Multilayer Machine Learning-Assisted Optimization-Based Robust Design and Its Applications to Antennas and Arrays

Abstract : An efficient multilayer machine learning-assisted optimization (ML-MLAO)-based robust design method is proposed for antenna and array applications. Machine learning methods are introduced into multiple layers of the robust design process, including worst-case analysis (WCA), maximum input tolerance hypervolume (MITH) searching, and robust optimization, considerably accelerating the whole robust design process. First, based on a surrogate model mapping between the design parameters and performance, the WCA is performed using a genetic algorithm to ensure reliability. MITH searching is then carried out using an MLAO-based framework to find the MITH of the given design point. Next, based on the training set obtained using MITH searching, correlations between the design parameters and the MITH are learned. The robust design is carried out using surrogate models for both the performance and the MITH, and these models are updated online following the ML-MLAO scheme. Finally, two examples, including an array synthesis problem and an antenna design problem, are used to verify the proposed ML-MLAO method. The numerical results and computation time are discussed to demonstrate the effectiveness of the proposed method.
 ? This review aims to provide an overview of the existing optimization and numerical methods and tools, which can enhance the robust multiobjective optimization procedures, where the emphasis is placed on finding a robust frontier for electrical machine design related problems . ? The second part of the paper highlights the role and possibilities of the robust design optimization based tools in the case of some recent technologies, 3D printed and superconductor based machines, and the role of robust design optimization in the development of electric vehicles and digital twin based modeling.
 • In contrast to the array synthesis problem discussed above, the solution of the antenna design problem relies on the prediction accuracy of the surrogate models trained with the datasets established by full-wave EM simulations. • For antennas with a large design parameter range, acquiring accurate surrogate models for the entire design space is difficult if time is limited. Therefore, local surrogate models surrounding the possible optimal design points should be established and updated online during the robust design process rather than surrogate models suitable for the entire design space. • The robust antenna design algorithm is divided into two phases: the optimization phase and the robust optimization phase.
 • They proposed to start the calculation with a relatively small sample size and increase the number of individuals with the number of generations. • Other adaptation methodologies can use a higher sample size for those individuals that have a higher estimated variance or simply calculate the fitness by averaging over the neighborhood of the evaluated individuals. • Another possibility to reduce the noise is implicit averaging because the area of a possible solution is sampled repeatedly, and this information can be used for an implicit averaging
 • The predicted optimization results of the MITHs are verified using the proposed DL-MLAO method, and the predicted antenna performance is verified using EM simulations. • The termination criterion, such as the maximum number of iterations iML or the maximum number of unchanged iterations, is then checked. • If one of the termination conditions is met, the process is stopped; otherwise, the database is updated, and Step 4 is repeated. • The ML-MLAO method uses the MITH search strategy as the HF simulation procedure in the MLAO scheme. • The accuracy and robustness of the results are ensured by the accuracy of DL-MLAO MITH searching.
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