TY - CHAP

T1 - Median based algorithm as an entropy function for noise detection in wavelet trees for data reconciliation

AU - Mercorelli, Paolo

PY - 2012/1/1

Y1 - 2012/1/1

N2 - The noise detection and the data cleaning find application in data compressions for images and voice as well as in their analysis and recognition, data transmission, data reconciliation, fault detection and in general in all application area of the signal processing and measurements. The content of this paper can offer the possibility to improve the state of the art of all those procedures with denoising methods which use a thresholding technique implying a free thresholding one, running in wavelet packets. The author presents a technique which deals with a free thresholding method related to the on-line peak noise variance estimation even for signals with a small S/N ratio. The second innovative aspect consists of use of wavelet packets which give more elasticity to the technique. The basic idea is to characterize the noise like an incoherent part of the measured signal. It is performed through the wavelet tree by choosing the subspaces where the median value of the wavelet components has minimum. In this sense the proposed median based algorithm can be seen as an entropy function and this analogy is shown. The paper provides to show general properties of the wavelet packets on which the proposed procedure is based. The developed algorithm is totally general even though it is applied by using Haar wavelet packets and it is present in some industrial software platforms to detect sensor outliers because of their easy structure. More, it is currently integrated in the inferential modeling platform of the Advanced Control and Simulation Solution Responsible Unit within ABB’s (Asea Brown Boveri) industry division.

AB - The noise detection and the data cleaning find application in data compressions for images and voice as well as in their analysis and recognition, data transmission, data reconciliation, fault detection and in general in all application area of the signal processing and measurements. The content of this paper can offer the possibility to improve the state of the art of all those procedures with denoising methods which use a thresholding technique implying a free thresholding one, running in wavelet packets. The author presents a technique which deals with a free thresholding method related to the on-line peak noise variance estimation even for signals with a small S/N ratio. The second innovative aspect consists of use of wavelet packets which give more elasticity to the technique. The basic idea is to characterize the noise like an incoherent part of the measured signal. It is performed through the wavelet tree by choosing the subspaces where the median value of the wavelet components has minimum. In this sense the proposed median based algorithm can be seen as an entropy function and this analogy is shown. The paper provides to show general properties of the wavelet packets on which the proposed procedure is based. The developed algorithm is totally general even though it is applied by using Haar wavelet packets and it is present in some industrial software platforms to detect sensor outliers because of their easy structure. More, it is currently integrated in the inferential modeling platform of the Advanced Control and Simulation Solution Responsible Unit within ABB’s (Asea Brown Boveri) industry division.

KW - Data reconciliation

KW - Fault detection

KW - Haar functions

KW - Noise detection

KW - Signal processing

KW - Variance

KW - Wavelets

KW - Wavelets’ packets

KW - Engineering

UR - http://www.scopus.com/inward/record.url?scp=85048686664&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:85048686664

SN - 9781613242520

SN - 1613242522

T3 - Mathematics Research Developments

SP - 85

EP - 104

BT - New Developments in Mathematics Research

A2 - Clarke, Natalie L.

A2 - Ronson, Alex P.

PB - Nova Science Publishers, Inc.

ER -