Water turbine top cover reinforcement design and modal optimization method

Abstract

The invention provides a water turbine top cover reinforcement design and modal optimization method, and belongs to the field of hydroelectric generating set structural dynamics and intelligent optimization design. The method comprises the following steps: firstly, carrying out radial-circumferential rib plate collaborative reinforcement top cover structure design, defining a parameter set and constructing an adjustable geometric model, and forming a'structure parameter-modal frequency 'data set through modal simulation; a machine learning modal prediction model based on physical constraints is built, rapid and accurate prediction of multi-order frequency is achieved, and physical consistency is guaranteed; and finally, a sparrow algorithm is adopted to complete structural parameter global optimization, and a closed-loop optimization system is formed through finite element back substitution verification. According to the method, limitation of a traditional reinforcing scheme is broken through, overall improvement and directional regulation and control of the multi-order modal frequency of the top cover are achieved, it is tested that the average improvement amplitude of the inherent frequency of the first ten orders reaches 2451%-54.52%, the difference between the optimization result and the target frequency is smaller than 0.15%, and the dynamic performance and operation safety of the water turbine top cover can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of hydropower unit structural dynamics and intelligent optimization technology, and in particular to a method for reinforcing the turbine top cover and modal optimization. Background Technology

[0002] The turbine top cover is a core load-bearing and flow-through component of large hydropower units. Its natural frequency and modal distribution directly determine the vibration response and dynamic-static interference safety of the unit. With the increase in unit capacity, operating head, and size, the dynamic characteristics of the top cover have become a key factor in design verification.

[0003] In existing technologies, structural design often employs methods such as local thickening, sealing holes, or unidirectional rib reinforcement to improve local stiffness. These methods can only improve static performance and cannot establish a correspondence between design parameters and modal characteristics. The improvement of multiple frequencies is limited and the distribution is disordered, making it difficult to achieve directional control of specific modes. In terms of numerical analysis, traditional finite element simulation is cumbersome and computationally intensive, making it difficult to support large-scale optimization. Empirical fitting and data regression methods, due to the lack of physical constraints, are prone to modal order confusion or non-monotonic distortion. In the field of optimization design, genetic algorithms, particle swarm optimization, and other algorithms have low convergence efficiency in high-dimensional multi-peak spaces and insufficient coupling with physical models, failing to form a closed loop of "strengthening design - modal prediction - parameter optimization". Summary of the Invention

[0004] This invention provides a method for reinforcing the top cover of a water turbine and optimizing its modal characteristics. By controlling the parameters of each stage in a refined manner, and through the coordinated reinforcement of radial and circumferential stiffeners, physical constraint machine learning prediction, sparrow algorithm global optimization, and closed-loop verification, the overall improvement and controllable distribution of the multi-order modal frequencies of the top cover are achieved.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for reinforcing and modally optimizing the top cover of a water turbine includes the following steps: Step 1: Design of a roof structure reinforced with radial and circumferential stiffeners: 1. Structural Parameter Definition: Based on the geometric characteristics and stress patterns of the roof, the parameter set P is defined as { p 1, p 2, … p n}, the p i Do not describe the geometric dimensions, arrangement angles, quantity, rounded corner transitions, and circumferential position characteristics of the stiffeners, and the parameter set should be able to continuously adjust the design variables while keeping the overall topology of the top cover unchanged.

[0006] 2. Geometric Model Construction: Based on the principle of parametric modeling, the generating function is established as G=f The adjustable geometric model (P) is defined, where G represents the top cover geometry and P represents the design parameters. The model includes the top cover base, radial stiffeners, circumferential stiffeners, and transition regions. The radial stiffeners are arranged at equal angles along the top cover plane, and the circumferential stiffeners are distributed with a set radius and thickness and continuously connected to the radial stiffeners, ensuring topological stability and reconfigurability of the model under different parameter combinations. This step can be accomplished by using a Python script to call the Abaqus modeling interface.

[0007] 3. Modal Simulation: Modal analysis was performed on the roof with different parameter combinations. The simulation satisfied the linear free vibration equation. By solving the stiffness matrix [K] and mass matrix [M], the front... m Set of first-order natural frequencies { f 1, f 2,…, f m} and corresponding mode shapes { φ 1, φ 2,…, φ m Establish a functional mapping relationship between parameters and modes. During simulation, the material property can be set to Young's modulus. E =2.11×10 11 Pa, density ρ =7800 kg / m 3 Poisson's ratio ν =0.30, solved using Abaqus / Standard.

