Fuel cell compressor impeller design optimization method

Abstract

The invention relates to the technical field of impeller design optimization, in particular to a fuel cell compressor impeller design optimization method, which comprises the following steps of: firstly constructing a parameter system of compressor impeller design, defining a design variable set and generating an impeller geometric model through parametric modeling; establishing a multi-objective function system, coordinating aerodynamic efficiency, structural strength and quality objective conflicts, and setting manufacturing and safety constraint conditions; then, key design variables are screened through global sensitivity analysis, and the space is optimized in a dimensionality reduction mode; a Pareto optimal solution set is generated by adopting a gradient enhanced NSGA-II algorithm, and convergence is accelerated in combination with gradient information; and finally, verifying the candidate solution through a multi-level verification system, and correcting the design space. According to the method, the design efficiency and performance of the fuel cell compressor impeller can be effectively improved, the method has wide application prospects in high-speed impeller mechanical design in the fields of aviation, automobiles and the like, and cross-platform multiplexing design criteria and empirical formula libraries are supported.

Description

Technical Field

[0001] The present invention relates to the technical field of impeller design optimization, and specifically to a method for optimizing the design of a fuel cell compressor impeller. Background Art

[0002] A fuel cell compressor, also known as a fuel cell air compressor, is an important component in a hydrogen fuel cell system. Fuel cells are recognized as one of the new energy sources with great development prospects. The air supply subsystem is an important part to ensure the efficient, stable and reliable operation of the fuel cell. As the core equipment of the air supply system, the main function of the air compressor is to provide the oxygen required for the electrochemical reaction of the hydrogen fuel cell. By compressing air and delivering it to the cathode of the fuel cell stack, the power density and efficiency of the fuel cell can be increased, and at the same time, the overall size of the system can be reduced.

[0003] In the prior art, for the impeller, an important component of the fuel cell compressor, the design parameters of the impeller largely depend on the experience of the designers. If the experience is sufficient, the product designed for the first time may meet the design objectives; otherwise, repeated design and simulation may be required, resulting in a long design cycle and consuming a large amount of manpower and material resources. Second, physical simulation is usually used. Due to the complexity of the system, when simulating multiple parameters, many parameters need to be carefully set during the simulation process. Once the simulation experience is insufficient, it is easy to cause a large error in the simulation results. Therefore, a method for optimizing the design of a fuel cell compressor impeller is proposed to solve the above problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for optimizing the design of a fuel cell compressor impeller to solve the problems raised in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A method for optimizing the design of a fuel cell compressor impeller includes the following steps:

[0007] S1. Construct a parameter system for the design of the compressor impeller, define a set of design variables, and generate an impeller geometric model through parametric modeling;

[0008] S2. Establish a multi-objective function system, convert the aerodynamic efficiency, structural strength and mass objectives into numerical indicators, coordinate the objective conflicts, and set manufacturing and safety constraint conditions;

[0009] S3. Screen key design variables through global sensitivity analysis to reduce the dimensionality of the optimization space;

[0010] S4. Use a multi-objective optimization algorithm to generate a Pareto optimal solution set and accelerate convergence in combination with gradient information;

[0011] S5. Verify the candidate solutions through a multi-level verification system, correct the design space, and ensure performance and reliability.

[0012] As a preferred solution, the set of design variables is:

[0013] X = [Z, β1, β2, D1, D2, b, t, γ, R hub , where Z is the number of blades, β1 is the blade inlet angle, β2 is the blade outlet angle, D1 is the inlet diameter, D2 is the outlet diameter, b is the blade height, t is the thickness distribution function, γ is the leading edge sweep angle, and R hub is the hub ratio.

[0014] As a preferred solution, in step S2, the multi-objective function system includes:

[0015] The pressure ratio objective function, the efficiency objective function, and the equivalent stress criterion. The pressure ratio objective function is defined as:

[0016] where π is the pressure ratio, Δh is the enthalpy change, c p is the specific heat at constant pressure, T in is the inlet temperature, and η is the efficiency;

[0017] The efficiency objective function is defined as:

[0018] where ∑Δs i is the total entropy increase, and k is the adiabatic index;

[0019] The equivalent stress criterion is defined as:

[0020] where σ eq is the equivalent stress, σ θ is the circumferential stress, σ r is the radial stress, and τ is the shear stress;

[0021] The multi-objective optimization problem is:

[0022] min X [-η(X), σ max (X), mass(X)], where min X represents optimizing the set of design variables X to find the objective function vector. X is the set of design variables, η(X) is the function of efficiency with respect to the design variables, σ max (X) is the function of the maximum stress with respect to the design variables, and mass(X) is the function of mass with respect to the design variables.

[0023] As a preferred solution, in step S1, the parametric modeling uses the NURBS surface equation, and its expression is:

[0024] Among them, S(u, v) is the value of the NURBS surface at the parameter (u, v), and N i,p (u) is the basis function of order i and degree p in the u direction, and N j,q (v) is the basis function of order j and degree q in the v direction, and P i,j is the control point coordinate, and n and m are the numbers of control points in the u and v directions respectively;

[0025] And the design parameters are associated with the control point coordinates by the least squares method, and the objective function is:

[0026] Among them, S(u, v; X) is a function of the NURBS surface with respect to the parameters (u, v) and the design variable X, and S target is the target surface, λ is the regularization parameter, is the gradient of the surface.

