Abstract
This paper presents the possibilities of the processing of indicator diagrams by means of the moving approximation objectsdeveloped by the author, which are based on the least squares method. The rules of creating the approximating objects withthe use of the spline knots have been discussed: glued, riveted and broken knots as well as multiple approximation. Byusing the example of the processing of indicator diagrams of the medium-speed marine engine, the quality of the mileageapproximation for a few types of the approximating objects has been compared. Some examples of curve smoothing and determining of derivatives and separating the high-frequency noise and disturbances caused by gas channels have beenpresented as well.
Highlights
S3owa kluczowe: ruchoma aproksymacja, funkcje giête, metoda najmniejszych kwadratów, wyg3adzanie, generowanie pochodnych, dekompozycja zak3óceñ, wykres indykatorowy, silnik spalinowy
The processing of indicator diagrams with the use of the moving approximating objects This paper presents the possibilities of the processing of indicator diagrams by means of the moving approximation objects developed by the author, which are based on the least squares method
Some examples of curve smoothing and determining of derivatives and separating the high-frequency noise and disturbances caused by gas channels have been presented as well
Summary
Dane pomiarowe zawieraj informacjê o wartoœciach wielkoœci mierzonej w punktach pomiarów oraz o przebiegu zale¿noœci wielkoœci mierzonej od argumentu. S1 one obarczone ró¿nego rodzaju b3êdami i zak3óceniami. Celem obróbki danych pomiarowych jest oszacowanie wartoœci rzeczywistych wielkoœci pomierzonych lub poszukiwanie zale¿noœci funkcyjnych, których model matematyczny jest znany lub tak¿e poszukiwany. Je¿eli nie udaje siê stworzyæ adekwatnego modelu matematycznego przebiegu wielkoœci mierzonej, to najczêœciej jest on przybli¿any kombinacj liniow wybranych funkcji elementarnych:. Gdzie: y – funkcja aproksymuj1ca, f1, f2, ... Fk – liniowo niezale¿ne funkcje elementarne, a1, a2, ... Spoœród funkcji elementarnych dobierane s1 najczêœciej wielomiany potêgowe lub trygonometryczne. Te ostatnie s1 na ogó stosowane, gdy poszukiwane jest widmo czêstotliwoœciowe przebiegu. Wspó3czynniki ak w równaniu (1) s1 z regu3y wyznaczane z warunku minimum funkcjona3u stanowi1cego definicjê metody najmniejszych kwadratów: MIN(S)
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