Fan blade design method for improving discrete grid mapping

Abstract

The invention relates to a fan blade design method based on improved discrete grid mapping, and belongs to the field of pneumatic optimization design of turbomachinery. The method comprises the following steps: acquiring a key design variable of a blade; establishing an agent model based on a CFD simulation result, and introducing multi-target coupling sensitivity analysis to dynamically adjust the discrete increment of a variable; the static pressure difference and zero pressure difference flow under the rated flow serve as optimization targets, an improved discrete grid mapping algorithm is adopted for iterative optimization, and the algorithm adaptively selects the search center and range of the next generation in each iteration; and finally outputting a Pareto optimal solution set for engineering decision. The method improves the search efficiency and global optimization capability of a discrete grid method, solves the problems that a conventional method is large in calculation amount and is liable to fall into local optimum, and is especially suitable for aerodynamic design of multi-working-condition blades of an automobile cooling fan and the like.

Description

Technical Field

[0001] This invention belongs to the field of turbomachinery aerodynamic optimization design, specifically involving an improved fan blade design method based on discrete mesh mapping. Background Technology

[0002] As a core component of fluid machinery, fan blades are widely used in automotive cooling, industrial ventilation, and thermal management of new energy batteries. Their aerodynamic performance directly determines the heat dissipation efficiency, energy consumption, and noise level of the equipment. With the rapid development of industries such as new energy vehicles, higher requirements have been placed on the design of fan blades. They need to increase the static pressure difference at rated flow to enhance airflow driving capability, while ensuring high flow characteristics when the pressure difference is zero, achieving multi-objective synergistic optimization.

[0003] Current fan blade design methods primarily rely on parametric modeling combined with computational fluid dynamics (CFD) simulation and optimization algorithms. Among these, discrete mesh mapping optimization has become one of the mainstream optimization methods due to its suitability for the discrete characteristics of blade design variables. However, this type of method still faces several technical bottlenecks in engineering applications: First, the discrete increments are mostly fixed values, failing to dynamically adjust based on the degree of influence of variables on the optimization objective. This results in insufficient search accuracy for high-sensitivity variables and excessive redundant calculations for low-sensitivity variables, making it difficult to balance optimization efficiency and accuracy. Second, the lack of multi-objective coupled sensitivity analysis makes it impossible to quantify the interaction effects between variables, easily overlooking key variable combinations and affecting the reliability of optimization results. Third, the surrogate model and mesh search have poor synergy; sample collection often employs traditional methods such as uniform design, resulting in insufficient uniformity of sample distribution and low model fitting accuracy, making it difficult to accurately replace time-consuming CFD simulations. Fourth, the selection of grid center nodes during iteration is often arbitrary, lacking diversity protection mechanisms, easily falling into local optima, and the uneven distribution of Pareto optimal solutions fails to provide a comprehensive performance trade-off solution for engineering decisions.

[0004] Furthermore, traditional optimization algorithms often suffer from problems such as search stagnation and slow convergence when dealing with multi-objective optimization of fan blades, especially when facing coupled scenarios involving multiple variables such as maximum airfoil thickness and installation angle, making it difficult to efficiently explore the design space. These shortcomings result in existing design methods having long optimization cycles, limited performance improvements, and poor engineering practicality, failing to meet the design requirements of high-performance fan blades. Therefore, developing an improved discrete mesh mapping design method that can dynamically adapt to variable characteristics and balance optimization efficiency and accuracy has become an urgent technical challenge in the field of fan blade design. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides an improved fan blade design method based on discrete mesh mapping. The objective of this invention can be achieved through the following technical solutions: Improved fan blade design methods based on discrete mesh mapping include: S1: Obtain the design variables of the fan blade, including the maximum airfoil thickness factor, the mid-blade installation angle factor, the tip installation angle factor, and the tip chord factor; S2: Based on computational fluid dynamics simulation results, a proxy model between design variables and optimization objectives is established, and multi-objective coupling sensitivity analysis is introduced in the modeling process to dynamically adjust the discrete increments of design variables; S3: Using the static pressure difference at rated flow rate and the flow rate corresponding to zero pressure difference as optimization objectives, the surrogate model is optimized using an improved discrete grid mapping optimization design algorithm. The optimization process iteratively divides and searches the design space using the discrete increments of the design variables, and adaptively selects the grid center node and search range for the next iteration step based on the objective function value of the current grid node in each iteration. S4: Output the optimized combination of design variables and the corresponding optimization target value to obtain the optimized design scheme of the fan blades.

[0006] As a preferred technical solution of the present invention, the step of obtaining the design variables of the fan blades specifically includes: based on the initial three-dimensional model of the fan, extracting the characteristic parameters of the blade cross section through parametric modeling, determining the design variables, and defining the initial values ​​and allowable variation ranges of each variable.

[0007] Specifically, the computational fluid dynamics simulation results include: establishing a fluid calculation model that includes a rotating fan domain, setting the rated flow inlet and pressure outlet boundary conditions, using a shear stress transmission turbulence model to solve the steady-state flow field, and obtaining performance data of static pressure difference and flow rate corresponding to zero pressure difference under different design variables.

[0008] The sample database construction specifically includes: selecting multiple sample points in the design space using a space-filling design method, performing computational fluid dynamics simulation on each sample point to obtain the static pressure difference at the corresponding rated flow rate and the flow rate value corresponding to zero pressure difference, thus forming a sample database for training the surrogate model.

[0009] Establishing a proxy model specifically includes: based on the sample database, constructing an approximate mapping relationship model from design variables to static pressure difference and flow rate values.

[0010] Multi-objective coupled sensitivity analysis is introduced, specifically including: based on the surrogate model, a global sensitivity analysis method is used to quantify the influence of each design variable on the static pressure difference and flow rate value and the interaction effect between variables, and according to the degree of influence, an initial discrete increment negatively correlated with the degree of influence is set for each variable.

[0011] Iterative mesh generation specifically includes: using the current center node as a reference, expanding along the coordinate axes of each design variable with the current discrete increment as the step size to generate a new set of mesh nodes for evaluation.

[0012] The improved discrete grid mapping optimization design algorithm dynamically adjusts the discrete increment during the iteration process based on the convergence of the solution and the sensitivity information of the variables. Specifically, the increment of variables that are actively exploring the solution space is reduced, while the increment of variables that change slowly is maintained or increased.

[0013] The selection of the grid center node for the next iteration step is adaptive, specifically by performing a multi-objective Pareto sort on all currently evaluated nodes and selecting nodes from the optimal frontier that promote search diversity based on the density of solution distribution.

[0014] When selecting the center node of the grid, a taboo list is also used to record the recently selected center nodes. When the search stalls, non-optimal nodes are accepted with a probability that is dynamically adjusted with temperature based on the idea of ​​simulated annealing, thus escaping the local optimal region.

[0015] The optimized design scheme for the fan blades is obtained, specifically including: the optimized design scheme is a Pareto optimal solution set, where each solution corresponds to a set of design variables and their predicted static pressure difference and flow rate performance.

[0016] It also includes: filtering the Pareto optimal solution set according to engineering constraints, and selecting the final implementation scheme from the filtered solutions based on preset performance weights for static pressure difference and flow rate value.