[0027] As a preferred solution, in step S3, the global sensitivity analysis adopts the Sobol method, which specifically includes:

[0028] Generate Sobol sequence samples and input them into the high-fidelity model to calculate the target values;

[0029] Calculate the first-order sensitivity index S i and the total sensitivity index S Ti ;

[0030] Screen the key variables that satisfy S Ti > 0.05, and eliminate the secondary variables with S Ti > 0.01.

[0031] As a preferred solution, in step S4, the multi-objective optimization algorithm is the gradient-enhanced NSGA-II algorithm, including:

[0032] The population initialization adopts Latin hypercube sampling;

[0033] Non-dominated sorting and crowding degree calculation;

[0034] Combine the mixed search direction of the objective function gradient and the constraint gradient;

[0035] Adaptive crossover and mutation strategies, where the mutation probability is dynamically adjusted with the number of iterations as:

[0036] Among them, p m is the mutation probability, gen is the current number of iterations, and gen max is the maximum number of iterations.

[0037] As a preferred solution, in step S5, the multi-level verification system includes:

[0038] Level 1: Fast aerodynamic performance evaluation based on the quasi-3D streamline curvature method;

[0039] Level 2: 3D RANS simulation using the SST k-ω turbulence model, outputting the flow field structure and efficiency correction amount;

[0040] Level 3: Fluid-structure interaction analysis, bidirectionally transferring pressure loads and displacements to verify stress distribution and vibration characteristics.

[0041] As a preferred solution, the method accelerates the optimization process through the Kriging surrogate model, and the surrogate model expression is:

[0042] where is the surrogate model prediction value, μ is the global mean, θ Ⅰ is the coefficient, φ Ⅱ is the correlation parameter, x Ⅱ is the second component of the input variable, x Ⅰ,Ⅱ is the second component of the first sample, § is the number of samples, d is the dimension of the input variable, and ε is the random error.

[0043] As a preferred solution, the manufacturing and safety constraint conditions include:

[0044] Equivalent stress constraint: where σ eq is the equivalent stress, σ yield is the yield stress, and SF is the safety factor;

[0045] Surge constraint: where is the derivative of efficiency with respect to mass flow rate, and ε is the surge constraint threshold;

[0046] Vibration constraint: ω critical ≥1.3ω operating where ω critical is the critical speed, and ω operating is the operating speed;

[0047] where the critical speed ω critical is calculated based on the first natural frequency of the impeller simplified beam model.

[0048] As can be seen from the technical solutions provided by the present invention above, for a fuel cell compressor impeller design optimization method provided by the present invention, the beneficial effects are:

[0049] Optimized Design Efficiency Improvement: By constructing a parameter system, defining a set of design variables, and performing parametric modeling, the geometric model of the impeller can be quickly generated, laying a solid foundation for subsequent optimization. In particular, by using the NURBS surface equation in combination with the least squares method to correlate design parameters with control point coordinates, the model construction becomes more accurate and efficient, greatly shortening the design cycle.

[0050] Multi-objective Balanced Optimization: The established multi-objective function system converts the aerodynamic efficiency, structural strength, and mass objectives into numerical indicators and effectively coordinates objective conflicts. By setting manufacturing and safety constraint conditions, such as equivalent stress, surge, and vibration constraints, etc., while improving aerodynamic efficiency, it ensures the structural strength and operation safety of the impeller, and also takes into account quality control, achieving comprehensive balanced optimization of multiple objectives and improving the overall performance of the product.

[0051] Precise Screening of Key Variables: The Sobol method is used for global sensitivity analysis to accurately screen out key design variables, eliminate secondary variables, and effectively reduce the dimensionality of the optimization space. This enables subsequent optimization to focus on key factors, reduces the amount of calculation and complexity, and improves the efficiency and accuracy of the optimization algorithm.

[0052] Efficient Convergence of the Optimization Algorithm: The gradient-enhanced NSGA-II algorithm determines the hybrid search direction by combining the objective function gradient and the constraint gradient, and cooperates with the adaptive crossover and mutation strategies to accelerate the generation speed of the Pareto optimal solution set. Latin hypercube sampling is used in population initialization to ensure good coverage of the design space by the initial population, enhance the global search ability of the algorithm, and make the optimization process converge faster to the vicinity of the optimal solution.

[0053] Verification System Ensures Reliability: The multi-level verification system gradually and comprehensively verifies candidate solutions from the rapid aerodynamic performance evaluation based on the quasi-3D streamline curvature method, to the 3D RANS simulation using the SSTk-ω turbulence model, and then to the fluid-structure interaction analysis. It can not only accurately evaluate aerodynamic performance, but also verify stress distribution and vibration characteristics. By modifying the design space, it effectively ensures the reliability of the design and reduces the product development risk.

[0054] Strong Versatility and Reusability: This method is applicable to the design of high-speed impeller machinery in the aviation and automotive fields, and supports cross-platform reuse of design criteria and empirical formula libraries. It has broad application prospects and versatility, providing an efficient and reliable solution for impeller design in different fields, saving design resources and costs. Brief Description of the Drawings

[0055] Figure 1 It is a schematic flow chart of the steps of a method for optimizing the design of a fuel cell compressor impeller according to the present invention. Detailed Embodiment

[0056] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0057] To better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the specification drawings and specific implementation manners.

