Calculation of transient sinusoidal signal amplitudes using the Morlet wavelet

Osofsky, S.S.

doi:10.1109/78.806091

Cited by 12 publications

(4 citation statements)

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“…Hence, the combination of wavelet transform and BPNN has the advantage of both wavelet analysis and neural network; the data is transmitted forward and the prediction error is propagated backward, so as to achieve a more accurate predictive data. Generally, prediction accuracy and generalization ability will be affected by the choice of wavelet base function; compared to orthogonal wavelet, Gauss spline wavelet and Mexico hat wavelet, the Morlet wavelet has the smallest error and the reliable computational stability [46,47], thus this study employed Morlet wavelet as the activation function of hidden layer nodes, the formula is given below, 0 500 1000 1500 2000 2500 3000 3500 -50…”

Section: Wavelet Neural Network Algorithmmentioning

confidence: 99%

“…Sampling point Generally, prediction accuracy and generalization ability will be affected by the choice of wavelet base function; compared to orthogonal wavelet, Gauss spline wavelet and Mexico hat wavelet, the Morlet wavelet has the smallest error and the reliable computational stability [46,47], thus this study employed Morlet wavelet as the activation function of hidden layer nodes, the formula is given below, y = cos(1.75x)e −x 2 /2 (43) In Figure 4, the input data are represented by X 1 , X 2 , . .…”

Section: Wavelet Neural Network Algorithmmentioning

confidence: 99%

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Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

Liang

2018

Symmetry

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The ability to accurately track the degradation trajectories of rotating machinery components is arguably one of the challenging problems in prognostics and health management (PHM). In this paper, an intelligent prediction approach based on asymmetric penalty sparse decomposition (APSD) algorithm combined with wavelet neural network (WNN) and autoregressive moving average-recursive least squares algorithm (ARMA-RLS) is proposed for degradation prognostics of rotating machinery, taking the accelerated life test of rolling bearings as an example. Specifically, the health indicators time series (e.g., peak-to-peak value and Kurtosis) is firstly decomposed into low frequency component (LFC) and high frequency component (HFC) using the APSD algorithm; meanwhile, the resulting non-convex regularization problem can be efficiently solved using the majorization-minimization (MM) method. In particular, the HFC part corresponds to the stable change around the zero line of health indicators which most extensively occurs; in contrast, the LFC part is essentially related to the evolutionary trend of health indicators. Furthermore, the nonparametric-based method, i.e., WNN, and parametric-based method, i.e., ARMA-RLS, are respectively introduced to predict the LFC and HFC that focus on abrupt degradation regions (e.g., last 100 points). Lastly, the final predicted data could be correspondingly obtained by integrating the predicted LFC and predicted HFC. The proposed methodology is tested using degradation health indicator time series from four rolling bearings. The proposed approach performed favorably when compared to some state-of-the-art benchmarks such as WNN and largest Lyapunov (LLyap) methods.

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Section: Wavelet Neural Network Algorithmmentioning

confidence: 99%

Section: Wavelet Neural Network Algorithmmentioning

confidence: 99%

Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

Liang

2018

Symmetry

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“…(1) Initialization: In the initialization, the evaluation of B-spline coefficients that interpolates the input signal as well as convolves with the kernel representing the basis functions for the wavelet transform, which can be mathematically expressed as: (11) (2) Iterated Moving Sum: Then, the signal can be dilated or compressed with the factor shown as follows: (12) where can be obtained by times convolution of . The following equation indicates such an operation: (13) Then, the moving sum filter can be employed as follows: (14) where is an appropriate offset, and the initial condition is equal to .…”

Section: Computation Proceduresmentioning

confidence: 99%

An Application of B-Spline Wavelet Transform for Notch Detection Enhancement

Huang

2004

IEEE Trans. Power Delivery

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In this paper, the B-spline wavelet transform is applied for the enhancement of notch detection capability. By embodying the B-spline wavelet function, the time-frequency information of the notch waveform is seen presented in an integrated manner, thereby improving the monitoring capability of disturbances at different intervals. To validate the effectiveness of the method, this proposed approach was employed for the detection of notch signals, the identification of sag and swell, and the examination of electric drive-generated signals. A virtual instrument approach was also made to facilitate the visualization of the method. Test results demonstrated the practicality and advantages of the proposed approach for the applications.Index Terms-B-spline wavelet, disturbances, notch.

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“…It performs what is called a time–frequency analysis of the signal, which means the estimation of the spectral characteristics of the signal as a function of time. In some sense, wavelet analysis is close to the windowed short-term Fourier transform, especially when using the Morlet wavelet (Osofsky, 2000), but the major difference is that the size of the window is fixed for the short-term Fourier, and it is adapted to the frequency of the signal in wavelet analysis. Because of this difference, wavelet analysis has a more accurate time–frequency resolution (Lachaux et al, 2000, Bonato et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

The research of constructing dynamic cognition model based on brain network

Fang

2017

Saudi Journal of Biological Sciences

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Estimating the functional interactions and connections between brain regions to corresponding process in cognitive, behavioral and psychiatric domains is a central pursuit for understanding the human connectome. Few studies have examined the effects of dynamic evolution on cognitive processing and brain activation using brain network model in scalp electroencephalography (EEG) data. Aim of this study was to investigate the brain functional connectivity and construct dynamic programing model from EEG data and to evaluate a possible correlation between topological characteristics of the brain connectivity and cognitive evolution processing. Here, functional connectivity between brain regions is defined as the statistical dependence between EEG signals in different brain areas and is typically determined by calculating the relationship between regional time series using wavelet coherence. We present an accelerated dynamic programing algorithm to construct dynamic cognitive model that we found that spatially distributed regions coherence connection difference, the topologic characteristics with which they can transfer information, producing temporary network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time after variation audio stimulation, dynamic programing model gives the dynamic evolution processing at different time and frequency. In this paper, by applying a new construct approach to understand whole brain network dynamics, firstly, brain network is constructed by wavelet coherence, secondly, different time active brain regions are selected by network topological characteristics and minimum spanning tree. Finally, dynamic evolution model is constructed to understand cognitive process by dynamic programing algorithm, this model is applied to the auditory experiment, results showed that, quantitatively, more correlation was observed after variation audio stimulation, the EEG function connection dynamic evolution model on cognitive processing is feasible with wavelet coherence EEG recording.

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Calculation of transient sinusoidal signal amplitudes using the Morlet wavelet

Cited by 12 publications

References 1 publication

Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

An Application of B-Spline Wavelet Transform for Notch Detection Enhancement

The research of constructing dynamic cognition model based on brain network

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