Application of L1 Trend Filtering Technology on the Current Time Domain Spectroscopy of Dielectrics

Abstract

The current time domain spectroscopy of dielectrics provides important information for the analysis of dielectric properties and mechanisms. However, there is always interference during the testing process, which seriously affects the analysis of the test results. Therefore, the effective filtering of current time domain spectroscopy is particularly necessary. L1 trend filtering can estimate the trend items exactly in a set of time series. It has been widely used in the fields of economics and sociology. Therefore, this paper attempts to apply L1 trend filtering to the current time domain spectroscopy. Firstly, polarization and depolarization currents are measured in the laboratory. Then the test results are filtered by L1 trend filtering and the filtering effects are compared with several common filtering algorithms, such as a sliding mean filter and Savitzky–Golay smoothing filter. Finally, the robustness and time complexity of L1 trend filtering are analyzed. The filtering results show that because the polarization currents vary in a wide range of the time domain (about 2–3 orders of magnitude), smooth and undistorted curves in the whole test time range can hardly be obtained through common filtering algorithms, while they can be obtained by L1 trend filtering. The results of robustness analysis and time complexity analysis show that L1 trend filtering can extract the trend items accurately in the time series under given different noise levels, and the execution time is also lower than 176.67 s when the number of tested points is no more than 20,000. Those results show that L1 trend filtering can be applied to the time domain current spectroscopy of dielectrics.

$$\ell _{1}$$ Common Trend Filtering

“…1 Figure 1 illustrates a continuous piecewise linear trend. The filter and its variants have been subsequently applied in various fields, including astronomy (Politsch et al 2020), climatology (Khodadadi and McDonald 2019), economics (Yamada and Jin 2013;Yamada and Yoon 2014;Winkelried 2016;Yamada 2017;Klein 2018), electronics (Suo et al 2019), environmental science (Brantley et al 2019), finance (Mitra and Rohit 2018), and geophysics (Wu et al 2018).…”

Trend Analysis of Modal Identification based Real-time Power System Oscillations using L1 Trend Filtering

“…When is small and is close to zero, it is changed to the original data. In [13,28], the parameterization of the factor is presented through simulations and empirical tests. It is established that it depends on the type of data and the size of the window.…”

“…With an adequate speed in the processing, multidisciplinary tasks require mathematical, statistical, and computer science concepts in an integrated way [8,12]. Following this precept, the 1 filter has been applied to financial and electronics data in [12,13] in order to establish the trend value of high-dimensional data. Based on its good performance for determining the trend of a large volume of data, 1 filter is adapted in this paper to allow monitoring the oscillatory trend behavior of an electric power system in real-time.…”

New measurement method of displacement susceptibility based on time‐domain current and potential combined spectra

“…The background noise is bad for the determination of the current density and electric field before and after the sample is opened, leading to the increase in relative error of displacement susceptibility or even error. To reduce or eliminate the effect of background noise, the PCDP and DCRP combined spectra is pre‐treated by the data fitting or the trend filtering [22]. The low sampling frequency is unfavourable for obtaining $$j\left({t}_{1}^{-}\right)$$ and $$j\left({t}_{2}^{-}\right)$$, resulting in an increase in the relative error of PCDP and DCRP.…”