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Sleep Stage Classification Using DWT and Dispersion Entropy Applied on EEG Signals
Published in Varun Bajaj, G.R. Sinha, Computer-aided Design and Diagnosis Methods for Biomedical Applications, 2021
Rajeev Sharma, Sitanshu Sekhar Sahu, Abhay Upadhyay, Rishi Raj Sharma, Ajit Kumar Sahoo
There are several methods for analyzing non-stationary signals like biomedical, earthquake, financial, and mechanical signals, etc. The wavelet transform is considered a powerful method for decomposing non-stationary signals into different scales, and provides a time-scale representation [38]. The wavelet transform is used for resolving the fixed time-frequency resolution problem of the short-time Fourier transform (STFT) [39]. The wavelet transform consists of two properties, namely space and frequency localization and multi-resolution analysis. Theoretically, the wavelet transform is broadly classified as the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). The CWT of signal y(t) is computed as follows [40]: YCWTτ,s=∫−∞∞ytψτ,s*tdt
Engineering Monitoring and Diagnosis Using Wavelet Transforms
Published in Cornelius Leondes, Computer-Aided Design, Engineering, and Manufacturing, 2019
Wavelet transform is a recently developed signal processing method. It has been successfully applied in many areas, for example; image processing, speech recognition, and data compression. This chapter introduces the basic principles of wavelet transforms and its applications for engineering monitoring and diagnosis. The chapter contains seven sections. Section 8.1 briefly introduces the history of wavelet transform along with its basic idea. Section 8.2 describes the mathematical backgrounds of wavelet transforms and several commonly used wavelet transforms, followed by a demonstration example. Section 8.3 describes the critical step of engineering monitoring and diagnosis: feature extraction. Through feature extraction, the characteristics of sensor signals are captured and related to the system conditions. Sections 8.4 and 8.5 present the methods for engineering monitoring and diagnosis, respectively. Section 8.6 presents two application examples of wavelet transform in engineering monitoring and diagnosis: one is chatter monitoring in a turning and the other is tool condition in drilling. Finally, Section 8.7 contains the conclusion.
Frames and Wavelets: A New Perspective on Sampling Theorems
Published in Ahmed I. Zayed, Advances in Shannon’s Sampling Theory, 2018
From the standpoint of signal analysis, the wavelet transform is a mathematical technique that can be used to split a signal into different frequency components and then studies each component with a resolution matched to its scale, thus providing a very good frequency and spatial resolution. Unlike other techniques used to study signals in the time-frequency domain, such as the windowed Fourier transform, in the wavelet transform the analyzing wavelets have time-width adapted to their frequency: high frequency wavelets are very narrow, while low frequency wavelets are much broader. This is in contrast with the windowed Fourier transform, where the analyzing signals all have the same envelope function, but translated to the proper time location and filled with higher frequency oscillations. This adaptability property of wavelets is especially useful for certain classes of signals, e.g., voiced speech signals as the energy is concentrated at lower frequencies, while the higher frequencies contain very little energy.
A Method to Predict Random Time-Delay of Networked Control System
Published in IETE Journal of Research, 2022
Wavelet transform has the characteristics of multi-resolution. It can decompose the non-stationary time series into several components [31]. In recent years, many scholars apply wavelet transform to the prediction of some objects. In [32], the authors use wavelet decomposition and ARIMA model to predict the number of arriving tasks in Internet. In their study, the authors proposed a growing deep belief network (DBN) with transfer learning to improve the prediction performance [33]. In [34], the authors proposed an innovative integrated prediction method that combines stochastic configuration networks with Savitzky–Golay smoothing filter and wavelet decomposition to predict workload in Cloud services. The idea of this paper is to use wavelet transform technology, but there are some differences with the previous literature. First of all, these results are decomposed by wavelet transform, and then a single prediction model is used to predict the component. The method of this paper is to use ARIMA and fractal autoregressive integrated moving average (FARIMA) to predict different components. Secondly, this paper uses Hurst parameter to select the prediction model, which makes ARIMA and FARIMA reasonable. Finally, the research object is different. The research object of this paper is the time-delay in a networked control system.
A combination model of wavelet analysis and neural network for predicting oil and gas exploration accidents
Published in Petroleum Science and Technology, 2022
Bo Zhang, Yunrui Zhang, Xi Chen, Shiyuan Dai, Zuoling You
When the historical OGE accident statistic materials are used, it should be aware that factors such as inconsistency of accidental statistic standards, data error or lack of original information often result in the incapability of precisely representing of some accidents’ essential characteristics. For the noise in the history OGE accident statistic data, the wavelet transform is a superior method to deal with the interference problem of noise data, which has proved feasible in electrocardiogram denoising, image processing, and many other fields(Bal et al. 2019). Wavelet transform is a signal time-frequency analysis method. It has the characteristics of multi-resolution analysis, and it can characterize the local characteristics of the signal in both time-frequency domains. This characteristic of wavelet analysis is known as the mathematical microscope (Wang, Ding, et al. 2015). In recent years, wavelet analysis has provided an effective way for signal filtering, signal-noise separation, and feature extraction, especially in signal denoising which shows its unique advantages(Peng, Peng et al. 2020). In recent studies, the wavelet denoising was used in the wind speed forecasting modeling research and greatly improved the prediction accuracy. The method was also used to denoise the extracted signal of gearbox failure to accurately and quickly identify the damage situation of the gear crack (Yang and Chen 2019). In this work, the wavelet analysis will be employed for denoising the OGE accident dataset.
Proactive maintenance of small wind turbines using IoT and machine learning models
Published in International Journal of Green Energy, 2022
Yoganand Selvaraj, Chithra Selvaraj
Dhiman, Harsh, Deb Dipankar & Anand Pritam [2018, 9] demonstrated the performance of a hybrid forecasting method comprising of wavelet transform and different variants of Support Vector Regression (SVR) like ε-SVR, Least Square Support Vector Regression (LS-SVR), Twin Support Vector Regression (TSVR) and ε-Twin Support Vector Regression (ε-TSVR) is analyzed. Wavelet transform is used to filter the raw wind speed data from any kind of stochastic volatility, Wavelet transform (WT) is a multi-resolution decomposition technique used in various fields of engineering applications like image processing, feature extraction for image segmentation, and noise reduction. Wavelet transform is of two types; that is, Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). Owing to its computational advantage DWT is more often used than CWT. WT decomposes a given input signal into an approximation signal and a detail signal with the former containing low-frequency components of the main signal.