Adaptive wavelet filtering for bearing monitoring based on block bootstrapping and white noise test

2011 ◽  
Vol 226 (9) ◽  
pp. 2345-2360 ◽  
Author(s):  
Du Wenliao ◽  
Yuan Jin ◽  
Li Yanming ◽  
Liu Chengliang
Keyword(s):  
White Noise ◽  
Wavelet Coefficient ◽  
Vibration Signal ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Decomposition Level ◽  
Wavelet Filtering ◽  
Adaptive Wavelet ◽  
Noise Test ◽  
Bearing Monitoring

This study describes a novel scheme of adaptive wavelet filtering for bearing monitoring based on block bootstrapping and white noise test. The scheme consists of three main steps. First, the vibration signal is decomposed into wavelet domain, and the correlations between the wavelet coefficients are measured by lag autocorrelations. Second, according to the intensity of correlation at each level, either the block bootstrapping or general bootstrapping procedure is adopted to produce new pseudo-samples from the original wavelet coefficient series. Finally, as actual signal and noise have different translating characters along the levels in wavelet domain, the optimal decomposition level is achieved through whitening test on the wavelet coefficients, and the accuracy of the test is also obtained by the pseudo-samples. The simulation and experimental results show that the proposed procedure can be used to adaptively determine the optimal decomposition level and obtain superior filtering capability.

A New Approach for Optimal Decomposition Level Selection in Wavelet De-Noising

2013 ◽  
Vol 333-335 ◽  
pp. 540-545
Author(s):  
Yong Xin Zhang ◽  
Li Chen ◽  
Jian Jia ◽  
Ding Yi Fang
Keyword(s):  
White Noise ◽  
Wavelet Coefficient ◽  
Maximum Energy ◽  
Wavelet Coefficients ◽  
Decomposition Level ◽  
New Approach ◽  
Noise Test ◽  
Novel Algorithm

The paper introduces a novel algorithm to determine the optimal decomposition level in wavelet de-noising. The algorithm selects the optimal decomposition level by comparing the sparsity of wavelet coefficients at adjacent levels. The level whose wavelet coefficient has the maximum sparsity can be confirmed as the optimal decomposition level. We demonstrate experimentally that wavelet de-noising performs better using optimal decomposition level determined by our proposed algorithm than White Noise Test (WNT) method and Maximum Energy (ME) method.

Locally Adaptive Wavelet Thresholding for Speech Enhancement

2013 ◽  
Vol 380-384 ◽  
pp. 3618-3622
Author(s):  
Kang Liu ◽  
Jian Zheng Cheng ◽  
Li Cheng
Keyword(s):  
White Noise ◽  
Speech Enhancement ◽  
Speech Signal ◽  
Bayesian Framework ◽  
Threshold Function ◽  
Wavelet Thresholding ◽  
Wavelet Coefficients ◽  
Edge Preservation ◽  
Adaptive Wavelet ◽  
Locally Adaptive

There are strong dependencies between wavelet coefficients of speech signal,in this article,based on that,a new corresponding nonlinear threshold function derived in Bayesian framework is proposed to decrease the effect of the ambient noise.Analysis of the data shows the effectiveness of the proposed method that it removes white noise more effectually and gets better edge preservation.

MATHEMATICAL IMPLEMENTATION OF HYBRID FAST FOURIER TRANSFORM AND DISCRETE WAVELET TRANSFORM FOR DEVELOPING GRAPHICAL USER INTERFACE USING VISUAL BASIC FOR SIGNAL PROCESSING APPLICATIONS

2012 ◽  
Vol 12 (05) ◽  
pp. 1240031 ◽  
Author(s):  
MOUSA K. WALI ◽  
M. MURUGAPPAN ◽  
R. BADLISHAH AHMMAD
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Input Signal ◽  
Wavelet Decomposition ◽  
Wavelet Coefficient ◽  
Visual Basic ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
End User ◽  
Decomposition Level

In recent years, the application of discrete wavelet transform (DWT) on biosignal processing has made a significant impact on developing several applications. However, the existing user-friendly software based on graphical user interfaces (GUI) does not allow the freedom of saving the wavelet coefficients in .txt or .xls format and to analyze the frequency spectrum of wavelet coefficients at any desired wavelet decomposition level. This work describes the development of mathematical models for the implementation of DWT in a GUI environment. This proposed software based on GUI is developed under the visual basic (VB) platform. As a preliminary tool, the end user can perform "j" level of decomposition on a given input signal using the three most popular wavelet functions — Daubechies, Symlet, and Coiflet over "n" order. The end user can save the output of wavelet coefficients either in .txt or .xls file format for any further investigations. In addition, the users can gain insight into the most dominating frequency component of any given wavelet decomposition level through fast Fourier transform (FFT). This feature is highly essential in signal processing applications for the in-depth analysis on input signal components. Hence, this GUI has the hybrid features of FFT with DWT to derive the frequency spectrum of any level of wavelet coefficient. The novel feature of this software becomes more evident for any signal processing application. The proposed software is tested with three physiological signal — electroencephalogram (EEG), electrocardiogram (ECG), and electromyogram (EMG) — samples. Two statistical features such as mean and energy of wavelet coefficient are used as a performance measure for validating the proposed software over conventional software. The results of proposed software is compared and analyzed with MATLAB wavelet toolbox for performance verification. As a result, the proposed software gives the same results as the conventional toolbox and allows more freedom to the end user to investigate the input signal.

