Showing papers on "Harmonic wavelet transform published in 2020"

Fault Detection of VFD-Fed Induction Motor Under Transient Conditions Using Harmonic Wavelet Transform

Abstract: Among a myriad of techniques in motor current analysis for fault detection in transient regime, the discrete wavelet transform (DWT) was widely implemented in the embedded online condition monitoring system (CMS) of the direct online (DOL)-fed induction motor (IM). However, the use of DWT-based CMS faces practical problems with variable frequency drive (VFD)-fed IM due to the required continuous redefinition of the decomposition tree to cope with the variable spectral content. To overcome this major limitation, an approach based on a novel DWT called multiple-windowed harmonic wavelet packet transform (MWHWPT) is then presented in this article. The originality of the proposed approach lies in the use of drive’s data to continuously tune the programmable MWHWPT in order to adapt to the varying spectral content of the motor current. The new approach has been validated experimentally under transient conditions covering both random variations of load and fundamental frequency with broken rotor bar fault on a VFD-fed 3-kW double-cage IM. Fault feature extraction results show the robustness and flexibility of the proposed approach through a clear distinction between healthy and faulty motor conditions for both steady and transient modes.

Classification of Hydroacoustic Signals Based on Harmonic Wavelets and a Deep Learning Artificial Intelligence System

Abstract: This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients of the harmonic wavelet transform (fast computation), short-time Fourier transform (spectrogram) and Fourier transform using a kNN-algorithm. Classification quality metrics (precision, recall and accuracy) are given for different signal-to-noise ratios. ROC curves were also obtained. The use of the deep neural network for classification of whales’ sounds is considered. The effectiveness of using harmonic wavelets for the classification of complex non-stationary signals is proved. A technique to reduce the feature space dimension using a ‘modulo N reduction’ method is proposed. A classification of 26 individual whales from the Whale FM Project dataset is presented. It is shown that the deep-learning-based approach provides the best result for the Whale FM Project dataset both for whale types and individuals.

Phase retrieval of bandlimited functions for the wavelet transform

Abstract: We study the problem of phase retrieval in which one aims to recover a function $f$ from the magnitude of its wavelet transform $|\mathcal{W}_\psi f|$. We consider bandlimited functions and derive new uniqueness results for phase retrieval, where the wavelet itself can be complex-valued. In particular, we prove the first uniqueness result for the case that the wavelet $\psi$ has a finite number of vanishing moments. In addition, we establish the first result on unique reconstruction from samples of the wavelet transform magnitude when the wavelet coefficients are complex-valued

Two-wavelet theory in Weinstein setting

Abstract: In this paper we introduce the notion of a Weinstein two-wavelet. Then we establish and prove the resolution of the identity formula for the Weinstein continuous wavelet transform. Next, we give results on Calderon's type reproducing formula in the context of the Weinstein two-wavelet.

Abelian theorems for the Bessel wavelet transform

Abstract: Abelian theorems of ordinary and distributional types are investigated exploiting the theory of the Bessel wavelet transform.

VFD fed Induction Motor Fault Detection using Drive's data and Harmonic Wavelet Transform

Abstract: Although the successful use of various variants of the Discrete Wavelet Transform (DWT) in the field of fault detection in Direct On-Line (DOL) fed Induction Motors, new challenges rise with the widespread use of Variable Frequency Drive (VFD) in industrial application. Regardless of the fault detection technique, the permanent variation in the fundamental frequency and therefore the fault frequencies of the analyzed signal imply a permanent re-tuning of DWT in terms of coefficient bandwidth and mother wavelet parameter. This tuning is a trial-and-error process which rises practical problem in the context of on-line Condition Monitoring Systems (CMS). Considering these limitations, the DWT use is non-tailored to the context of a VFD fed IM on-line CMS. In this paper, a novel auto-tunable DWT called the Windowed Harmonic Wavelet Packet Transform (WHWPT) using drive's data is presented in order to overcome the aforementioned drawbacks. The new approach has been validated experimentally using broken rotor bar fault in a VFD fed 3-kW Double Cage IM under a power supply at different fundamental frequencies. Fault feature extraction results show the robustness and the flexibility of the proposed approach through clear distinction between healthy and faulty motor conditions even for several fundamental frequencies.

Solution of the Problem of Classification of Hydroacoustic Signals Based on Harmonious Wavelets and Machine Learning

Abstract: Two types of real hydroacoustic signals of whales are classified based on the harmonic wavelet transform (HWT) coefficients (fast implementation), windowed Fourier transform (FT) (spectrogram), and conventional FT using the k-NN algorithm. The accuracy of the classification is estimated for various signal-to-noise ratios (SNRs). In order to reduce the dimension of the feature space during classification using the k-NN algorithm, the use of the modulo N reduction method is proposed. The efficiency of the use of harmonic wavelets in the classification of complex nonstationary signals is experimentally proved. The applicability of speech processing methods for the classification of underwater bioacoustic signals is confirmed. The discussed methods are initially developed taking into account the characteristics of human speech, but, nevertheless, showed good results even without being tuned to the characteristics of the classified signals. The problem of classifying two types of whales by the sounds they make using a neural network is solved.