Kriging Surrogate-based Optimization for Shape Design of Thin Electric Propeller

Nantiwat Pholdee; Sujin Bureerat; Weerapon Nuantong; Boonrit Pongsatitpat

doi:10.5614/j.eng.technol.sci.2024.56.3.8

Kriging Surrogate-based Optimization for Shape Design of Thin Electric Propeller

Published: 2024-01-01 | DOI: 10.5614/j.eng.technol.sci.2024.56.3.8 | Vol 56, Issue 3 (2024) | Cited by: 6

Authors

Nantiwat Pholdee

Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailand

ORCID: 0000-0002-4370-5241 · OpenAlex: A5059825118

Sujin Bureerat

Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailand

ORCID: 0000-0002-6332-1202 · OpenAlex: A5014397651

Weerapon Nuantong

Department of Mechatronics Engineering, Faculty of Engineering, Rajamangala University of Technology Isan Khon Kaen Campus, Khon Kaen 40000, Thailand

ORCID: 0000-0003-3663-3136 · OpenAlex: A5032631210

Boonrit Pongsatitpat

Department of Mechatronics Engineering, Faculty of Engineering, Rajamangala University of Technology Isan Khon Kaen Campus, Khon Kaen 40000, Thailand

OpenAlex: A5100019269

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Abstract

This paper outlines an optimized propeller design for an unmanned aerial vehicle (UAV) employing a Kriging surrogate model-based optimization approach. The primary objective was to maximize propeller efficiency while adhering to the thrust-to-torque ratio constraint at a rotational speed of 6,500 rpm. The design variables encompassed the twist angle and the ratio of blade thickness to chord length across the twenty-section airfoil of the propeller. A comprehensive analysis was conducted using computational fluid dynamics to assess the aerodynamics of the propeller. The Kriging surrogate model serves as a valuable tool for approximating objective and constraint functions. The optimal Latin hypercube sampling technique was employed for design of experiment, generating a set of sampling points to construct a Kriging surrogate model. To tackle the optimization problem, seven metaheuristic optimizers were employed, including a genetic algorithm, particle swarm optimization, population-based incremental learning, differential evolution, teaching-learning based optimization, ant colony optimization, and an evolution strategy with covariance matrix adaptation. The obtained results revealed that Kriging surrogate model-based differential evolution optimization stood out as the most efficient method for addressing the propeller optimization problem. The propeller efficiency experienced improvement of approximately 0.6% compared to the maximum result obtained from the sampling points.

Keywords

meta model; optimal design; optimization; propeller; surrogate model

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Research Intelligence

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Citations

1.41

FWCIfield-weighted

83th

Percentilevs same year + field

Article

Work type

GOLD

Open Access

Topics

Advanced Multi-Objective Optimization Algorithms Primary

1.00

Computational Theory and Mathematics › Computer Science › Physical Sciences

Advanced Aircraft Design and Technologies

0.99

Metaheuristic Optimization Algorithms Research

0.99

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2024

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Year	Citations
2026	3
2025	1
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Core Domains

Kriging 0.81

level 2

Surrogate model 0.80

level 2

Mathematical optimization 0.52

level 1

Secondary Topics

Propeller 0.52 Differential evolution 0.51 Particle swarm optimization 0.48 Metaheuristic 0.48 Computer science 0.41 Engineering 0.33 Mathematics 0.32

Institution Network

Khon Kaen University TH
Nantiwat Pholdee · Sujin Bureerat
Rajamangala University of Technology Isan TH
Weerapon Nuantong · Boonrit Pongsatitpat