[0058] As Figure 1 shown, an embodiment of the present invention provides a method for optimizing the design of a fuel cell compressor impeller, including the following steps:

[0059] S1. Construct a parameter system for the design of the compressor impeller, define a set of design variables, and generate an impeller geometric model through parametric modeling;

[0060] S2. Establish a multi-objective function system, convert the aerodynamic efficiency, structural strength and mass objectives into numerical indicators, coordinate the objective conflicts, and set manufacturing and safety constraint conditions;

[0061] S3. Screen key design variables through global sensitivity analysis to reduce the dimensionality of the optimization space;

[0062] S4. Use a multi-objective optimization algorithm to generate a Pareto optimal solution set and accelerate convergence in combination with gradient information;

[0063] S5. Verify candidate solutions through a multi-level verification system, correct the design space, and ensure performance and reliability.

[0064] In this embodiment, the specific operation steps of step S1 are as follows:

[0065] Step S1-1: Construct a parameter system for the design of the compressor impeller:

[0066] Constructing a parameter system is the cornerstone of the design optimization of the entire fuel cell compressor impeller; it is necessary to comprehensively and deeply analyze various parameters that affect the impeller performance and consider them from multiple dimensions;

[0067] Geometric shape parameters: The outer dimensions and contours of the impeller directly determine the shape and spatial layout of its internal flow channels, thereby affecting the gas flow characteristics; for example, parameters such as the length, width, and bending degree of the blades will change the gas flow path and velocity distribution inside the impeller, thereby affecting the efficiency and pressure ratio of the compressor;

[0068] Flow characteristic parameters: These parameters reflect the flow state and energy conversion process of the gas inside the impeller; such as the inlet velocity, pressure, temperature of the gas, and the corresponding parameters at the outlet. The variation relationships among them directly reflect the working performance of the compressor; at the same time, the flow velocity distribution, pressure distribution, etc. of the gas are also important flow characteristic parameters, which have crucial guiding significance for the design and optimization of the impeller;

[0069] Material-related parameters: The material properties of the impeller play a decisive role in its structural strength and reliability; the density of the material affects the mass of the impeller, and thus affects its moment of inertia and energy consumption; the mechanical property parameters such as the elastic modulus and yield strength of the material determine the structural stability and safety of the impeller under high-speed rotation and high-pressure environment;

[0070] Step S1-2: Define the set of design variables:

[0071] Defining the set of design variables is a key step in clarifying the optimization direction and scope; the set of design variables X = [Z, β1, β2, D1, D2, b, t, γ, R hub given in claim 2, where b is the blade height, t is the thickness distribution function, γ is the leading edge sweep angle, and R hub is the hub ratio, and each variable plays an important role in the impeller design;

[0072] Number of blades Z: The number of blades directly affects the compression ability of the impeller for the gas and the flow stability; a larger number of blades can increase the contact area between the gas and the blades, improving the compression efficiency, but at the same time increasing the flow resistance and energy loss; a smaller number of blades may lead to insufficient gas compression, affecting the performance of the compressor;

[0073] Blade inlet angle β1 and blade outlet angle β2: β1 determines the initial flow direction of the gas when it enters the impeller. A reasonable inlet angle can reduce the impact loss at the inlet and improve the intake efficiency; β2 affects the state of the gas when it leaves the impeller and the energy conversion efficiency. A suitable outlet angle can make the gas flow out of the impeller at the best speed and direction, improving the overall performance of the compressor;

[0074] Inlet / outlet diameters D1 and D2: The sizes of the inlet / outlet diameters are directly related to the gas flow rate and the flow velocity distribution inside the impeller; a larger inlet diameter can increase the gas intake volume, but may lead to a decrease in the flow velocity; a larger outlet diameter can reduce the outlet flow velocity of the gas, reducing the kinetic energy loss, but may affect the pressure ratio;

[0075] Blade height b: The blade height is closely related to the work capacity of the impeller and the internal flow field structure. A higher blade height can increase the gas flow area and improve the flow rate, but it may also lead to a reduction in the structural strength of the blade. A lower blade height can improve the structural strength of the blade, but it may limit the gas flow rate.

[0076] Thickness distribution function t: The thickness distribution function determines the thickness of the blade at different positions and has an important impact on the structural strength and mass of the impeller. A reasonable thickness distribution can minimize the mass of the impeller and reduce energy consumption while ensuring the structural strength of the impeller.

[0077] Leading edge sweep angle γ: The leading edge sweep angle can improve the gas flow condition at the leading edge of the impeller and reduce flow separation. An appropriate sweep angle can make the gas enter the impeller more smoothly, reduce the intake loss, and improve the efficiency of the compressor.

[0078] Hub ratio R hub : The hub ratio reflects the ratio of the hub diameter to the outer diameter of the impeller and has a certain impact on the overall structure and flow field of the impeller. A suitable hub ratio can optimize the flow channel shape inside the impeller, improve the gas flow uniformity and compression efficiency.

[0079] Step S1-3: Generate the impeller geometric model through parametric modeling:

[0080] Using the parametric modeling method can accurately generate the impeller geometric model according to the design variable set, providing a basis for subsequent analysis and optimization.

