A common problem in many complex physical systems is the determination of pulsation modes from irregularly sampled time-series, and there is a wealth of signal processing techniques that are being applied to post-pulse and real-time data analysis in such complex systems. The aim of this report is studying the problem of detecting discrete spatial periodicities in the spectrum of magnetic fluctuations in tokamaks, for which the optimization of the algorithm performance is essential, particularly when multiple sensors are used with different measurement uncertainties, and some of the processed output signals are then used in real-time for discharge control. The main tool used hereafter will be the SparSpec algorithm, initially devised for astrophysical purposes and already applied to the analysis of magnetic fluctuations in various tokamaks. In its baseline version, dubbed SS-H2, the SparSpec algorithm runs in currently or previously operating tokamaks (JET, TCV and Alcator C-mod), and is foreseen to be deployed for data analysis in tokamak under construction (ITER, DTT). For JET, SS-H2 regularly runs also in real-time on a 1ms clock for detecting Alfvn Eigenmodes using synchronously-measured magnetic perturbations. On JET and TCV, it was noted that often a reduced set of sensors had to be used as the measurement uncertainties were not the same for all available sensors, somewhat deteriorating the overall performance of the algorithm. Hence, as part of a major update of the SparSpec algorithm, specifically intended for accelerating the real-time performance, use of the measurement uncertainties to weight the data, the spectral window and the ensuing penalization criterion was introduced. The behaviour of this new version of the SparSpec algorithm under a variety of simulated circumstances is analysed. It is found that the implementation of SparSpec using such error weighting produces superior results to those obtained with SS-H2, both in terms of the speed and the accuracy of the calculations. A test on actual data from the JET tokamak also shows a clear improvement in the performance of the algorithm.

许多复杂物理系统中的一个常见问题是脉动模式的确定来自不规则采样的时间序列，并且有大量的信号处理技术被应用于这种复杂系统中的后脉冲和实时数据分析。本报告的目的是研究检测托卡马克磁涨落谱中离散空间周期性的问题，对此算法性能的优化至关重要，特别是当使用具有不同测量不确定性的多个传感器时，以及一些处理过的然后实时使用输出信号进行放电控制。此后使用的主要工具将是 SparSpec 算法，该算法最初是为天体物理学目的而设计的，并已应用于各种托卡马克的磁涨落分析。在其被称为 SS-H2 的基线版本中，SparSpec 算法在当前或以前运行的托卡马克（JET、TCV 和 Alcator C-mod）中运行，预计将部署在建设中的托卡马克（ITER、DTT）中进行数据分析。对于 JET，SS-H2 也在 1ms 时钟上定期实时运行，以使用同步测量的磁扰来检测 Alfvn 本征模式。在 JET 和 TCV 上，注意到通常必须使用一组减少的传感器，因为所有可用传感器的测量不确定性都不同，这在一定程度上降低了算法的整体性能。因此，作为 SparSpec 算法主要更新的一部分，专门用于加速实时性能，引入了使用测量不确定性来加权数据、光谱窗口和随后的惩罚标准。分析了这种新版本的 SparSpec 算法在各种模拟环境下的行为。发现使用这种误差加权的 SparSpec 实现产生优于使用 SS-H2 获得的结果，无论是在计算速度还是准确性方面。对来自 JET 托卡马克的实际数据的测试也显示了算法性能的明显改进。