A denoising procedure using wavelet packets for instantaneous detection of pantograph oscillations Paolo Mercorelli n Leuphana University of Lueneburg, Institute of Product and Process Innovation (PPI), Volgershall 1, D-21339 Lueneburg, Germany article info Article history: Received 30 August 2010 Received in revised form 14 August 2012 Accepted 4 September 2012 Available online 12 October 2012 Keywords: Noise detection Oscillation detection Wavelets Pantograph control abstract This paper presents a robust online denoising algorithm for use in the online, instantaneous detection of changing harmonic signals. This algorithm uses a classical time correlation function (scalar product). For instantaneous frequency detection, a short window is considered. It is known that cleaned signals are required to determine the correct correlation between short signals. The measured signal is cleaned by the proposed noise removal algorithm, which uses wavelet packets. The proposed cleaning method avoids classical thresholding techniques. Computer simulations that validate the procedure are shown. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction and motivation The paper presents a new general denoising procedure, which can be applied to various industrial applications, such as the identification of signals and parameters for models, fault detection, data reconciliation, compression, and harmonic detection. In these applications, an online denoising procedure is often necessary. In particular, this algorithm was developed and implemented in a wavelets-based outlier package that is currently being integrated into the inferential model platform of the advanced control and simulation solution responsible unit within ABB’s Industry division. Moreover, the paper combines and advances knowledge and methods already present in a technical form in [1,2]. In particular, here, the denoising algorithm is used to detect frequency oscillations in the pantograph control. Fig. 1 shows the whole structure of the application considered in this paper. One of the pioneer methods, known as VisuShrink, was proposed by Donoho and Johnstone [3] and this work and its implementation are available in [4]. Another group of popular wavelet denoising methods is the Bayesian approach, often based on minimising the expected risk, with the expectation taken over a postulated prior distribution supposedly governing the underlying true signal [5–7]. A different approach to wavelet denoising is based on the ‘‘minimum description length’’ (MDL) principle, as proposed in [8,9]. This approach is based on comparisons of the ‘‘description lengths’’ of the data. The description length, which is an information theory criterion, is calculated for different subspaces of the basis. The method suggests choosing the noise variance and the subspace for which the description length of the data is minimal. In other words, noise is defined to be the part of the data in which the given model class cannot find any regular features. Ideally, this definition of noise does not include any assumptions of the noise distribution, even though a Gaussian noise model is usually assumed. The currently used (state of the art) algorithms for estimating noise using wavelets could be summarised as follows:  Apply the wavelet transform to a noisy signal, and obtain the noise wavelet coefficients.  Threshold those elements in the wavelet coefficients that are believed to be attributed to noise.  To reconstruct the noise, apply the inverse wavelet transform to the thresholded wavelet coefficients. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2012.09.001 n Tel.: þ49 4131 677 5571; fax: þ49 4131 677 5300. E-mail address: mercorelli@uni.leuphana.de Mechanical Systems and Signal Processing 35 (2013) 137–149