Nonlinear time series analysis of Kepler Space Telescope data: Mutually beneficial progress

Abstract

Nonlinear time series analysis, though a powerful tool, has not been used widely in astronomy and astrophysics because the principle requirements that the data be sampled uniformly and continuous are rarely met. Kepler Space Telescope variable-star light curves satisfy these and almost all other requirements. These data have allowed a more systematic study of the methodology and yielded new information. Nonlinear noise reduction is the aspect we focus on here. Nonlinear time series power spectra often have relevant information across all the frequencies in a spectrum. As opposed to traditional filtering that results in a loss of information at the high frequencies, nonlinear local projective noise reduction allows us to significantly reduce noise while keeping high-frequency information. Nonlinear noise reduction is discussed for a number of Kepler Space Telescope targets with different power-spectral characteristics. The extremely high quality of the Kepler data has also allowed us to explore the novel use of average mutual information (AMI) for distinguishing signal from noise in broadband spectra. We report on noise reduction for targets with power spectra that contain a fundamental and harmonics, power spectra with no such lines and spectra with high-frequency lines.

The noise wars in helio‐ and asteroseismology

“…Figure 1 represents an example of an efficient noise reduction (right panel) of the more "chaotic" raw light curve (left panel). The power spectrum of the filtered time series has a reduction of noise at high frequency that could reach typical values of a few order of magnitude till a factor of 10 4 in the best cases (see Jevtić et al 2012). Figure 2 shows an example of the power spectrum obtained using raw data (gray lines) and the one issued of the local projective nonlinear noise reduction (black lines).…”

“…In the case of Kepler, most of the data is obtained at a rate of ∼30 min (usually called long-cadence data), Fig. 1 (online colour at: www.an-journal.org) Phase-space portraits for KIC 8054179 for the raw data (left) and the data after nonlinear noise reduction (right) for a delay of 1 (for more details see Jevtić et al 2012). while at any time 512 targets can be sampled at a shorter cadence of ∼1 min (see for further details, e.g., García et al 2011a).…”

Fault Diagnosis of Rolling Bearing Based on a Novel Adaptive High‐Order Local Projection Denoising Method

“…The noise is reduced by requiring locally linear relations among the delay coordinates and moving delay vectors closer to smooth manifolds. Then, the local projective filters had been employed in spheres ranging from biology signal analysis [30] to space signal analysis [31]; the general framework of local projection was adopted to analyze signals from particular systems, such as being applied to remove interferential artifacts from an electroencephalography (EEG) signal among them. A local projection stabilized and characteristic decoupled scheme aiming at the fluid-fluid interaction problems was proposed.…”

Automated preparation of Kepler time series of planet hosts for asteroseismic analysis

“…With some corrections being applicable to large samples of stars, while other are more targeted towards specific types of stars (see e.g. Jevtić, Stine & Schweitzer 2012;Danielski, Kacprzak & Tinetti 2013). However, asteroseismic analysis of planetary host stars presents some unique complications compared to pure asteroseismic targets.…”