[0081] Using the NURBS surface equation: The NURBS surface equation is a powerful geometric modeling tool. By adjusting the control point coordinates P i,j and the parameters of the basis functions N i,p (u) and N j,q (v), various complex-shaped impeller surfaces can be flexibly constructed. This method has high flexibility and accuracy and can meet different design requirements. Among them, S(u, v) is the value of the NURBS surface at the parameters (u, v), N i,p (u) is the basis function of order p of degree i in the u direction, N j,q (v) is the basis function of order q of degree j in the v direction, P i,j is the control point coordinate, and n and m are the numbers of control points in the u and v directions respectively.

[0082] Relate the design parameters to the control point coordinates: The design parameters are related to the control point coordinates through the least squares method, and the objective function is The purpose of this objective function is to make the generated NURBS surface S(u, v; X) as close as possible to the target surface Starget , while considering the smoothness of the surface (through ), where S(u, v; X) is a function of the NURBS surface with respect to the parameters (u, v) and the design variable X, and S target is the target surface, λ is the regularization parameter, is the gradient of the surface; by solving this objective function, the optimal control point coordinates corresponding to the design parameters can be obtained, thereby generating an impeller geometric model that meets the design requirements; the model generated in this way can accurately reflect the influence of the design variables on the impeller geometry and provide a reliable basis for subsequent performance analysis and optimization.

[0083] In this embodiment, step S2 is to establish a multi-objective function system, convert the aerodynamic efficiency, structural strength, and mass objectives into numerical indicators, coordinate the objective conflicts, and set manufacturing and safety constraint conditions. The following is a detailed step analysis:

[0084] Step S2-1: Determine the components of the multi-objective function system:

[0085] The multi-objective function system mainly includes the pressure ratio objective function, the efficiency objective function, and the equivalent stress criterion; these functions evaluate the performance of the fuel cell compressor impeller from different aspects;

[0086] Pressure ratio objective function:

[0087] The formula is (where π is the pressure ratio, Δh is the enthalpy change, c p is the specific heat capacity at constant pressure, T in is the inlet temperature, and η is the efficiency); this function describes the quantitative relationship between the pressure ratio and other design parameters, and the pressure ratio can be changed by adjusting these parameters to meet different working requirements;

[0088] Efficiency objective function:

[0089] The formula is (where ∑Δs i is the total entropy increase, and k is the adiabatic index); this function is used to measure the energy utilization efficiency of the compressor during the gas compression process, and the entropy increase is reduced and the efficiency is improved by optimizing the design parameters;

[0090] Equivalent stress criterion:

[0091] The formula is (where σ eq is the equivalent stress, σ θ is the circumferential stress, σ r is the radial stress, and τ is the shear stress); the equivalent stress is an important indicator for judging whether the impeller structural strength meets the requirements;

[0092] Step S2-2: Convert the target into numerical indicators:

[0093] Through the above objective functions, convert the aerodynamic efficiency, structural strength, and mass objectives into specific numerical values; for example, the efficiency objective function directly gives the numerical value of efficiency, the equivalent stress criterion calculates the numerical value of equivalent stress, and the mass can be calculated through the geometric model and material density of the impeller; these numerical indicators provide a clear quantitative basis for subsequent optimization and evaluation;

[0094] Step S2-3: Coordinate objective conflicts:

[0095] In actual design, there are often conflicts among the aerodynamic efficiency, structural strength, and mass objectives; for example, to improve aerodynamic efficiency, it may be necessary to increase the number of blades or change the shape of the blades, but this may lead to an increase in the mass of the impeller and may also affect the structural strength; therefore, it is necessary to coordinate the conflicts among these objectives;

[0096] The method of multi-objective optimization can be adopted to combine multiple objective functions into a comprehensive objective function, such as the multi-objective optimization problem min X [-η(X), σ max (X), mass(X)] (where min X represents optimizing the set of design variables X to find the objective function vector, X is the set of design variables, η(X) is the function of efficiency with respect to the design variables, σ max (X) is the function of the maximum stress with respect to the design variables, and mass(X) is the function of mass with respect to the design variables); by solving the optimal solution of this comprehensive objective function, find a balance among different objectives;

[0097] Step S2-4: Set manufacturing and safety constraints:

[0098] To ensure the feasibility and safety of the designed impeller during actual manufacturing and operation, a series of constraints need to be set;

[0099] Equivalent stress constraint:

[0100] The formula is (where σ eq is the equivalent stress, σ yield is the yield stress, and SF is the safety factor); this constraint ensures that the equivalent stress of the impeller during operation does not exceed the allowable stress of the material, preventing the impeller from undergoing plastic deformation or damage;

[0101] Surge constraint:

[0102] The formula is (where is the derivative of efficiency with respect to mass flow rate, and ε is the surge constraint threshold. Surge is an unstable phenomenon during the operation of a compressor, which can lead to a decline in compressor performance or even damage. This constraint condition avoids the compressor entering the surge operating condition by restricting the rate of change of efficiency with respect to mass flow rate.

[0103] Vibration constraint:

[0104] The formula is ω critical ≥1.3ω operating (where ω critical is the critical speed and ω operating is the operating speed). This constraint condition ensures that the critical speed of the impeller is higher than the operating speed by a certain proportion, avoiding resonance of the impeller during operation and ensuring the operating stability of the impeller.

