High-dimensional multi-objective multi-condition optimization method and system for fuel cell centrifugal air compressor

Abstract

This application belongs to the field of fuel cell technology, specifically relating to a high-dimensional multi-objective, multi-condition optimization method and system for fuel cell centrifugal air compressors. The method includes: constructing a performance analysis and optimization system for fuel cell air compressors; improving simulation and optimization efficiency by building a comprehensive performance testing platform, establishing a multi-physics coupled CFD simulation model, and combining machine learning algorithms; defining pressure ratio and isentropic efficiency as optimization objectives based on fuel cell system requirements, and evaluating air compressor performance through experimental and simulation data; and establishing an MMPS algorithm by integrating multi-objective, multi-population optimization methods, archive sharing technology, and genetic algorithms to perform high-dimensional multi-objective optimization of relevant structural parameters of the impeller, volute, and diffuser. This application solves the technical problems of existing fuel cell centrifugal air compressors, such as the difficulty in meeting multi-objective collaborative optimization requirements, the high difficulty in optimizing high-dimensional variables, and the difficulty in controlling complex flow characteristics.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell technology, and more specifically, relates to a high-dimensional multi-objective multi-condition optimization method and system for fuel cell centrifugal air compressors. Background Technology

[0002] Fuel cell technology has garnered significant global attention and rapid development due to its high efficiency, cleanliness, and low emissions. As a crucial supporting technology for achieving green and low-carbon goals, it demonstrates broad application potential in transportation, stationary power generation, and portable energy. The centrifugal air compressor is the core air supply unit of a fuel cell system, responsible for providing high-pressure air to the fuel cell stack. Its performance directly impacts the fuel cell's power generation efficiency, power density, durability, and overall system performance. Therefore, optimizing the performance of centrifugal air compressors has become a key research direction for improving the efficiency of fuel cell systems.

[0003] The current status of fuel cell centrifugal air compressor technology is as follows:

[0004] 1. Difficulty in meeting multi-objective collaborative optimization requirements: Fuel cell systems often face complex operating conditions in practical applications, such as instantaneous load changes, high dynamic response, and long-term stability. This requires centrifugal air compressors to maintain efficient and stable performance under various operating conditions. However, traditional optimization methods are usually oriented towards a single objective or static operating condition, making it difficult to take into account dynamic multi-objective requirements, thus limiting the performance of air compressors in complex scenarios.

[0005] 2. High-dimensional variable optimization is challenging: The design of centrifugal air compressors involves multi-dimensional variables such as geometric parameters, hydrodynamic characteristics, speed, and load. These variables exhibit highly nonlinear and strongly coupled relationships. Achieving global optimization in a multi-dimensional design space requires efficient algorithms. However, traditional optimization methods are often limited to local optima, making it difficult to meet engineering requirements in terms of accuracy and efficiency.

[0006] 3. Challenges in controlling complex flow characteristics: The complex flow characteristics inside centrifugal air compressors, such as turbulence and boundary layer separation, necessitate that optimization design consider the nonlinearity and dynamic changes of the flow field. Traditional optimization tools struggle to fully capture these complex characteristics, thus failing to achieve systemic performance improvements.

[0007] For example, patent CN118013658A discloses an optimization design method for a turbine air compressor based on fuel cell exhaust energy recovery. This scheme determines the matching points and weights corresponding to typical operating conditions through cluster analysis, and combines the coupling characteristics of the pressure end and vortex end to simulate and optimize the air compressor performance using a CFD (Computational Fluid Dynamics) model. Specific methods include: establishing a performance prediction model based on enthalpy loss, using the Monte Carlo method to perform sensitivity analysis on turbine geometric parameters, and optimizing using a particle swarm optimization algorithm with the goal of maximizing the overall efficiency of the vortex end. Although this technical solution improves air compressor performance to some extent, it still has the following shortcomings: 1. Limitations of single-objective optimization: Improving the overall efficiency of the vortex end may lead to a decrease in other air compressor performance, failing to achieve multi-objective collaborative optimization. 2. Shortcomings of the optimization algorithm: The particle swarm optimization algorithm suffers from problems such as local convergence, poor balance between search accuracy and convergence speed, and weak adaptability and diversity maintenance. Compared with advanced optimization algorithms developed in recent years, its efficiency and applicability are insufficient. 3. High computational resource requirements: Although CFD simulation models have high accuracy, they have high computational complexity and low optimization efficiency, making it difficult to meet the high efficiency requirements of actual engineering.

[0008] In summary, existing optimization technologies for centrifugal air compressors in fuel cells still face significant challenges in areas such as multi-objective collaborative optimization, high-dimensional variable optimization, and complex flow field control. To further improve the overall performance of fuel cell systems, it is urgent to develop more efficient and comprehensive optimization methods to overcome current technological bottlenecks. Summary of the Invention

[0009] This invention addresses the shortcomings of existing technologies by proposing a high-dimensional, multi-objective, multi-condition optimization method and system for fuel cell centrifugal air compressors. This method utilizes comprehensive performance test data, CFD simulation, and data-driven modeling, combined with a multi-objective, multi-population optimization framework and the MMPS algorithm, to achieve high-dimensional, multi-objective performance optimization of fuel cell centrifugal air compressors under complex multi-conditions, providing scientific guidance and practical basis.

[0010] On the one hand, this invention provides a high-dimensional, multi-objective, multi-condition optimization method for fuel cell centrifugal air compressors, the method comprising:

[0011] Step 1: Construct a fuel cell air compressor performance analysis and optimization system. This involves building a comprehensive performance testing platform, establishing a multi-physics coupled CFD simulation model, verifying the consistency between simulation results and test data, determining the optimization direction of the geometric model, generating multi-condition data through batch simulation based on orthogonal experimental design, and combining machine learning algorithms to construct and verify a data-driven model to improve simulation and optimization efficiency.

[0012] Step 2: Based on the requirements of the fuel cell system and multi-condition data analysis, the optimization objectives are defined as pressure ratio and isentropic efficiency, and the compression capacity and efficiency performance of the air compressor are evaluated through experimental and simulation data calculations.

[0013] Step 3: Integrate multi-objective and multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm, and K-means clustering method to establish the MMPS algorithm. Use the MMPS algorithm to perform high-dimensional multi-objective optimization on impeller, volute, diffuser and related structural parameters to improve their performance under multiple operating conditions.

[0014] Further, step 1 includes:

[0015] Step 1.1: Build a comprehensive performance testing platform for fuel cell air compressors and collect performance parameters of fuel cell air compressors under different operating conditions through this platform;

[0016] Step 1.2: Create a geometric model of the fuel cell air compressor. Based on the fluid dynamics model, thermodynamics model and turbulence model, perform multiphysics simulation analysis on the geometric model, set the boundary conditions of each model, run multiphysics simulation to cover a variety of operating conditions, and complete the convergence and accuracy verification of the geometric model.

[0017] Step 1.3: Based on the fluid dynamics model, thermodynamics model and turbulence model, set boundary conditions for each model and establish a multiphysics coupled CFD simulation model of the fuel cell air compressor;

[0018] Step 1.4: Compare the simulation results with the performance parameters collected by the test platform one by one to verify whether the error of each performance index is within the set acceptance range;

[0019] Step 1.5: Based on the comparative analysis of simulation results and test data, determine the optimization direction of the impeller, volute and diffuser in the geometric model of the fuel cell air compressor;

[0020] Step 1.6: Based on the geometric model of the fuel cell air compressor, construct a CFD integrated simulation framework for the fuel cell air compressor. Based on orthogonal experimental design, perform batch simulations on different combinations of structural parameters to generate representative simulation data covering multiple working conditions, and preprocess the simulation data.

[0021] Step 1.7: Based on the acquired batch simulation data, construct a data-driven model of the fuel cell centrifugal air compressor using machine learning algorithms, complete the model construction using the training set, and verify the model performance using the test set.

[0022] Further, step 2 includes:

[0023] Step 2.1: Based on the comprehensive analysis of the fuel cell system's gas supply demand, multi-condition operation, thermodynamic and aerodynamic theories, and experimental and simulation data, the optimization objectives of the fuel cell air compressor are defined as pressure ratio and isentropic efficiency.

[0024] Step 2.2: Under a fixed speed ratio, collect inlet and outlet pressure and temperature data of the air compressor at different speeds, calculate the pressure ratio and isentropic efficiency, and evaluate the compression capacity and efficiency performance of the air compressor based on the calculation results.

