Carlosena, Alfonso

Gómez, Marisol

Lecumberri, Pablo

UPCommons. Portal del coneixement obert de la UPC

Instrumentation ViewPoint. Autumn 2005361. IntroductionThe goal of the work reported in thiscommunication is the development of a methodfor recovering impact signals, or transientimpulsive source signals in general, from sensormeasurements. These techniques are to beincorporated into the design of smartaccelerometers.The classical approach for recovering impactingforce signals consists in applying deconvolutiontechniques to the output signals, given a previousestimation of the system response, which mustaccount for the effects of mechanical propagationand sensor response [1]. Therefore, the overallsystem response depends of the underlyingmechanical structure and the position of impactand sensor, which may be unknown. As a result,in many cases that previous estimation isunavailable and the need for blind deconvolutiontechniques arises.Blind identification / deconvolution is an activefield of research, boosted by its application inwireless communications. Most methodsdeveloped in this area assume some statisticaldistribution for the input signal samples andcompute statistics from the output signals timesamples in order to deconvolve the signals [e.g. 2]. However, in the case of transient signals,we cannot rely on time averages to obtain validstatistics. Deterministic methods that do notassume any statistical prior, still require anestimation of the impulse response of thechannels [e.g. 3, 4].We propose a new blind deconvolution methodfor transient impulsive signals in a single input– multiple output (SIMO) system. The methodexploits the data redundancy inherent to SIMOmultichannel systems to obtain an estimationof the input signal. The method is built upon theassumptions of finite-length signals and channeldiversity.2. Results and Discussion.When the assumptions of the proposed methodare met, it can be shown that the input signalis actually the greatest common divisor (GCD)of the polynomials built with the time samplesof the output signals as coefficients. Thus, areliable numerical method for the computationof the GCD would allow to estimate the inputsignal blindly.In [5], specialized matrices are studied in relationto the computation of the GCD. From resultsreported in that work we have derived a singularmatrix pencil formulation of the problem. Themethod proposed ion [5] and solutions availablefor matrix pencils rely on matrix decompositionswhich are very sensitive to small changes in thedata and thus not suitable for computingestimations from noisy data. Our methodprovides an estimation through the minimizationof the pseudospectra [6] to avoid such instability.The proposed method has been tested with bothsinthetic and real data. Figure 1 shows one ofthe experimental set-ups for the acquisition ofreal signals, which consists of a steel cantileverbeam hit by a sensorized hammer (DytranImpulse Hammer 5850B). Table I shows thedimensions of the beam. Technical data ofhammer and sensors employed can be seen inTable II.Computation of Greatest Common Divisor for theBlind Deconvolution of Transient Impulsive SignalsPablo Lecumberri, Marisol Gómez, Alfonso Carlosena (1)Universidad Pública de NavarraDepartment of Mathematics and Computer Science(1) Department of Electric and Electronic EngineeringCampus de ArrosadíaE-31006 Pamplonapablo.lecumberri@unavarra.esTable I. Steel cantilever beam dimensionsTable II. Equipment data.Figure 1. Cantilever beam with accelerometersand sensorized hammer.Instrumentation ViewPoint.Autumn 200537Piezoelectric accelerometers (Endevco Isotron751-10 Accelerometer) placed upon the beam ondiferent positions provide the output signals ofthe SIMO multichannel system.Signals are sampled at 1066 samples/second.Figure 2 (a) shows one of the output signals. Inorder to obtain finite-length signals so that theproposed method can be applied, the poles ofthe system are first estimated and their contributionfiltered out. The result are finite-length signalsmodelling the zeros of the original ones (Figure2 (b)).Figure 2 (c) shows the impact signal provided bythe sensor placed inside the hammer and theestimated one, obtained by the proposed method(after convenient delaying and scaling). The resultis satisfactory in the sense that it approximatesthe shape of the excitation signal and allows toestimate its duration.3. ConclusionsMotivated by the deconvolution of impact signalsin mechanical systems, we have developed anovel numerical method for the computation ofthe GCD of polynomials. The experimental testsshow the applicability of this method for estimatingtransient impulsive source signals blindly fromsensor measurements. This is a problem thatcould not be resolved with previous blinddeconvolution algorithms. 4. References[1] E. Jacquelin, A. Benani, and P.Hameling, “Force reconstruction. Analysis andregularization of a deconvolution problem”,Journal of Sound and Vibration, vol. 265, pp.81 – 107, 2003.[2] E. Moulines, P. Duhamel, J.-F. Cardoso,and S. Mayrargue, “Subspace methods for theblind identification of multichannel FIR filters”,IEEE Trans. Signal Processing, vol. 43, pp. 516– 525, 1995.[3] G. Xu, H. Liu, L. Tong, and T. Kailath,“A least-squares approach to blind channelidentification”, IEEE Trans. Signal Processing,vol. 43, pp. 2982 – 2993, 1995.[4] Y. Hua, “Fast maximum likelihood forblind identification of multiple FIR channels”,IEEE Trans. Signal Processing, vol. 44, pp.661– 672, 1996.[5] R. R. Bitmead, S.-Y. Kung, B. D. O.Anderson, and T. Kailath, “Greatest commondivisor via generalized sylvester and bezoutmatrices”, IEEE Trans. Automatic Control, vol.23, pp. 1043 – 1047, 1978.[6] G. Boutry, M. Elad, G. H: Golub, and P.Milanfar, “The generalized eigenvalue problemfor non-square pencils using a minimalperturbation approach”, accepted for publicationin SIAM Journal on Matrix Analysis andApplications.Figure 2. (a) Output signal provided by one accelerometer. (b) Output signal afterremoving poles contribution. (c) Measured (dashed) and estimated (solid) sourcesignal.

Computation of Greatest Common Divisor for the Blind Deconvolution of Transient Impulsive Signals

Abstract

Similar works

Full text

Available Versions

UPCommons. Portal del coneixement obert de la UPC