Light curve analysis of variable stars using Fourier decomposition and principal component analysis

In the present study, an adaptive Fourier Decomposition Method (FDM) is applied to identify damage at connections. For that purpose, an experimental single-story plane frame model is considered. The beam and columns of the frame are connected by angles and bolts, and the damage is introduced by loosening bolts at different locations. The frame is excited at the right top corner using a hammer, and strain time histories are collected from different points. The FDM and Empirical Mode Decomposition (EMD) algorithm are applied to characterize the damage sensitive features. The results obtained from the FDM are compared with the EMD algorithm, which shows that the performance of FDM is better, which motivates to extend its application further to estimate the amount of bolt loosening in terms of extracted damage sensitive features.

We show how Principal Component Analysis can be used to analyse the structure of Cepheid light curves. This method is more efficient than Fourier analysis at bringing out changes in light curve shape as a function of period. Using this technique, we study the shape of fundamental and first overtone mode Cepheid light curves in the Galaxy, LMC and SMC over a wide period range. For fundamentals, we find evidence for structural changes at log P ≈ 1.55, 2.1. It is suggested that the feature at log P ≈ 2.1 is associated with a resonance in the Cepheid normal mode spectrum. For overtones, we recover the Z shape in the R21 period plane and reproduce the metallicity dependence of this Z shape.

The number of known periodic variable stars has increased rapidly in recent years. As an all-sky transit survey, the Transiting Exoplanet Survey Satellite (TESS) plays an important role in detecting low-amplitude variable stars. Using 2 minute cadence data from the first 67 sectors of TESS, we find 72,505 periodic variable stars. We used 19 parameters including period, physical parameters, and light-curve (LC) parameters to classify periodic variable stars into 12 subtypes using the random forest method. Pulsating variable stars and eclipsing binaries are distinguished mainly by period, LC parameters, and physical parameters. Classical Cepheids, Type-II Cepheids, rotational variable stars, eruptive variable stars of the UV Ceti type, and young stellar objects are distinguished mainly by period and physical parameters. Compared to previously published catalogs, 63,106 periodic variable stars (87.0%) are newly classified, including 13 Cepheids, 27 RR Lyrae stars,​​​​​​ ~4600 δ Scuti variable stars, ~1600 eclipsing binaries, ~34,000 rotational variable stars, and about 23,000 other types of variable star. The purity of eclipsing binaries and pulsation variable stars ranges from 94.2% to 99.4% when compared to the variable star catalogs of Gaia Data Release 3 and Zwicky Transient Facility Data Release 2. The purity of rotational variable stars is relatively low at 83.3%. The increasing number of variables stars is helpful to investigate the structure of the Milky Way, stellar physics, and chromospheric activity.

Light curves are time series of the brightness of astronomical objects and are fundamental to analyze variable stars. RR Lyrae are a particular type of variable stars that exhibit periodic behavior in their light curves. The Vista Variable in the Via Lactea (VVV) survey aims to understand how our galaxy was formed and finding large quantities of RR Lyrae is key to accomplish this. In this work we evaluate convolutional neural networks for the automatic classification of RR Lyrae using a subset of the light curves of the VVV survey. To address the differences in length between light curves we compare padding, partial-convolution and subsampling based strategies. The experiments show that the best test-set results are achieved using conventional convolutional layers with a global max pooling operator over zero-padded light curves. Future work includes testing with continuous-time convolutions, exploring synergies with feature-based models and evaluating on more classes of periodic variable star.

Peak envelope spectrum Fourier decomposition method and its application in fault diagnosis of rolling bearings

Photometric methods for identifying dark companion binaries – binary systems hosting quiescent black holes (BHs) and neutron stars (NSs) – operate by detecting ellipsoidal variations caused by tidal interactions. The limitation of this approach is that contact and semidetached binaries can produce similarly looking light curves. In this work, we address the degeneracy of ellipsoidal light curves by studying the differences between synthetically generated light curves of dark companion, semidetached, and contact binary systems. We inject the light curves with various levels of uncorrelated and correlated Gaussian noise to simulate the effects of instrumental noise and stellar spots. Using principal component analysis (PCA) and Fourier decomposition, we construct low-dimensional representations of the light curves. We find that the first three to five PCA components are sufficient to explain 99% of variance in the data. The PCA representations are generally more informative than the Fourier representation for the same number of coefficients as measured by both the silhouette scores of the representations and the macro recalls of random forest classifiers trained on the representations. The random forest classifiers reach macro recalls from 0.97 in the complete absence of noise to 0.67 in the presence of spots and strong instrumental noise, indicating that the classes remain largely separable even under adverse conditions. We find that instrumental noise significantly impacts the class separation only when its standard deviation exceeds 10−3 mag, whereas the presence of spots can markedly reduce the class separation even when they contribute as little as 1% of the light curve amplitude. We discuss the application of our method to real ellipsoidal samples, and we show that we can increase the purity of a sample of dark companion candidates by a factor of up to 25 if we assume a prior purity of 1%, significantly improving the cost efficiency of follow-up observations.

