Proceedings of SerbiaTrib '13

Serbian TribologySocietySERBIATRIB‘1313th International Conference onTribologyKragujevac,Serbia, 15 – 17 May 2013Faculty of Engineeringin KragujevaccUSING OFKALMAN FILTER ASA PROGNOSTIC TOOLFOR TRIBOLOGY PROCESSESIvanMačužić 1 , Petar Todorović 1 , Marko Đapan 1 , Milan Radenković 1 , Branislav Jeremić 11 Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia,ivanm@kg.ac.rs, petar@ @kg.ac.rs, djapan@kg.ac.rs, radenkovic@ @kg.ac.rs, bane@kg.ac.rsAbstract: The paper consider possibilities for performing ofprognostic procedure pfor tribology processes inhydraulic equipment using advanced mathematical tool called Kalman filter. It is an algorithmthat uses aseries of measurementsobserved over time, containing noiseand other inaccuracies,, and produces estimatessof monitored parameter that tend to be more precise than those based on a single measurement alone.Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimateeof the underlying system state.This type of procedure could be usedd for prognostic of state of chosenparameter of tribologysystem with significantly accuracy. Efficiencyy of Kalman filter were tested onexperimental results of hydraulic oill contamination monitoring performed in laboratory conditions.Keywords: Kalman filter, prognostic, tribology processes, hydraulic equipment1. INTRODUCTIONPrognostics is a set of activities aimedd atassessing the remaining time tofailure for aparticular technical system or risk of presencee oroccurrence of one or more failuremodes in thefuture. Prognosticsefficiency can be quitesatisfactory for the failure modes that haverepeating time characteristics,followed byprogressive degradation of keyexploitationcharacteristics [1].In casess of failure modes with random andunexpected events, prognostic is a very difficulttask with uncertain results.Prognostic process could be based on the model,or on the measurement results. Prognostic basedd onthe measurement resultss includes the use of variousmathematical tools for monitoring and predicting,such as for example Kalman filter and its simplifiedversion known as alpha-beta-gammaa filter [2].2. KALMAN FILTERSignal filtering, and extracting the t useful signalfrom noise is a traditional problemin science andtechnology.Significant number of models andalgorithms was proposed and developed for solvingof this problem. In case when signal and noise384spectra lies inn different frequency bands, theirseparation cann be made with appropriate bandfilters.Another problem arises when the spectra of thesignal and noise overlapp and thenstatisticalmethods for the assessment and evaluation of thesignal should be b used to extract the signal. In suchcircumstancesit is not possible toobtain anaccurate absolute value off the signal, and all themethods of filtration are made only to t minimizeinterference.The first such analog signals filter suggested s byNorbet Winer in 1940. using the method of leastsquares. New stage in the development of thetheory of filtration began Rudolf Emill Kalman in1960., with publication of his capital work, "A NewApproach to Linear Filtering and PredictionProblems" in which w it was first introduced methodwill become known in science as the Kalman filter[3].The Kalmann filter is a mathematical tool thattcanbe used too assess thee value of variables indifferent formss of real situation. Mathematicallyspeaking Kalman filter evaluates the condition oflinear systems. It is a statistical technique thattcombines the statistical nature of systemfaults withknowledge of the systemm dynamics, , and those13 th International Conference C onn Tribology – Serbiatrib’13