Application of wavelets and neural networks to diagnostic system development, 1, feature extraction(8)

卷积神经网络和一些独立成分分析的外文文献

B.H.Chenetal./ComputersandChemicalEngineering23(1999)899–906903

Fig.2.The‘least-Asymmetric’scalefunctionandwaveletfunction.

Fig.3.Signal(a)anditsextrema(b)ofwaveletanalysisusingDaubechies’eightcoef cientswavelet.

Fig.5andFig.6illustratethisidea.InFig.5,threedifferentnoisefrequenciesarestudied.Thewaveletmulti-resolutionanalysisisshownontheleftandex-tremaofwaveletanalysisareontheright.Clearly,theextremawilldecreaseandthendisappearasthescaleincreases.

Fig.6showsasignalwhichisbasicallythesineinFig.3acorruptedbywhitenoiseaswellasthewaveletmulti-scaleextremaanalysis.Noisecomponentsarere-ducedandthendisappearasthescaleincreases.Theresultsforscales-4and-5aresimilartothatofFig.3bwhichisnoise-free.Thisshowsthattheextremaofthetrendsignalareretainedwhilenoiseextremaare ltered.

theextremarepresentationinscale-4isavectorofdimension70,

Scale-4=(…x5…x23…x37…x53…)

wherex5standsforanon-zerodatumincolumn5.Whileinscale-5,itbecomes

3.4.Piece-wiseprocessing

Twoobservationsaremadeabouttheabovediscus-sions.Firstly,extremaanalysisusingwaveletmultireso-lutionanalysisremainssteadywiththeincreaseofscales,sotherepresentationissteady.Forexample,inFig.6whenthescaleisincreasedfromfourto ve,thefourextremaremain.Secondly,thelocationofextremamayslightlyshiftwithtimeasscaleincreases.InFig.6,

Fig.4.ExtremaofwaveletanalysisusingDaubechies’tencoef cientswavelet.