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Because the modulating frequency and its magnitude of gearbox vibration signals relate to gear faults, demodulation analysis methods are commonly used to diagnose gear fault. The conventional envelope spectrum helps us to identify the dominant amplitude modulation frequency. However, it fails to locate the gear fault precisely when the modulation frequency corresponds to multiple gears. To address this issue, a gear fault diagnosis method is proposed to locate the faulty gear precisely based on the Fourier decomposition and demodulation analysis. Firstly, the Fourier decomposition is employed to extract analytical Fourier intrinsic band functions (FIBFs) from the given signal. Then, some FIBFs including modulation information are selected for further demodulation analysis. Finally, the faulty gear is detected by jointly considering the dominant modulation frequency and modulation strength. Simulated and experimental signal analysis results verify the effectiveness of the proposed method in obtaining modulation information in a specific frequency band and locating the faulty gear precisely.

Context . The space mission CoRoT (Convection, Rotation, and planetary Transiting) still holds a wealth of high-quality, yet largely unexplored data that can be analysed in terms of signal-to-noise ratio and continuous time coverage. Aims . This work is the first in a series focused on identifying and classifying variable stars observed by CoRoT whose light-curve signals have not yet been studied or reported in the main variable star repositories. Methods . We employed simulations alongside real-world data to assess the effectiveness of the moving average method in handling instrumental jumps and detecting short-period signals (lasting less than one day) within time series spanning approximately 20 days. To classify the newly identified variable stars, we used the light curves of known variable stars as a training set. A supervised selection method was developed, introducing a novel classifier based on features extracted from the folded light curve using the double period. Results . We identified 9272 variable stars, of which 6249 are not yet listed in the SIMBAD and VSX repositories. From our preliminary classification, we identified various types of variable stars, including 309 β Cepheis, 3105 δ Scutis, 599 Algol-type eclipsing binaries, 844 β Lyrae eclipsing binaries, 497 W Ursae Majoris eclipsing binaries, 1443 γ Doradus, 63 RR Lyraes, and 32 T Tauri stars. The template-based models created serve as a new classifier for variable stars with well-sampled light curves. This catalogue introduces CoRoT variable stars into widely used astronomical repositories. Conclusions . By comparing the properties of the identified variables in the inner and outer regions of the Milky Way, we observed notable differences in several variable star types, likely reflecting metallicity and age gradients. The identification of signals with periods shorter than one day also enables us to propose new approaches for detecting longer period variability through automated methods, which will be explored in forthcoming papers in this series.

Fourier decomposition (FD) is a noninvasive method for assessing ventilation and perfusion-related information in the lungs. However, the technique has a low signal-to-noise ratio (SNR) in the lung parenchyma. We present an approach to increase the SNR in both morphological and functional images. The data used to create functional FD images are usually acquired using a standard balanced steady-state free precession (bSSFP) sequence. In the standard sequence, the possible range of the flip angle is restricted due to specific absorption rate (SAR) limitations. Thus, using a variable flip angle approach as an optimization is possible. This was validated using measurements from a phantom and six healthy volunteers. The SNR in both the morphological and functional FD images was increased by 32%, while the SAR restrictions were kept unchanged. Furthermore, due to the higher SNR, the effective resolution of the functional images was increased visibly. The variable flip angle approach did not introduce any new transient artifacts, and blurring artifacts were minimized. Both a gain in SNR and an effective resolution gain in functional lung images can be obtained using the FD method in conjunction with a variable flip angle optimized bSSFP sequence.

Factor analysis aims to reduce the amount of information from the original variable without losing important information. A factor is a collection of reduced variables. Several methods can be used in factor analysis, the most common of which are principal component analysis and maximum likelihood. The principal component analysis technique was used in this study. This technique was chosen because it better represents the purpose of the analysis than others. A case study of beef gravel is used to supplement the explanation of factor analysis using the Principal Component Analysis (PCA) technique. The goal of this study was to identify the most important factors influencing beef gravel quality to maintain product quality. The main factor is the volume of soaking water, and the second is the volume of soaking two dishes. These two factors have a cumulative variance proportion of 55%, indicating that they can influence the quality of the gravel. In contrast, the rest can be influenced by other factors not revealed in the research model.

Urmia Lake in the northwestern of Iran is a hypersaline water body and has become an environmentally important issue especially due to the presence of an infrequent aquatic species, Artemia Urmiana. During the last three decades, several considerable man-made changes including river damming and construction of a causeway across the lake affected the lake salinity. This article aims to propose a new approach of salinity modeling using a reduced-order model based on MIKE21 simulation model, in conjunction with principal component analysis (PCA) technique. At first, spatial variation of salinity in the lake was simulated by MIKE21 to prepare the input information for the PCA. Then, the dominant modes of salinity were determined by PCA technique while MIKE21 simulated results were compared with the output of developed reduced order model. Findings indicated that MIKE21's results closely matched the experimental data collected by field study. Also, the first 10 PCs among 974 modes computed by the reduced order model conserved approximately over 93% of the system variance. Therefore, the reduced order model was sufficient to capture the variation of salinity in the lake using a few first PCs. In other words, it was generally found that improvements in the simulated salinity in the lake provided by reduced order model were comparable to MIKE21 simulations.