[0017] The beneficial effects of this invention are as follows: Balancing optimization efficiency and search accuracy, the design cycle is significantly shortened: Multi-objective coupled sensitivity analysis quantifies the influence of variables, setting small discrete increments for high-sensitivity variables to ensure local accuracy, and setting large increments for low-sensitivity variables to improve global exploration efficiency; simultaneously, the increments are dynamically adjusted during iteration to avoid redundant calculations and accuracy loss. Compared to traditional fixed-increment methods, optimization efficiency is greatly improved, effectively balancing the core contradiction between "global exploration" and "refined local search."

[0018] To improve the reliability and comprehensiveness of optimization results: Multi-objective coupling sensitivity analysis is introduced to accurately identify key variables and strongly coupled variable groups, avoiding omission of core variable combinations; the optimization algorithm ensures that the Pareto optimal solution is evenly distributed through fast non-dominated sorting and congestion analysis, covering the entire performance trade-off range of "static pressure difference-flow rate"; the diversity protection mechanism combining tabu lists and simulated annealing effectively avoids premature convergence of the algorithm and improves the probability of obtaining the global optimal solution.

[0019] Reduce design costs and improve engineering practicality: A sample library is built using space-filling design to improve the fitting accuracy of surrogate models and replace a large number of time-consuming CFD simulations with high-precision surrogate models; the Pareto optimal solution set output after optimization can be quickly screened by combining engineering constraints and performance weights, and directly outputs feasible design schemes and 3D parametric files, realizing a seamless connection between "design-optimization-engineering decision-making" and significantly reducing the cost of subsequent trial production and verification.

[0020] High adaptability and broad application scenarios: The core optimization framework can flexibly adapt to the design requirements of different types of fan blades (such as ordinary blades and blades with guide vanes) and different application scenarios (automotive cooling, battery thermal management, industrial ventilation) by adjusting design variables and optimization objectives; for the adaptability design of discrete and continuous mixed variables, there is no need to make continuous approximations of discrete variables, avoiding the generation of infeasible solutions, and further improving the engineering adaptability of the technical solution.

[0021] The optimization algorithm exhibits excellent stability and convergence: The improved discrete grid mapping optimization algorithm ensures stable progress of the iteration process by adaptively selecting the grid center node and dynamically adjusting the search range; the quantitative design of the iteration termination condition and convergence criterion avoids search stagnation or excessive iteration. Compared with the traditional NSGA-II algorithm and orthogonal experimental optimization method, the convergence speed is greatly improved, providing a stable and reliable design basis for mass production. Attached Figure Description

[0022] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0023] Figure 1 This is a flowchart illustrating the improved discrete mesh mapping fan blade design method of the present invention. Figure 2 This is a diagram of the improved discrete mesh mapping optimization design algorithm architecture of the present invention; Figure 3 This is a schematic diagram showing the maximum thickness of the leaf shape. Figure 4 This is a schematic diagram of the blade mounting angle. Detailed Implementation

[0024] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided.

[0025] Please see Figure 1-4 An improved method for designing fan blades using discrete mesh mapping includes: S1: Obtain the design variables of the fan blade, including the maximum airfoil thickness factor, the mid-blade installation angle factor, the tip installation angle factor, and the tip chord factor; S2: Based on computational fluid dynamics simulation results, a proxy model between design variables and optimization objectives is established, and multi-objective coupling sensitivity analysis is introduced in the modeling process to dynamically adjust the discrete increments of design variables; S3: Using the static pressure difference at rated flow rate and the flow rate corresponding to zero pressure difference as optimization objectives, the surrogate model is optimized using an improved discrete grid mapping optimization design algorithm. The optimization process iteratively divides and searches the design space using the discrete increments of the design variables, and adaptively selects the grid center node and search range for the next iteration step based on the objective function value of the current grid node in each iteration. S4: Output the optimized combination of design variables and the corresponding optimization target value to obtain the optimized design scheme of the fan blades.

[0026] Specifically, obtaining the design variables of the fan blades includes: based on the initial three-dimensional model of the fan, extracting the characteristic parameters of the blade cross section through parametric modeling, determining the design variables, and defining the initial values ​​and allowable variation ranges of each variable.

[0027] This embodiment takes the vehicle cooling fan of a certain pickup truck model as the optimization object, and determines the maximum thickness coefficient of the airfoil, the installation angle coefficient at the blade mid-blade, the installation angle coefficient at the blade tip, and the chord length coefficient at the blade tip based on the relevant parameter acquisition method of this invention.

[0028] Figure 3 This is a schematic diagram of the maximum thickness coefficient of an airfoil. The straight-line distance between the leading and trailing edges of the airfoil is represented by the symbol. This indicates that the diameter of the largest inscribed circle of the leaf shape is equal to the maximum thickness, denoted by the symbol [symbol missing]. The airfoil maximum thickness factor represents the ratio of the blade's maximum thickness to its chord length. The factor is expressed as... express.

[0029] Figure 4 This is a schematic diagram of the blade installation angle. The blades are arranged into a blade cascade. The blade installation angle is the angle between the chord line and the header line. This angle indicates the installation position of the blade in the blade cascade. This represents the installation angle at the tip of the leaf; This represents the installation angle at the center of the blade; This represents the installation angle at the blade base. The mid-section installation angle coefficient describes the change in the installation angle at the blade's mid-section relative to the blade base installation angle, and is usually expressed as... The blade tip installation angle factor is a parameter describing the change in the blade tip installation angle relative to the blade base installation angle, and is usually expressed as... It represents the chord length factor at the leaf tip. ) and the chord length at the base of the leaf ( The ratio of ) is usually expressed as express.

[0030] The specific implementation steps are as follows: Step 1: Initial 3D Model Preparation. Obtain the initial 3D model of the cooling fan (in STEP format). The model includes the complete structure such as blades and hub. The blades adopt the common C4 airfoil, and the initial design is adapted to the heat dissipation requirements under the engine's rated operating conditions. Import the model into the 3D modeling software (SolidWorks), create a new parametric design project, and ensure that the model's feature tree is editable, laying the foundation for subsequent cross-sectional parameter extraction.

[0031] Step 2: Extraction of Blade Section Feature Parameters. Section parameters are extracted using a "uniformly truncated along the blade span" method. The specific steps are as follows: ① Determine the section selection rules: Starting from the fan hub center, uniformly select 10 feature sections along the blade span direction (from the hub to the blade tip). The spacing between adjacent sections is 1 / 9 of the blade span to ensure coverage of the aerodynamic characteristics of the entire blade area; ② Extract airfoil coordinates: Using the "section properties" function of the 3D modeling software, export the airfoil profile coordinate data (including the leading edge, trailing edge, and key points of the airfoil surface) for each of the 10 sections and save them as txt format; ③ Calculate the maximum airfoil thickness coefficient (t), which is the ratio of the maximum blade thickness to the chord length. Import the exported coordinate data into MATLAB software and automatically calculate the maximum airfoil thickness coefficient for each section using a self-developed airfoil analysis program; ④ Calculate the installation angle coefficient (θ). middle This describes the change in the blade tip installation angle relative to the bottom installation angle, and the blade tip installation angle coefficient (θ). tip ) Describe the change in the blade tip installation angle relative to the bottom installation angle. Based on the transformation relationship between the blade installation coordinate system and the global coordinate system, the transformation matrix between the two coordinate systems is used for accurate calculation; ⑤ Calculate the blade tip chord length coefficient. The blade tip chord length coefficient (λ) is the ratio of the chord length at the blade tip to the chord length at the blade root. It is calculated by obtaining relevant chord length data using the "measurement" tool of the 3D modeling software.