References

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Naser, M.Z. & Kodur, V.K., Concepts and Applications for Integrating Unmanned Aerial Vehicles (UAV’s) in Disaster Management, Adv. Comput. Des., 5(1), pp. 91-109, Jan. 2020.
Sreelakshmi, K. & Jagadeeswar, K.K., Aerodynamic Analysis Over Unmanned Aerial Vehicle (UAV) using CFD, IOP Conf. Ser. Mater. Sci. Eng., pp. 1–10, 2018.
Zhang, J., Campbell, J.F., Sweeney II, D.C. & Hupman, A.C., Energy Consumption Models for Delivery Drones: A Comparison and Assessment, Transp. Res. Part D, 90, pp. 1-23, Jan. 2021.
Chodnicki, M., Siemiatkowska, B., Stecz, W. & Stępień, S., Energy Efficient UAV Flight Control Method in an Environment with Obstacles and Gusts of Wind, Energies, 15(10), pp. 1-31, 2022.
Ucgun, H., Yuzgec, U. & Bayilmis, C., A Review on Applications of Rotary-Wing Unmanned Aerial Vehicle Charging Stations, Int. J. Adv. Robot. Syst., 18(3), pp. 1-20, May 2021.
MacNeill, R., Verstraete, D. & Gong, A., Optimisation of Propellers for UAV Powertrains, The 53rd AIAA/SAE/ASEE Joint Propulsion Conference, pp. 1-25, 2017.
Hwang, M., Cha, H.R. & Jung, S.Y., Practical Endurance Estimation for Minimizing Energy Consumption of Multirotor Unmanned Aerial Vehicles, Energies, 11(9), pp. 1-11, 2018.
Dahal, C., Dura, H.B. & Poudel, L., Design and Analysis of Propeller for High-Altitude Search and Rescue Unmanned Aerial Vehicle, Int. J. Aerosp. Eng., pp. 1-13, 2021.
You, K., Zhao, X., Zhao, S.Z. & Faisal, M., Design and Optimization of a High-altitude Long Endurance UAV Propeller, IOP Conf. Ser. Mater. Sci. Eng., pp. 1-6, 2020.
Svorcan, J., Hasan, S., Baltić, M. & Simonović, A., Optimal Propeller design for future HALE UAV, Sci. Tech. Rev., 69(2), pp. 25-31, 2019.
Stevenson, R., Chandra, C., Christon, J., Wiryanto, W., Virginio, R. & Adiprawita, W., Energy Consumption Comparison of Static Pitch Propeller and Variable Pitch Propeller using Maximum Thrust Equation Approach in Small Scale Electric Unmanned Aerial Vehicle, AIP Conf. Proc., 2020.
Gürses, D., Mehta, P., Patel, V., Sait, S.M. & Yildiz, A.R., Artificial Gorilla Troops Algorithm for the Optimization of a Fine Plate Heat Exchanger, Mater. Test., 64(9), pp. 1325-1331, Sep. 2022.
Gürses, D., Mehta, P., Sait, S.M. & Yildiz, A.R., African Vultures Optimization Algorithm for Optimization of Shell and Tube Heat Exchangers, Mater. Test., 64(8), pp. 123-1241, Aug. 2022.
Sait, S.M., Mehta, P., Gürses, D. & Yildiz, A.R., Cheetah Optimization Algorithm for Optimum Design of Heat Exchangers, Mater. Test., 65(8), pp. 1230-1236, Aug. 2023.
Mehta, P., Yıldız, B.S., Sait, S.M. & Yıldız, A.R., Gradient-Based Optimizer for Economic Optimization of Engineering Problems, Mater. Test., 64(5), pp. 690-696, May 2022.
Mehregan, M., Sheykhi, M., Kharkeshi, B.A., Emamian, A., Aliakbari, K. & Rafiee, N., Performance Analysis and Optimization of Combined Heat And Power System Based on PEM Fuel Cell and β Type Stirling Engine, Energy Convers. Manag., 283, 116874, May 2023.
Mehregan, M., Sheykhi, M., Emamian, A. & Delpisheh, M., Technical and Economic Modeling and Optimization of a Ford-Philips Engine for Power Production, Appl. Therm. Eng., 213, 118761, Aug. 2022.