[0008] 4. Dataset Construction: The system samples within the preset parameter space, and combines multiple sets of parameter samples and corresponding modal frequencies into a training dataset. After normalization and filtering, a high-dimensional mapping sample set of "structural parameters - modal frequencies" is formed to provide data support for subsequent model training and algorithm calls.

[0009] Step 2: Building a machine learning modality prediction model based on physical constraints: 1. Data preprocessing and standardization: The input parameter vector and output multi-order frequency vector of the above sample set are standardized with zero mean and unit variance. Random stratified sampling is used to divide the sample into 70% training set, 15% validation set, and 15% test set. At the same time, the scaler and meta-information are saved for destandardization recovery in the inference stage.

[0010] 2. Model Structure and Mapping Relationship: A multi-layer fully connected feedforward network is constructed, employing a multi-output structure with shared intermediate representations. The structural parameter space is mapped to the modal frequency space, establishing a functional relationship from input P to output F. , where θ is the set of trainable parameters. The network is configured with a medium capacity, and batch normalization and weight decay are used to suppress overfitting. Training is completed in the normalized space, and inference is performed by denormalizing to restore the output to the physical domain.

[0011] 3. Physical Constraints and Loss Function Design: A modal increasing order penalty is introduced in addition to the main loss. The total loss function includes the main loss term and a physical constraint term. The physical constraint term ensures the modal increasing pattern by limiting the frequency difference between adjacent orders. Simultaneously, a weighted progressive strategy is used to avoid early training convergence difficulties. The total loss function is... ,in N This represents the number of training samples; m Let be the predicted modal order; for the th i There are n samples, and the true frequency vector is... The predicted frequency vector is The main loss term is defined as: The physical constraint term is used to constrain the predicted frequency to follow an increasing pattern, and it is defined as follows: ,in The minimum frequency interval threshold is defined as the difference between predicted frequencies of adjacent orders being less than [a certain value]. A penalty is applied periodically to reduce the risk of modal order violation. To avoid overly strong constraints in early training that could lead to convergence difficulties, a weighted gradual approach is adopted. ,in t The number of iterations. α This is the growth factor. Numerical accuracy is monitored synchronously during model training. The system combines physical consistency (RMSE) and physical consistency (violation rate and minimum interval deviation) with early stop control based on dual criteria.

[0012] 4. Model Training and Performance Evaluation: Training is performed using an adaptive gradient algorithm combined with a learning rate decay strategy. After training, network weights, scalers, and modal information are encapsulated to form prediction packets. A confidence evaluation mechanism is introduced during the inference phase: for any input parameter vector, its nearest neighbor distance in the training samples is calculated in the standardized parameter space. d NN Then, select its K nearest neighbor samples, take the maximum relative error of the first m frequencies of the nearest neighbor samples as the statistical object, take the neighborhood average of the maximum relative error and normalize it to obtain the local residual. Define confidence score. ,in β This is a penalty coefficient used to quantify extrapolation risk. When... c Below the preset threshold c minWhen the input parameter combination is triggered, a finite element modal simulation verification is performed to obtain the true modal frequencies. The verification samples are then added to the training dataset to incrementally update or retrain the prediction model, thereby improving the prediction reliability and closed-loop optimization stability of the model in the extrapolation region.

[0013] Step 3: Global optimization and closed-loop verification of modal frequencies based on the sparrow algorithm: 1. Optimization Objective and Constraint Definition: Define the objective frequency vector T, construct a composite objective function that includes a frequency matching error term and a modal increment penalty term, and simultaneously constrain the design parameter range P. min ≤P≤P max This ensures that the optimization results closely match the target frequency and conform to the laws of dynamics and engineering feasibility.

[0014] 2. Global Search Based on Sparrow Algorithm: The sparrow algorithm is used for global parameter optimization. The algorithm employs three cooperative individuals: discoverers, foragers, and watchdogs, to achieve an adaptive balance between global exploration and local development. A boundary repair mechanism is introduced to ensure parameter feasibility, a re-initialization mechanism is implemented to restore population diversity, and hyperparameters and early stopping criteria are configured to achieve stable convergence.