[0032] Step 3: Determining Design Variables and Parameter Ranges. Based on the extracted cross-sectional characteristic parameters, four design variables for this optimization are identified. Combining existing design experience with similar fans, manufacturing limitations, and aerodynamic performance requirements, the initial values ​​and allowable variation ranges for each variable are defined: ① Maximum airfoil thickness coefficient (t): initial value 0.070, allowable variation range (0.010, 0.130); ② Blade installation angle coefficient (θ) middle ): Initial value is 0.110, allowable variation range is (0.105, 0.115); ③ Tip installation angle coefficient (θ) tip): Initial value is 0.100, and the allowable range of variation is (0.095, 0.105); ④ Tip chord length coefficient (λ): Initial value is 0.100, and the allowable range of variation is (0.060, 0.140).

[0033] This embodiment effectively improves the accuracy and reliability of design variable acquisition through standardized parametric modeling tool operation, precise cross-section extraction process, and reasonable parameter range setting. It avoids subsequent optimization failures caused by ambiguous variable definitions or unreasonable parameter ranges, laying a solid foundation for subsequent sample collection, surrogate model construction, and optimization calculation.

[0034] Specifically, the computational fluid dynamics simulation results include: establishing a fluid calculation model that includes a rotating fan domain, setting the rated flow inlet and pressure outlet boundary conditions, using a shear stress transmission turbulence model to solve the steady-state flow field, and obtaining performance data of static pressure difference and flow rate ("transparent point" flow rate) corresponding to zero pressure difference under different design variables.

[0035] This embodiment takes the onboard cooling fan of a pickup truck as the optimization object. Based on the computational fluid dynamics (CFD) simulation method, it obtains the static pressure difference and the flow rate value at the "transparent point" under different combinations of design variables. The specific implementation steps are as follows: Step 1: Establish a fluid computation model including the rotating fan domain. ① Computational domain construction: Referring to the national standard GB / T 1236-2017, a C-type device (pipe inlet - free outlet) is used to construct the fluid computation model. The pipe inlet allows for clearly defined boundary conditions, while the outlet is free, which can accurately simulate the fan's suction characteristics and reduce the computational domain and computational cost. With the fan's 3D model as the core, a complete fluid computational domain is constructed, consisting of "inlet extension domain - rotating fan domain - outlet extension domain". The rotating fan domain precisely encompasses the fan blades and hub, and its size perfectly matches the actual fan structure. ② Interaction settings between rotating and stationary domains: A multiple reference frame (MRF) model is used to handle the interaction between the rotating and stationary domains (inlet and outlet extension domains). The rotating domain is defined as the motion region, and the speed is set to be consistent with the engine's rated operating condition (2430 r / min). The interface between the stationary and rotating domains uses the default adjacent surface setting to ensure a smooth transition of airflow between the two domains.

[0036] Step 2: Mesh Generation and Quality Check. ① Mesh Type Selection and Generation: An unstructured mesh is used to discretize the entire computational domain. The mesh quality in the rotating fluid region is crucial for the convergence and accuracy of the simulation results. Mesh generation is performed using STAR-CCM+ software. Mesh refinement is applied to areas with drastic airflow changes, such as the blade surface, hub surface, and the interface between the rotating and stationary domains. The mesh size is appropriately increased in non-critical areas to balance accuracy and computational efficiency. ② Key Mesh Parameters: The total number of mesh nodes in the entire computational domain is controlled within a reasonable range to ensure mesh quality meets standards. A boundary layer mesh is set near the blade wall, and the Y+ value near the wall is strictly controlled to ≤10 to accurately capture the viscous effect of the airflow in the near-wall region of the blade. ③ Quality Check: After generation, the mesh quality is checked to ensure that key indicators such as mesh distortion rate and aspect ratio meet the requirements of steady-state solutions, avoiding simulation distortion due to mesh quality issues.

[0037] Step 3: Boundary Condition Setting and Solution Parameter Configuration. ① Boundary Condition Definition: Set the rated flow inlet and pressure outlet boundary conditions; the specific value of the rated flow inlet is determined based on the heat dissipation requirements of the engine under rated operating conditions for this vehicle model, and is set to 2296.08m. 3 / h, the inlet medium is ambient air (25℃); the pressure outlet is set to atmospheric pressure (101325Pa) to ensure that the simulation conditions are consistent with the actual engineering scenario. ② Turbulence model selection: The k-ε turbulence model is adopted, and the solution is based on the Reynolds-averaged Navier-Stokes equations (RANS) to meet the steady-state solution requirements of the fan flow field. ③ Solution parameter settings: A steady-state solver is selected for flow field solution; in terms of discretization scheme, the momentum equation, energy equation, and turbulence equation are all in the second-order upwind scheme, and the pressure correction method is set to SIMPLE; the convergence criterion is set as follows: the convergence threshold of all residuals (continuity equation, momentum equation, turbulence equation, etc.) is reduced to 1×10 -3 The following steps involve simultaneously monitoring the inlet air flow and the outlet static pressure. When the fluctuation range of both meets the requirements within consecutive iterations, the simulation is considered to have converged. The maximum number of iterations is 1000.

[0038] Step 4: Simulation Solution and Performance Data Extraction. ① Steady-State Solution: After completing the above settings, start the simulation solution. The system automatically iterates until the convergence criterion is met. During this process, the residual curve and the changing trend of key performance parameters are monitored in real time to ensure the stability of the solution process. ② Static Pressure Difference Extraction: After the simulation converges, the area-weighted average total pressure of the fan inlet and outlet sections is extracted using post-processing software. The difference between the inlet total pressure and the outlet total pressure is taken as the static pressure difference (ΔP) corresponding to the rated flow rate under this design variable combination. 额 ), accurately obtain static pressure difference performance data. ③ Obtain the "transparent point" flow rate value: calculate using the Language interpolation method, with a flow rate interval of 764.64m³.3 / h, record the flow values ​​corresponding to the left (positive pressure difference) and right (negative pressure difference) of the target flow rate respectively, and then perform Language interpolation in MATLAB to obtain the flow value (Q) corresponding to a pressure difference of 0.

[0039] Specifically, S2 includes sample database construction, which specifically includes: selecting multiple sample points in the design space using a space-filling design method, performing computational fluid dynamics simulation on each sample point to obtain the static pressure difference at the corresponding rated flow rate and the flow rate value corresponding to zero pressure difference, forming a sample database for training the surrogate model.

[0040] This embodiment is based on the four design variables of the pickup truck vehicle cooling fan mentioned above (maximum airfoil thickness factor, mid-blade installation angle factor, tip installation angle factor, and tip chord factor). It uses the NOLH experimental design method to select sample points and combines this with CFD simulation to obtain performance data, ultimately forming a sample database for training the surrogate model. The specific implementation steps are as follows: Step 1: Define the design space boundaries. Based on the four design variables and their corresponding allowable variation ranges identified above, define the design space range for this sample collection: ① Maximum airfoil thickness coefficient (t): (0.010, 0.130); ② Blade installation angle coefficient (θ) middle : (0.105, 0.115); ③ Tip installation angle coefficient (θ) tip : (0.095, 0.105); ④ Tip chord length coefficient (λ): (0.060, 0.140). This design space fully covers the engineering feasible range of variables, ensuring that the sample points can fully reflect the influence of variable changes on the optimization objectives (static pressure difference at rated flow rate, "transparent point" flow rate value).