Mehta, P., Yildiz, B.S., Sait, S.M. & Yildiz, A.R., Hunger Games Search Algorithm for Global Optimization of Engineering Design Problems, Mater. Test., 64(4), pp. 524–532, Apr. 2022.
Cha, K. & Kinnas, S. A., Application of a Comprehensive Design Method to Counter-Rotating Propellers, SNAME 27th Offshore Symposium, 2022.
Go, Y.J., Bae, J.H., Ryi, J., Choi, J.S. & Lee, C.R., A Study on the Scale Effect According to the Reynolds Number in Propeller Flow Analysis and a Model Experiment, Aerospace, 9(10), pp. 1-19, 2022.
Hoyos, J.D., Jiménez, J.H., Echavarría, C., Alvarado, J.P. & Urrea, G., Aircraft Propeller Design through Constrained Aero-Structural Particle Swarm Optimization, Aerospace, 9(3), pp. 1-23, 2022.
Liu, Y., Chen, J., Cheng, J. & Xiang, H., Aerodynamic Optimization of Transonic Rotor Using Radial Basis Function Based Deformation and Data-Driven Differential Evolution Optimizer, Aerospace, 9(9), pp. 1-19, 2022.
Nguyen, C.C., Bui, M.D., Nguyen, N.K. & Nguyen, V.T., Optimal Design of V-Shaped Fin Heat Sink for Active Antenna Unit of 5G Base Station, J. Eng. Technol. Sci., 54(3), pp. 568-579, 2022.
Sun, B., Ge, W., Wang, Y., Tan, C. & Li, B., Research on Flow Characteristics of Electronically Controlled Injection Device Developed for High-Power Natural Gas Engines, J. Eng. Technol. Sci., 51(4), pp. 443-462, 2019.
Hantoro, R., Sarwono, S., Panjaitan, F.P., Septyaningrum, E. & Hidayati, N., Site Test Performance and Numerical Study of Vertical Axis Hydrokinetic Turbine Straight Blade Cascaded (VAHT–SBC), J. Eng. Technol. Sci., 53(1), pp. 28-43, 2021.
Abed, I.A. & Hamza, R.A., Modeling and Experimental Investigation of Laminar Ceiling Air Distribution System for Operating Room in Merjan Teaching Hospital, J. Eng. Technol. Sci., 50(6), pp. 870-883, Dec. 2018.
Pholdee, N., Kumar, S., Bureerat, S., Nuantong, W. & Dongbang, W., Sweep Blade Design for an Axial Wind Turbine using a Surrogate-‎assisted Differential Evolution Algorithm, J. Appl. Comput. Mech., 9(1), pp. 217-225, Jan. 2023.
Maulana, F.A., Amalia, E. & Moelyadi, M.A., Computational Fluid Dynamics (CFD) based Propeller Design Improvement for High Altitude Long Endurance (HALE) UAV, Int. J. Intell. Unmanned Syst., pp. 1-14, 2022.
Seeni, A., Effect of Groove Size on Aerodynamic Performance of a Low Reynolds Number UAV Propeller, INCAS Bulletin, 14(1), pp. 171-186, 2022.
Yiğit, Ş., Abuhanieh, S. & Biçer, B., An Open-Source Aerodynamic Shape Optimization Application for an Unmanned Aerial Vehicle (UAV) Propeller, J. Aeronaut. Space Technol., 15(2), pp.1-12, Jul. 2022.
Hantoro, R. & Septyaningrum, E., Novel Design of a Vertical Axis Hydrokinetic Turbine - Straight-Blade Cascaded (VAHT-SBC): Experimental and Numerical Simulation, J. Eng. Technol. Sci., 50(1), pp. 73-86, Mar. 2018.
Howell, R., Qin, N., Edwards, J. & Durrani, N., Wind Tunnel and Numerical Study of a Small Vertical Axis Wind Turbine, Renew. Energy, 35(2), pp. 412-422, Feb. 2010.
Gaur, N. & Raj, R., Aerodynamic Mitigation by Corner Modification on Square Model Under Wind Loads Employing CFD and Wind Tunnel, Ain Shams Eng. J., 13(1), pp. 1-19, 2022.
Lee, K.H., Jeon, Y.H., Kim, K.H., Lee, D.H. & Lee, K.T., Three-Dimensional Micro Propeller Design by Using Efficient Two Step Optimization, J. Fluid Sci. Technol., 2(2), pp. 334-345, 2007.