[0025] Furthermore, step 3 includes:

[0026] Step 3.1: Construct a multi-objective, multi-population optimization framework. By dividing the optimization objective into 10 subpopulations for parallel optimization, and combining crossover and mutation operators based on genetic algorithms to generate and improve solutions, the diversity of solution sets and global search capabilities are enhanced, thereby achieving efficient solution set exploration and optimization in complex multi-objective optimization problems.

[0027] Step 3.2: The crossover operator uses a priority crossover operation, which achieves gene recombination by sorting individuals with high fitness values ​​and using a double-optimal crossover strategy, thereby improving the population's fitness and solution set diversity; the mutation operator uses an insertion mutation operation, which enhances the population's diversity and global search capability by inserting and optimizing genes for individuals with low fitness values, ensuring the stability of the optimization results and performance improvement.

[0028] Step 3.3: By constructing a database sharing technology, excellent solutions are stored and shared in database A within a multi-objective, multi-population optimization framework, which assists in information exchange and priority crossover operations among populations, thereby achieving adaptive search and population co-evolution.

[0029] Step 3.4: A database update strategy is proposed. By filtering, perturbing, and performing diversity preservation operations based on K-means clustering on the solution set of the newly generated population, the database is updated to improve the convergence and quality of elite solutions, thereby enhancing the co-evolutionary ability and optimization efficiency of the population in the multi-objective multi-population optimization framework.

[0030] Step 3.5: By integrating multi-objective multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm and K-means clustering method, the MMPS algorithm is established. The population is randomly initialized and updated through priority crossover and insertion mutation operations. The solution set is optimized by combining the archive update strategy, and finally the elite solution in the archive is output as the optimization result.

[0031] Furthermore, the fuel cell air compressor comprehensive performance testing platform can simulate typical operating conditions including different flow rates, different speeds, different pressures, different cooling conditions, start-up and steady-state conditions, and comprehensive conditions.

[0032] Furthermore, in step 1.4, the simulation results are compared one by one with the experimental data in step 1.1 to verify whether the error of each performance index is controlled within 5%.

[0033] Furthermore, the optimization directions for impellers include increasing the blade inlet angle to improve inflow performance and decreasing the outlet angle to improve airflow uniformity; the optimization directions for volutes include optimizing the volute tongue angle to reduce turbulence and adjusting the ellipticity of the volute cross section to reduce flow separation; the optimization directions for diffusers include increasing the outlet radius to improve pressure recovery and adjusting the width to improve the uniformity of the outlet flow field.

[0034] Furthermore, the pressure ratio (σ) is determined by the following formula:

[0035] σ=p out / p in

[0036] In the formula: p out p indicates the outlet pressure of the air compressor. in This indicates the inlet pressure of the air compressor;

[0037] The isentropic efficiency (η) is determined by the following formula:

[0038]

[0039] In the formula: T in Indicates the inlet temperature of the air compressor; T out This indicates the air compressor outlet temperature; k represents the isentropic exponent.

[0040] On the other hand, the present invention also provides a high-dimensional multi-objective multi-condition optimization system for a fuel cell centrifugal air compressor, comprising:

[0041] The performance analysis and modeling module is used to build a performance analysis and optimization environment for fuel cell air compressors. By building a comprehensive performance testing platform and establishing a multi-physics coupled CFD simulation model, the consistency between simulation results and test data is verified. Multi-condition data is generated based on orthogonal experimental design. At the same time, machine learning algorithms are combined to build and verify data-driven models to improve simulation and optimization efficiency.

[0042] The optimization target definition module is used to define optimization targets based on fuel cell system requirements and multi-condition data analysis, including pressure ratio and isentropic efficiency, and to evaluate the air compressor's compression capacity and efficiency performance through experimental and simulation data calculations.

[0043] The high-dimensional multi-objective optimization module is used to integrate multi-objective multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm and K-means clustering method to construct the MMPS algorithm. Based on this algorithm, the structural parameters of the impeller, volute and diffuser are optimized in a high-dimensional multi-objective manner to improve the performance of the fuel cell centrifugal air compressor under multiple operating conditions.

[0044] The beneficial effects of this invention are:

[0045] First, based on comprehensive performance test data, multi-physics coupled CFD simulation model, CFD integrated simulation framework and orthogonal experimental design, this invention has obtained a large amount of high-quality test and simulation data, and established an efficient and accurate data-driven model for fuel cell centrifugal air compressor through data-driven algorithms, providing a solid model foundation for realizing high-dimensional multi-objective multi-condition performance optimization of air compressor.

[0046] Secondly, this invention introduces a multi-objective, multi-population optimization framework, dividing the population into multiple subpopulations. Each subpopulation works independently or collaboratively, exploring different objectives, thereby more effectively finding Pareto optimal solutions in complex multi-objective problems. Through an information exchange mechanism, solutions are shared and transferred, balancing global search and local exploitation, preventing the population from getting trapped in local optima and maintaining population diversity. This allows the algorithm to better adapt to complex, high-dimensional, and multi-objective optimization environments.

[0047] Third, this invention proposes the MMPS algorithm for optimizing air compressor performance under different operating conditions, forming a high-dimensional multi-objective optimization framework. This enables efficient solutions to complex multi-objective problems and significantly improves the superiority of the final solution set. Simultaneously, it fully considers the performance requirements of air compressors under different operating conditions, providing scientific guidance and practical basis for the development of high-performance fuel cell centrifugal air compressors, thus meeting practical engineering needs. Attached Figure Description

[0048] Figure 1 This is a flowchart of the high-dimensional multi-objective multi-condition optimization method for fuel cell centrifugal air compressors of the present invention;

[0049] Figure 2 This is a schematic diagram of the layout of the monitoring system for the comprehensive performance testing platform of the fuel cell air compressor according to an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the structure of a three-dimensional model of a fuel cell air compressor according to an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of the CFD integrated simulation framework of the fuel cell air compressor according to an embodiment of the present invention;

[0052] Figure 5This is a flowchart of the MMPS algorithm according to an embodiment of the present invention. Detailed Implementation

[0053] To enable those skilled in the art to better understand the technical solutions of this application, the following will provide a more detailed description of this application in conjunction with the accompanying drawings and embodiments.

[0054] In the description of this application, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more unless otherwise expressly defined. The terms "install," "connect," "link," and "fix" should be interpreted broadly. For example, "connect" can mean a fixed connection, a detachable connection, or an integral connection; "link" can mean a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0055] In the description of this application, it should be understood that the terms "upper", "lower", "left", "right", "front", "rear", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or unit referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0056] In the description of this specification, the terms "one embodiment / mode," "some embodiments / modes," "specific embodiment / mode," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment / mode or example, which is included in at least one embodiment / mode or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples.

[0057] As per the instruction manual Figure 1 The purpose of this invention is to provide a high-dimensional, multi-objective, multi-condition optimization method for a fuel cell centrifugal air compressor, comprising:

[0058] Step 1: Construct a fuel cell air compressor performance analysis and optimization system. This involves building a comprehensive performance testing platform, establishing a multi-physics coupled CFD simulation model, verifying the consistency between simulation results and test data, determining the optimization direction of the geometric model, generating multi-condition data through batch simulation based on orthogonal experimental design, and combining machine learning algorithms to construct and verify a data-driven model to improve simulation and optimization efficiency.

[0059] The purpose of Step 1 is to construct a systematic process for performance analysis and optimization of fuel cell air compressors. Through comprehensive performance testing, CFD simulation modeling, data verification, and optimization direction determination, combined with orthogonal experimental design and machine learning algorithms, representative simulation data under multiple operating conditions are generated, and an efficient data-driven model is established to provide scientific basis and technical support for subsequent air compressor structure optimization and performance improvement.

[0060] It should be noted that a fuel cell air compressor includes an impeller, volute, diffuser, motor, bearings and lubrication system, inlet and outlet, cooling system, and control system. The impeller, as the core component, converts mechanical energy into the kinetic and pressure energy of the gas. Key structural parameters include the blade inlet angle, outlet angle, and blade thickness. The volute, the outer casing surrounding the impeller, guides gas flow and converts kinetic energy into pressure energy. Key structural parameters include the volute's cross-sectional shape, outlet diameter, and volute tongue angle. The diffuser, installed between the impeller and volute, decelerates and pressurizes the gas, improving compression efficiency. Key structural parameters include the diffuser's outlet radius, inlet diameter, and outlet width. The motor, connected to the impeller, provides the necessary mechanical energy and typically uses a high-speed motor to drive the impeller's high-speed rotation. The bearings and lubrication system support the rotation of the impeller and shaft, reducing friction and ensuring stable operation. The inlet and outlet connect to the fuel cell system, handling gas input and output. The cooling system, including cooling water or air cooling designs, dissipates heat and maintains the operating temperature. The control system includes sensors and control modules for real-time monitoring and adjustment of the air compressor's operating status, such as temperature, pressure, and flow rate.