[0105] In this embodiment, step S3 screens key design variables through global sensitivity analysis to reduce the dimensionality of the optimization space. The following is a detailed description of this step:

[0106] Step S3-1: Select the global sensitivity analysis method:

[0107] The present invention uses the Sobol method for global sensitivity analysis. The Sobol method is a global sensitivity analysis method based on variance decomposition. It can comprehensively consider the interaction between design variables and their influence on the objective function. Compared with local sensitivity analysis methods, it can more accurately evaluate the importance of each design variable in the entire design space.

[0108] Step S3-2: Generate Sobol sequence samples:

[0109] The Sobol sequence is a low-discrepancy sequence that can evenly distribute sample points in the design space, enabling the sample points to better represent the entire design space. By generating Sobol sequence samples, the design space can be sampled efficiently, reducing the required number of samples and improving the accuracy of the analysis. During specific operations, the number and distribution of samples are determined according to the value range and accuracy requirements of the design variables, and a series of Sobol sequence sample points are generated.

[0110] Step S3-3: Input the high-fidelity model to calculate the target value:

[0111] Take the generated Sobol sequence samples as input and substitute them into the high-fidelity model for calculation; the high-fidelity model can be a complex numerical model established based on physical principles, such as a computational fluid dynamics (CFD) model, a finite element analysis (FEA) model, etc. It can accurately simulate the performance of the fuel cell compressor impeller and calculate the target values corresponding to the sample points, such as pressure ratio, efficiency, equivalent stress, etc.; these target values reflect the performance of the impeller under different combinations of design variables and provide a data basis for subsequent sensitivity analysis;

[0112] Step S3-4: Calculate the first-order sensitivity index S i and the total sensitivity index S Ti :

[0113] Using the Monte Carlo integration method, based on the sample points and the corresponding target values, calculate the first-order sensitivity index S of each design variable i and the total sensitivity index S Ti ;

[0114] The first-order sensitivity index S i : It measures the direct contribution of a single design variable to the variance of the objective function and reflects the degree of influence of this design variable on the objective function when acting independently;

[0115] The total sensitivity index S Ti : It considers the contribution of the interaction between this design variable and other design variables to the variance of the objective function and more comprehensively reflects the importance of this design variable in the entire design system;

[0116] Step S3-5: Screen key variables and eliminate secondary variables:

[0117] According to the calculated total sensitivity index S Ti screen the design variables:

[0118] Screen key variables: Select the design variables that satisfy S Ti > 0.05 as key variables; these variables have a greater impact on the objective function and need to be focused on and adjusted during the optimization process; by optimizing the key variables, the performance of the impeller can be improved more effectively;

[0119] Eliminate secondary variables: Eliminate the design variables with S Ti > 0.01; these variables have a very small impact on the objective function and can be ignored during the optimization process, thereby reducing the dimension of the optimization problem, reducing the calculation amount and optimization time, and improving the optimization efficiency;

[0120] Through the above steps, the screening of key design variables and the dimensionality reduction of the optimization space are completed, providing a more concise and effective set of design variables for the subsequent multi-objective optimization algorithm, which helps to improve the accuracy and efficiency of optimization.

[0121] In this embodiment, step S4 is to generate a Pareto optimal solution set using a multi-objective optimization algorithm and accelerate convergence by combining gradient information. The following is a detailed step description:

[0122] Step S4-1: Select a multi-objective optimization algorithm:

[0123] The present invention selects the gradient-enhanced NSGA-II algorithm; NSGA-II (Non-dominated Sorting Genetic Algorithm II) is a classic multi-objective genetic algorithm with good global search ability and population diversity maintenance ability; while the gradient-enhanced NSGA-II algorithm combines the gradient information of the objective function on this basis, which can more efficiently guide the search direction and accelerate the convergence process;

[0124] Step S4-2: Population initialization:

[0125] The Latin Hypercube Sampling (LHS) method is used for population initialization; Latin Hypercube Sampling is a stratified sampling technique that can uniformly sample within the value range of design variables to ensure that the initial population can better cover the entire design space. The specific steps are as follows:

[0126] The value range of each design variable is divided into N non-overlapping intervals, where N is the size of the population;

[0127] A value is randomly selected from each interval to form a sample point;

[0128] Repeat the above steps N times to obtain N sample points, and these sample points constitute the initial population;

[0129] Step S4-3: Non-dominated sorting and crowding degree calculation:

[0130] Non-dominated sorting: Perform non-dominated sorting on the individuals in the initial population to divide the population into different non-dominated ranks; if an individual is not inferior to another individual in all objective functions and is superior to that individual in at least one objective function, then it is said that this individual dominates the other individual; through non-dominated sorting, the individuals in the population can be stratified according to their superiority and inferiority, so that the individuals within the same layer do not have a domination relationship with each other;

[0131] Crowdedness calculation: For each individual within a non-dominated rank, calculate its crowdedness; crowdedness is an indicator measuring the density of individuals around an individual, used to maintain the diversity of the population; individuals with a larger crowdedness indicate fewer individuals around them and better distribution; in the selection operation, individuals with a larger crowdedness will be preferentially selected to avoid the algorithm converging to a local optimal solution prematurely;

[0132] Step S4-4: Determine the hybrid search direction:

[0133] Combine the objective function gradient and the constraint gradient to determine the hybrid search direction; the objective function gradient reflects the change trend of the objective function at the current point, and the constraint gradient reflects the change situation of the constraint conditions at the current point; by combining the two, it is possible to search in the direction of the optimal objective function while satisfying the constraint conditions; the specific method can be to perform a weighted combination of the objective function gradient and the constraint gradient to obtain a comprehensive search direction;

[0134] Step S4-5: Adaptive crossover and mutation strategies:

[0135] Crossover operation: Select a certain number of individuals in the population for the crossover operation to generate new individuals; the crossover operation is an important means of generating new individuals in the genetic algorithm. It generates offspring individuals with different gene combinations by exchanging part of the genes of the parent individuals;

[0136] Mutation operation: Perform a mutation operation on the offspring individuals generated by crossover to introduce new gene information; the mutation probability p m is dynamically adjusted with the number of iterations, and the formula is where p m is the mutation probability, gen is the current number of iterations, and gen max is the maximum number of iterations; at the beginning of the iteration, the mutation probability is larger, which helps the algorithm explore in a larger search space; as the number of iterations increases, the mutation probability gradually decreases, enabling the algorithm to perform a more refined search locally;

[0137] Step S4-6: Generate the Pareto optimal solution set:

[0138] By continuously performing selection, crossover, and mutation operations, the population is iteratively updated until the termination conditions are met (such as reaching the maximum number of iterations, the objective function value converges, etc.); the non-dominated individuals in the finally obtained population constitute the Pareto optimal solution set; the individuals in the Pareto optimal solution set achieve a balance among multiple objective functions, that is, it is impossible to improve the value of a certain objective function without reducing the values of other objective functions; users can select the most suitable design scheme from the Pareto optimal solution set according to actual needs.

[0139] In this embodiment, step S5 verifies the candidate solutions through a multi-level verification system, modifies the design space, and ensures performance and reliability. The following is a detailed step description:

[0140] Step S5-1: Level 1 - Fast Aerodynamic Performance Evaluation Based on Quasi-3D Streamline Curvature Method:

[0141] Method Principle: The quasi-3D streamline curvature method is a method for approximately calculating the internal flow field of an impeller. It simplifies the three-dimensional flow field into a series of two-dimensional problems along the streamlines and obtains the flow field parameters by solving the streamline curvature equation. Compared with the fully three-dimensional numerical simulation, the computational cost of this method is greatly reduced, and it can quickly give a preliminary evaluation of the aerodynamic performance of the impeller.

[0142] Specific Operation: Input the impeller geometric model corresponding to the candidate solution into the calculation program based on the quasi-3D streamline curvature method. The program first determines the starting position and approximate direction of the streamlines according to the geometric shape of the impeller. Then, along each streamline, according to the given boundary conditions (such as the velocity, pressure, temperature, etc. of the inlet air flow), the streamline curvature equation is solved iteratively to gradually calculate the air flow parameters at each point on the streamline, such as velocity, pressure, density, etc. Finally, based on these parameters on the streamlines, the overall aerodynamic performance indicators of the impeller are calculated, such as the preliminary estimated values of flow rate, pressure ratio, efficiency, etc. These estimated values can quickly help determine whether the candidate solution has potential feasibility in terms of aerodynamic performance. If the results deviate significantly from the expected performance range, the candidate solution can be preliminarily excluded, reducing the workload of subsequent high-cost calculations.

[0143] Step S5-2: Level 2 - 3DRANS Simulation Using SSTk-ω Turbulence Model:

[0144] Basis for Model Selection: The SSTk-ω turbulence model combines the accuracy of the k-ω model in the near-wall region and the advantages of the k-ε model in the far field, and has good simulation ability for the complex internal turbulent flow of the impeller. The Reynolds-averaged Navier-Stokes (RANS) equation can accurately simulate the turbulent flow field at a reasonable computational cost by time-averaging the Navier-Stokes equation, and is suitable for analyzing complex three-dimensional flow phenomena inside the impeller.

[0145] Simulation process: For the impeller geometric models corresponding to the candidate solutions considered potential after Level 1 screening, use professional computational fluid dynamics (CFD) software to establish a three-dimensional computational model; set the boundary conditions of the model, including inlet boundary conditions (such as velocity, temperature, turbulent kinetic energy, etc.), outlet boundary conditions (such as pressure, etc.), and wall boundary conditions (no-slip conditions, etc.); select the SST k-ω turbulence model as the turbulence closure model in the software and start the computational solver for numerical calculation; during the calculation process, gradually converge to obtain the three-dimensional flow field structure inside the impeller, including detailed information such as velocity field, pressure field, temperature field, and turbulent kinetic energy distribution by iteratively solving the RANS equation and the turbulence model equation; based on this flow field information, accurately calculate the aerodynamic efficiency of the impeller and compare it with the results of Level 1 to obtain the efficiency correction amount; at the same time, by analyzing the velocity field and pressure field, abnormal phenomena such as flow separation and recirculation that may exist in the flow field can be found to further evaluate the aerodynamic performance advantages and disadvantages of the candidate solutions.