Boulkeraa, T., Ghenaiet, A. & Benini, E., Optimum Operating Parameters and Blade Setting of a High-Speed Propeller, J. Aircr., 59(2), pp. 484-501, 2022.
Park, K., Jung, J. & Jeong, S., Multi-objective Shape Optimization of Airfoils for Mars Exploration Aircraft Propellers, Int. J. Aeronaut. Space Sci., Aug. 2022.
Poggi, C., Rossetti, M., Bernardini, G., Iemma, U., Andolfi, C., Milano, C. & Gennaretti, M., Surrogate Models for Predicting Noise Emission and Aerodynamic Performance of Propellers, Aerosp. Sci. Technol., 125, pp. 1-12, 2022.
Kovačević, A., Svorcan, J., Hasan, M.S., Ivanov, T. & Jovanović, M., Optimal Propeller Blade Design, Computation, Manufacturing and Experimental Testing, Aircr. Eng. Aerosp. Technol., 93(8), pp. 1323-1332, Jan. 2021.
Pholdee, N., Bureerat, S. & Nuantong, W., Kriging Surrogate-Based Genetic Algorithm Optimization for Blade Design of a Horizontal Axis Wind Turbine, Comput. Model. Eng. Sci., 126(1), pp. 261-273, 2021.
Yamazaki, W., Experiment / Simulation Integrated Shape Optimization using Variable Fidelity Kriging Model Approach, J. Adv. Mech. Des. Syst. Manuf., 11(5), pp. 1-9, 2017.
Pholdee, N. & Bureerat, S., An Efficient Optimum Latin Hypercube Sampling Technique based on Sequencing Optimisation using Simulated Annealing, Int. J. Syst. Sci., 46(10), pp. 1780-1789, Jul. 2015.
Mosetti, G., Poloni, C. & Diviacco, B., Optimization of Wind Turbine Positioning in Large Windfarms by Means of a Genetic Algorithm, J. Wind Eng. Ind. Aerodyn., 51(1), pp. 105-116, Jan. 1994.
Pal, J. & Banerjee, S., A Combined Modal Strain Energy and Particle Swarm Optimization for Health Monitoring of Structures, J. Civ. Struct. Health Monit., 5(4), pp. 353-363, Sep. 2015.
Yang, S. & Yao, X., Population-Based Incremental Learning with Associative Memory for Dynamic Environments, IEEE Trans. Evol. Comput., 12(5), pp. 542-561, Oct. 2008.
Storn, R. & Price, K., Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, J. Glob. Optim., 11(4), pp. 341-359, Dec. 1997.
Rao, R.V., Savsani, V.J. & Vakharia, D.P., Teaching–learning-based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems, Comput.-Aided Des., 43(3), pp. 303–315, Mar. 2011.
Socha, K. & Dorigo, M., Ant Colony Optimization for Continuous Domains, Eur. J. Oper. Res., 185(3), pp. 1155–1173, Mar. 2008.
Hansen, N., Müller, S.D. & Koumoutsakos, P., Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), Evol. Comput., 11(1), pp. 1-18, Mar. 2003.
Brandt, J. B., Small-scale Propeller Performance at Low Speeds, MSc thesis, University of Illinois, Urbana-Champaign, 2005.
Schwartzenberger, A., RCbenchmark 2407 2300kv 9x4 propeller, Tyto Robotics, https://database.tytorobotics.com/tests/76n/rcbenchmark-2407-2300kv-9x4-propeller, (18 November 2019).
Alexander, I. J. F., Andras, S., & Andy, J. K., Engineering Design via Surrogate Modelling, John Wiley & Sons Ltd., 2008.
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[ref-1] Esakki, B., Raj, P.G., Yang, L.J., Khurana, E., Khute, S. & Vikram, P., Computational Fluid Dynamic Analysis of Amphibious Unmanned Aerial Vehicle, J. Appl. Comput. Mech., 8(2), pp. 475-484, Apr. 2022.