[0061] During air compressor operation, the motor drives the impeller to rotate at high speed. The blades, through centrifugal force, throw the gas outward from the center, increasing the gas's kinetic energy. The high-speed gas flows into the diffuser, where the gradually expanding structure slows the airflow, converting kinetic energy into pressure energy and significantly increasing the gas pressure. The pressurized gas then enters the volute, where the curved design further optimizes the gas pressure and flow distribution before finally being output from the outlet. The control system adjusts the motor speed and impeller parameters in real time (such as variable frequency speed control or blade angle adjustment) to adapt to different load requirements and operating conditions. Ultimately, the air compressor provides high-pressure air to the fuel cell, where the oxygen in the air reacts with the hydrogen inside the fuel cell to generate electricity and water.

[0062] Specifically, step 1 includes:

[0063] Step 1.1: Build a comprehensive performance testing platform for fuel cell air compressors and collect performance parameters of fuel cell air compressors under different operating conditions through this platform.

[0064] As per the instruction manual Figure 2The comprehensive performance testing platform for fuel cell air compressors includes the air compressor and its motor, air circuit system, water cooling system, power supply, and control system.

[0065] The air path system is the core component of the test platform, used to guide air through the air compressor and measure relevant performance parameters. It includes an air filter, intake valve, intercooler, and exhaust valve. The air filter filters particulate matter from the air, protecting the air compressor. The intake valve controls the flow rate of gas entering the air compressor. The intercooler reduces the temperature of the compressed air. The exhaust valve controls the output of compressed air. The air filter is connected to the air compressor's inlet via the intake valve and piping. A pressure sensor (PT) and a temperature sensor (THA) are installed at the air compressor's inlet to monitor the pressure and temperature of the input air. Driven by a motor, the air compressor compresses air. Its outlet is connected to the intercooler's inlet via piping. A pressure sensor (PT) and a temperature sensor (THA) are installed at the air compressor's outlet to monitor the compressed air's outlet parameters. The intercooler's outlet is connected to the exhaust pipe via the exhaust valve and piping, and is equipped with a temperature sensor (THA) and a flow sensor (FS) to monitor the cooling effect.

[0066] The water-cooling system maintains the thermal management performance of the air compressor and intercooler, dissipating heat through circulating water. It includes a water tank, water pump, cooling water flow path, and multiple sensors. Cooling water is stored in the water tank, and the water pump, connected to the tank, provides the circulating water flow. The water pump is connected to the intercooler and the air compressor cooling circuit inlet via piping. Cooling water enters the intercooler through pipes, carrying away heat from the compressed air. Water flowing out of the intercooler returns to the water tank through pipes, forming a closed loop. The multiple sensors in the water system include a flow sensor (FS) to measure the cooling water flow rate, a pressure sensor (PT) to monitor the water pressure, and a temperature sensor to monitor the cooling water temperature.

[0067] The power supply and control system, which drives the air compressor and collects data, includes DC power modules, controllers, and sensors. The DC power modules (Q-100V adjustable power supply and 12V power supply) are connected to the air compressor motor via control lines. The Q-100V adjustable power supply drives the main air compressor motor, while the 12V power supply powers auxiliary equipment such as sensors and controllers. The controller is directly connected to all sensors and actuators to monitor inlet and outlet pressure, flow, and temperature data, and to adjust motor speed, intake valve opening, and exhaust valve opening in real time.

[0068] In the implementation of this application, the typical operating conditions that the fuel cell air compressor comprehensive performance testing platform can simulate include different flow rate conditions, different speed conditions, different pressure conditions, different cooling conditions, start-up and steady-state conditions, and comprehensive conditions.

[0069] The different flow rate conditions simulate low, medium, and high flow rate operation, testing the air compressor's efficiency, pressure ratio, compression power, and other performance indicators at different flow rates. Specifically, the intake air volume is controlled by adjusting the intake valve opening, and the system flow balance is adjusted in conjunction with the exhaust valve. Under different flow rate conditions, the low flow rate can be set to 10-30 g / s, the medium flow rate to 30-50 g / s, and the high flow rate to 50-70 g / s (maximum design flow rate). The air compressor speed is set to a fixed value (e.g., 40,000 rpm), and the air compressor outlet pressure is maintained at the design pressure (e.g., 2 bar).

[0070] The different operating speeds are tested by adjusting the motor's drive voltage and frequency to assess the air compressor's efficiency, noise, vibration, and other performance indicators at different speeds. Specifically, an adjustable DC power supply (Q-100V) is used to adjust the motor's input voltage and frequency to ensure the motor operates within a stable range. Under different speed conditions, the low speed can be set to 20,000 rpm, the medium speed to 40,000 rpm, and the high speed to 60,000 rpm (the air compressor's design limit speed), while maintaining a medium flow rate (e.g., 40 g / s) and keeping the air compressor's outlet pressure at the design pressure (e.g., 2 bar).

[0071] Different pressure operating conditions are tested by simulating low-pressure, medium-pressure, and high-pressure conditions to assess the air compressor's performance indicators, such as compression ratio, efficiency, and power consumption, at different outlet pressures. Specifically, the outlet pressure is controlled by adjusting the opening of the exhaust valve to ensure that the compression ratio meets the operating condition requirements during normal operation. Under different pressure conditions, the low-pressure condition can be set to 1 bar (close to atmospheric pressure), the medium-pressure condition to 2 bar, and the high-pressure condition to 3 bar (the upper limit of the air compressor's design), while maintaining a medium flow rate (e.g., 40 g / s) and setting the air compressor speed to a fixed value (e.g., 40,000 rpm).

[0072] Different cooling conditions are used to verify the thermal management performance of the air compressor, including cooling efficiency, outlet temperature, and thermal stability. Specifically, the cooling water temperature is adjusted by regulating the water pump output flow rate and setting the water tank temperature control device. Under different cooling conditions, the cooling water flow rate can be set to 1L / min for low flow, 3L / min for medium flow, and 5L / min for high flow. The cooling water temperature is 10℃ for cold water operation, 25℃ for normal temperature operation, and 40℃ for high temperature operation. The air compressor speed is set to a fixed value (e.g., 40,000 rpm), and the air compressor outlet pressure is maintained at the design pressure (e.g., 2 bar).

[0073] Start-up and steady-state operation tests the air compressor's performance from a standstill to normal operation, as well as its long-term performance under stable operating conditions. Specifically, the air compressor is initially stopped. By adjusting the opening of the intake and exhaust valves and dynamically changing the motor speed using power control, the air compressor gradually increases flow and pressure until it reaches a steady-state condition. This allows for monitoring of the acceleration time, settling time, and initial vibration during startup. After reaching a steady-state condition, load changes are simulated by instantaneously increasing or decreasing the flow rate (±20%) and instantaneously adjusting the outlet pressure (±0.5 bar). This allows for testing the system's response time, pressure fluctuation amplitude, and flow rate stability. Throughout the process, the air compressor speed is dynamically adjusted (e.g., 20,000 rpm → 60,000 rpm), while the cooling water temperature is maintained at a constant level (e.g., 25°C).

[0074] Comprehensive operating conditions are used to evaluate the overall performance of an air compressor under combined operating conditions. Specifically, first, parameter combinations are set, for example: setting the speed to medium speed (40000 rpm), the flow rate to medium flow rate (40 g / s), the pressure to medium pressure (2 bar), the cooling water temperature to 25℃, and the cooling water flow rate to 3 L / min. By dynamically adjusting individual parameters (such as flow rate ±10%, pressure ±0.2 bar), the comprehensive performance is verified.

[0075] Through these detailed test conditions, the performance testing of fuel cell air compressors can comprehensively cover various real-world operating scenarios and provide high-quality experimental data support for subsequent modeling and optimization.

