Simultaneous Noise and Impedance Fitting to Transition-Edge Sensor Data Using Differential Evolution
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Simultaneous Noise and Impedance Fitting to Transition‑Edge Sensor Data Using Differential Evolution A. P. Helenius1 · T. A. Puurtinen1 · K. M. Kinnunen1 · I. J. Maasilta1 Received: 5 August 2019 / Accepted: 6 June 2020 © The Author(s) 2020
Abstract We discuss a robust method to simultaneously fit a complex multi-body model both to the complex impedance and the noise data for transition-edge sensors. It is based on a differential evolution (DE) algorithm, providing accurate and repeatable results with only a small increase in computational cost compared to the Levenberg–Marquardt (LM) algorithm. Test fits are made using both DE and LM methods, and the results compared with previously determined best fits, with varying initial value deviations and limit ranges for the parameters. The robustness of DE is demonstrated with successful fits even when parameter limits up to a factor of 10 from the known values were used. It is shown that the least squares fitting becomes unreliable beyond a 10% deviation from the known values. Keywords Thermal model · Genetic algorithm · Differential evolution · Transitionedge sensor
1 Introduction Transition-edge sensors (TES) are versatile, state-of-the-art radiation detectors [1, 2], currently used in many applications, such as particle-induced X-ray emission spectroscopy [3, 4], and ground- and space-borne telescopes [5, 6]. However, the modelling of transition-edge sensors and finding fits to data has sometimes proven quite challenging in practice, due to the complexities of the thermal circuit of the device [7–12], as two- and three-block thermal models [13] need to be employed at times. Fitting these models by the commonly used least squares fitting methods or with certain initial guesses manually, as was done in references [7, 8], has proven to be tedious or even unreliable. Here, we propose a different approach to fit TES thermal models, which is independent of the initial parameters given, and can fit both the complex impedance and * A. P. Helenius [email protected] 1
Nanoscience Center, Department of Physics, University of Jyvaskyla, 40014 Jyvaskyla, Finland
13
Vol.:(0123456789)
Journal of Low Temperature Physics
the noise data simultaneously, even for three-block models, producing more reliable results than the more commonly used Levenberg–Marquardt method [15]. It is based on the differential evolution (DE) algorithm [14], a branch of genetic algorithms. In this study, we fit previously measured data from Ref. [7] both with the DE algorithm and with the LM algorithm and use the published manual fits in that paper as the control to evaluate the performance.
2 Two‑ and Three‑Block Thermal Models In Ref. [7], it was shown that for good fitting of the complex impedance and noise data, three-block thermal models had to be employed. The models chosen for study here are the so-called hanging (H) model for two-block and intermediate–hanging (IH) model of Ref. [13], see Fig.1. In the IH model, in addition to the heat capacity of the TES sensor element, Ctes , th
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