[ref-2] Naser, M.Z. & Kodur, V.K., Concepts and Applications for Integrating Unmanned Aerial Vehicles (UAV’s) in Disaster Management, Adv. Comput. Des., 5(1), pp. 91-109, Jan. 2020.

[ref-3] Sreelakshmi, K. & Jagadeeswar, K.K., Aerodynamic Analysis Over Unmanned Aerial Vehicle (UAV) using CFD, IOP Conf. Ser. Mater. Sci. Eng., pp. 1–10, 2018.

[ref-4] Zhang, J., Campbell, J.F., Sweeney II, D.C. & Hupman, A.C., Energy Consumption Models for Delivery Drones: A Comparison and Assessment, Transp. Res. Part D, 90, pp. 1-23, Jan. 2021.

[ref-5] Chodnicki, M., Siemiatkowska, B., Stecz, W. & Stępień, S., Energy Efficient UAV Flight Control Method in an Environment with Obstacles and Gusts of Wind, Energies, 15(10), pp. 1-31, 2022.

[ref-6] Ucgun, H., Yuzgec, U. & Bayilmis, C., A Review on Applications of Rotary-Wing Unmanned Aerial Vehicle Charging Stations, Int. J. Adv. Robot. Syst., 18(3), pp. 1-20, May 2021.

[ref-7] MacNeill, R., Verstraete, D. & Gong, A., Optimisation of Propellers for UAV Powertrains, The 53rd AIAA/SAE/ASEE Joint Propulsion Conference, pp. 1-25, 2017.

[ref-8] Hwang, M., Cha, H.R. & Jung, S.Y., Practical Endurance Estimation for Minimizing Energy Consumption of Multirotor Unmanned Aerial Vehicles, Energies, 11(9), pp. 1-11, 2018.

[ref-9] Dahal, C., Dura, H.B. & Poudel, L., Design and Analysis of Propeller for High-Altitude Search and Rescue Unmanned Aerial Vehicle, Int. J. Aerosp. Eng., pp. 1-13, 2021.

[ref-10] You, K., Zhao, X., Zhao, S.Z. & Faisal, M., Design and Optimization of a High-altitude Long Endurance UAV Propeller, IOP Conf. Ser. Mater. Sci. Eng., pp. 1-6, 2020.

[ref-11] Svorcan, J., Hasan, S., Baltić, M. & Simonović, A., Optimal Propeller design for future HALE UAV, Sci. Tech. Rev., 69(2), pp. 25-31, 2019.

[ref-12] Stevenson, R., Chandra, C., Christon, J., Wiryanto, W., Virginio, R. & Adiprawita, W., Energy Consumption Comparison of Static Pitch Propeller and Variable Pitch Propeller using Maximum Thrust Equation Approach in Small Scale Electric Unmanned Aerial Vehicle, AIP Conf. Proc., 2020.

[ref-13] Gürses, D., Mehta, P., Patel, V., Sait, S.M. & Yildiz, A.R., Artificial Gorilla Troops Algorithm for the Optimization of a Fine Plate Heat Exchanger, Mater. Test., 64(9), pp. 1325-1331, Sep. 2022.

[ref-14] Gürses, D., Mehta, P., Sait, S.M. & Yildiz, A.R., African Vultures Optimization Algorithm for Optimization of Shell and Tube Heat Exchangers, Mater. Test., 64(8), pp. 123-1241, Aug. 2022.

[ref-15] Sait, S.M., Mehta, P., Gürses, D. & Yildiz, A.R., Cheetah Optimization Algorithm for Optimum Design of Heat Exchangers, Mater. Test., 65(8), pp. 1230-1236, Aug. 2023.

[ref-16] Mehta, P., Yıldız, B.S., Sait, S.M. & Yıldız, A.R., Gradient-Based Optimizer for Economic Optimization of Engineering Problems, Mater. Test., 64(5), pp. 690-696, May 2022.

[ref-17] Mehregan, M., Sheykhi, M., Kharkeshi, B.A., Emamian, A., Aliakbari, K. & Rafiee, N., Performance Analysis and Optimization of Combined Heat And Power System Based on PEM Fuel Cell and β Type Stirling Engine, Energy Convers. Manag., 283, 116874, May 2023.

[ref-18] Mehregan, M., Sheykhi, M., Emamian, A. & Delpisheh, M., Technical and Economic Modeling and Optimization of a Ford-Philips Engine for Power Production, Appl. Therm. Eng., 213, 118761, Aug. 2022.

[ref-19] Mehta, P., Yildiz, B.S., Sait, S.M. & Yildiz, A.R., Hunger Games Search Algorithm for Global Optimization of Engineering Design Problems, Mater. Test., 64(4), pp. 524–532, Apr. 2022.

