Obtain the first data characterizing the uncertainty of creep settlement of the rockfill below the dam. The first data is a probability field, which includes the expected value and variance of creep settlement. S2: Based on the geometric model of the dam panel, generate second data representing the optimal force transmission path inside the panel. The second data is the initial reinforcement topology network. S3: Based on the first and second data, the data is processed by the structural robustness efficiency Pareto front solver to generate an indicator signal that characterizes the trade-off between material efficiency and structural robustness of the reinforced topology network. The indicator signal is the Pareto front curve. S4: Generate reinforcement network optimization instructions based on the operating point selected on the Pareto front curve; S5: In response to the reinforcement network optimization command, adjust the initial reinforcement topology network to output the final reinforcement configuration scheme.

2. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 1, characterized in that, The first data in S1 is based on the on-site settlement monitoring data and material creep test data of the dam. Through a Bayesian inference process, the expected settlement value and settlement variance are calculated for each discrete unit of the rockfill. The first set of data is analyzed and processed, and a pre-set material creep model is loaded as the prior distribution. The parameters of the material creep model are derived from indoor experiments, and the model reads real-time or historical data from settlement monitoring instruments deployed during construction as observational evidence. The Markov chain Monte Carlo algorithm is used to update the prior distribution posteriorly, outputting a three-dimensional probability field, where each voxel corresponds to a physical region of the rockfill and is assigned an expected settlement value. and settlement variance The two attributes together constitute the first data.

3. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 2, characterized in that, The second data in S2 is based on the finite element model of the dam panel and is generated iteratively through a topology optimization algorithm with the goal of minimizing structural flexibility. By receiving the geometric model and material properties of the dam panel and setting an initial, uniform material pseudo-density field, the SIMP topology optimization algorithm is used for iteration under the condition of only considering the expected settlement load: finite element analysis is performed on the current pseudo-density field to calculate the sensitivity of each element and update the pseudo-density field accordingly until convergence; thresholding is performed on the pseudo-density field, and the extracted high-density region connectivity map constitutes the initial reinforcement topology network.

4. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 3, characterized in that, The three-dimensional probability field calculates the expected value and variance of settlement through Bayesian inference; it also includes calculating the fourth-order statistical moment of the settlement probability distribution in the three-dimensional probability field, namely the settlement kurtosis factor. The initial reinforcement topology network includes a baseline efficiency network generated based on the expected settlement value and through a topology optimization algorithm aimed at minimizing structural flexibility. Based on the settlement variance and settlement kurtosis factor in the three-dimensional probability field, an adaptive enhancement process is applied to the baseline efficiency network to adjust the baseline efficiency network.

5. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 4, characterized in that, The Pareto front solver in S3 generates the Pareto front curve by simultaneously optimizing two conflicting objective functions through a multi-objective optimization algorithm: First objective function: Minimize the expected settlement value. The total material consumption of the reinforced topology network is as follows; The second objective function is to minimize the conditional risk value of the reinforced topology network under a three-dimensional probability field, specifically the maximum principal stress.

6. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 5, characterized in that, The second objective function is constrained to minimize the conditional risk value of the maximum principal stress of the reinforced topology: The calculation of the maximum principal stress of the conditional risk value includes the following steps: Based on the probabilistic settlement scenario set, which is a data set containing multiple deterministic settlement displacement fields, finite element analysis is performed on each scenario to obtain the maximum principal stress set of the scenario. Based on the preset risk quantile level, the stress risk value of the stress set is calculated; Filter out all stress values ​​in the stress set that are not less than the stress risk value, and calculate the arithmetic mean of the stress values; The multi-objective optimization algorithm is a non-dominated sorting genetic algorithm, whose selection mechanism is based on Pareto rank and crowding distance.

7. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 6, characterized in that, The reinforcement network optimization command in S4 is generated as follows: The Pareto front curve is displayed on the visualization interface, and the user selects the operating point, which corresponds to a specific combination of material efficiency and structural robustness. Based on the operating point, reinforcement network optimization instructions containing target topology and member size parameters are generated.

8. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 7, characterized in that, The adjustment process in S5 in response to reinforcement network optimization commands is as follows: The topology and member dimensions of the final reinforcement configuration scheme are adjusted in conjunction with the position of the working point on the Pareto front curve; as the working point moves towards the high robustness region, the redundant connections of the reinforcement network increase and the member dimensions increase.

9. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 8, characterized in that, The specific control steps for reinforcement network optimization commands are as follows: The location information of the working point contained in the reinforcement network optimization command directly determines the characteristics of the final reinforcement configuration scheme. By selecting a high-efficiency, low-robust working point located on the Pareto front curve, the reinforcement network optimization command will drive the generation of a lightweight network with sparse members, direct paths, and truss-like structure. Conversely, if an operating point located in a low-efficiency, high-robust position is selected, the reinforcement network optimization command will drive the generation of a redundant network with dense members, complex connections, and similar to a ribbed plate. The continuous movement of the operating point on the Pareto front curve will cause a smooth, global change in the topology and dimensional parameters of the final reinforcement configuration.

10. The method for optimizing the crack-resistant reinforcement configuration of high concrete panel dam panels according to claim 9, characterized in that, The steps for generating reinforcement network optimization instructions are as follows: Based on the two nearest Pareto optimal solutions on both sides of the working point, a hybrid reinforcement scheme is generated in real time through a dynamic interpolation generator; The interpolation process performed by the dynamic interpolation generator is a topology-size hybrid weighted interpolation algorithm; The topology-size hybrid weighted interpolation algorithm specifically includes: The topological existence of the interpolation scheme is determined by performing a logical union operation on the pseudo-density fields of two neighboring solutions. For all elements with known topology, the pseudo-density value of the interpolation scheme is determined by linearly weighting the pseudo-density values ​​of two neighboring solutions.

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