不确定条件下四极谐振腔的多目标优化设计
Multi-objective design optimization of a Quadrupole Resonator under uncertainties
摘要：
为了精确测定超导材料的射频（RF）特性，借助于所谓的四极谐振器（QPR）进行量热测量。这一过程受到某些系统测量误差的影响，这些误差具有各种不确定性来源。为了减小几何不确定性对测量偏差的影响，本文采用改进的最速下降法对QPR {在期望测度方面}进行多目标形状优化。因此，几何参数的变化是由多项式混沌（PC）扩展技术建模。然后，所产生的麦克斯韦特征值问题与随机输入数据的解决，使用基于PC的随机配置方法（PC-SCM）。此外，为了评估特定几何参数的贡献，提出了基于方差的灵敏度分析。这允许修改最速下降算法，从而减少找到最优解所需的计算负荷。最后，优化结果的形式的一个有效的近似的帕累托前的三维（3D）模型的QPR。
英文摘要：
For a precise determination of the radio frequency (RF) properties of superconducting materials, a calorimetric measurement is carried out with the aid of a so-called Quadrupole Resonator (QPR). This procedure is affected by certain systematic measurement errors with various sources of uncertainties. In this paper, to reduce the impact of geometrical uncertainties on the measurement bias, the modified steepest descent method is used for the multi-objective shape optimization of a QPR {in terms of an expectation measure}. Thereby, variations of geometrical parameters are modeled by the Polynomial Chaos (PC) expansion technique. Then, the resulting Maxwell's eigenvalue problem with random input data is solved using the PC-based stochastic collocation method (PC-SCM). Furthermore, to assess the contribution of the particular geometrical parameters, the variance-based sensitivity analysis is proposed. This allows for modifying the steepest descent algorithm, which results in reducing the computational load needed to find optimal solutions. Finally, optimization results in the form of an efficient approximation of the Pareto front for a three dimensional (3D) model of the QPR are shown.
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