Proceedings of SerbiaTrib '13

3. KALMAN FILTERAPPLICATION FORRPROGNOSTIC OFTRIBOLOGYPROCESSES IN HYDRAULICThe essence of the idea for theapplicationn ofKalman filter for forecasting andprognosticc oftribology processes liesin the fact that it is a toolthat is least dependent on the accuracy of the modelof tribology system that is considered.Theprocedure involves projections toprognosticc inmathematical modelling of the behaviour oftribology parameters in time, whichh severely limitsthe application of other, model-based, prognostictools, sincethey are directly dependent on thecharacteristics of the model for a specific system.On the other hand, Kalman filter will providevery useful results even for very approximatemodels andalso for some standard, general modelsof system behaviour in time (that do not even havedirect link with the observed system),.It is clear that the Kalman filter works onlyy atdiscrete points in time, and its use is relatedd todigital signal processing. Complexmath, matrixtransformations and calculations, represent an easytask for modern computers and processors to thestabile and to mobile devices, which also allowedthe installation of Kalman filters in numerousportable monitoring devices.As an example of application of Kalman filterfor prognostic of tribology processes, trendingg ofcontamination level in hydraulic equipment will bepresented.Method of hydraulic oil contamination valuesprognostic (based on ISO4406 contamination levelcode) usingKalman filter is shown on Figuree 1.From 200 measured points, that define the values ofcontamination level, forparticles off defined size, 9points was allocated (8 is shown from T1 to T8) .ISO 4406 class of oil contaminationT9PT5PT7T7PT6T4T7T8PT3PT6PT5T4PT2T3projectionerrorT1T2PT1,Kalman filter defines point T2P so that t its valueis the same as the t value of the point T1. This is theinitial assumption that nothing will change.At the time of obtainingg the measured values ofother points - T2, T the projection error is i calculatedas the difference in point values T2 and T2P. Onthe basis of the projection error values andmeasured values point T2, Kalman filter performsthe projection of o the value e of the thirdpoint T3P.Then a new measured valuee of contamination T3 isreceived and new projectionn error is calculated andthe cycle is repeated.Practically the value of each new projected pointis function of the previous measuredvalue andprojection errors in the previous point.At Figure 2, , diagram obtained by the projectionof contamination using a Kalman filter for thecurve related to the measured contamination ofhydraulic oil is shown, together with diagram oferror projections. Prognostic process is i conducteddfor 40 points, which define thevalue ofcontamination,in first attempt and 10 points insecond one.ISO 4406class of oil contaminationprojection errorISO 4406class of oil contaminationprojection errornumber of f cyclesnumber off cyclesnumber of cyclesmeasured valuesprojection valuesmeasured valuesprojection valuesnumber of cyclesFigure 1. Kalman filter prognostic processIn this case, those are equidistant points,although, ingeneral, donot have to t be. Basedd onthe value ofthe first point of T1 andset parametersof Kalmanfilter define the value of the firstprojected point in the future (T2P). Since there isno additional information other than the valuee of386number of cyclesFigure 2. Kalman filter prognostic and projection errorAt Figure 3. diagrams obtained by the projectionof contamination using the Kalman filter f for oilsample from the test with the externall addition ofcontamination in i the contact zone is shown.Total of 3 diagrams are shown in Figure 3.refers to variants of Kalman filters with different13 th International Conference C onn Tribology – Serbiatrib’13