[ref-20] Cha, K. & Kinnas, S. A., Application of a Comprehensive Design Method to Counter-Rotating Propellers, SNAME 27th Offshore Symposium, 2022.

[ref-21] Go, Y.J., Bae, J.H., Ryi, J., Choi, J.S. & Lee, C.R., A Study on the Scale Effect According to the Reynolds Number in Propeller Flow Analysis and a Model Experiment, Aerospace, 9(10), pp. 1-19, 2022.

[ref-22] Hoyos, J.D., Jiménez, J.H., Echavarría, C., Alvarado, J.P. & Urrea, G., Aircraft Propeller Design through Constrained Aero-Structural Particle Swarm Optimization, Aerospace, 9(3), pp. 1-23, 2022.

[ref-23] Liu, Y., Chen, J., Cheng, J. & Xiang, H., Aerodynamic Optimization of Transonic Rotor Using Radial Basis Function Based Deformation and Data-Driven Differential Evolution Optimizer, Aerospace, 9(9), pp. 1-19, 2022.

[ref-24] Nguyen, C.C., Bui, M.D., Nguyen, N.K. & Nguyen, V.T., Optimal Design of V-Shaped Fin Heat Sink for Active Antenna Unit of 5G Base Station, J. Eng. Technol. Sci., 54(3), pp. 568-579, 2022.

[ref-25] Sun, B., Ge, W., Wang, Y., Tan, C. & Li, B., Research on Flow Characteristics of Electronically Controlled Injection Device Developed for High-Power Natural Gas Engines, J. Eng. Technol. Sci., 51(4), pp. 443-462, 2019.

[ref-26] Hantoro, R., Sarwono, S., Panjaitan, F.P., Septyaningrum, E. & Hidayati, N., Site Test Performance and Numerical Study of Vertical Axis Hydrokinetic Turbine Straight Blade Cascaded (VAHT–SBC), J. Eng. Technol. Sci., 53(1), pp. 28-43, 2021.

[ref-27] Abed, I.A. & Hamza, R.A., Modeling and Experimental Investigation of Laminar Ceiling Air Distribution System for Operating Room in Merjan Teaching Hospital, J. Eng. Technol. Sci., 50(6), pp. 870-883, Dec. 2018.

[ref-28] Pholdee, N., Kumar, S., Bureerat, S., Nuantong, W. & Dongbang, W., Sweep Blade Design for an Axial Wind Turbine using a Surrogate-‎assisted Differential Evolution Algorithm, J. Appl. Comput. Mech., 9(1), pp. 217-225, Jan. 2023.

[ref-29] Maulana, F.A., Amalia, E. & Moelyadi, M.A., Computational Fluid Dynamics (CFD) based Propeller Design Improvement for High Altitude Long Endurance (HALE) UAV, Int. J. Intell. Unmanned Syst., pp. 1-14, 2022.

[ref-30] Seeni, A., Effect of Groove Size on Aerodynamic Performance of a Low Reynolds Number UAV Propeller, INCAS Bulletin, 14(1), pp. 171-186, 2022.

[ref-31] Yiğit, Ş., Abuhanieh, S. & Biçer, B., An Open-Source Aerodynamic Shape Optimization Application for an Unmanned Aerial Vehicle (UAV) Propeller, J. Aeronaut. Space Technol., 15(2), pp.1-12, Jul. 2022.

[ref-32] Hantoro, R. & Septyaningrum, E., Novel Design of a Vertical Axis Hydrokinetic Turbine - Straight-Blade Cascaded (VAHT-SBC): Experimental and Numerical Simulation, J. Eng. Technol. Sci., 50(1), pp. 73-86, Mar. 2018.

[ref-33] Howell, R., Qin, N., Edwards, J. & Durrani, N., Wind Tunnel and Numerical Study of a Small Vertical Axis Wind Turbine, Renew. Energy, 35(2), pp. 412-422, Feb. 2010.

[ref-34] Gaur, N. & Raj, R., Aerodynamic Mitigation by Corner Modification on Square Model Under Wind Loads Employing CFD and Wind Tunnel, Ain Shams Eng. J., 13(1), pp. 1-19, 2022.