[0041] Step 2: Selection of Space Filling Design Method and Generation of Sample Points. ① Method Selection: Considering the multidimensional optimization scenario of the four design variables for the fan blades, the Nearly Orthogonal Latin Hypercube (NOLH) experimental design was selected as the specific method. Compared with traditional Latin Hypercube Sampling (LHS) and uniform sampling, this method has better uniformity and a certain degree of orthogonality within the design space, and can utilize sample points more effectively. ② Determination of Sample Point Quantity: Considering the four dimensions of the design variables, the accuracy requirements of the surrogate model fitting, and the cost of CFD simulation calculation, the number of sample points was determined to be 17. ③ Sample Point Generation: Using the NOLH module of the relevant design software, the boundary ranges of the four design variables were imported, and the number of sample points was set to 17, generating 17 sets of independent design variable combinations. Each combination corresponds to one sample point. All sample points showed no obvious clustering across the variable dimensions and were evenly distributed.

[0042] Step 3: Sample Point CFD Simulation and Performance Data Acquisition. For the 17 generated sample points, the CFD simulation process described in claim 3 and above is executed one by one: ① For each sample point's design variable combination, parametric geometric reconstruction is completed using 3D modeling software (SolidWorks) to generate the corresponding fan 3D model; ② The fluid computation domain is constructed according to a unified standard, unstructured meshes are generated, and boundary conditions and solution parameters (k-ε turbulence model, steady-state solver, residual convergence threshold 1×10⁻⁶) are set. -3 ); ③ After the simulation converges, extract the static pressure difference and the "transparent point" flow rate value at the rated flow rate corresponding to each sample point to ensure that the acquisition standards of the two sets of performance data are completely consistent, and avoid data deviation due to differences in simulation operation.

[0043] Step 4: Sample Database Organization and Formatting. The design variable combinations and corresponding two sets of performance data from the 17 sample points are structured and organized to construct a sample database: ① Stored in Excel spreadsheet format, with columns for "Sample Point Number," "Maximum Airfoil Thickness Coefficient (t)," and "Airfoil Mounting Angle Coefficient (θ)." middle "Tilt installation angle coefficient (θ)" tip "Tip chord length coefficient (λ) "Static pressure difference at rated flow rate (ΔP)" 额 / Pa) "Transparent point flow rate (Q / m)" 3 ·h -1 ① Perform validity checks on all data and remove abnormal data (such as simulation distortion data caused by mesh quality issues) to ensure the integrity and reliability of the database; ② Convert the organized Excel spreadsheet into txt format so that subsequent proxy model training software (such as MATLAB) can directly read and call it.

[0044] This embodiment constructs a sample database with uniform distribution, accurate data, and standardized format through a clear space filling design selection, a scientific method for determining the number of sample points, and a standardized CFD simulation process, which can effectively improve the fitting accuracy of subsequent surrogate models.

[0045] Specifically, the establishment of the proxy model includes: based on the sample database, constructing an approximate mapping relationship model from design variables to static pressure difference and flow rate values.

[0046] Specifically, the introduction of multi-objective coupled sensitivity analysis includes: based on the surrogate model, using a global sensitivity analysis method to quantify the influence of each design variable on the static pressure difference and flow rate value and the interaction effect between variables, and ranking them according to the degree of influence, setting an initial discrete increment for each variable that is negatively correlated with the degree of influence.

[0047] This embodiment, based on the sample database of 17 sample points constructed above, completes the construction of the Kriging surrogate model and multi-objective coupling sensitivity analysis, and finally determines the initial discrete increment of each design variable. The specific implementation steps are as follows: Step 1: Surrogate Model Construction (Kriging Model). ① Rationale for Method Selection: Considering the weakly nonlinear mapping characteristics of the four design variables and two optimization objectives of the fan blades, the Kriging model is chosen to construct the surrogate model. This method, by considering the spatial correlation between sample points, can not only provide response value predictions but also give the prediction uncertainty, possessing strong nonlinear fitting capabilities. ② Core Parameter Settings: A quadratic polynomial is chosen as the trend function, which can effectively fit the nonlinear relationship between the variables and the objectives; a Gaussian function is chosen as the correlation function, as this type of function has good smoothness and fast convergence speed, and can adapt to the mapping requirements of multi-dimensional design space; the parameter fitting process is implemented through relevant toolboxes in MATLAB, and the hyperparameters of the Gaussian correlation function are optimized using the maximum likelihood estimation method, automatically iteratively solving to minimize the deviation between the model's predicted values ​​and the actual sample values. ③ Model training: Divide the sample database into a training set (13 sample points) and a test set (4 sample points) in an 8:2 ratio, import them into the toolbox to complete the model training, and build two independent surrogate models for "design variable - static pressure difference under rated flow" and "design variable - transparent point flow value" to achieve synchronous prediction of the two optimization objectives.

[0048] Step 2: Accuracy Verification of the Surrogate Model. To ensure that the model accuracy meets the requirements of subsequent optimization, the coefficient of determination R is used. 2 The root mean square error (RMSE) was used as a validation metric to evaluate the accuracy of the two surrogate models: ① Data calculation: By comparing the model predictions with the actual CFD simulation values ​​using four sample points from the test set, the errors of both models were found to be within 3%; ② Accuracy judgment: An error ≤3% indicates that the model prediction accuracy meets the requirements and can effectively replace time-consuming CFD simulations for subsequent optimization calculations and sensitivity analysis.

[0049] Step 3: Multi-objective Coupling Sensitivity Analysis (Sobol Index Method). ① Method Selection: The Sobol index method is selected as the global sensitivity analysis method. Based on the principle of variance decomposition, this method can quantify the first-order influence of a single design variable on the optimization objective, as well as the influence of the interaction effect between any two variables. Compared with local sensitivity analysis methods, it can more comprehensively capture the global coupling characteristics of variables and is suitable for multi-objective collaborative optimization scenarios. ② Calculation Process: Based on two trained surrogate models, Monte Carlo sampling is performed using the Sobol toolbox in MATLAB. 1000 sets of design variable combinations are randomly generated in the design space and input into the surrogate models to obtain the corresponding target prediction values. The first-order sensitivity index (influence of a single variable) and the second-order interaction sensitivity index (coupling effect between variables) of each variable are calculated through variance decomposition. Finally, the sensitivity quantification results of each variable to the two optimization objectives are output.

[0050] Step 4: Ranking the Influence of Variables and Setting Initial Discrete Increments. ① Ranking the Influence: Based on the sensitivity analysis results of the two optimization objectives, the four design variables are ranked in descending order according to the first-order sensitivity index. The ranking result is: Tip chord length coefficient (λ) > Tip installation angle coefficient (θ). tip > Maximum airfoil thickness coefficient (t) > Blade installation angle coefficient (θ) middle Among them, the tip chord length coefficient and tip installation angle coefficient have the most significant impact on the two targets. ② Initial discrete increment setting: Based on the principle that "the degree of influence is negatively correlated with the initial discrete increment", that is, the higher the sensitivity index (the more significant the influence), the smaller the initial discrete increment, so as to ensure local search accuracy; the lower the sensitivity index (the weaker the influence), the larger the initial discrete increment, so as to improve global exploration efficiency. Based on engineering practice experience, the correspondence between the variable sensitivity index and the initial discrete increment and the specific values ​​are set as shown in the table below: Meanwhile, for the strongly coupled variable group (tip chord length coefficient and tip installation angle coefficient, second-order interaction sensitivity index > 0.1) identified by sensitivity analysis, the initial discrete increments of the two are associated and marked to ensure that their combined effect can be examined simultaneously in the subsequent optimization search process, and to avoid missing the interaction effects of key variables.

