TY - CHAP

T1 - Industrial applications using wavelet packets for gross error detection

AU - Mercorelli, P.

AU - Frick, Alexander

N1 - Export Date: 22 May 2012 Source: Scopus doi: 10.1007/978-3-540-71078-3_4 Language of Original Document: English Correspondence Address: Mercorelli, P.; Dep. of Vehicles, Production and Control Engineering, University of Applied Sciences Wolfsburg, Robert-Koch-Platz 12, 38440 Wolfsburg, Germany; email: p.mercorelli@fh-wolfsburg.de References: Menold, P.H., Pearson, R.K., Allgwer, F., Online outlier detection and removal (1999) Mediterranean Control Conference, , Israel; Donoho, D.L., Johnstone, I.M., Adapting to unknown smoothness via wavelet shrinkage (1994) Journal of the American Statistical Association, 90 (432), pp. 1220-1224; Donoho, D.L., Denoising by soft thresholding (1995) IEEE Transaction On Information Theory, 41 (3), pp. 613-627; Donoho, D.L., Johnstone, I.M., Ideal spatial adaptation by wavelet shrinkage (1994) Biometrika, 81 (3), pp. 425-455; Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D., Density estimation by wavelet thresholding (1996) Annals of Statistics, 24 (2), pp. 508-539; Shao, R., Jia, F., Martin, E.B., Morris, A.J., Wavelets and non linear principal component analysis for process monitoring (1999) Control Engineering Practice, 7, pp. 865-879; Coifman, R.R., Wickerhauser, M.V., Entropy based algorithm for best basis selection (1992) IEEE Information Theory, 32, pp. 712-718; Isermann, R., Modellgesttzte berwachung und Fehlerdiagnose Technischer Systeme (1996) Automatisierungstechnische Praxis, 5, pp. 9-20; P. Mercorelli, M. Rode, P. Terwiesch, (2000) A Wavelet Packet Algorithm for OnLine Detection of Pantograph Vibration, In: Proc. IFAC Symposium on Transportation. Braunschweig, Germany, 13-15 JuneMercorelli, A.F., (2006) Noise Level Estimation Using Haar Wavelet Packet Trees for Sensor Robust Outlier Detection, , Lecture Note in Computer Sciences. Springer-Verlag publishing; http://www-stat.stanford.edu/wavelabDaubechies, I., (1995) Ten Lectures on Wavelets, , Publisher Society for Industrial and Applied Mathematics, Philadelphia Pennsylvania; Albuquerque, J.S., Biegler, L.T., Data Reconciliation and Gross-Error Detection for Dynamic Systems (1996) AIChE Journal, 42, pp. 2841-2856; Beheshti, S., Dahleh, M.A., On denoising and signal representation (2002) Proc. of the 10th Mediterranean Control Conference on Control and Automation; Beheshti, S., Dahleh, M.A., Noise variance and signal denoising (2003) Proc. of IEEE International Conference on Acustic. Speech, and Signal Processing, , ICASSP; Coifman, R.R., Wickerhauser, M.V., Entropy based algorithm for best basis selection (1992) IEEE Trans. Inform. Theory, 32, pp. 712-718; Shao, R., Jia, F., Martin, E.B., Morris, A.J., Wavelets and non linear principal component analysis for process monitoring (1999) Control Engineering Practice, 7, pp. 865-879; Pearson, R.K., Exploring process data (2001) J. Process Contr, 11, pp. 179-194; Pearson, R.K., Outliers in Process Modelling and Identification IEEE Transactions on Control Systems Technology, 10, pp. 55-63

PY - 2007/1/1

Y1 - 2007/1/1

N2 - This chapter addresses Gross Error Detection using uni-variate signal-based approaches and an algorithm for the peak noise level determination in measured signals. Gross Error Detection and Replacement (GEDR) may be carried out as a pre-processing step for various model-based or statistical methods. More specifically, this work presents developed algorithms and results using two uni-variate, signal-based approaches regarding performance, parameterization, commissioning, and on-line applicability. One approach is based on the Median Absolute Deviation (MAD) whereas the other algorithm is based on wavelets. In addition, an algorithm, which was developed for the parameterization of the MAD algorithm, is also utilized to determine an initial variance (or peak noise level) estimate of measured variables for other model-based or statistical methods. The MAD algorithm uses a wavelet approach to set the variance of the noise in order to initialize the algorithm. The findings and accomplishments of this investigation are: 1. Both GEDR algorithms, MAD based and wavelet based, show good robustness and sensitivity with respect to one type of Gross Errors (GEs), namely outliers. 2. The MAD based GEDR algorithm, however, performs better with respect to both robustness and sensitivity. 3. The algorithm developed to detect the peak noise level is accurate for a wide range of S/N ratios in the presence of outliers. © Springer-Verlag Berlin Heidelberg 2007.

AB - This chapter addresses Gross Error Detection using uni-variate signal-based approaches and an algorithm for the peak noise level determination in measured signals. Gross Error Detection and Replacement (GEDR) may be carried out as a pre-processing step for various model-based or statistical methods. More specifically, this work presents developed algorithms and results using two uni-variate, signal-based approaches regarding performance, parameterization, commissioning, and on-line applicability. One approach is based on the Median Absolute Deviation (MAD) whereas the other algorithm is based on wavelets. In addition, an algorithm, which was developed for the parameterization of the MAD algorithm, is also utilized to determine an initial variance (or peak noise level) estimate of measured variables for other model-based or statistical methods. The MAD algorithm uses a wavelet approach to set the variance of the noise in order to initialize the algorithm. The findings and accomplishments of this investigation are: 1. Both GEDR algorithms, MAD based and wavelet based, show good robustness and sensitivity with respect to one type of Gross Errors (GEs), namely outliers. 2. The MAD based GEDR algorithm, however, performs better with respect to both robustness and sensitivity. 3. The algorithm developed to detect the peak noise level is accurate for a wide range of S/N ratios in the presence of outliers. © Springer-Verlag Berlin Heidelberg 2007.

KW - Engineering

KW - Outlier Detection

KW - Lipschitz Constant

KW - Wavelet Packet

KW - Median Absolute Deviation

KW - Quality Module

UR - http://www.scopus.com/inward/record.url?scp=34248373209&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f20c2089-afa8-3b7c-8e1c-712283a9a400/

U2 - 10.1007/978-3-540-71078-3_4

DO - 10.1007/978-3-540-71078-3_4

M3 - Contributions to collected editions/anthologies

SN - 978-3-540-71077-6

SN - 3-540-71077-9

T3 - Studies in Computational Intelligence

SP - 89

EP - 127

BT - Computational Intelligence in Information Assurance and Security

A2 - Nedjah, Nadia

A2 - Macedo Mourelle, Luiza

A2 - Abraham, Ajith

PB - Springer Verlag

CY - Berlin, Heidelberg

ER -