SIGNAL DENOISING USING WAVELETS AND BLOCK HIDDEN MARKOV MODEL

2005 ◽  
Vol 19 (05) ◽  
pp. 681-700 ◽  
Author(s):  
ZHIWU LIAO ◽  
Y. Y. TANG
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Mean Squared Error ◽  
Hidden Markov ◽  
Wavelet Coefficient ◽  
Gaussian Mixture ◽  
Signal Denoising ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
New Framework

This paper presents a new framework for signal denoising based on wavelet-domain hidden Markov models (HMMs). The new framework enables us to concisely model the statistical dependencies and non-Gaussian statistics encountered in real-world signals, and enables us to get a more reliable and local model using blocks. Wavelet-domain HMMs are designed with the intrinsic properties of wavelet transform and provide powerful yet tractable probabilistic signal models. In this paper, we propose a novel wavelet domain HMM using blocks to strike a delicate balance between improving spatial adaptability of contextual HMM (CHMM) and modeling a more reliable HMM. Each wavelet coefficient is modeled as a Gaussian mixture model, and the dependencies among wavelet coefficients in each subband are described by a context structure, then the structure is modified by blocks which are connected areas in a scale conditioned on the same context. Before denoising a signal, efficient Expectation Maximization (EM) algorithms are developed for fitting the HMMs to observational signal data. Parameters of trained HMM are used to modify wavelet coefficients according to the rule of minimizing the mean squared error (MSE) of the signal. Then, reverse wavelet transformation is utilized to modified wavelet coefficients. Finally, experimental results are given. The results show that block hidden Markov model (BHMM) is a powerful yet simple tool in signal denoising.

scholarly journals A New Method of Denoising of Vibration Signal and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Feng Miao ◽  
Rongzhen Zhao ◽  
Xianli Wang
Keyword(s):  
White Noise ◽  
Wavelet Packet ◽  
Median Filter ◽  
Vibration Signal ◽  
New Method ◽  
Mixed Complex ◽  
Denoising Method ◽  
Adaptive Wavelet ◽  
Vibration Signals ◽  
Window Width

In order to improve the performance of the denoising method for vibration signals of rotating machinery, a new method of signal denoising based on the improved median filter and wavelet packet technology is proposed through analysing the characteristics of noise components and relevant denoising methods. Firstly, the window width of the median filter is calculated according to the sampling frequency so that the impulse noise and part of the white noise can be effectively filtered out. Secondly, an improved self-adaptive wavelet packet denoising technique is used to remove the residual white noise. Finally, useful vibration signals are obtained after the previous processing. Simulation signals and rotor experimental vibration signals were used to verify the performance of the method. Experiment results show that the method can not only effectively eliminate the mixed complex noises but also preserve the fault character details, which demonstrates that the proposed method outperforms the method based on the wavelet-domain median filter.

scholarly journals Mechanical Vibration Signal Denoising Using Quantum-Inspired Standard Deviation Based on Subband Based Gaussian Mixture Model

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Aidong Xu ◽  
Wenqi Huang ◽  
Peng Li ◽  
Huajun Chen ◽  
Jiaxiao Meng ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Mechanical Vibration ◽  
Vibration Signal ◽  
Gaussian Mixture ◽  
Wavelet Coefficients ◽  
Denoising Method ◽  
Reduction Effect ◽  
Thresholding Function

Aiming at improving noise reduction effect for mechanical vibration signal, a Gaussian mixture model (SGMM) and a quantum-inspired standard deviation (QSD) are proposed and applied to the denoising method using the thresholding function in wavelet domain. Firstly, the SGMM is presented and utilized as a local distribution to approximate the wavelet coefficients distribution in each subband. Then, within Bayesian framework, the maximum a posteriori (MAP) estimator is employed to derive a thresholding function with conventional standard deviation (CSD) which is calculated by the expectation-maximization (EM) algorithm. However, the CSD has a disadvantage of ignoring the interscale dependency between wavelet coefficients. Considering this limit for the CSD, the quantum theory is adopted to analyze the interscale dependency between coefficients in adjacent subbands, and the QSD for noise-free wavelet coefficients is presented based on quantum mechanics. Next, the QSD is constituted for the CSD in the thresholding function to shrink noisy coefficients. Finally, an application in the mechanical vibration signal processing is used to illustrate the denoising technique. The experimental study shows the SGMM can model the distribution of wavelet coefficients accurately and QSD can depict interscale dependency of wavelet coefficients of true signal quite successfully. Therefore, the denoising method utilizing the SGMM and QSD performs better than others.