[0051] The reliability of subsequent analyses was ensured through the construction and accuracy verification of a standardized surrogate model; the multi-objective coupling sensitivity analysis based on the Sobol exponent method accurately identified the degree of influence and coupling relationship of variables; and the initial discrete increment set by the negative correlation principle laid the foundation for the efficient search of the subsequent improved discrete grid mapping optimization algorithm.

[0052] Specifically, the iterative mesh generation includes: taking the current center node as a reference, expanding along the coordinate axes of each design variable, and using the current discrete increment as a step size to generate a new set of mesh nodes for evaluation.

[0053] This embodiment is based on the optimization scenario of the onboard cooling fan of a pickup truck mentioned earlier. It continues with the four determined design variables (maximum airfoil thickness coefficient, mid-blade installation angle coefficient, tip installation angle coefficient, and tip chord length coefficient) and their corresponding initial discrete increments to complete the generation of mesh nodes for a certain iteration. The specific implementation steps are as follows: Step 1: Define the basic parameters for iteration. ① Determine the current center node: Select the optimal non-dominated solution selected in the previous iteration as the center node for this mesh generation. The corresponding design variable combination is: maximum airfoil thickness coefficient 0.070, mid-blade installation angle coefficient 0.110, tip installation angle coefficient 0.100, and tip chord length coefficient 0.100; ② Determine the current discrete increment: Based on the multi-objective coupling sensitivity analysis results above, the current effective discrete increments for each variable are: tip chord length coefficient 0.005, tip installation angle coefficient 0.003, maximum airfoil thickness coefficient 0.008, and mid-blade installation angle coefficient 0.004. This increment parameter is the core basis for subsequent expansion step size.

[0054] Step 2: Specific Operations of Discrete Increment Expansion. The expansion rule of "bidirectional expansion along the coordinate axes of each design variable, with a single step size in each direction" is adopted. The specific operations are as follows: ① Setting the Expansion Direction and Step Size: Based on the values ​​of each variable corresponding to the central node, expand by one current discrete increment step size in both the positive and negative directions along the coordinate axes of each design variable. The setting of expanding by only one step size in each direction ensures the exploration range of the design space while avoiding node redundancy caused by over-expansion, balancing exploration efficiency and computational accuracy; ② Calculating the Expansion Range of Each Variable: Calculate the expanded numerical ranges of the four design variables respectively, as shown in the table below: Step 3: Generation of a new set of grid nodes. ① Node combination rules: The expanded values ​​of the four design variables (each variable contains three values: "negative expansion value - center value - positive expansion value") are fully combined to generate new grid nodes; ② Node set composition: The new set of grid nodes generated this time only includes the newly added nodes obtained by the full combination, and does not include nodes that have been evaluated in the historical iteration (including the current center node and grid nodes from previous rounds), avoiding repeated evaluation of historical nodes and effectively improving iteration efficiency; ③ Node quantity calculation: Each of the four design variables contains three values, and a total of 3×3×3×3=81 new grid nodes are generated after the full combination, forming the discrete grid node set to be evaluated in this round.

[0055] Step 4: Duplicate Node Avoidance Measures. To further ensure that there are no duplicate nodes in the new node set (including duplicates with historical nodes and duplicates among new nodes), the following verification process is implemented: ① Establish a historical node database: Enter the design variable combination information of nodes (including central nodes and newly generated nodes in each round) that have been evaluated in all previous iterations into the database, using structured tables for easy retrieval; ② New node coordinate matching verification: For the 81 new nodes generated in this full combination, extract the numerical combination of their four design variables one by one and match and compare it with the data in the historical node database; ③ Duplicate node removal: If the variable combination of a new node is completely consistent with that of a historical node, it is determined to be a duplicate node and is directly removed from the set to be evaluated; After verification, none of the 81 new nodes generated in this round are duplicates, and the 81 valid new nodes are finally determined as the evaluation objects for this round.

[0056] Step 5: Preprocessing of nodes to be evaluated. The 81 finalized valid new nodes are organized into a structured file in the format of "node number + value of each design variable" and imported into the Kriging proxy model built earlier. Subsequently, the static pressure difference and "transparent point" flow value corresponding to each node will be quickly predicted through the model, providing data support for the selection of the grid center node in the next iteration.

[0057] Specifically, during the iteration process, the improved discrete grid mapping optimization design algorithm dynamically adjusts the discrete increment based on the convergence of the solution and the sensitivity information of the variables. Specifically, the increment of variables that are actively exploring the solution space is reduced, while the increment of variables that change slowly is maintained or increased.

[0058] This embodiment is based on the multi-objective optimization scenario of the pickup truck vehicle cooling fan described above. It continues with the four core design variables (maximum airfoil thickness coefficient, mid-blade installation angle coefficient, tip installation angle coefficient, and tip chord length coefficient), the Kriging surrogate model, and the initial discrete incremental parameters. For the fourth iteration of the improved discrete mesh mapping optimization algorithm, dynamic adjustment of discrete increments is performed. The specific implementation steps are as follows: Step 1: Define the basic parameters for iteration. ① Iteration phase: The current iteration is the 4th iteration. The mesh generation, node evaluation, and Pareto optimal solution selection for the first 3 iterations have been completed. Historical data includes the optimal solution set and corresponding objective function values ​​(static pressure difference, "transparent point" flow rate value) for the first 3 iterations. ② Current discrete increment: The initial discrete increment determined by the sensitivity analysis above is adopted, specifically: tip chord length coefficient 0.005, tip installation angle coefficient 0.003, airfoil maximum thickness coefficient 0.008, and mid-blade installation angle coefficient 0.004. ③ Core basis: This adjustment is based on both "the convergence of solutions in the 3rd and 2nd iterations" and "the variable sensitivity information updated based on the current iteration data," strictly following the principle of "reducing the increment for active variables and maintaining or increasing the increment for variables with gradual changes."

[0059] Step 2: Determine the convergence status of the solution. The "Pareto front movement distance" is used as the convergence criterion. The specific steps are as follows: ① Data extraction: Extract the Pareto optimal solution sets obtained from the 2nd and 3rd iterations from the historical database, and construct the Pareto fronts for each iteration (a two-dimensional distribution curve with static pressure difference as the vertical axis and the "transparent point" flow rate value as the horizontal axis); ② Movement distance calculation: Calculate the average Euclidean distance between the two Pareto fronts using MATLAB. This distance reflects the overall movement of the optimal solution distribution in the two iterations; the smaller the distance, the higher the degree of convergence; ③ Convergence criterion: The preset convergence threshold is 0.05 (after dimensionless processing). If the average Euclidean distance ≤ 0.05, it is determined that "the solution is approaching convergence"; if the distance > 0.05, it is determined that "the solution is still in the exploratory stage." In this calculation, the average Euclidean distance is 0.07 > 0.05, therefore, the current solution is determined to be in the exploratory stage, and the ability to perform fine-grained searches on key variables needs to be retained.

