TY - JOUR

T1 - A black box identification in frequency domain

AU - Mercorelli, Paolo

AU - Terwiesch, P.

N1 - Cited By (since 1996): 4 Export Date: 22 May 2012 Source: Scopus Language of Original Document: English Correspondence Address: Mercorelli, P.; Inst. fur Automatisierung/Informatik, Schlachthofstraße 4, 38855 Wernigerode, Germany; email: mercorelli@iai-wr.de References: Terwiesch, P., Menth, S., Schmidt, S., Analysis of transients in electrical railway networks using wavelets (1998) IEEE Trans. on Ind. Electron., 45 (6), pp. 955-959; Jawerth, B., Sweldens, W., Biorthogonal smooth local trigonometric bases (1995) J. Fourier Anal. Appl., 2 (2), pp. 109-133; Auscher, P., Weiss, G., Wickerhauser, M.V., Wavelet- A tutorial in theory and applications (1992) Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets, , Boston/USA: Academic Press; Coifman, R.R., Wickerhauser, M.V., Entropy-based algorithms for best basis selection (1992) IEEE Trans. on Inform. Theory, IT-38 (2), pp. 713-718; Joost, M., Schiffmann, W., Speeding up backpropagation algorithms by using cross-entropy combined with pattern normalization (1999) Int. J. of Uncertainity, Fuzziness and Knowledge-based Syst. (IJUFKS), 6 (2), pp. 117-126; Saito, N., Coifman, R.R., Local discriminant bases (1994) Mathematical Imaging: Wavelet Applications in Signal and Image Processing II Conf. (SPIE), 2303, pp. 2-14. , San Diego/California/USA, proc; Zhang, Q., Using wavelet network in nonparametric estimation (1997) IEEE Trans. on Neural Networks, 8 (2), pp. 227-236; Mallat, S., Zhang, Z., (1993) Matching Pursuit with Time-Frequency Dictionaries, , Computer Science Department: New York/USA, Tech. Rep. 619; Juditsky, A., Hjalmarsson, H., Benveniste, A., Delyon, B., Ljung, L., Sjöberg, J., Zhang, Q., Nonlinear black-box models in system identification: Mathematical foundations (1995) J. Automatica, 31 (12), pp. 1725-1750; Daubechies, I., (1995) Ten Lectures on Wavelets, , Philadelphia/USA: Society for Industrial and Applied Mathematics; Hess-Nielsen, N., Wickerhauser, M.V., Wavelets and time-frequency analysis (1996) IEEE Proc., 84 (4), pp. 523-540; Daubechies, I., The wavelet transform, time-frequency localization and signal analysis (1990) IEEE Trans. on Inform. Theory, IT-36 (5), pp. 961-1005; Ruck, D.W., Rogers, S.K., Kabrisky, M., Oxley, M.E., Suter, B.W., The multilayer perceptron as an approximation to a Bayes optimal discriminant function (1990) IEEE Trans. on Neural Networks, 1 (4), pp. 296-298; Donoho, D., (1996), http://playfair.stanford.eduUR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0037285523&partnerID=40&md5=ec20fb77a0c4242cfc52ba2ec8992107

PY - 2003

Y1 - 2003

N2 - Harmonic oscillations as integer multiples of the fundamental frequency in a power system are caused by nonlinear physical effects such as switching or saturation. Modelling and detection of these harmonics are crucial for power system control and protection. The present paper proposes the use of wavelet networks with smooth local trigonometric functions as activation functions. A new algorithm is proposed, together with the use of the Cross Entropy function as a tool for evaluating the model quality. The algorithm consists of recursive dual iterations with biorthogonal smooth local sine and cosine wavelet packets in order to calculate the adjustable parameters related to the activation functions. The algorithm efficiently minimizes the Shannon Entropy function by adaptively choosing the best time-frequency cells on the wavelet packet tree. During every loop the Cross Entropy function between estimated outputs and target outputs is checked. A procedure by using trigonometric wavelet packets is proposed as an effective tool for disturbance detection, power quality analysis and non-linear harmonic circuit modelling. Simulations of a converter bridge for traction drives are included to illustrate the effectiveness of the algorithm and the choice of the activation function.

AB - Harmonic oscillations as integer multiples of the fundamental frequency in a power system are caused by nonlinear physical effects such as switching or saturation. Modelling and detection of these harmonics are crucial for power system control and protection. The present paper proposes the use of wavelet networks with smooth local trigonometric functions as activation functions. A new algorithm is proposed, together with the use of the Cross Entropy function as a tool for evaluating the model quality. The algorithm consists of recursive dual iterations with biorthogonal smooth local sine and cosine wavelet packets in order to calculate the adjustable parameters related to the activation functions. The algorithm efficiently minimizes the Shannon Entropy function by adaptively choosing the best time-frequency cells on the wavelet packet tree. During every loop the Cross Entropy function between estimated outputs and target outputs is checked. A procedure by using trigonometric wavelet packets is proposed as an effective tool for disturbance detection, power quality analysis and non-linear harmonic circuit modelling. Simulations of a converter bridge for traction drives are included to illustrate the effectiveness of the algorithm and the choice of the activation function.

KW - Engineering

U2 - 10.1002/etep.4450130105

DO - 10.1002/etep.4450130105

M3 - Journal articles

VL - 13

SP - 29

EP - 40

JO - International Transactions on Electrical Energy Systems

JF - International Transactions on Electrical Energy Systems

SN - 2050-7038

IS - 1

ER -