[0015] 3. Closed-loop verification and dynamic update: Output the optimal parameter combination P * The predicted frequency is then substituted back into the finite element module to complete the accurate modal solution, and the predicted result is compared with the true frequency F. FE The relative error. If the error meets the engineering tolerance, the solution is solidified; if not, the source of the deviation is analyzed, the sample set is expanded, and the solution is re-optimized to form a closed-loop improvement system.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. At the structural design level, the radial and circumferential stiffeners combined reinforcement scheme breaks through the limitations of traditional unidirectional stiffening, expands the parametric design space, and realizes active control and distribution optimization of multi-order modal frequencies. The average improvement of the first ten natural frequencies can reach 24.51%–54.52%, which is far better than the 4.17%–20.06% of the traditional reinforcement scheme.

[0017] 2. At the modal prediction level, the physical constraint machine learning model balances prediction accuracy and physical consistency, with a validation set mean square error of less than 1.2 × 10⁻⁶. -3 The coefficient of determination R² = 0.9999, and the order-preserving violation rate decreased from 0.6204 to 0.0012, avoiding the problems of order disorder and extrapolation distortion.

[0018] 3. In terms of optimization control, the Sparrow Algorithm combines boundary repair and re-initialization strategies to achieve stable global optimization in a high-dimensional coupled space. The final optimization result is less than 0.15% different from the target frequency, which improves the controllability of modal distribution.

[0019] 4. At the system level, an integrated closed-loop process of "design-simulation-prediction-optimization-verification" is formed, which has good efficiency, reliability and scalability, and can effectively improve the modal control capability and operational safety margin of the turbine top cover. Attached Figure Description

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the turbine top cover reinforcement design and modal optimization process proposed in this invention; Figure 2 This is a schematic diagram comparing the radial and circumferential coordinated reinforcement of the turbine top cover proposed in this invention with the traditional reinforcement by sealing the opening of long stiffener plates; Figure 3 This is a schematic diagram of the main design parameters of the turbine top cover reinforcement structure in an embodiment of the present invention; Figure 4 This is a comparison of the natural frequencies of the top cover under different reinforcement schemes in the embodiments of the present invention; Figure 5 This is a schematic diagram of the structure of a physical constraint multi-output machine learning modality prediction model according to an embodiment of the present invention; Figure 6 The training and prediction performance results of the physical constraint machine learning model in the embodiments of the present invention; Figure 7 This is a comparison of model performance before and after introducing physical constraints in an embodiment of the present invention; Figure 8 This is a schematic diagram of the modal frequency optimization process based on the sparrow algorithm in an embodiment of the present invention; Figure 9 This is a schematic diagram of the modal frequency optimization results based on the sparrow algorithm in an embodiment of the present invention. Detailed Implementation

[0021] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0022] This invention proposes a reinforcement design and modal optimization method for the top cover of a hydro turbine. The method first establishes a parameterized geometric model of the top cover and calculates multiple natural frequencies under different parameter conditions through finite element simulation, establishing a mapping relationship between structural parameters and modal responses. Subsequently, a machine learning model incorporating physical constraints is introduced to achieve rapid prediction of multiple modal frequencies and maintain physical consistency. Based on this, the sparrow algorithm is used to globally optimize the structural parameters, obtaining a reinforcement scheme that satisfies the target modal distribution, which is then verified through finite element calculations (e.g., ...). Figure 1(As shown). This method realizes a unified process of top cover reinforcement design, modal prediction and parameter optimization, which can significantly improve computational efficiency and design accuracy, and is applicable to the dynamic performance optimization of top covers of large-scale water turbines and pumped storage units.

[0023] Specifically, it includes the following steps: Step 1: Design method for roof structure reinforced by radial and circumferential stiffeners.

[0024] This embodiment takes the turbine top cover as the object and proposes a reinforcement structure design method based on the coordinated arrangement of radial and circumferential stiffeners. Figure 2 This method enables the adjustable and automated generation of the roof structure geometry through parametric modeling. Taking the Abaqus and Python script interface as an example, it realizes the full-process control from parameter definition, geometric modeling, mesh generation to modal analysis, providing a unified geometric and data foundation for subsequent modal prediction and optimization.

