Optimum design of permanent magnet synchronous generator based on MaxPro sampling and kriging surrogate model

Numerical investigations are carried out to investigate the reduction in the aerodynamic drag of a vehicle by employing a dimpled non-smooth surface. The computational scheme was validated by the experimental data reported in literature. The mechanism and the effect of the dimpled non-smooth surface on the drag reduction were revealed by analysing the flow field structure of the wake. In order to maximize the drag reduction performance of the dimpled non-smooth surface, an aerodynamic optimization method based on a Kriging surrogate model was employed to design the dimpled non-smooth surface. Four structure parameters were selected as the design variables, and a 16-level design-of-experiments method based on orthogonal arrays was used to analyse the sensitivities and the influences of the variables on the drag coefficient; a surrogate model was constructed from these. Then a multi-island genetic algorithm was employed to obtain the optimal solution for the surrogate model. Finally, the surrogate model and the simulation results showed that the optimal combination of design variables can reduce the aerodynamic drag coefficient by 5.20%.

Multi-objective optimization of crashworthiness in automobile front-end structure was performed, and finite element model (FEM) was validated by experimental results to ensure that FEM can predict the response value with sufficient accuracy. Seven design variables and four crashworthiness indicators were defined. Through orthogonal design method, 18 FEMs were established, and the response values of crashworthiness indicators were extracted. By using the variable-response specimen matrix, Kriging surrogate model (KSM) was constructed to replace FEM to reflect the function correlation between variables and responses. The accuracy of KSM was also validated. Finally, the simulated annealing optimization algorithm was implemented in KSM to seek optimal and reliable solutions. Based on the optimal results and comparison analysis, the 9096-th iteration point was the optimal solution. Although the intrusion of firewall and the mass of optimal structure increased slightly, the vehicle acceleration of the optimal solution decreased by 6.9%, which effectively reduced the risk of occupant injury.

Creep rupture life prediction for the A231 T91 alloy steel has been optimized using the Kriging surrogate model. Creep rupture data published by NIMS data sheet was used in this optimization, and isothermal creep rupture life-stress and TTP(Time-Temperature Parameter)-stress curves were optimized with Kriging model. The creep rupture data having the rupture life of less than 10,000 hours was interpolated with the K海ing surrogate model and theKriging extrapolation to the creep life of 100,000 hours was verified by comparing with experimental data. It was found that the Kriging model could fit to the data within 3% of relative error. Furthermore, the Kriging surrogate model was compared to Wilshire, Manson-Brown, Manson-Haferd, and MCX models. It can be found that the creep rupture stress extrapolated to 100,000 hours by Kriging surrogate showed a relatively good accuracy and uncertainty of 4% - 16%.

High-speed forming processes, such as electrohydraulic forming, have recently attracted attention with the development of forming technology. However, because the high-speed operation (above 100 m/s) raises safety concerns, most experiments are conducted in a closed die, which hides the forming process. Therefore, the experimental process can only be observed in a numerical simulation with accurate material properties. The conventional quasistatic material properties are improper for high-speed forming simulations with high strain rates (>102 s−1). In this study, the material properties of Al 6061-T6, which reflect the deformation behavior in the high-strain-rate region, were investigated in a numerical approach based on a reduced order model and a surrogate model in which the numerical results resemble the experimental results. The strain rate effect on the material was determined by the Cowper–Symonds constitutive equation, and two strain rate parameters were predicted. The surrogate model takes two material parameters as inputs and outputs a weighting coefficient calculated by the reduced order model. The surrogate model is based on the Kriging method to reduce the simulation cost. Next, the optimal material parameters that minimize the error between the surrogate model and the experiments are estimated by nonlinear least-squares optimization using a genetic algorithm and the constructed surrogate model. The predicted optimal parameters were verified by comparing the results of the experiment, numerical simulation, and surrogate model.

This paper discusses the use of surrogate modelling focusing on the performance comparison of different Kriging surrogate models. The different Kriging surrogate models are investigated and applied to design of superconducting magnetic energy storage system and switched reluctance motor. Finally, some comments on selection of proper surrogate model are given for optimal design of electromagnetic problems.

An improved lump mass stick model of a nuclear power plant based on the Kriging surrogate model

The purpose of the current work is to develop e cient and yet accurate design optimization framework using variabledelity aerodynamic analysis. Basic idea of the variabledelity method is to maximize e ciency of the analysis while maintaining accuracy of the highdelity analysis. To explore a large design space with relatively many design variables, an e cient global optimization (EGO) is selected. However, the number of function evaluations for the global search process is often too expensive to directly carry out aerodynamic analysis using computational uid dynamics (CFD). The Kriging surrogate model is introduced as an e cient alternative. To facilitate the variabledelity analysis, a corresponding variabledelity Kriging surrogate model is developed. Gradient data are directly utilized to improve the accuracy of the Kriging surrogate model and reduces considerably the total number of function evaluations. The variabledelity and gradient-enhanced Kriging surrogate model is constructed and regression e ect is also taken into account to mitigate the errors from the lowdelity analysis to better predict the trend of the function of interest. The validity of the proposed Kriging surrogate model is validated for an analytic function with varying number of samples and its lowdelity functions. Finally, practical design applications of two-dimensional RAE2822 airfoil and three-dimensional UCAV are carried out using the proposed surrogate model-based EGO design framework.