[0076] Step 1.2: Create a geometric model of the fuel cell air compressor. Based on the fluid dynamics model, thermodynamics model and turbulence model, perform multiphysics simulation analysis on the geometric model, set the boundary conditions of each model, run multiphysics simulation to cover a variety of operating conditions, and complete the convergence and accuracy verification of the geometric model.

[0077] It should be noted that the geometric model of the fuel cell air compressor created in step 1.2 is the same as the geometric structure of the fuel cell air compressor tested on the fuel cell air compressor comprehensive performance test platform in step 1.1. The fluid dynamics model describes the motion behavior of the fluid inside the fuel cell air compressor, helping to understand the distribution characteristics of gas flow and its impact on air compressor performance. The thermodynamic model describes the temperature changes and heat transfer behavior of the fluid inside the fuel cell air compressor, which is key to analyzing the compression process and thermal management performance. The turbulence model describes the turbulence characteristics in complex flow fields, including eddies, turbulent energy dissipation, and turbulent kinetic energy transfer, which is crucial for simulating flow losses and pressure recovery inside the air compressor.

[0078] Specifically, first, use CAD software (such as SolidWorks or CATIA) to create a three-dimensional geometric model of the air compressor. (See the instruction manual attached.) Figure 3 The geometric model of a fuel cell air compressor includes an impeller, volute, diffuser, inlet duct, and outlet duct. The impeller's geometric model parameters include the blade inlet installation angle, outlet installation angle, and blade thickness. The volute's geometric model parameters include the cross-sectional ellipticity, volute outlet diameter, and volute tongue angle. The diffuser's geometric model parameters include the diffuser's inlet diameter, outlet radius, and outlet width. The inlet duct guides fluid into the impeller, and the outlet duct guides fluid out of the diffuser.

[0079] Then, a professional meshing tool (such as ANSYS Meshing or ICEM CFD) is used to mesh the geometric model of the fuel cell air compressor. In the implementation of this application, an unstructured mesh (such as a tetrahedral mesh) is used in the impeller region to refine the blade surface; the number of mesh elements is controlled within a reasonable range (such as 5 million to 10 million elements). A structured mesh (such as a hexahedral mesh) is used in the volute region to optimize the calculation accuracy within the flow channel. The diffuser region has its mesh refined at the inlet and outlet to ensure the accuracy of flow deceleration and pressure recovery.

[0080] Step 1.3: Based on the fluid dynamics model, thermodynamics model and turbulence model, set boundary conditions for each model and establish a multiphysics coupled CFD simulation model of the fuel cell air compressor.

[0081] Specifically, suitable fluid dynamics, thermodynamics, and turbulence models are selected from the existing models, and boundary conditions are set for each model. The boundary conditions for the fluid dynamics model include inlet conditions, outlet conditions, and wall conditions. Inlet conditions control the flow rate or velocity, providing the driving force for the flow field; outlet conditions limit the range of the pressure field, ensuring the stability of the computational domain; and wall conditions define the interaction behavior between the fluid and the solid. The boundary conditions for the thermodynamic model include inlet temperature and wall heat exchange. Inlet temperature controls the initial state of the compressed air; wall heat exchange determines the thermal management effect of the air compressor. The boundary conditions for the turbulence model include turbulence parameters, which provide initial disturbance information and influence the turbulence distribution of the flow.

[0082] For example: Assume the fuel cell air compressor operates under the following conditions: inlet flow rate 30 g / s, outlet pressure 2 bar, and air inlet temperature 25°C. Set the boundary conditions: Fluid dynamics: inlet flow rate 30 g / s, outlet pressure 2 bar, wall impeller rotation speed 40000 rpm, no slip condition. Thermodynamic model: inlet air temperature 25°C, wall volute adiabatic, diffuser convective heat exchange (cooling water temperature 20°C). Turbulence model: turbulence intensity 10%, turbulent viscosity ratio 20.

[0083] Furthermore, to meet the actual operating requirements of the fuel cell air compressor, the following operating conditions are set: 1. Flow range: 10g / s, 20g / s, 30g / s, 40g / s; 2. Outlet pressure range: 1.5bar, 2.0bar, 2.5bar; 3. Impeller speed range: 30000rpm, 40000rpm, 50000rpm; 4. Cooling conditions: cooling water temperature of 15℃, 20℃, 25℃.

[0084] Run the simulation using multiphysics simulation software (such as ANSYS Fluent or CFX). Set the simulation convergence criterion: the residual convergence criterion is 10. -5 Key performance indicators (such as total pressure ratio, efficiency, and flow rate) are stable. Then, convergence is checked, and the stability of key performance indicators (such as total pressure ratio, flow rate, temperature rise, and efficiency) is monitored. Data such as velocity field, pressure field, and temperature field are extracted, and performance indicators such as total pressure ratio, flow-pressure curve, isentropic efficiency, turbulence intensity distribution, and pressure recovery coefficient are calculated.

[0085] It should be noted that the velocity field is used to analyze the velocity distribution within the impeller, volute, and diffuser; the pressure field is used to evaluate pressure recovery efficiency; and the temperature field is used to observe the temperature rise during airflow compression. The total pressure ratio reflects compression performance, the flow-pressure curve evaluates regulation capability, isentropic efficiency quantifies energy loss during compression, temperature rise observes temperature changes during compression, turbulence intensity distribution reveals the sources of eddies and flow losses, and the pressure recovery coefficient evaluates the effectiveness of the diffuser and volute geometry design.

[0086] Step 1.4: Compare the simulation results with the performance parameters collected by the test platform one by one to verify whether the error of each performance index is within the set acceptance range.

[0087] In the implementation of this application, the simulation results are compared one by one with the experimental data in step 1.1 to verify whether the error of each performance index is controlled within 5%. The error formula can be expressed as:

[0088]

[0089] Step 1.5: Based on the comparative analysis of simulation results and test data, determine the optimization direction of the impeller, volute and diffuser in the geometric model of the fuel cell air compressor.

[0090] Impeller optimization includes increasing the blade inlet angle to improve inflow performance and decreasing the outlet angle to enhance airflow uniformity. Volute optimization includes optimizing the volute tongue angle to reduce turbulence and adjusting the ellipticity of the volute cross-section to reduce flow separation. Diffuser optimization includes increasing the outlet radius to improve pressure recovery and adjusting the width to improve outlet flow field uniformity.

[0091] Step 1.6: Based on the geometric model of the fuel cell air compressor, construct a CFD integrated simulation framework for the fuel cell air compressor. Based on orthogonal experimental design, perform batch simulations on different combinations of structural parameters to generate representative simulation data covering multiple working conditions, and preprocess the simulation data.

[0092] It should be noted that CFD (Computational Fluid Dynamics) for fuel cell air compressors refers to the simulation and analysis of the flow field inside an air compressor using computational fluid dynamics methods. Using CFD technology, the airflow distribution, pressure field, velocity field, and temperature field of key components such as the impeller, volute, and diffuser of the air compressor can be accurately calculated, allowing for the evaluation of performance parameters such as efficiency, pressure ratio, and flow characteristics.

[0093] As per the instruction manual Figure 4 Specifically, the key to constructing a CFD integrated simulation framework for fuel cell air compressors lies in achieving efficient management of parametric input, automated operation, and result data. First, based on the geometry and operating conditions of the fuel cell air compressor, key design parameters (such as blade inlet angle, volute angle, and diffuser outlet width) and operating parameters (such as inlet flow rate, outlet pressure, and speed) are tabulated to form an adjustable input parameter table, providing a foundation for automated simulation. Second, through scripting tools (such as Python or ANSYS Workbench Automation), the entire CFD simulation process is automated, including geometric parameter input, mesh generation, boundary condition setting, and simulation task scheduling. In the simulation framework, boundary conditions cover typical operating conditions, such as various combinations of flow rate, pressure, and speed, ensuring a comprehensive evaluation of air compressor performance. After simulation completion, key performance indicators (such as total pressure ratio, efficiency, flow rate, and temperature rise) are automatically extracted, and these data are associated with the corresponding input parameters and stored in a unified database. The framework also integrates data validation and noise reduction functions to ensure the reliability and quality of simulation results. It also supports visualization analysis to intuitively display the distribution of velocity, pressure, and temperature fields, as well as the relationship between geometric parameters and performance indicators. This framework enables efficient, flexible, and highly scalable batch CFD simulations of fuel cell air compressors, providing a solid technical foundation for optimized design.