[0025] The first step is to define the structural parameters. Based on the geometric characteristics and stress patterns of the roof, a set of parameters P={ representing the relationship between the geometric dimensions and arrangement of the stiffeners is defined. p 1, p 2, p 3, p 4}, of which p 1 represents the radius of the fillet radius of the radial stiffener opening (20–120 mm). p 2 represents the thickness of the radial stiffener (20–120 mm). p 3 represents the thickness of the radial short stiffener (10–280 mm). p 4 represents the thickness of the circumferential stiffener (0–200 mm), see Figure 3 The fixed parameter set includes a circumferential stiffener height of 950 mm, an outer diameter of 2118 mm, an inner diameter of 3630 mm, and 12 radial and circumferential stiffeners, as well as connection transition relationships. This parameter system, while ensuring topological continuity, enables continuous adjustment of key geometric features, providing a unified design basis for modeling and modal optimization of the roof's collaborative stiffener structure under different reinforcement schemes.

[0026] The second step is geometric model construction. A three-dimensional geometric model is created by calling the Abaqus modeling interface using a Python script. This model consists of the roof base, radial long stiffeners, radial short stiffeners, circumferential stiffeners, and their transition regions. The model generation function can be represented as G= f (P), where G is the geometry of the top cover. Radial stiffeners are arranged at equal angles along the plane of the top cover, and circumferential stiffeners are distributed according to a set radius and thickness, and are continuously connected with the radial stiffeners to achieve geometric synergistic constraints between the two, ensuring the topological stability and reconfigurability of the model under different parameter combinations.

[0027] The third step is modal simulation. After the geometric model is established, modal analysis is performed on the roof under different parameter combinations in Abaqus / Standard, with the material property set as Young's modulus. ,density Poisson's ratio Apply constraints and boundary conditions, mesh the data, and solve for its first 10 natural frequencies. f 1, f 2,…, f 10} and corresponding mode shapes { φ 1, φ 2, …, φ 10 Modal solutions satisfy the linear free vibration equation. Where [K] and [M] are the stiffness matrix and mass matrix of the structure, respectively. For the first i angular frequency, This represents the corresponding mode vector. A functional mapping relationship between parameters and modes is then established. This reflects the influence of structural design parameters on the modal characteristics of the top cover.

[0028] The fourth step is dataset construction. System sampling is performed within a pre-defined parameter design space, and multiple sets of parameter samples and their corresponding modal frequency results are combined to form a training dataset. After normalization and filtering, a high-dimensional mapping sample set of "structural parameters – modal frequencies" is formed, which can be used for subsequent training of physical constraint machine learning models and calling optimization algorithms, providing unified data support for modal prediction and global optimization.

[0029] Calculation results show that within this parameter space, the natural frequencies of the radial and circumferential stiffener-reinforced structure are significantly higher than those of the traditional closed-stiffener-opening reinforcement scheme. The average increase in the first ten natural frequencies is approximately 24.51%–54.52%, while the traditional scheme only increases by 4.17%–20.06%. Simultaneously, the multi-modal spacing is more uniform, verifying the superiority of the synergistic stiffener design in improving the dynamic performance and modal adjustability of the roof. Figure 4 ).

[0030] Step 2: Machine learning modality prediction model based on physical constraints.

[0031] Based on the structural parameter-modal frequency dataset established in step 1, a multi-output machine learning modal prediction model based on physical constraints is proposed. This model introduces modal increment constraints into the traditional feedforward neural network structure, enabling the prediction results to possess both numerical accuracy and physical consistency, achieving rapid prediction and response evaluation of multiple natural frequencies of the roof. The overall process includes data preprocessing, model construction, physical constraint design, and model training and evaluation. Figure 5 ).

[0032] The first step is data preprocessing and standardization. This involves processing the parameter-frequency sample set obtained in step 1. Perform standardization. Input parameter vector P=[ p 1, p 2, p 3, p 4], corresponding to the structural geometric parameters (radial long stiffener opening radius, radial long stiffener thickness, radial short stiffener thickness, circumferential stiffener thickness), the output vector F=[ f 1, f 2, …, f 10 [Corresponds to the first ten intrinsic frequencies.] The dataset contains 1000 valid samples, with 70% used for training, 15% for validation, and 15% for testing. Both inputs and outputs are standardized with zero mean and unit variance, and scaler parameters are saved to ensure consistency and reproducibility during the prediction phase. All scalers and metadata are packaged and saved after training to form a model encapsulation package, used for destandardization recovery during the subsequent inference phase to ensure that the model's prediction results are consistent with the physical domain dimensions.