[0146] Step S5-3: Level 3 - Fluid-structure interaction analysis:

[0147] Analysis purpose: During the operation of the impeller, the pressure in the internal flow field will exert a force on the impeller structure, causing the impeller to deform, and the deformation of the impeller will in turn affect the flow field distribution. This phenomenon of interaction between the flow field and the structure is called fluid-structure interaction; through fluid-structure interaction analysis, the stress distribution and vibration characteristics of the candidate solutions under actual working conditions can be accurately verified to ensure the structural reliability of the impeller.

[0148] Two-way transfer process: First, take the flow field pressure load obtained in Level 2 as the boundary condition for structural analysis and input it to the impeller structure model established in the finite element analysis (FEA) software; in the FEA software, divide appropriate finite element meshes according to the material properties (such as elastic modulus, Poisson's ratio, etc.) and geometric shape of the impeller; then, solve the structural mechanics equation to obtain the deformation and stress distribution of the impeller under the action of the flow field pressure; next, reverse transfer the deformation result of the impeller back to the flow field model in the CFD software to update the boundary conditions of the flow field and perform flow field calculation again to obtain the new flow field distribution considering the structural deformation; repeat the two-way data transfer and calculation like this until the flow field and structural responses reach a convergent state; finally, through the evaluation of the fluid-structure interaction analysis results, judge whether the stress distribution of the candidate solutions is within the allowable range of the material and whether the vibration characteristics meet the design requirements, such as whether the vibration frequency avoids the resonance frequency, etc.; if problems such as excessive stress or abnormal vibration are found, correct or redesign the candidate solutions, further modify the design space to ensure that the finally designed impeller meets the actual application requirements in terms of performance and reliability.

[0149] In this embodiment, the method accelerates the optimization process through the Kriging surrogate model, and the expression of the surrogate model is:

[0150] Where, is the predicted value of the surrogate model, μ is the global mean, θ Ⅰ is the coefficient, φ Ⅱ is the correlation parameter, x Ⅱ is the second component of the input variable, x Ⅰ,Ⅱ is the second component of the first sample, § is the number of samples, d is the dimension of the input variable, and ε is the random error;

[0151] Furthermore, in the fuel cell compressor impeller design optimization method of the present invention, the Kriging surrogate model plays a key role in accelerating the optimization process. The following is a detailed description of it:

[0152] 1. Principle of Kriging surrogate model

[0153] The Kriging surrogate model is also called the Gaussian process regression model. It is a statistical interpolation method used to establish an approximate relationship between input variables (design variables) and output responses (objective function values). Its basic idea is to use the information of known sample points to predict the response values of unknown points by constructing a model that includes a global trend term and a local deviation term;

[0154] The expression of the Kriging surrogate model is:

[0155]

[0156] 2. Steps to construct the Kriging surrogate model:

[0157] 2.1 Sample data collection:

[0158] Within the value range of the design variables, a certain number of sample points are selected using a suitable sampling method (such as Latin hypercube sampling); for each sample point, the corresponding objective function values (such as pressure ratio, efficiency, equivalent stress, etc.) are calculated through a high-fidelity model (such as CFD model, finite element model, etc.). These sample points and their corresponding objective function values constitute the training data for constructing the Kriging surrogate model;

[0159] 2.2 Determine model parameters:

[0160] Using the training data, methods such as maximum likelihood estimation are used to determine the parameters μ, θ Ⅰ and φ ⅡSpecifically, it is to find a set of parameter values that make the surrogate model have the best fitting effect on the training data, that is, the error between the predicted value and the actual value is minimized;

[0161] 2.3 Model verification:

[0162] To evaluate the accuracy and reliability of the Kriging surrogate model, it is necessary to use a part of the sample points (verification set) that did not participate in the training to verify the model; calculate the error metrics (such as mean square error, mean absolute error, etc.) between the predicted values and the actual values of the sample points in the verification set. If the error metrics are within an acceptable range, it is considered that the surrogate model has a good fitting effect and can be used for subsequent optimization processes; otherwise, it is necessary to readjust the sampling strategy or model parameters until the model meets the requirements.

[0163] 3. Accelerate the optimization process using the Kriging surrogate model:

[0164] 3.1 Reduce the number of high-fidelity model calculations:

[0165] In the optimization process, traditional methods need to frequently call the high-fidelity model to calculate the objective function value, and the calculation of the high-fidelity model is usually very time-consuming; the Kriging surrogate model can replace the high-fidelity model to predict the objective function value in most cases; in each iteration, first quickly predict the objective function values under different combinations of design variables through the surrogate model, then screen out potential design schemes according to the prediction results, and then only use the high-fidelity model to perform accurate calculations on these schemes; this can greatly reduce the number of calls to the high-fidelity model, thereby significantly shortening the calculation time of the optimization process.

[0166] 3.2 Guide the search direction:

[0167] The Kriging surrogate model can not only provide the predicted value of the objective function, but also give the uncertainty information of the predicted value (such as prediction variance); in the optimization process, this information can be used to guide the search direction; for example, preferentially select the regions with larger prediction variances for search because there may be better solutions in these regions; at the same time, combined with the predicted value of the objective function, select the direction with a better objective function value under the premise of meeting the constraints, so as to improve the optimization efficiency and find the Pareto optimal solution set faster.

[0168] 3.3 Model update:

[0169] As the optimization process progresses, new design solutions are continuously obtained through high-fidelity model calculations with accurate objective function values; these new sample points are added to the training data to reconstruct the Kriging surrogate model to improve the accuracy and adaptability of the model; by continuously updating the surrogate model, the true distribution of the objective function in the design space can be better reflected, further accelerating the optimization process and ensuring that the final design solution has high performance and reliability.