[0094] Furthermore, the orthogonal experimental design process includes: determining the geometric parameters to be optimized and their levels, such as: blade inlet angle (20°, 25°, 30°), volute tongue angle (40°, 45°, 50°), and diffuser outlet radius (60mm, 65mm, 70mm). An orthogonal array (such as the L9 array) is used to design the experiment, simplifying the full factorial test (27 trials) into 9 simulation trials. Each set of geometric parameters is simulated under different operating conditions, such as: flow rate: 10g / s, 20g / s, 30g / s, 40g / s; outlet pressure: 1.5bar, 2.0bar, 2.5bar; impeller speed: 30000rpm, 40000rpm, 50000rpm. Representative simulation data covering multiple operating conditions is generated through simulation.

[0095] It should be noted that representative simulation data refers to high-quality data generated through carefully designed simulation experiments, covering the design parameter space and operating condition range. This data can reflect the performance characteristics and variation patterns of fuel cell air compressors under typical operating conditions. It can cover the main variation ranges of air compressor geometric parameters (such as blade angles, volute shape, diffuser dimensions) and operating parameters (such as flow rate, pressure, and speed). It possesses sufficient breadth and accuracy to guide optimization design and the construction of data-driven models.

[0096] For example: blade inlet angle (20°, 25°, 30°), volute tongue angle (40°, 45°, 50°), diffuser width (20mm, 25mm, 30mm). Operating parameters: flow rate (20g / s, 30g / s), outlet pressure (2bar, 2.5bar). Through orthogonal experimental design, simulations were performed using 9 sets of parameter combinations, generating the following data:

[0097]

[0098] Furthermore, multi-scale wavelet denoising, simple cross-validation, and standardization methods are used to preprocess representative simulation data.

[0099] Step 1.7: Based on the acquired batch simulation data, construct a data-driven model of the fuel cell centrifugal air compressor using machine learning algorithms, complete the model construction using the training set, and verify the model performance using the test set.

[0100] The model construction process includes feature selection, data preprocessing, algorithm selection and parameter tuning, and model performance evaluation to ensure that the data-driven model is efficient and accurate, thereby achieving efficient performance prediction and optimization of fuel cell centrifugal air compressors.

[0101] Specifically, key features and target variables are extracted from representative datasets generated by batch simulations to construct a dataset. Geometric parameters include blade inlet angle, volute angle, diffuser outlet width, etc., while operating parameters include flow rate, outlet pressure, impeller speed, etc. Target variables are performance indicators such as total pressure ratio, efficiency, temperature rise, and pressure recovery coefficient. Correlation analysis (e.g., Pearson correlation coefficient or mutual information) is used to screen features highly correlated with the target variables, removing redundant features and reducing model complexity. The dataset is divided into a training set (70%-80%) and a test set (20%-30%) to ensure no overlap between the test and training data. All features are normalized or standardized to a mean of 0 and a variance of 1, removing outliers and noisy data.

[0102] Furthermore, based on the data characteristics and prediction objectives, select a suitable machine learning algorithm. For example, XGBoost: a gradient boosting-based tree model suitable for small, high-dimensional datasets with strong fitting capabilities; AdaBoost: improves model accuracy by weighted combination of multiple weak classifiers (such as decision trees); Random Forest: suitable for situations with high feature diversity and strong resistance to overfitting; Neural Networks: suitable for large datasets with complex nonlinear relationships, but training time is long. If the data volume is small and the nonlinear relationship is weak, XGBoost is preferred; if the data volume is large and highly nonlinear fitting is required, neural networks can be used.

[0103] Then train the data-driven model on the training set using the selected algorithm; set hyperparameters and tune them using grid search or Bayesian optimization to optimize model performance.

[0104] Furthermore, the model is validated using a test set, and its performance is measured using various evaluation metrics. Commonly used evaluation metrics include: mean squared error (MSE) and coefficient of determination (R²). 2 ), Mean Absolute Error (MAE). Use k-fold cross-validation (such as 5-fold or 10-fold cross-validation) to evaluate the model's generalization performance and ensure its predictive ability for unknown data. Analyze data points with large errors to identify potential model deficiencies or data quality issues; adjust feature selection, data preprocessing, or algorithm parameters to optimize the model.

[0105] After training, the model can be used to predict performance indicators under new geometric parameters and operating conditions. When applied to the design optimization of fuel cell air compressors, it can quickly assess the impact of different parameter combinations on performance. It plots the relationship curves between features and performance indicators, visually demonstrating the impact of geometric parameters (such as blade inlet angle) on total pressure ratio, efficiency, etc.; uses error distribution plots to show the reliability of the model's predictions; and generates 3D scatter plots or contour plots to describe the combined impact of multiple parameters on performance.

[0106] Step 2: Based on the requirements of the fuel cell system and multi-condition data analysis, the optimization objectives are defined as pressure ratio and isentropic efficiency, and the compression capacity and efficiency performance of the air compressor are evaluated through experimental and simulation data calculations.

[0107] The purpose of step 2 is to define the optimization objectives as pressure ratio and isentropic efficiency based on the gas supply requirements and multi-condition operation of the fuel cell system. Through experimental testing and simulation calculations, the compression capacity and efficiency performance of the air compressor are comprehensively evaluated under a fixed speed ratio, thereby providing data support and performance evaluation basis for subsequent multi-objective optimization and performance improvement.

[0108] Step 2 specifically includes:

[0109] Step 2.1: Based on the comprehensive analysis of the fuel cell system's gas supply demand, multi-condition operation, thermodynamic and aerodynamic theories, and experimental and simulation data, the optimization objectives of the fuel cell air compressor are defined as pressure ratio and isentropic efficiency.

[0110] Specifically, the pressure ratio (σ) characterizes the ratio of the air compressor's outlet pressure to its inlet pressure, and is used to measure compression capacity; the pressure ratio (σ) is determined by the following formula:

[0111] σ=p out / p in (1)

[0112] In the formula: p out p indicates the outlet pressure of the air compressor. in This indicates the inlet pressure of the air compressor.

[0113] Isentropic efficiency (η) characterizes the thermodynamic efficiency of an air compressor and reflects the energy loss during the compression process; isentropic efficiency (η) is determined by the following formula:

[0114]

[0115] In the formula: T in Indicates the inlet temperature of the air compressor; T out This indicates the air compressor outlet temperature; k represents the isentropic index.

[0116] Step 2.2: Under a fixed speed ratio, collect inlet and outlet pressure and temperature data of the air compressor at different speeds, calculate the pressure ratio and isentropic efficiency, and evaluate the compression capacity and efficiency performance of the air compressor based on the calculation results.

[0117] It should be noted that the sources of the inlet and outlet pressures, inlet and outlet temperatures, and other key performance parameters of the air compressor at various operating speeds include experimental testing or CFD simulation calculations.

[0118] In the implementation of this application, the fixed speed ratio condition is: the actual speed of the fuel cell air compressor is 12.7 times the motor speed, ensuring stable speed conditions during testing or simulation. The motor speed range is 3000, 5000, 7000, 9000, and 11000 rpm, corresponding to an actual air compressor speed of 38100–139700 rpm. In the comprehensive performance testing platform, the air compressor inlet pressure p is collected in real time. in The outlet pressure p of the air compressor out Air compressor inlet temperature T in Air compressor outlet temperature T out The operating conditions of the air compressor were simulated using multiphysics simulation software (such as ANSYS Fluent). Simulation boundary conditions (inlet pressure, outlet pressure, inlet temperature, speed, etc.) were set to simulate the fluid field and extract performance parameters such as flow rate, pressure ratio, and temperature rise. Then, the pressure ratio and isentropic efficiency were calculated according to formulas (1) and (2). Under different speed conditions (5 motor speeds), the pressure ratio and isentropic efficiency of the air compressor were calculated respectively, forming a total of 10 optimization objectives. The changes in pressure ratio and isentropic efficiency under different speed conditions were compared to analyze the stability of performance. Under high speed (11000 rpm) conditions, the pressure ratio and efficiency were evaluated to ensure that they meet the requirements of high-performance fuel cell systems. Under low speed (3000 rpm) conditions, the stability and efficiency of the air compressor operation were ensured.

[0119] Step 3: Integrate multi-objective and multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm, and K-means clustering method to establish the MMPS algorithm. Use the MMPS algorithm to perform high-dimensional multi-objective optimization on impeller, volute, diffuser and related structural parameters to improve their performance under multiple operating conditions.