A hyperparameter-optimized Kriging surrogate model was developed for the structural collapse behavior framework presented in this paper. The assessment is conducted on a stiffened panel subject to axial load and lateral pressure, typical of the deck structure of a bulk carrier ship. This behavior is characterized using nonlinear finite element analysis to determine the collapse response. The surrogate model’s hyperparameters were optimized using a Genetic Algorithm to achieve the best performance, and the trained framework can predict ultimate strength. By following this approach, the problem can be reformulated as a multi-objective optimization task. This framework involves associating the Kriging surrogate model with a multi-objective evolutionary optimization algorithm based on Genetic Algorithms to balance the trade-off between the weight and ultimate strength of the stiffened panel. The results confirm the applicability of the Kriging surrogate framework to predict the ultimate strength and assess the collapse analysis of the stiffened panels, ensuring accuracy through GA-based hyperparameter optimization.

It is hard to simultaneously improve the peak efficiency (η *) and the width of the high-efficiency region ( Gη) for a hydrodynamic torque converter. A combination of comprehensive CFD simulation and multi-objective optimization was pretested. The elaborate CFD simulation calculation included a reasonable mesh layout, a robust algorithm and a correct turbulence model, whose results were also experimentally verified. In our study, the Kriging surrogate model was first used to construct a nonlinear relationship between the inlet and outlet angle and the economic performance index of the hydrodynamic torque converter. To ensure that the accuracy of the surrogate model meet the requirements, we also used 10 sets of sample points to verify the accuracy of our surrogate model. The accuracy is found to meet the requirements, which shows that the accuracy of the constructed surrogate model is relatively high. We choose to apply the second-generation non-dominant sorting genetic algorithm (NSGA-II) to solve our problem. After solving the Pareto frontier solution set, we obtain a set of global optimal solutions on the Pareto frontier solution set. The optimization results show that the η * is increased by 2.49% and that the Gη is increased by 14.23%. We extracted the flow field structure near the turbine region, characterized the difference between original and optimal model from the flow field perspective, and demonstrated the accuracy of our optimization results. Finally, we used CFD to verify our optimization results, further illustrating the accuracy of the optimization results prediction. Literature research indicates that a large amount of experiments to optimize the η * and the Gη of the hydrodynamic torque converter will bring huge trial cost and time cost. We conclude from our research that the proposed calculation method can solve such problems well.

Multi-objective optimization of reverse osmosis desalination units using different adaptations of the non-dominated sorting genetic algorithm (NSGA)

Particle swarm algorithm with adaptive constraint handling and integrated surrogate model for the management of petroleum fields

Electromagnetic acoustic transducers (EMATs) are non-contact ultrasonic transducers used to generate ultrasonic waves directly in the tested metal samples, suitable for special situations like testing moving or hot metal solids. EMATs rely on electromagnetic coupling, and the transduction efficiency of EMATs is relatively low, so it’s crucial to improve their performance through building accurate models and implementing structural optimisations. Modern evolutionary optimization algorithms involve a number of evaluations of the objective function of the optimization problem, so it’s necessary to explore surrogate models to reduce the time consumption during evaluation of the computationally expensive objective function, especially when the function corresponds to complex numerical models, like the EMAT model. We focused on the application of Kriging surrogate model (DACE) in EMAT modeling in this work. The formulations of the DACE model were reviewed, then the model of an omnidirectional EMAT was introduced. Three methods to calculate the amplitudes of the displacement components were discussed and compared, including the time-domain method, the multifrequency method (with FFT/IFFT processing), and the single frequency method applying directly the phasors. The DACE model of the EMAT was then built to predict outputs on a discrete grid of the design variables. Finally the obtained DACE model was used as the surrogate model in the optimization of the EMAT driven by the simulated annealing algorithm. With the DACE model, the total time consumption of optimization of the EMAT was reduced greatly.

Thermal protection system (TPS) is one of the most important subsystems for vehicle reentry. Because of the uncertainties in thermal loads, material properties, and manufacture tolerances, the thermal response of TPS has strong randomness, which brings great challenges to the engineering design and reliability evaluation. Because the uncertain aerodynamic heating loads are stochastic processes in time history, it is difficult to model them in the conventional surrogate models that usually take scalar random variables as input. This paper thus proposes an effective characterization method that can represent the uncertainties of aerodynamic heating by a set of random variables using Karhunen–Loève expansion. The random variables that describe the uncertainty of thermal loads, material properties, and geometric thickness are taken as inputs for probabilistic analyses. A kriging surrogate model is constructed to solve the transient heat conduction with high accuracy. Taking a typical multilayer TPS as an example, the probabilistic thermal analyses are carried out considering different degrees of heat rate uncertainties. The results show that the uncertainties of aerodynamic heating intensify the randomness of the thermal response of TPS, and thus have a great impact on the thermal reliability. The sensitivities of temperature response to various uncertain parameters are investigated as well, which provide a reference for system design and reliability improvement.

In this study, we developed an efficient computer-aided design tool for scaling combustor designs. From a limited number of fluid simulations, an original design is scaled while preserving most of the flow properties, using a multi-objective optimization method and deep neural network or kriging surrogate models. The accuracy and robustness of the method were first tested with a simple geometry. Investigations have shown a strong sensitivity of the surrogate models to the sample distribution, which can be reduced using a strategic sampling method. Subsequently, the geometry was scaled down to a factor of two using both surrogate models while preserving most of the flow features.

Structural dynamic reanalysis method for transonic aeroelastic analysis with global structural modifications