Application of wavelets and neural networks to diagnostic system development, 1, feature extraction(9)

卷积神经网络和一些独立成分分析的外文文献

904B.H.Chenetal./ComputersandChemicalEngineering23(1999)899–906

Fig.5.Noisesignal,itswavelettransformationandtheextremaofwaveletanalysis.

Scale-5=(…x7…x22…x38…x54…)

Itisobviousthatnon-zerodatumintheposition5ofscale-4isshiftedtotheposition7ofscale-5.Thisinconsistencyshouldbeavoided.Forinstance(2,0…0,3)and(2,0…3,0)shouldbeconsidereddif-ferent.Thisisnecessaryespeciallywhenthetrendsofavariableatdifferentoperationsconditionsareconsidered.

Theextremarepresentationcanbehighlysparsevec-tors.Thisistrueforprocessdynamicresponseswhichare

slowinfrequency.Themethodweusediscalledpiece-wiseprocessing.Theideaistomapahighlysparsevectortoadenservectorbydimensionreduction.Forexample,withscale-4andscale-5discussedabove,ifthepiece-wisesub-regionis xedasfourdatapoints,thenscale-4andscale-5willbetransformedtovectorsofdimension18.Scale-4%=(…x2…x6…x10…x13…)Scale-5%=(…x2…x6…x10…x13…)

Itisclearthatafterpiece-wiseprocessing,thedimen-