[0060] Step 3: Update variable sensitivity information. During the iteration process, a dynamic update method based on "recalculation based on the current surrogate model" is adopted, rather than using the fixed initial sensitivity. The specific process is as follows: ① Model update preparation: Collect all design variable combinations and corresponding surrogate model predictions (including some validated CFD real values) of all evaluated nodes in the first three iterations, and supplement them to the original sample database to form an expanded sample library, improving the model's fitting accuracy to the current exploration area; ② Sensitivity recalculation: Based on the updated Kriging surrogate model, recalculate the global sensitivity index of each variable using the Sobol exponent method to ensure that the sensitivity information matches the current iteration's design space exploration state; ③ Result comparison: The sensitivity ranking obtained after this update is still "tip chord length coefficient (λ) > tip installation angle coefficient (θ)". tip > Maximum airfoil thickness coefficient (t) > Blade installation angle coefficient (θ) middleHowever, the sensitivity index of the leaf tip chord length coefficient increased slightly from the initial 0.32 to 0.36, indicating that the variable has a more significant impact in the current exploration area.

[0061] Step 4: Quantitatively determine the exploration status of variables. The quantification standard is "the variance of the variable's values ​​in the most recent three rounds of optimal solutions." Specific operations include: ① Data extraction: Extracting all values ​​corresponding to each design variable from the first three rounds of Pareto optimal solutions (each round's optimal solution set contains 35 non-dominated solutions, therefore each variable yields 915 values); ② Variance calculation: Calculating the variance of each variable's value set. A larger variance indicates more drastic fluctuations in the optimal solution, i.e., "active exploration"; a smaller variance indicates smoother fluctuations, i.e., "smooth change"; ③ State determination threshold: Preset variance thresholds (based on normalization of the variable's allowable range of change), with a threshold of 0.02 for high-sensitivity variables and 0.03 for medium- and low-sensitivity variables. The calculation results are shown in the table below: Step 5: Perform dynamic adjustment of discrete increments. Based on the convergence results and variable exploration status, formulate and implement adjustment strategies: ① Actively exploring variables (tip chord length coefficient, tip installation angle coefficient): Since the current solution is still in the exploration stage and the variables fluctuate drastically, the increment needs to be reduced to improve local search accuracy. The adjustment range is 80% of the original increment; ② Slowly changing variables (maximum airfoil thickness coefficient, mid-blade installation angle coefficient): The variables fluctuate little. To improve global exploration efficiency, the maximum airfoil thickness coefficient is kept unchanged, while the mid-blade installation angle coefficient is appropriately increased (120% of the original increment); ③ Adjusted discrete increments: The final discrete increments for the 4th iteration are: tip chord length coefficient 0.004, tip installation angle coefficient 0.0024, maximum airfoil thickness coefficient 0.008, and mid-blade installation angle coefficient 0.0048.

[0062] Step 6: Result Validation. The adjusted discrete increments were applied to the fourth round of mesh generation. The generated new mesh nodes were more focused on the finer exploration areas of the tip chord length coefficient and tip installation angle coefficient. Simultaneously, the increased increment of the mid-blade installation angle coefficient expanded the design space coverage. Subsequent surrogate model evaluation and validation confirmed that the adjusted increments effectively improved the targeting of the iterative search and avoided ineffective exploration.

[0063] Specifically, the adaptive selection of the grid center node for the next iteration step includes: performing a multi-objective Pareto sort on all currently evaluated nodes and selecting nodes from the optimal frontier that promote search diversity based on the distribution crowding of solutions.

[0064] This embodiment is based on the multi-objective optimization scenario of the pickup truck's onboard cooling fan described above. For the 81 new grid nodes evaluated in the fourth iteration (combined with historical nodes evaluated in the first three iterations, forming a total of 106 nodes to be sorted), the grid center node for the next iteration is determined through multi-objective Pareto sorting, congestion calculation, SOM visualization, and a diversity selection strategy. The specific implementation steps are as follows: Step 1: Data Preparation for Nodes to be Sorted. Core data for 106 nodes to be sorted were extracted from the surrogate model evaluation database to form a structured dataset, including "node number," "values ​​of four design variables," "static pressure difference at rated flow rate (predicted value)," and "transparent point flow rate (predicted value)." Among these, the two aerodynamic performance parameters are the core basis for multi-objective sorting, perfectly consistent with the core setting of "optimization objectives based on static pressure difference and 'transparent point' flow rate."

[0065] Step 2: Multi-objective Pareto sorting (using the fast non-dominated sorting algorithm). The specific process is as follows: ① Initialize the layer parameters: Create a "Frontline Layer Number" label, with an initial value of 0; define "Domination Count" (the number of times a node is dominated by other nodes) and "Dominated Node List" (the set of other nodes dominated by a node), with initial values ​​of empty. ② Filter the first frontline non-dominated solution: Traverse each node to be sorted, and compare it with all other nodes one by one with the two optimization objectives (the larger the static pressure difference, the better; the larger the "transparent point" flow value, the better); if node A is not inferior to node B in both objectives, and is superior to node B in at least one objective, then node A is determined to dominate node B; count the domination count of each node, mark the node with a domination count of 0 as the first frontline layer (optimal frontline), and record the list of nodes it dominates. ③ Layered iteration: For each node in the first front layer, traverse its list of dominated nodes and decrement the dominance count of each node in the list by 1; if the dominance count of a node is reduced to 0, mark it as the next front layer (second front layer); repeat this process until all nodes are assigned to the corresponding front layer. Finally, 106 nodes are divided into 5 front layers, of which the first front layer contains 12 nodes.

[0066] Step 3: Calculation of the distribution congestion of the solution. The calculation logic of "sum of distances between adjacent nodes in each target dimension" is adopted, and the specific operations are as follows: ① Target data normalization: The static pressure difference and "transparent point" flow value of the 12 nodes in the first front layer are normalized (converted to the [0,1] interval) to eliminate the influence of the difference in the two target dimensions on the distance calculation. ② Determining adjacent nodes: The two normalized targets are sorted separately to obtain the sorting position of each node in the static pressure difference dimension and the "transparent point" flow value dimension; for each node, its adjacent nodes in a certain target dimension are the nodes immediately before and after the sorted position (for the first and last nodes of the front layer, only one-sided adjacent nodes are taken). ③ Congestion calculation: The congestion of a single node = distance between adjacent nodes in the static pressure difference dimension + distance between adjacent nodes in the "transparent point" flow value dimension; where the distance is the difference (absolute value) between the normalized values ​​of the two nodes corresponding to the target; if it is the first or last node of the front layer, the distance in the corresponding dimension is calculated as 0 (to avoid overestimating the congestion of boundary nodes). For example, if a node has a normalized value of 0.6 for its preceding neighbor and 0.8 for its following neighbor in the static pressure difference dimension, and 0.5 for its preceding neighbor and 0.7 for its following neighbor in the "transparent point" flow value dimension, then its congestion level = (0.8-0.6) + (0.7-0.5) = 0.4.

[0067] Step 4: SOM Visualization-Assisted Analysis. Self-Organizing Map (SOM) technology is applied to the 106 nodes to be sorted for cluster analysis, reducing the high-dimensional data of the four-dimensional design variables and two-dimensional objective variables to a two-dimensional visual representation. The correlation between design variables and the objective function is identified through color coding in the SOM diagram: the larger the tip chord length coefficient (λ), the larger the static pressure difference at rated flow; the larger the airfoil maximum thickness coefficient (t), the smaller the "transparent point" flow rate value; the tip installation angle coefficient (θ)... tip The smaller the value, the lower the static pressure difference under the rated flow rate and the higher the flow rate value at the "transparent point", providing a data correlation basis for the selection of the central node.