[0170] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the design of a fuel cell compressor impeller, characterized in that: It includes the following steps: S1. Construct a parameter system for compressor impeller design, define a set of design variables, and generate an impeller geometric model through parametric modeling; S2. Establish a multi-objective function system, convert the aerodynamic efficiency, structural strength, and mass objectives into numerical indicators, coordinate objective conflicts, and set manufacturing and safety constraint conditions; S3. Screen key design variables through global sensitivity analysis to reduce the dimensionality of the optimization space; S4. Use a multi-objective optimization algorithm to generate a Pareto optimal solution set and accelerate convergence by combining gradient information; S5. Verify candidate solutions through a multi-level verification system, correct the design space, and ensure performance and reliability.

2. The design optimization method of a fuel cell compressor impeller according to claim 1, wherein: The set of design variables is: X = [Z, β1, β2, D1, D2, b, t, γ, R hub , where Z is the number of blades, β1 is the blade inlet angle, β2 is the blade outlet angle, D1 is the inlet diameter, D2 is the outlet diameter, b is the blade height, t is the thickness distribution function, γ is the leading edge sweep angle, and R hub is the hub ratio.

3. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: In step S2, the multi-objective function system includes: A pressure ratio objective function, an efficiency objective function, and an equivalent stress criterion. The pressure ratio objective function is defined as: where, π is the pressure ratio, Δh is the enthalpy change, c p is the specific heat capacity at constant pressure, T in is the inlet temperature, and η is the efficiency; The efficiency objective function is defined as: Among them, ∑Δs i is the total entropy increase, and k is the adiabatic index; The equivalent stress criterion is defined as: Among them, σ eq is the equivalent stress, σ θ is the circumferential stress, σ r is the radial stress, and τ is the shear stress; The multi-objective optimization problem is: min X [-η(X), σ max (X), mass(X)], where min X represents optimizing the set of design variables X to find the objective function vector, X is the set of design variables, η(X) is the function of efficiency with respect to the design variables, σ max (X) is the function of the maximum stress with respect to the design variables, and mass(X) is the function of mass with respect to the design variables.

4. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: In step S1, the parametric modeling uses the NURBS surface equation, and its expression is: where S(u, v) is the value of the NURBS surface at the parameter (u, v), N i,p (u) is the basis function of degree i and order p in the u-direction, N j,q (v) is the basis function of degree j and order q in the v-direction, P i,j are the control point coordinates, and n and m are the numbers of control points in the u- and v-directions respectively; And the design parameters are associated with the control point coordinates through the least squares method. The objective function is: where \(S(u, v; X)\) is a function of the NURBS surface with respect to the parameters \((u, v)\) and the design variable \(X\), and \(S\) target is the target surface, \(\lambda\) is the regularization parameter, is the gradient of the surface.

5. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: In step S3, the global sensitivity analysis uses the Sobol method, which specifically includes: Generate Sobol sequence samples and input them into the high-fidelity model to calculate the objective values; Calculate the first-order sensitivity index S by Monte Carlo integration i and the total sensitivity index S Ti ; Screen for key variables where S Ti > 0.05, and eliminate secondary variables where S Ti > 0.

01.

6. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: In step S4, the multi-objective optimization algorithm is the gradient-enhanced NSGA-II algorithm, which includes: The population initialization uses Latin hypercube sampling; Non-dominated sorting and crowding degree calculation; A hybrid search direction that combines the gradients of the objective function and the constraints; An adaptive crossover and mutation strategy, where the mutation probability is dynamically adjusted with the number of iterations as: Among them, p m is the mutation probability, gen is the current iteration number, and gen max is the maximum iteration number.

7. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: In step S5, the multi-level verification system includes: Level 1: Fast aerodynamic performance evaluation based on the quasi-3D streamline curvature method; Level 2: 3D RANS simulation using the SST k-ω turbulence model, outputting the flow field structure and efficiency correction amount; Level 3: Fluid-structure interaction analysis, bidirectionally transferring pressure loads and displacements to verify the stress distribution and vibration characteristics.

8. A method for optimizing the design of a fuel cell compressor impeller according to claim 1, characterized in that: The method accelerates the optimization process through the Kriging surrogate model, and the expression of the surrogate model is: Among them, is the predicted value of the proxy model, μ is the global mean, and θ Ⅰ is the coefficient, and φ Ⅱ is the correlation parameter, x Ⅱ is the second component of the input variable, and x Ⅰ,Ⅱ is the second component of the first sample, § is the number of samples, d is the dimension of the input variable, and ε is the random error.

9. The fuel cell compressor impeller design optimization method according to claim 1, characterized in that: The manufacturing and safety constraint conditions include: Equivalent stress constraint: Among them, σ eq is the equivalent stress, σ yield is the yield stress, and SF is the safety factor; Surge constraint: where is the derivative of efficiency with respect to mass flow rate, and ε is the surge constraint threshold; Vibration constraint: ω critical ≥1.3ω operating , where ω critical is the critical speed and ω operating is the operating speed; Among them, the critical speed ω critical Calculation of the first natural frequency based on the simplified beam model of the impeller.

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