[0033] The second step is to define the model structure and mapping relationships. The prediction model employs a multi-layer fully connected feedforward network, which maps the structural parameter space... Mapped to modal frequency space Establish a functional relationship between the input vector P and the output frequency vector F. θ represents the set of trainable parameters. The model employs a multi-output structure with a shared intermediate representation, mapping from four input nodes (corresponding to four design parameters) through four hidden layers to ten output nodes (corresponding to the first ten modal frequencies). Each layer is fully connected, with 128 neurons in the hidden layers and ReLU activation function. To enhance model stability and generalization ability, batch normalization and weight decay mechanisms are introduced during network training to suppress gradient vanishing and overfitting. In the implementation, training is performed in the standardized parameter space, and the loss function includes numerical error and physical constraint terms. The optimization algorithm uses Adam, with an initial adaptive learning rate of 0.001. After training, the model parameters... θ ∗ The optimal solution is solidified, and the prediction results are transformed to the physical frequency domain through the de-standardization process during the inference stage, so as to realize the rapid prediction of multi-mode frequencies under any combination of design parameters.

[0034] The third step is the design of physical constraints and the loss function. A penalty for modal increasing order is introduced in addition to the main loss. The total loss function includes the main loss term and a physical constraint term. The physical constraint term ensures the modal increasing pattern by limiting the frequency difference between adjacent orders, and a weighted progressive strategy is used to avoid early training convergence difficulties. The total loss function is... ,in N =1000 represents the number of training samples; m =10 represents the predicted modal order; for the th i There are n samples, and the true frequency vector is... The predicted frequency vector is The main loss term is defined as: The physical constraint term is used to constrain the predicted frequency to follow an increasing pattern, and it is defined as follows: ,in =0.1 Hz is the minimum frequency interval threshold. When the difference between the predicted frequencies of adjacent orders is less than 0.1 Hz, the minimum frequency interval threshold is reached. A penalty is applied periodically to reduce the risk of modal order violation. To avoid overly strong constraints in early training that could lead to convergence difficulties, a weighted gradual approach is adopted. ,in t Let λ be the number of iterations. max =0.1, α= 0.0055 is the growth factor. Numerical accuracy is monitored synchronously during model training. The system combines physical consistency (RMSE) and physical consistency (violation rate and minimum interval deviation) with early stop control based on dual criteria.

[0035] The fourth step is model training and performance evaluation. Model training employs an adaptive gradient algorithm combined with a learning rate decay strategy, ensuring that the numerical loss and physical constraint loss decrease synchronously and converge stably. After training, the network weights, input / output scalers, and modal information are encapsulated into a prediction package, forming a standard inference interface. To improve engineering reliability, this invention introduces a confidence evaluation mechanism in the inference phase: for any input parameter vector, its nearest neighbor distance in the training samples is calculated in the standardized parameter space. d NN The 20 nearest neighbor samples were selected, and the maximum relative error of the top 10 frequencies of the nearest neighbor samples was taken as the statistical object. The neighborhood average of the maximum relative error was taken and normalized to obtain the local residual. Define confidence score. ,in β =1.5 is the penalty coefficient, used to quantify extrapolation risk. When c Below the preset threshold c minWhen the value is 0.70, a finite element modal simulation verification of the input parameter combination is triggered to obtain the true modal frequencies. The verification samples are then added to the training dataset to incrementally update or retrain the prediction model, thereby improving the prediction reliability and closed-loop optimization stability of the model in the extrapolation region.

[0036] Test results show that the model's mean squared error on the validation set is less than [value missing]. Overall Determinance Coefficient ( Figure 6 Compared to the model without physical constraints, the prediction accuracy of each mode in this embodiment is higher than that of the model without physical constraints, and the order-preserving violation rate decreases from 0.6204 to 0.0012. Figure 7 This demonstrates that the physical constraint mechanism effectively guarantees the modal increase law. Statistical analysis shows that the prediction error for all samples is less than 0.5%, indicating that the model achieves a high level in both physical consistency and prediction accuracy, and can serve as an efficient evaluation core for the optimization process.

[0037] Step 3: Global optimization and closed-loop verification method for modal frequencies based on the sparrow algorithm.

[0038] This embodiment proposes a global optimization and closed-loop verification method for modal frequencies based on the Sparrow Algorithm, building upon the aforementioned physical constraint machine learning prediction model. This method uses the prediction model as the core for rapid evaluation. By constructing a composite objective function containing the target modal frequencies and safety interval constraints, it leverages the global search capability of the Sparrow Algorithm in a multi-peak, strongly coupled design space to achieve intelligent optimization of the roof structure parameters and reverse control of modal distribution, forming a closed-loop optimization framework of "prediction—optimization—back-substitution—verification". Figure 8 ).

