Surrogate-Assisted Adaptive Design Optimization of Magnetorheological Fluid Brake-Integrated AFPM Machine With Different Brake Torque Ratios

This article proposes an improved surrogate-assisted adaptive design optimization method to optimize the magnetorheological fluid brake integrated axial flux permanent magnet machine (MRFBI-AFPMM) with different brake torque ratios (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{m}$</tex-math></inline-formula>). The proposed method addresses two critical challenges in design optimization: 1) To alleviate the calculation burden of repeated finite-element (FE) simulations, the local cascade ensemble (LCE) learning technique is introduced to build accurate surrogate models. The LEC learning method effectively addresses the bias-variance trade-off in the regression of MRFBI-AFPMM, ensuring efficient and accurate surrogate modeling. 2) The unknown axial outer radius (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{OA}$</tex-math></inline-formula>) of AFPM part poses great convergence challenges for optimization under target <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_m</i> constraint. To mitigate it, this article proposes an adaptive optimization strategy. It incorporates iterative <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_OA</i> search to improve the optimization efficiency of the non-dominated sorting genetic algorithm-II (NSGA-II). Additionally, simplified analytical models of different torque indexes are derived and analyzed before optimization, providing clear guidance for defining design objectives and selecting sensitive structural parameters. The proposed method is applied to several cases with different <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_m</i>. A statistical comparison of the total time consumption for different optimization methods is conducted, validating the proposed method's superiority in computational efficiency. Finally, the FE and experimental results from Case 2 demonstrate the feasibility of proposed optimization method.