Multicollinearity refers to the presence of collinearity between multiple variables and renders the results of statistical inference erroneous (Type II error). This is particularly important in environmental health research where multicollinearity can hinder inference. To address this, correlated variables are often excluded from the analysis, limiting the discovery of new associations. An alternative approach to address this problem is the use of principal component analysis. This method, combines and projects a group of correlated variables onto a new orthogonal space. While this resolves the multicollinearity problem, it poses another challenge in relation to interpretability of results. Standard hypothesis testing methods can be used to evaluate the association of projected predictors, called principal components, with the outcomes of interest, however, there is no established way to trace the significance of principal components back to individual variables. To address this problem, we investigated the use of sparse principal component analysis which enforces a parsimonious projection. We hypothesise that this parsimony could facilitate the interpretability of findings. To this end, we investigated the association of 20 environmental predictors with all-cause mortality adjusting for demographic, socioeconomic, physiological, and behavioural factors. The study was conducted in a cohort of 379,690 individuals in the UK. During an average follow-up of 8.05 years (3,055,166 total person-years), 14,996 deaths were observed. We used Cox regression models to estimate the hazard ratio (HR) and 95% confidence intervals (CI). The Cox models were fitted to the standardised environmental predictors (a) without any transformation (b) transformed with PCA, and (c) transformed with SPCA. The comparison of findings underlined the potential of SPCA for conducting inference in scenarios where multicollinearity can increase the risk of Type II error. Our analysis unravelled a significant association between average noise pollution and increased risk of all-cause mortality. Specifically, those in the upper deciles of noise exposure have between 5 and 10% increased risk of all-cause mortality compared to the lowest decile.

Time-domain astronomy is progressing rapidly with the ongoing and upcoming large-scale photometric sky surveys led by the Vera C. Rubin Observatory project (LSST). Billions of variable sources call for better automatic classification algorithms for light curves. Among them, periodic variable stars are frequently studied. Different categories of periodic variable stars have a high degree of class imbalance and pose a challenge to algorithms including deep learning methods. We design two kinds of architectures of neural networks for the classification of periodic variable stars in the Catalina Survey’s Data Release 2: a multi-input recurrent neural network (RNN) and a compound network combing the RNN and the convolutional neural network (CNN). To deal with class imbalance, we apply Gaussian Process to generate synthetic light curves with artificial uncertainties for data augmentation. For better performance, we organize the augmentation and training process in a “bagging-like” ensemble learning scheme. The experimental results show that the better approach is the compound network combing RNN and CNN, which reaches the best result of 86.2% on the overall balanced accuracy and 0.75 on the macro F1 score. We develop the ensemble augmentation method to solve the data imbalance when classifying variable stars and prove the effectiveness of combining different representations of light curves in a single model. The proposed methods would help build better classification algorithms of periodic time series data for future sky surveys (e.g., LSST).

view Abstract Citations (40) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS RR Lyrae Stars in Local Group Galaxies. II. NGC 147 Saha, A. ; Hoessel, John G. ; Mossman, Amy E. Abstract Deep CCD images of NGC 147 taken with the "4-shooter" on the Hale 5 m telescope have been processed to find and photometrically measure RR Lyrae stars. 36 variable stars have been found, of which 32 are surmised to be RR Lyrae stars. Finding charts, periods, and light curves are presented. The mean magnitude of the RR Lyraes is determined to be <g> = 25.25 mag. A distance modulus 23.92 is derived, based on the best currently available values of foreground extinction and mean absolute magnitudes of RR Lyrae stars. A wide range of periods is seen for the RR Lyrae stars, indicating a correspondingly wide range of metallicities for the stars in NGC 147. The distance modulus derived here places NGC 147 at a distance of 154 kpc from the center of M31, and in conjunction with the line sight velocities of these two galaxies, this implies a lower limit of 7.2X10^11^ M_sun_ for the mass of M31. Publication: The Astronomical Journal Pub Date: July 1990 DOI: 10.1086/115495 Bibcode: 1990AJ....100..108S Keywords: Astronomical Photometry; Galaxies; Local Group (Astronomy); Variable Stars; Charge Coupled Devices; Light Curve; Metallicity; Stellar Magnitude; Astrophysics; STARS: RR LYRAE; GALAXIES: INDIVIDUAL; GALAXIES: LOCAL GROUP; GALAXIES: STELLAR CONTENT full text sources ADS | data products SIMBAD (39) NED (36) Related Materials (3) Part 1: 1990AJ.....99...97S Part 3: 1992AJ....103...84S Part 4: 1992AJ....104.1072S