Classical reliability assessment methods have predominantly focused on probability and statistical theories, which are insufficient in assessing the operational reliability of individual mechanical equipment with time-varying characteristics. A new approach to assess machinery operational reliability with normalized lifting wavelet entropy from condition monitoring information is proposed, whic...

Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing a given time series both in time and frequency domain. However, in practice one frequently observes nonstationary time series. In order to apply spectral analysis to these processes, an extension of the...

Classical wavelet thresholding methods suffer from boundary problems caused by the application of the wavelet transformations to a finite signal. As a result, large bias at the edges and artificial wiggles occur when the classical boundary assumptions are not satisfied. Although polynomial wavelet regression and local polynomial wavelet regression effectively reduce the risk of this problem, th...

Aims. We investigate the nature of the classical low-velocity structures in the local velocity field, i.e. the Pleiades, Hyades and Sirius moving groups. After using a wavelet transform to locate them in velocity space, we study their relation with the open clusters kinematically associated with them. Methods. By directly comparing the location of moving group stars in parallax space to the iso...

Wavelet transform is a well-known multi-resolution tool to analyze the time series in time-frequency domain. basis diverse but predefined by manual without taking data into consideration. Hence, it great challenge select an appropriate wavelet separate low and high frequency components for task on hand. Inspired lifting scheme second-generation wavelet, updater predictor are learned directly fr...

Performance of standard Direction Arrival (DOA) estimation techniques degraded under real-time signal conditions. The classical algorithms are Multiple Signal Classification (MUSIC), and Estimation Parameters via Rotational Invariance Technique (ESPRIT). There many conditions hamper on its performance, such as closely spaced coherent signals caused due to the multipath propagations results in a...

We introduce the theory of frames and develop wavelet theory as a natural extension of the Classical Sampling Theorem. This material serves as background for our applications to periodicity detection, noise reduction, and multidimensional irregular sampling.

in general, energy prices, such as those of crude oil, are affected by deterministic events such as seasonal changes as well as non-deterministic events such as geopolitical events. it is the non-deterministic events which cause the prices to vary randomly and makes price prediction a difficult task. one could argue that these random changes act like noise which effects the deterministic variat...

Interesting signals are often contaminated by heavy-tailed noise that has more outliers than Gaussian noise. Under the introduction of probability model for heavy-tailed noises, a robust wavelet threshold based on the minimax description length principle is derived in the εcontaminated normal family for maximizing the entropy. The performance and their measurement criterion for the robust wavel...