[0068] Step 5: A strategy for selecting central nodes to promote search diversity. Specific implementation: ① Selection scope limitation: Select only from the first frontier layer (optimal frontier) to ensure that the selected central nodes have the best aerodynamic performance potential, conforming to the optimization logic of "prioritizing the exploration of optimal regions". ② Core principle of diversity: Prioritize nodes with high congestion and distributed in high-potential regions in the SOM diagram. These nodes are sparsely distributed in the optimal frontier, and their design variable combinations are more likely to bring performance breakthroughs. Selecting them as centers allows the next round of mesh generation to accurately cover insufficiently explored areas, avoiding the search from being concentrated in a localized area. ③ Determine the number of central nodes and the final result: Combining iteration efficiency and exploration needs, the number of central nodes for the next round of grid is set to 3; the 12 nodes of the first leading edge layer are sorted by "crowding score + SOM area potential score", and the top 3 nodes with the highest scores are selected as the grid central nodes for the next iteration step. The corresponding design variable combinations are as follows: maximum airfoil thickness coefficient 0.068, mid-blade installation angle coefficient 0.112, tip installation angle coefficient 0.098, tip chord length coefficient 0.103; maximum airfoil thickness coefficient 0.075, mid-blade installation angle coefficient 0.113, tip installation angle coefficient 0.102, tip chord length coefficient 0.105; maximum airfoil thickness coefficient 0.072, mid-blade installation angle coefficient 0.108, tip installation angle coefficient 0.101, tip chord length coefficient 0.101.

[0069] Step 6: Select and Verify Results. A visualization tool is used to plot the distribution cloud map of the 12 nodes in the first front layer (with static pressure difference as the vertical axis and the flow rate of the "transparent point" as the horizontal axis). It can be seen that the three selected central nodes are evenly distributed in the optimal front, without significant clustering. Combined with the SOM plot, it is verified that the design variable combinations are all in the performance-sensitive region. Using this as the benchmark for the next round of mesh generation ensures that the newly generated mesh nodes fully cover the sparse region of the optimal front, effectively improving the search diversity of subsequent iterations while ensuring that the search direction always focuses on the optimal performance region.

[0070] Specifically, when selecting the center node of the grid, a taboo list is also used to record the recently selected center nodes. When the search stalls, non-optimal nodes are accepted with a probability that is dynamically adjusted with temperature based on the idea of ​​simulated annealing, thus escaping the local optimal region.

[0071] This embodiment continues the optimization scenario for the onboard cooling fan of a pickup truck. For the selection of the center node in the 5th iteration of the mesh, based on Pareto sorting, congestion selection, and SOM visualization, it incorporates a hybrid strategy of tabu lists and simulated annealing to avoid duplicate point selection and search stagnation. The specific steps are as follows: Step 1: Basic Data and Parameter Preparation. ① Basic Data: After the 4th iteration, the 15 optimal nodes in the first leading edge layer are ranked to obtain 5 candidate nodes; historical data includes the 12 selected center nodes from the previous 4 iterations. ② Parameter Initialization: Combine the optimization framework with preset core parameters to ensure that the strategy adapts to the fan blade optimization requirements; simulated annealing initial temperature 1.0, linear decay coefficient 0.9, termination condition T≤0.1; taboo length 3 (nodes selected in the most recent 3 iterations are included in the taboo).

[0072] Step 2: Taboo List Construction and Update. ① Core Settings: Taboo objects are identified by a dual identifier of "node index + design variable combination," and the storage format includes the taboo node index, variable combination, and start and end rounds. ② Initialization: Enter the 9 selected nodes from rounds 2-4. The taboo expires in round number 3 (starting round). ③ Real-time Updates: After each round of selection, enter new nodes and mark the expired round. Delete expired nodes to simplify the list.

[0073] Step 3: Taboo Validation of Candidate Nodes. Each of the 5 candidate nodes is matched against the taboo list: ① Search Logic: First match the index; if no match is found, match the variable combination (allowing a small error of no more than 10% of the discrete increment); ② Judgment Rule: If a match is successful, the node is removed; ③ Result: 2 candidate nodes are removed because they were recently selected, leaving 3 valid nodes (A, B, C).

[0074] Step 4: Determining Search Stagnation. Using the distance traveled along the Pareto front over multiple rounds as an indicator: ① Calculate the average Euclidean distance (normalized) along the front in rounds 3-4; ② Set a stagnation threshold of 0.05; ③ Result: If the travel distance is 0.04 < the threshold, the search is considered stagnant, and the simulated annealing strategy is initiated.

[0075] Step 5: Simulated Annealing Strategy Implementation. ① Core Rule: The higher the temperature, the greater the probability of accepting a non-optimal node, adapting to the transition from global exploration to local search. ② Temperature Parameter: The current temperature T=0.7, which is in the transition range from the exploration phase to the fine search phase. ③ Acceptance Probability: Related to the target difference (Δf) and the current temperature (T). The smaller Δf and the higher T, the greater the probability. Two second-frontier layer nodes (D, E) are added, and their target differences with the optimal node are calculated, yielding acceptance probabilities of 0.65 and 0.42, respectively. ④ Implementation Selection: A random number 0.58 is generated between 0 and 1. D is accepted (0.65>0.58), E is rejected, and D is added to the candidate set.

[0076] Step 6: Determine the final central node. After verifying that none of the four candidate nodes (A, B, C, D) have any contraindications, and considering the objectives of "optimality + diversity + SOM regional potential", A, C, and D are selected as the central nodes for the fifth round. The inclusion of D can break the search stagnation.

[0077] Step 7: Effect Verification. Three central nodes were applied to the fifth round of mesh generation. The new nodes take into account both the fine exploration of the optimal region and the expansion of the new design space. The surrogate model evaluation shows that the front-end movement distance was increased to 0.08, successfully escaping the local optimum. After optimization, the static pressure difference under rated flow rate increased by 35.15%, and the flow rate value of the "transparent point" increased by 13.07%, verifying the effectiveness of the hybrid strategy.

[0078] Specifically, the optimized design scheme for the fan blades described herein includes: the optimized design scheme is a Pareto optimal solution set, wherein each solution corresponds to a set of design variables and their predicted static pressure difference and flow rate performance.

[0079] Specifically, it also includes: filtering the Pareto optimal solution set according to engineering constraints, and selecting the final implementation scheme from the filtered solutions based on preset performance weights for static pressure difference and flow rate value.

[0080] This embodiment is based on the multi-objective optimization results of the pickup truck vehicle cooling fan mentioned above. The final iteration yields a Pareto optimal solution set containing 101 solutions (each solution corresponds to a set of design variables and predicted static pressure difference and "transparent point" flow rate values). The final implementation scheme is selected through engineering constraint filtering and performance weight scoring. The specific steps are as follows: Step 1: Pareto Optimal Solution Set Preparation. Extract the complete Pareto optimal solution set from the output of the optimization algorithm (improved discrete mesh mapping + NSGA-II) and organize it into a structured table, including "Solution Number", "Maximum Airfoil Thickness Coefficient (t)", and "Blade Mounting Angle Coefficient (θ)". middle "Tilt installation angle coefficient (θ)" tip "Immune tip chord length coefficient (λ) "Static pressure difference at rated flow rate (Pa) "Transparent point flow rate (m³) 3 ·h -1 This ensures that the data is complete and traceable, consistent with the setting of "design variables, static pressure difference, and 'transparent point' flow rate as the core indicators".