[0120] Step 3 aims to develop a high-efficiency multi-objective multi-population optimization algorithm (MMPS algorithm). By integrating a multi-objective multi-population optimization framework, database sharing technology, database update strategy, genetic algorithm, and K-means clustering, it performs high-dimensional multi-objective optimization on key components (impeller, volute, diffuser) of the fuel cell air compressor, comprehensively improving the overall performance of the air compressor under various operating conditions. By optimizing multiple structural parameters, it addresses the trade-offs in performance indicators such as pressure ratio and isentropic efficiency of the air compressor, achieving an effective solution to complex multi-objective optimization problems, ultimately improving the operating efficiency and reliability of the fuel cell system.

[0121] Step 3 specifically includes:

[0122] Step 3.1: Construct a multi-objective, multi-population optimization framework. By dividing the optimization objective into 10 subpopulations for parallel optimization, and combining crossover and mutation operators based on genetic algorithms to generate and improve solutions, the diversity of solution sets and global search capabilities are enhanced, thereby achieving efficient solution set exploration and optimization in complex multi-objective optimization problems.

[0123] Multi-objective, multi-swarm optimization methods are a class of swarm intelligence algorithms designed for multi-objective optimization problems. They aim to improve the diversity of solution sets and global search capabilities by employing parallel search by multiple populations. The core of this method lies in dividing the population into multiple subpopulations, each working independently or collaboratively to explore different objectives, search regions, or optimization strategies, thereby more effectively finding Pareto optimal solutions in complex multi-objective problems. These populations can share and transfer solutions through information exchange mechanisms, enabling the algorithm to balance global exploration with local exploitation, avoid getting trapped in local optima, and maintain population diversity. The design of multi-swarm methods is often accompanied by different strategy choices, such as differentiated population splitting, mutation, and crossover operations, and adaptive parameter adjustment, making them adaptable to complex, high-dimensional, multi-objective optimization scenarios.

[0124] In a multi-objective, multi-population optimization framework, 10 populations are used to optimize 10 objectives. The performance of the solution in each population is evaluated by its corresponding optimization objective, rather than by Pareto optimality rules, because Pareto optimality is difficult to achieve in multi-objective, multi-population optimization and may slow down the evolutionary process. Genetic algorithm-based operators (i.e., crossover and mutation operators) are used as optimizers in each population to generate offspring.

[0125] Step 3.2: The crossover operator uses a priority crossover operation, which achieves gene recombination by sorting individuals with high fitness values ​​and using a double-optimal crossover strategy, thereby improving population fitness and solution set diversity; the mutation operator uses an insertion mutation operation, which enhances population diversity and global search capability by inserting and optimizing genes for individuals with low fitness values, ensuring the stability of optimization results and performance improvement.

[0126] Prioritized crossover (POX) is a selection and gene recombination strategy for specific individuals in a population during optimization. It aims to improve the overall fitness and convergence of the population while ensuring the diversity of the solution set. Therefore, the crossover operator chosen is prioritized crossover. The core of prioritized crossover is to prioritize individuals with high fitness values ​​for crossover, maximizing the preservation of excellent gene traits and promoting the population's evolution towards a high-quality solution set. The specific steps are: ① Individual priority ranking: Within the population, individuals are ranked according to their fitness values ​​(evaluation criteria may include a comprehensive score of multiple objectives such as compression efficiency, energy consumption, and stability). Individuals with higher rankings are prioritized for crossover to fully utilize the superior genes of high-fitness individuals. ② Double-fitness crossover strategy: Prioritized crossover employs a "double-fitness crossover strategy," randomly selecting two groups of high-fitness individuals from the prioritized individuals as parent individuals for crossover. This strategy is based on probabilistic selection and local search enhancement mechanisms to improve the diversity and potential fitness of newly generated individuals. ③ Crossover method selection: A hybrid gene crossover mechanism is used, employing a multi-point crossover approach, flexibly switching according to specific objectives and population status. In the crossover operation, emphasis is placed on preserving key gene segments from the parent individuals, while introducing appropriate gene perturbations to enhance population diversity. ④ Adaptive adjustment: New individuals generated through crossover undergo initial screening using a rapid adaptive assessment mechanism, retaining only those meeting multi-objective optimization requirements for subsequent iterations. Individuals that do not meet performance requirements are relabeled and entered into the next generation's mutation operation.

[0127] The mutation operator employs insertion mutation (IM), designed as a key means to enhance population diversity, break local convergence, and improve global search capabilities. Its purpose is to introduce new search directions and optimize the performance of centrifugal air compressors under multi-objective and multi-condition working conditions through a reasonable mutation strategy. The specific steps are as follows: ① Individual selection and location: Individuals with lower fitness are selected from the current population for mutation. By ranking the fitness values ​​of individuals within the population, those with lower rankings are prioritized as mutation targets, aiming to introduce new gene characteristics through mutation and improve the overall fitness of these individuals. ② Selection of insertion position: For the individual to be mutated, one or more gene loci are randomly selected as insertion positions. To enhance the flexibility of multi-objective optimization, a weighted random strategy is used for the selection of insertion positions to achieve a balance between global and local factors, ensuring good diversity and stability of the mutation results. ③ Generation of mutated genes: Gene fragments are extracted from superior individuals in other populations, and information sharing and recombination are achieved through insertion mutation, enhancing optimization efficiency. ④ Insertion strategy and control mechanism: The core of the insertion mutation operation lies in how to select and insert mutated genes. Specifically, this method employs flexible insertion strategies, including single-point insertion, segmented insertion, and multi-point insertion, to improve mutation effectiveness. By controlling mutation intensity and insertion frequency, it ensures population diversity and global search capability, avoiding solution set chaos and decreased convergence caused by excessive mutation. ⑤ Adaptability Evaluation and Update: After the mutation operation is completed, the newly generated individuals undergo an adaptation evaluation. A multi-objective comprehensive evaluation index is used to ensure that the performance of mutated individuals improves under different operating conditions and objectives.

[0128] Step 3.3: By constructing a database sharing technology, excellent solutions are stored and shared in database A within a multi-objective, multi-population optimization framework. This assists in information exchange and priority crossover operations among populations, enabling adaptive search and population co-evolution.

[0129] In a multi-objective, multi-population optimization framework, a repository denoted by A is used to store excellent solutions discovered during evolution. A is initialized with all randomly generated solutions from 10 populations, without repetition. A repository-sharing technique is then developed to exchange information between populations and assist crossover operators, thereby helping to achieve efficient population co-evolution. The repository-sharing technique aims to assist the crossover operator, specifically the preferred crossover operation in Algorithm 1. Specifically, for the k-th population (k∈[1,10]), each solution in population k is selected as p1, while a solution in A is randomly selected as p2 (lines 4-6). In each crossover operation, a random value r in the range [0,1] is generated. If r is less than or equal to the crossover probability Prc, a preferred crossover operation is performed on p1 and p2, generating offspring c1 and c2. Among p1, c1, and c2, the one performing best among the k objectives is retained to generate a new population (lines 8-11). Otherwise, the better performer of p1 and p2 will be retained (lines 12-14). Therefore, the adaptive search technique in the multi-objective multi-population optimization framework can not only retain the superior characteristics of its corresponding optimization objective, but also effectively utilize the information of the other nine objectives.

[0130] A specific embodiment includes the following process:

[0131]

[0132]

[0133] Step 3.4: A database update strategy is proposed. By filtering, perturbing, and performing diversity preservation operations based on K-means clustering on the solution set of the newly generated population, the database is updated to improve the convergence and quality of elite solutions, thereby enhancing the co-evolutionary ability and optimization efficiency of the population in a multi-objective, multi-population optimization framework.

[0134] In a multi-objective, multi-population optimization framework, a repository update strategy is proposed to update A based on the newly generated population, thereby generating better-performing solutions. The pseudocode for the repository update strategy is given in Algorithm 2. As the number of non-dominated solutions increases during evolution, a threshold is defined for the repository size. Therefore, in the multi-objective, multi-population optimization framework, the maximum repository size is set to NA. For each generation, all solutions from the current 10 populations are added to an empty set S (lines 2-4), and all elite solutions in A are also added to S (line 5). Then, each elite solution in A is perturbed and added to S (lines 6-10). The perturbation operation on A is implemented based on the insertion mutation operation (mutation operator). Based on local perturbation, the repository update strategy primarily improves the convergence of elite solutions, thereby enhancing the exploration capability of the multi-objective, multi-population optimization framework. Since solutions collected from the 10 populations and the repository may contain duplicates, the duplication elimination operation not only saves storage space but also helps retain more diverse solutions in the repository. If the size of S is less than or equal to a predefined size NA, all solutions in S are copied to A; otherwise, a K-means clustering-based ranking and diversity preservation method is performed on S, selecting NA elite solutions for A (lines 12-17). Archive update strategies can improve the quality of solutions in the archive, thereby helping archive sharing technologies better guide the co-evolutionary process among populations.

