COBEM99

S25 Métodos Numéricos

Title:

MULTIRESOLUTION ANALYSIS WITH WAVELETS OF A VIBRATION RECORDS DATA FROM A NAVAL ENGINE

Summary :

THE AIM OF THIS PAPER IS TO PROVIDE AN INTRODUCTION TO THE SUBJECT OF WAVELET ANALYSIS OF VIBRATION RECORDS DATA FROM A NAVAL ENGINE. THE PAPER SELECTS FROM THE MATHEMATICAL LITERATURE ON WAVELETS THE RESULTS NECESSARY TO DEVELOP WAVELET-BASED NUMERICAL ALGORITHMS. IN PARTICULAR, WE PROVIDE EXTENSIVE DETAILS OF DERIVATION OF DAUBECHIE’S WAVELET COEFFICIENTS, SINCE THESE ARE FUNDAMENTAL TO GAINING AN INSIGHT INTO THE PROPERTY OF WAVELETS. WAVELETS ARE MATHEMATICAL FUNCTIONS THAT CUP DATA INTO DIFFERENT FREQUENCY COMPONENTS AND THEN STUDY EACH COMPONENT WITH A RESOLUTION MATCHED TO ITS SCALE. THEY HAVE ADVANTAGES OVER TRADITIONAL FOURIER METHODS IN ANALYZING PHYSICAL SITUATIONS WHERE THE SIGNAL CONTAINS DISCONTINUITIES AND SHARP SPIKES. WAVELETS HAVE BEEN A VERY POPULAR TOPIC OF CONVERSATIONS IN MANY SCIENTIFIC AND ENGINEERING GATHERINGS THESE DAYS. A NATURAL FRAMEWORK FOR WAVELET THEORY IS MULTIRESOLUTION ANALYSIS (MRA) WHICH IS A MATHEMATICAL CONSTRUCTION THAT CHARACTERIZES WAVELETS IN GENERAL WAY. HOWEVER, CONCEPTUALLY, MULTIRESOLUTION IT IS INTIMATELY RELATED TO SUBBAND AND WAVELET DECOMPOSITIONS. THE BASIC IDEA IS SUCCESSIVE APPROXIMATION. A SIGNAL IS WRITTEN AS A COARSE APPROXIMATION (TYPICALLY A LOWPASS, SUBSAMPLED VERSION) PLUS A PREDICTION ERROR WHICH IS THE DIFFERENCE BETWEEN THE ORIGINAL SIGNAL AND A PREDICTION BASED ON THE COARSE VERSION. RECONSTRUCTION IS IMMEDIATE: SIMPLY ADD BACK THE PREDICTION TO THE PREDICTION ERROR. THE SCHEME CAN BE ITERATED ON THE COARSE VERSION. IT CAN BE SHOWN THAT IF THE LOWPASS FILTER MEETS CERTAIN CONSTRAINTS OF ORTHOGONALITY, THEN THIS SCHEME IS IDENTICAL APPROXIMATION APPROACH IS STILL AT LEAST CONCEPTUALLY IDENTICAL TO THE WAVELET DECOMPOSITION SINCE IT PERFORMS A MULTIRESOLUTION ANALYSIS OF THE VIBRATION RECORDS DATA. PRESENTING THE RESULTS OF OUR RESEARCH IN ONE-DIMENSIONAL VIBRATION RECORDS DATA ANALYSIS FROM A NAVAL ENGINE HIGHLIGHTS THE BENEFITS OF USING MULTIRESOLUTION ANALYSIS WITH WAVELETS.

Author :

POTERASU, VICTOR FLORIN
ZAGAN, REMUS 0

Paper View :