[ref-35] Lee, K.H., Jeon, Y.H., Kim, K.H., Lee, D.H. & Lee, K.T., Three-Dimensional Micro Propeller Design by Using Efficient Two Step Optimization, J. Fluid Sci. Technol., 2(2), pp. 334-345, 2007.

[ref-36] Boulkeraa, T., Ghenaiet, A. & Benini, E., Optimum Operating Parameters and Blade Setting of a High-Speed Propeller, J. Aircr., 59(2), pp. 484-501, 2022.

[ref-37] Park, K., Jung, J. & Jeong, S., Multi-objective Shape Optimization of Airfoils for Mars Exploration Aircraft Propellers, Int. J. Aeronaut. Space Sci., Aug. 2022.

[ref-38] Poggi, C., Rossetti, M., Bernardini, G., Iemma, U., Andolfi, C., Milano, C. & Gennaretti, M., Surrogate Models for Predicting Noise Emission and Aerodynamic Performance of Propellers, Aerosp. Sci. Technol., 125, pp. 1-12, 2022.

[ref-39] Kovačević, A., Svorcan, J., Hasan, M.S., Ivanov, T. & Jovanović, M., Optimal Propeller Blade Design, Computation, Manufacturing and Experimental Testing, Aircr. Eng. Aerosp. Technol., 93(8), pp. 1323-1332, Jan. 2021.

[ref-40] Pholdee, N., Bureerat, S. & Nuantong, W., Kriging Surrogate-Based Genetic Algorithm Optimization for Blade Design of a Horizontal Axis Wind Turbine, Comput. Model. Eng. Sci., 126(1), pp. 261-273, 2021.

[ref-41] Yamazaki, W., Experiment / Simulation Integrated Shape Optimization using Variable Fidelity Kriging Model Approach, J. Adv. Mech. Des. Syst. Manuf., 11(5), pp. 1-9, 2017.

[ref-42] Pholdee, N. & Bureerat, S., An Efficient Optimum Latin Hypercube Sampling Technique based on Sequencing Optimisation using Simulated Annealing, Int. J. Syst. Sci., 46(10), pp. 1780-1789, Jul. 2015.

[ref-43] Mosetti, G., Poloni, C. & Diviacco, B., Optimization of Wind Turbine Positioning in Large Windfarms by Means of a Genetic Algorithm, J. Wind Eng. Ind. Aerodyn., 51(1), pp. 105-116, Jan. 1994.

[ref-44] Pal, J. & Banerjee, S., A Combined Modal Strain Energy and Particle Swarm Optimization for Health Monitoring of Structures, J. Civ. Struct. Health Monit., 5(4), pp. 353-363, Sep. 2015.

[ref-45] Yang, S. & Yao, X., Population-Based Incremental Learning with Associative Memory for Dynamic Environments, IEEE Trans. Evol. Comput., 12(5), pp. 542-561, Oct. 2008.

[ref-46] Storn, R. & Price, K., Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, J. Glob. Optim., 11(4), pp. 341-359, Dec. 1997.

[ref-47] Rao, R.V., Savsani, V.J. & Vakharia, D.P., Teaching–learning-based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems, Comput.-Aided Des., 43(3), pp. 303–315, Mar. 2011.

[ref-48] Socha, K. & Dorigo, M., Ant Colony Optimization for Continuous Domains, Eur. J. Oper. Res., 185(3), pp. 1155–1173, Mar. 2008.

[ref-49] Hansen, N., Müller, S.D. & Koumoutsakos, P., Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), Evol. Comput., 11(1), pp. 1-18, Mar. 2003.

[ref-50] Brandt, J. B., Small-scale Propeller Performance at Low Speeds, MSc thesis, University of Illinois, Urbana-Champaign, 2005.

[ref-51] Schwartzenberger, A., RCbenchmark 2407 2300kv 9x4 propeller, Tyto Robotics, https://database.tytorobotics.com/tests/76n/rcbenchmark-2407-2300kv-9x4-propeller, (18 November 2019).

[ref-52] Alexander, I. J. F., Andras, S., & Andy, J. K., Engineering Design via Surrogate Modelling, John Wiley & Sons Ltd., 2008.

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