[0135] A specific embodiment includes the following process:

[0136]

[0137]

[0138] Step 3.5: By integrating multi-objective multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm and K-means clustering method, the MMPS algorithm is established. The population is randomly initialized and updated through priority crossover and insertion mutation operations. The solution set is optimized by combining the archive update strategy, and finally the elite solution in the archive is output as the optimization result.

[0139] The MMPS algorithm flowchart is shown in the attached manual. Figure 5 As shown. First, 10 populations of equal size are randomly initialized using an operation-based encoding method. Then, a database A is initialized with all solutions from the 10 populations. During iteration, the 10 populations each focus on optimizing 10 objectives. Database sharing techniques based on Priority Crossover (POX) and Insertion-Mutation (IM) are performed to update each population, and then A is updated by a database update strategy. The evolutionary process is repeated until a termination condition is met. The elite solutions in A are the final output of the MMPS algorithm.

[0140] One specific embodiment includes:

[0141] The optimization objective is to optimize the multi-objective performance of a fuel cell centrifugal air compressor. The objectives include 10 performance metrics, such as maximizing efficiency, minimizing compression power, minimizing noise, and minimizing vibration. The constraint is to meet the design parameter range under different flow rates, speeds, and pressures. An optimization framework based on the Multi-Objective Multi-Swarm Optimization (MMPS) algorithm is applied to find a highly efficient Pareto optimal solution set by optimizing the 10 objectives in parallel.

[0142] Step 3.1: Randomly generate 10 populations, each containing 50 individuals (solutions). The population's genetic encoding method is as follows: genetic information includes control variables such as air compressor flow rate (g / s), rotational speed (rpm), outlet pressure (bar), and cooling parameters (L / min and temperature °C); each individual represents a design scheme, initially randomly distributed within the parameter space. Each population optimizes for a specific objective, for example, population 1 optimizes for efficiency, population 2 for compression power, and population 3 for noise, etc. Population optimization is performed in parallel, with each population using crossover and mutation operators to generate new solutions. The initial solution set is stored in repository A for subsequent sharing and improvement.

[0143] Step 3.2: Prioritized Crossover Operation: In Population 1 (Efficiency Optimization), sort the 50 individuals from highest to lowest fitness value, and select the top 10 individuals with high fitness values ​​as priority crossover parent candidates. Randomly select two groups of individuals from the top 10 parents and generate offspring through multi-point crossover. Assume the parent genes are: Parent 1: [flow rate = 30g / s, rotation speed = 40000rpm, pressure = 2bar, cooling water flow rate = 3L / min, cooling water temperature = 25℃], Parent 2: [flow rate = 40g / s, rotation speed = 45000rpm, pressure = 2.5bar, cooling water flow rate = 5L / min, cooling water temperature = 30℃]; After multiple crossovers, the offspring are generated as follows: Offspring 1: [flow rate = 30g / s, rotation speed = 45000rpm, pressure = 2bar, cooling water flow rate = 5L / min, cooling water temperature = 25℃], Offspring 2: [flow rate = 40g / s, rotation speed = 40000rpm, pressure = 2.5bar, cooling water flow rate = 3L / min, cooling water temperature = 30℃]. A multi-point crossover mechanism is adopted, allowing alternating combinations of parental gene fragments. For example, key genes (such as cooling water temperature = 25℃) can be retained from the parent, and moderate perturbations (such as changes in cooling water flow rate) can be introduced. After preliminary evaluation, the new individuals generated by the crossover will retain only the solutions that meet the efficiency optimization objective; individuals that do not meet the conditions will enter the next generation of mutation operations.

[0144] Mutation Insertion: In population 2 (optimization objective: compression power), individuals are sorted from lowest to highest fitness value (compression power value). The bottom 10 individuals are selected as mutation targets to introduce new gene traits through mutation, thereby improving the overall fitness of these individuals. For example: Original individual 1: [flow rate = 50 g / s, rotation speed = 40000 rpm, pressure = 3 bar, cooling water flow rate = 3 L / min, cooling water temperature = 35℃], Original individual 2: [flow rate = 45 g / s, rotation speed = 45000 rpm, pressure = 2.8 bar, cooling water flow rate = 4 L / min, cooling water temperature = 32℃]. Using a weighted random strategy, cooling water temperature and cooling water flow rate genes are assigned higher weights (because these parameters significantly affect compression power), while other genes are assigned lower weights to achieve a balance between global and local optimization. For example: Original individual 1: cooling water flow rate (3 L / min) and cooling water temperature (35℃) are selected as mutation sites. Original individual 2: Flow rate (45 g / s) and rotation speed (45000 rpm) were selected as mutation sites. Gene fragments of superior individuals were extracted from other populations (e.g., population 1 with optimized efficiency) as mutation sources: for example, the superior genes extracted from population 1 were: cooling water flow rate = 4 L / min, cooling water temperature = 25℃, rotation speed = 40000 rpm. After mutation, the mutation results of original individual 1 and original individual 2 were: Mutant individual 1: [flow rate = 50 g / s, rotation speed = 40000 rpm, pressure = 3 bar, cooling water flow rate = 4 L / min, cooling water temperature = 25℃], Mutant individual 2: [flow rate = 45 g / s, rotation speed = 40000 rpm, pressure = 2.8 bar, cooling water flow rate = 4 L / min, cooling water temperature = 25℃]. A mutation strategy combining single-point and multi-point insertions was employed to control mutation intensity and frequency, ensuring optimal results: Single-point insertion: Mutating the cooling water flow rate (e.g., changing it from 3 L / min to 4 L / min) to improve cooling performance. Multi-point insertion: Simultaneously mutating both cooling water flow rate and cooling water temperature to ensure significant optimization of the impact on compression power. Control mechanism: Mutation intensity was adjusted by predefined weights to avoid excessive global search leading to solution set chaos. For example, cooling water temperature variation was only allowed within ±5℃. After mutation, multi-objective comprehensive evaluation indicators (such as compression power, efficiency, and stability) were used to evaluate the mutated individuals, ensuring performance improvement under multiple objectives. Evaluation results: Mutated individual 1 showed a 10% decrease in compression power and a 5% increase in efficiency, passing the evaluation; Mutated individual 2 showed no significant change in compression power and was marked as a low-fitness individual, entering the next generation of mutations.

[0145] Step 3.3: Archive A initially stores 100 solutions from all populations for information sharing. For example, in population 3 (noise optimization), each time, a solution from A is preferentially selected as the second parent in the crossover process. The current population solution p1: [flow rate = 35 g / s, rotation speed = 42000 rpm, pressure = 2.2 bar, cooling water flow rate = 4 L / min, cooling water temperature = 27℃], selects p2 from A: [flow rate = 30 g / s, rotation speed = 40000 rpm, pressure = 2 bar, cooling water flow rate = 3 L / min, cooling water temperature = 25℃], performs preferential crossover, generates offspring, and retains the optimal solution.

[0146] Step 3.4: Collect all new solutions from the current population and elite solutions from A, and store them together in set S. Through deduplication and fast non-dominated sorting, select the solution set that meets the requirements of multi-objective optimization. For the solution set with more repetitions in S, use K-means clustering to group them, select the solution closest to the center point in each group, and update the elite solutions in A.

[0147] Step 3.5: Perform priority crossover, insertion mutation, and database update in each generation. Optimize in parallel across 10 populations, repeating the iteration until convergence (e.g., the change in elite solutions is less than a threshold or the maximum number of generations is reached). Finally, the elite solutions in database A are output as the optimization results, for example: [flow rate = 40 g / s, rotational speed = 40000 rpm, pressure = 2 bar, cooling water flow rate = 3 L / min, cooling water temperature = 25℃].

[0148] Through the above steps, the multi-objective performance of the air compressor was successfully optimized, with significant improvements in efficiency, compression power, noise, and vibration. At the same time, a set of Pareto optimal solutions with engineering application value was generated.