[0081] Step 2: Define the specific engineering constraints. Based on the actual installation and operational requirements of the pickup truck's engine compartment, three core engineering constraints are identified: ① Space constraint: The actual tip chord length corresponding to the tip chord factor must be compatible with the reserved installation space in the engine compartment to avoid rotational interference; ② Structural strength constraint: The maximum airfoil thickness factor must meet the structural stability requirements of the blade during high-speed rotation to avoid the risk of breakage; ③ Power constraint: The corresponding fan operating power is ≤80W (matching the vehicle's power supply limit, indirectly derived from aerodynamic performance parameters).

[0082] Step 3: Pareto optimal solution set filtering. A "full constraint satisfaction" filtering logic is adopted, meaning only solutions that simultaneously satisfy all engineering constraints are retained. Specifically: ① Constraint verification is performed on each of the 101 Pareto solutions, checking whether the design variables of each solution meet spatial and strength constraints, and whether the power corresponding to aerodynamic performance meets power limits; ② Solutions that do not satisfy any constraint are eliminated: In this verification, some solutions were eliminated because the tip chord length coefficient was too large or the maximum airfoil thickness coefficient was too small, ultimately yielding valid solutions that meet the engineering constraints.

[0083] Step 4: Set the performance weights for static pressure difference and "transparent point" flow rate. The performance weights are set based on the actual cooling requirements of the pickup truck engine and are jointly determined by the engineering design team in conjunction with the system's cooling objectives: ① Requirements Analysis: Under high-temperature conditions in summer, the engine of this model needs to prioritize ensuring the static pressure difference at the rated flow rate to enhance cooling driving force; under high-speed conditions, it needs to prioritize reducing aerodynamic drag, i.e., increasing the "transparent point" flow rate value. Therefore, the static pressure difference weight is set to 0.6, and the "transparent point" flow rate value weight is set to 0.4; ② Weight Verification: This weight setting has been verified through multiple engineering tests and can effectively adapt to the cooling requirements under different operating conditions, ensuring that the fan performance matches the vehicle's cooling system.

[0084] Step 5: Complete Decision Example – Screening the Final Implementation Scheme. Valid solutions are screened using weighted scoring: ① Scoring Rules: First, normalize the static pressure difference and the "transparent point" flow rate value (convert to the [0,1] interval), then calculate the comprehensive score for each solution according to "Comprehensive Score = Normalized Static Pressure Difference Value × 0.6 + Normalized Transparent Point Flow Rate Value × 0.4". The higher the score, the better the overall performance. ② Final Selection: Among the valid solutions, the design scheme corresponding to the solution with the highest comprehensive score is the final implementation scheme. Specific parameters are: maximum airfoil thickness coefficient 0.017781, mid-blade installation angle coefficient 0.113568, tip installation angle coefficient 0.10073, and tip chord length coefficient 0.10927.

[0085] Step 6: Optimization Result Verification. The design variables of the final implementation scheme were imported into the fan parametric model, and recalculated according to the CFD simulation process described above. The static pressure difference at rated flow rate was found to be 214.3 Pa, and the "transparent point" flow rate was 7811.3 m³ / s. 3 ·h -1 Compared with the initial design, the static pressure difference increased by 35.15%, the "transparent point" flow rate increased by 13.07%, and the vortex area around the fan was significantly reduced with a more uniform velocity distribution. The additional aerodynamic drag under high-speed conditions was significantly reduced, verifying the effectiveness of the optimization scheme.

[0086] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. An improved fan blade design method based on discrete mesh mapping, characterized in that, include: S1: Obtain the design variables of the fan blade, including the maximum airfoil thickness factor, the mid-blade installation angle factor, the tip installation angle factor, and the tip chord factor; S2: Based on computational fluid dynamics simulation results, a proxy model between design variables and optimization objectives is established, and multi-objective coupling sensitivity analysis is introduced in the modeling process to dynamically adjust the discrete increments of design variables; S3: Using the static pressure difference at rated flow rate and the flow rate corresponding to zero pressure difference as optimization objectives, the improved discrete grid mapping optimization design algorithm is used to perform multi-objective optimization on the surrogate model; The optimization process iteratively divides and searches the design space using discrete increments of the design variables, and adaptively selects the grid center node and search range for the next iteration based on the objective function value of the current grid node in each iteration. S4: Output the optimized combination of design variables and the corresponding optimization target value to obtain the optimized design scheme of the fan blades.

2. The method according to claim 1, characterized in that, The acquisition of design variables for fan blades as described in S1 specifically includes: based on the initial three-dimensional model of the fan, extracting the characteristic parameters of the blade cross-section through parametric modeling, determining the design variables, and defining the initial values ​​and allowable variation ranges of each variable.

3. The method according to claim 1, characterized in that, The computational fluid dynamics simulation results described in S2 specifically include: establishing a fluid computational model that includes a rotating fan domain, setting the rated flow inlet and pressure outlet boundary conditions, using a shear stress transmission turbulence model to solve the steady-state flow field, and obtaining performance data of static pressure difference and flow rate corresponding to zero pressure difference under different design variables.

4. The method according to claim 1, characterized in that, The establishment of a surrogate model between design variables and optimization objectives described in S2 includes the construction of a sample database. The specific method is as follows: multiple sample points are selected in the design space using the space-filling design method, and computational fluid dynamics simulation is performed on each sample point to obtain the static pressure difference at the corresponding rated flow rate and the flow rate value corresponding to zero pressure difference, thereby forming a sample database for training the surrogate model.

5. The method according to claim 4, characterized in that, The establishment of the proxy model described in S2 specifically includes: based on the sample database, constructing an approximate mapping relationship model from design variables to static pressure difference and flow rate values.

6. The method according to claim 5, characterized in that, The multi-objective coupled sensitivity analysis introduced in S2 specifically includes: based on the surrogate model, using a global sensitivity analysis method to quantify the influence of each design variable on the static pressure difference and flow rate value and the interaction effect between variables, and ranking them according to the degree of influence, setting an initial discrete increment for each variable that is negatively correlated with the degree of influence.

7. The method according to claim 1, characterized in that, The iterative mesh generation described in S3 specifically includes: using the current center node as a reference, expanding along the coordinate axes of each design variable with the current discrete increment as the step size to generate a new set of mesh nodes for evaluation.

8. The method according to claim 1, characterized in that, The improved discrete grid mapping optimization design algorithm described in S3 dynamically adjusts the discrete increment during the iteration process based on the convergence of the solution and the sensitivity information of the variables. Specifically, the increment of variables that are actively exploring the solution space is reduced, while the increment of variables that change slowly is maintained or increased.

9. The method according to claim 7, characterized in that, The adaptive selection of the grid center node for the next iteration step described in S3 specifically includes: performing a multi-objective Pareto sort on all currently evaluated nodes and selecting nodes that promote search diversity from the optimal frontier based on the density of solution distribution.

10. The method according to claim 9, characterized in that, When selecting the center node of the grid, a taboo list is also used to record the recently selected center nodes. When the search stalls, non-optimal nodes are accepted with a probability that is dynamically adjusted with temperature based on the idea of ​​simulated annealing, thus escaping the local optimal region.

11. The method according to claim 1, characterized in that, The optimized design scheme for the fan blades described in S4 specifically includes: the optimized design scheme is a Pareto optimal solution set, where each solution corresponds to a set of design variables and their predicted static pressure difference and flow rate performance.

12. The method according to claim 11, characterized in that, Also includes: The Pareto optimal solution set is filtered according to engineering constraints, and the final implementation scheme is selected from the filtered solutions based on preset performance weights for static pressure difference and flow rate.

Images