[0039] The first step is to define the optimization objective and constraints. The optimization objective is to make the multi-order natural frequency distribution of the top cover as close as possible to the target frequency vector T={ t 1, t 2, …, t m In this embodiment, the frequency is [73.4, 73.5, 89.9, 90.0, 92.4, 136.5, 136.6, 177.2, 177.3, 178.2] Hz, ensuring that each frequency order increases and that the design parameters meet physical and manufacturing constraints. The design parameter vector P is defined, where... p 1, p 2, p 3, p 4 represents the radius of the opening fillet in the radial long stiffener, the thickness of the radial long stiffener, the thickness of the radial short stiffener, and the thickness of the circumferential stiffener, respectively. The parameter range remains consistent with step 1. Construct a composite objective function: ,in w kThese are the weighting coefficients. The output of the physical constraint prediction model is the first k First natural frequency, θ * This is the optimal set of parameters frozen after training. ,in =0.1 Hz is the minimum frequency interval threshold. To constrain the weighting coefficients, the optimization results are ensured to closely approximate the target frequency while also conforming to dynamic laws and engineering feasibility by jointly minimizing the error term and penalty term.

[0040] The second step involves a global search mechanism based on the sparrow algorithm. This embodiment employs the sparrow algorithm to globally optimize the design parameters. The algorithm simulates the foraging and vigilance behaviors of a sparrow flock to achieve an adaptive balance between global exploration and local development. The hyperparameters are set as follows: population size... N =Composed of 50 individuals, maximum number of iterations T max =1000, discoverer ratio 20%, vigilant ratio 10%, convergence early stopping window 30 generations, improved threshold 10. -6 In the first t In the nth iteration, the 1st i Individual position Let the set of candidate design parameters be defined by the objective function. The calculation is determined. The algorithm involves three types of cooperative individuals: the discoverer is responsible for the global search and guides the direction of the population, the foragers focus on the current optimal solution, and so on. A localized development layout is implemented, with the vigilant introducing perturbations to low-fitness individuals to prevent them from falling into local optima. After alternating updates to the positions of various individual parameters, a unified fitness evaluation and ranking are performed, forming an iterative optimization process. To ensure the feasibility of the updates, this invention introduces a boundary repair mechanism in each iteration, assuming the... t During the nth iteration i The design parameter vector for each individual is: ,when When the boundary is exceeded, boundary projection repair is performed on each component separately, that is, for any component ,according to The algorithm is modified to ensure that design variables always meet preset boundary conditions. Furthermore, to prevent premature convergence or search stagnation, a re-initialization mechanism is implemented. When the optimal fitness does not improve significantly after several generations or the population diversity drops below a threshold, global resampling or Gaussian perturbation reset is performed on some low-fitness individuals, and their fitness is recalculated immediately to restore population diversity and global exploration capabilities. Algorithm hyperparameters (population size, maximum number of iterations, proportional parameters, etc.) and early stopping criteria (window length, tolerance threshold) are all configurable for easy reproduction and parameter tuning.

[0041] The third step is closed-loop verification and dynamic updating. This occurs when the population converges or the maximum number of iterations is reached. T max When the optimal parameter combination P is output, the output is... * The system automatically combines these parameters and substitutes them back into the finite element analysis module for accurate modal solving to obtain the true frequency result F. FE The relative error between the predicted and simulated results is calculated. The optimization results are then validated for consistency. If the error meets the engineering tolerance requirement of 5%, the result is adopted as the final design scheme; if the error is too large, the source of the deviation is analyzed (such as boundary condition settings, parameter range, or extrapolation error), and the optimization cycle is re-executed after expanding the sample set if necessary. The optimization process records the optimal solution and optimal loss at checkpoints and outputs convergence curves and graded relative error diagrams for result review and archiving.

[0042] The results show that, under the above parameter settings, the algorithm converges stably, the individual loss decreases by more than 95%, and the difference between the first ten natural frequencies of the top cover and the target after optimization is less than 0.15%, and the modal distribution is more balanced. This verifies the efficiency and engineering feasibility of the method in multi-parameter coupled optimization and modal control. Figure 9 ).