[0149] Another objective of this invention is to provide a high-dimensional, multi-objective, multi-condition optimization system for a fuel cell centrifugal air compressor, comprising:

[0150] The performance analysis and modeling module is used to build a performance analysis and optimization environment for fuel cell air compressors. By building a comprehensive performance testing platform and establishing a multi-physics coupled CFD simulation model, the consistency between simulation results and test data is verified. Multi-condition data is generated based on orthogonal experimental design. At the same time, machine learning algorithms are combined to build and verify data-driven models to improve simulation and optimization efficiency.

[0151] The optimization target definition module is used to define optimization targets based on fuel cell system requirements and multi-condition data analysis, including pressure ratio and isentropic efficiency, and to evaluate the air compressor's compression capacity and efficiency performance through experimental and simulation data calculations.

[0152] The high-dimensional multi-objective optimization module is used to integrate multi-objective multi-population optimization methods, archive sharing technology, archive update strategy, genetic algorithm and K-means clustering method to construct the MMPS algorithm. Based on this algorithm, the structural parameters of the impeller, volute and diffuser are optimized in a high-dimensional multi-objective manner to improve the performance of the fuel cell centrifugal air compressor under multiple operating conditions.

[0153] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific structures and characteristics of the solutions is not described in detail here. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the present invention is defined by the appended claims rather than the foregoing description. Therefore, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A high-dimensional multi-objective multi-working condition optimization method for a fuel cell centrifugal air compressor, characterized in that, The method comprises: Step 1: Constructing a fuel cell air compressor performance analysis and optimization system, determining the optimization direction of the geometric model by building a comprehensive performance test platform, establishing a multi-physical field coupled CFD simulation model, verifying the consistency of the simulation results and the test data, generating multi-working condition data based on orthogonal experimental design, and combining machine learning algorithm to construct and verify the data-driven model to improve the simulation and optimization efficiency; Step 2: Based on the fuel cell system requirements and multi-working condition data analysis, the optimization target is defined as the pressure ratio and isentropic efficiency, and the compression capacity and efficiency performance of the air compressor are evaluated through experimental and simulation data calculation; Step 3: A multi-objective multi-population optimization algorithm is established by combining multi-objective multi-population optimization method, archive sharing technology, archive updating strategy, genetic algorithm and K-means clustering method, and the multi-objective multi-population optimization algorithm is used to optimize the impeller, volute and diffuser and related structure parameters to improve their performance in multi-working condition; Step 3 includes: Step 3.1: Constructing a multi-objective multi-population optimization framework, dividing the optimization target into 10 sub-populations for parallel optimization, combining the crossover operator and mutation operator based on genetic algorithm to generate and improve solutions, and improving the diversity and global search ability of the solution set to realize efficient solution exploration and optimization in complex multi-objective optimization problems; Step 3.2: The crossover operator adopts priority crossover operation, and the gene recombination is realized by sorting and double priority crossover strategy for high fitness individuals to improve the population fitness and solution set diversity; the mutation operator adopts insertion mutation operation, and the population diversity and global search ability are enhanced by inserting and optimizing the genes of low fitness individuals to ensure the stability and performance improvement of the optimization results; Step 3.3: By constructing an archive sharing technology, the archive A is used to store and share excellent solutions in the multi-objective multi-population optimization framework to assist the information exchange and priority crossover operation between populations, realize adaptive search and population cooperative evolution; Step 3.4: An archive updating strategy is proposed, which screens, disturbs and saves the diversity of the solution set of the newly generated population based on K-means clustering to update the archive and improve the convergence and quality of the elite solutions, thereby enhancing the cooperative evolution ability and optimization efficiency of the population in the multi-objective multi-population optimization framework; Step 3.5: By combining multi-objective multi-population optimization method, archive sharing technology, archive updating strategy, genetic algorithm and K-means clustering method, a multi-objective multi-population optimization algorithm is established to randomly initialize the population and update the population through priority crossover operation and insertion mutation operation, and the archive updating strategy is used to optimize the solution set, and finally the elite solutions in the archive are output as the optimization results.

2. The high dimensional multi-objective multi-condition optimization method of a fuel cell centrifugal air compressor according to claim 1, characterized in that, Step 1 includes: Step 1.1: Build a fuel cell air compressor comprehensive performance test platform to collect performance parameters of the fuel cell air compressor under different operating conditions through the platform; Step 1.2: Create a geometric model of the fuel cell air compressor, perform multi-physical field simulation analysis on the geometric model based on fluid dynamics model, thermodynamics model and turbulence model, set boundary conditions for each model, run multi-physical field simulation to cover multiple operating conditions, and verify the convergence and accuracy of the geometric model; Step 1.3: Based on the fluid dynamics model, thermodynamics model and turbulence model, set the boundary conditions for each model, and establish a multi-physical field coupling CFD simulation model for the fuel cell air compressor; Step 1.4: Compare the simulation results with the performance parameters collected by the test platform one by one, and verify whether the error of each performance index is within the set acceptance range; Step 1.5: Based on the comparison and analysis of simulation results and test data, determine the optimization direction of impeller, volute and diffuser in the geometric model of fuel cell air compressor; Step 1.6: Based on the geometric model of fuel cell air compressor, build a CFD integrated simulation framework for fuel cell air compressor, perform batch simulation on different structure parameter combinations based on orthogonal test design, generate representative simulation data covering multiple operating conditions, and preprocess the simulation data; Step 1.7: Based on the batch simulation data obtained, use machine learning algorithm to build data-driven model of fuel cell centrifugal air compressor, use training set to complete model construction, and use test set to verify model performance.

3. The high dimensional multi-objective multi-condition optimization method of a fuel cell centrifugal air compressor according to claim 1, characterized in that, Step 2 includes: Step 2.1: Based on the comprehensive analysis of fuel cell system gas supply demand, multi-condition operation condition, thermodynamics and aerodynamics theory, and experimental and simulation data, define the optimization target of fuel cell air compressor as pressure ratio and isentropic efficiency; Step 2.2: Under the condition of fixed speed increasing ratio, collect the inlet and outlet pressure and temperature data of air compressor under different rotating speed conditions, calculate the pressure ratio and isentropic efficiency, and evaluate the compression capacity and efficiency performance of air compressor according to the calculation results.

4. The high dimensional multi-objective multi-condition optimization method of a fuel cell centrifugal air compressor according to claim 2, characterized in that, The typical working conditions that can be simulated by the fuel cell air compressor comprehensive performance test platform include different flow rate conditions, different rotating speed conditions, different pressure conditions, different cooling conditions, start-up and steady-state conditions and comprehensive conditions.

5. The high dimensional multi-objective multi-condition optimization method of a fuel cell centrifugal air compressor according to claim 2, characterized in that, In step 1.4, the simulation results are compared with the experimental data of step 1.1 one by one, and it is verified whether the error of each performance index is controlled within 5%.

6. The high dimensional multi-objective multi-condition optimization method of a fuel cell centrifugal air compressor according to claim 2, characterized in that, The optimization direction of impeller includes increasing blade inlet angle to improve inflow performance and reducing outlet angle to improve airflow uniformity; the optimization direction of volute includes optimizing volute tongue angle to reduce turbulence and adjusting volute cross-section ellipticity to reduce flow separation; the optimization direction of diffuser includes increasing outlet radius to improve pressure recovery and adjusting width to improve outlet flow field uniformity.

7. A system for high dimensional multi-objective multi-condition optimization of a fuel cell centrifugal air compressor as claimed in any one of claims 1 to 6, characterized in that, It includes: Performance analysis and modeling module, used to build fuel cell air compressor performance analysis and optimization environment, by building comprehensive performance test platform, establishing multi-physical field coupling CFD simulation model, verifying the consistency of simulation results and test data, and generating multi-condition data based on orthogonal test design, and combining machine learning algorithm to build and verify data-driven model to improve simulation and optimization efficiency; An optimization target defining module is configured to define optimization targets including pressure ratio and isentropic efficiency based on fuel cell system requirements and multi-working condition data analysis, and to evaluate the compression capacity and efficiency performance of the air compressor through experimental and simulation data calculation; A high-dimensional multi-objective optimization module is configured to fuse a multi-objective multi-population optimization method, an archive sharing technique, an archive updating strategy, a genetic algorithm and a K-means clustering method, to construct a multi-objective multi-population optimization algorithm, and to perform high-dimensional multi-objective optimization on structure parameters of the impeller, the volute and the diffuser based on the algorithm, so as to improve the performance of the fuel cell centrifugal air compressor under multi-working conditions.

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