Steganographic Method with High Visual Concealment in Wavelet Domain

2013 ◽  
Vol 281 ◽  
pp. 47-50
Author(s):  
Zhi Hong Chen
Keyword(s):  
Wavelet Transformation ◽  
Experimental Results ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Local Neighborhood ◽  
The Impact

In this paper we propose a new steganographic method, which based on wet paper codes and wavelet transformation. The method is designed to embed secret messages in images' wavelet coefficients and depends on images' texture characters in local neighborhood. The receivers can extract secret bits from carrier images only by some matrix multiplications without knowing the formulas written by senders, which further improves steganographic security and minimizes the impact of embedding changes. The experimental results show that our proposed method has good robust and visual concealment performance and proves out it's a practical steganographic algorithm.

scholarly journals An adaptive wavelet transformation filtering algorithm for improving road anomaly detection and characterization in vehicular technology

2019 ◽  
Vol 9 (5) ◽  
pp. 3664
Author(s):  
Habeeb Bello-Salau ◽  
A. J. Onumanyi ◽  
B. O. Sadiq ◽  
H. Ohize ◽  
A. T. Salawudeen ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
False Alarm ◽  
Wavelet Transformation ◽  
Multiple Scales ◽  
Detection System ◽  
Spatial Filter ◽  
Adaptive Threshold ◽  
Wavelet Coefficients ◽  
Adaptive Wavelet ◽  
Vehicular Technology

Accelerometers are widely used in modern vehicular technologies to automatically detect and characterize road anomalies such as potholes and bumps. However, measurements from an accelerometer are usually plagued by high noise levels, which typically increase the false alarm and misdetection rates of an anomaly detection system. To address this problem, we have developed in this paper an adaptive threshold estimation technique to filter accelerometer measurements effectively to improve road anomaly detection and characterization in vehicular technologies. Our algorithm decomposes the output signal of an accelerometer into multiple scales using wavelet transformation (WT). Then, it correlates the wavelet coefficients across adjacent scales and classifies them using a newly proposed adaptive threshold technique. Furthermore, our algorithm uses a spatial filter to smoothen further the correlated coefficients before using these coefficients to detect road anomalies. Our algorithm then characterizes the detected road anomalies using two unique features obtained from the filtered wavelet coefficients to differentiate potholes from bumps. The findings from several comparative tests suggest that our algorithm successfully detects and characterizes road anomalies with high levels of accuracy, precision and low false alarm rates as compared to other known methods.

Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform and Its Application in Wind Turbine Gearbox Fault Diagnosis

2021 ◽  
Author(s):  
Zhaohong Yu ◽  
Cancan Yi ◽  
Xiangjun Chen ◽  
Tao Huang
Keyword(s):  
Wavelet Transform ◽  
Wind Turbine ◽  
Time Window ◽  
Vibration Signal ◽  
Second Order ◽  
Center Frequency ◽  
Wind Turbine Gearbox ◽  
Adaptive Wavelet ◽  
Time Frequency ◽  
Window Width

Abstract Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing Time-Frequency (TF) Analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated Time-Frequency Representation (TFR), this paper proposes a new TFA method, namely Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical Continuous Wavelet Transform (CWT), and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus Adaptive Wavelet Transform (AWT) is generated. Then, on the basis of the theoretical framework of Synchrosqueezing Transform (SST) and accurate Instantaneous Frequency (IF) estimation by the utilization of second-order local demodulation operator, Adaptive Second-order Synchrosqueezing Wavelet Transform (AWSST2) is formed. Considering that the quality of actual time-frequency analysis is greatly disturbed by noise components, through performing multiple Synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since Synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

Efficient and Adaptive Rotation Invariant Wavelet Transform

2003 ◽  
Vol 01 (03) ◽  
pp. 353-372
Author(s):  
Chi-Man Pun
Keyword(s):  
Wavelet Transform ◽  
Texture Classification ◽  
Wavelet Packet ◽  
Sampling Rate ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Information Cost ◽  
Image Size ◽  
Rotation Invariant ◽  
Adaptive Wavelet

It is well known that the sensitivity to translations and orientations is a major drawback in 2D discrete wavelet transform (DWT). In this paper, we have proposed an effective scheme for rotation invariant adaptive wavelet packet transform. During decomposition, the wavelet coefficients are obtained by applying a polar transform (PT) followed by a row-shift invariant wavelet packet decomposition (RSIWPD). In the first stage, the polar transform generates a row-shifted image and is adaptive to the image size to achieve complete and minimum sampling rate. In the second stage, the RSIWPD is applied to the row-shifted image to generate rotation invariant but over completed subbands of wavelet coefficients. In order to reduce the redundancy and computational complexity, we adaptively select some subbands to decompose and form a best basis representation with minimal information cost with respect to an appropriate information cost function. With this best basis representation, the original image can be reconstructed easily by applying a row-shift invariant wavelet packet reconstruction (RSIWPR) followed by an inverse polar transform (IPT). In the experiments, we study the application of this representation for texture classification and achieve 96.5% classification accuracy.

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