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for reinforcing the top cover of a water turbine and for modal optimization, characterized in that, Includes the following steps: Step 1: Design of a roof structure reinforced with radial and circumferential stiffeners: Define a parameter set P representing the geometric dimensions and arrangement of the stiffeners. Based on parametric modeling principles, construct an adjustable geometric model of the roof base, radial stiffeners, circumferential stiffeners, and transition regions. Perform modal simulations on roofs with different parameter combinations and solve the underlying geometry. m The first natural frequencies and their corresponding mode shapes are used to construct a "structural parameter-modal frequency" training dataset; Step 2: Training and Confidence Evaluation of the Physically Constrained Machine Learning Modal Prediction Model: The dataset from Step 1 is standardized and preprocessed to construct a multi-output feedforward network model. Modal incremental physical constraints are introduced into the loss function to train and encapsulate a prediction model that combines numerical accuracy and physical consistency. After the prediction model is trained, a confidence evaluation mechanism is introduced to calculate the confidence score based on the nearest neighbor distance and neighborhood residual statistics of the input parameters in the training sample space. When the confidence score is lower than a preset threshold, finite element modal simulation of the corresponding parameter combination is triggered, and the simulation results are added to the training dataset to update the prediction model. Step 3: Global optimization and closed-loop verification of modal frequencies based on the sparrow algorithm: Using the prediction model in Step 2 as the calculation engine, a composite objective function containing the target modal frequency and safety interval constraints is constructed. The sparrow algorithm is used to perform global optimization of structural parameters. The optimal parameters are then substituted back into the finite element module for verification, forming a closed-loop optimization system.

2. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The parameter set P = { in step 1) p 1, p 2,… p n }, the p i The parameters describe the geometric dimensions, arrangement angles, quantity, rounded corner transitions, and circumferential position characteristics of the stiffeners, and the parameter set enables continuous adjustment of design variables while keeping the overall topology of the top cover unchanged.

3. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The generating function of the adjustable geometric model mentioned in step 1) is G= f (P), where G is the geometry of the top cover and P is the design parameter; the radial stiffeners are arranged at equal angles along the plane of the top cover, and the circumferential stiffeners are distributed according to a set radius and thickness and are continuously connected with the radial stiffeners to achieve geometric co-constraint.

4. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The modal simulation described in step 1) satisfies the linear free vibration equation. ,in, Let i be the i-th order angular frequency. To obtain the corresponding modal vectors, the stiffness matrix [K] and mass matrix [M] are solved to obtain the front... m Set of first-order natural frequencies { f 1, f 2,…, f m } and the corresponding set of mode shapes { φ 1, φ 2,…, φ m } 5. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The dataset preprocessing described in step 2) adopts zero-mean, unit variance standardization. The training, validation and test data adopt a random stratified sampling strategy, and the scaler and meta-information are packaged and saved for destandardization recovery in the inference stage.

6. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The multi-output feedforward network described in step 2) adopts a shared intermediate representation structure, combined with batch normalization and weight decay to suppress overfitting; the loss function is total loss = main loss term + physical constraint term, the physical constraint term ensures the modal increase law by constraining the frequency difference between adjacent orders, and adopts a weight asymptotic strategy to avoid early convergence difficulties.

7. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, After the prediction model training described in step 2) is completed, a confidence evaluation mechanism is introduced to calculate the nearest neighbor distance of any input parameter vector in the training samples in the standardized parameter space. d NN The local residual is obtained based on the statistical analysis of the relative prediction errors of the K nearest neighbor samples. Define confidence score ,in β This is a penalty coefficient used to quantify extrapolation risk.

8. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The composite objective function mentioned in step 3) includes a frequency matching error term and a modal increment penalty term. The design parameter vector P has a range limited by P. min ≤P≤P max Physical and manufacturing constraints.

9. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The sparrow algorithm described in step 3) adopts a collaborative update mechanism that includes global search and local development, and includes a safety interval constraint term. It also introduces a boundary repair mechanism to ensure parameter feasibility and sets a re-initialization mechanism to restore population diversity.

10. The method for reinforcing and modal optimization of a turbine top cover as described in claim 1, characterized in that, The closed-loop verification described in step 3) involves calculating the predicted frequency and the actual frequency F from the finite element simulation. FE The relative error is used to determine whether it meets the engineering tolerance. If the error does not meet the standard, the sample set is expanded and the optimization loop is re-executed.

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