meranie v informatike · 2008-02-25 · lord kelvin: when you can measure what you are speaking...
TRANSCRIPT
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MERANIE
doc. Ing. Peter Kukuča, CSc. MIET
KMer FEI STU
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Hodnotenie predmetu
max. 50 bodov za semester– 30 bodov za prípravu na cvičenia a referáty
16 bodov za vstupné testy
14 bodov za odovzdané referáty
– 20 bodov za dve písomky na prednáškach
max. 50 bodov za skúšku
webmail.stuba.sk/~peter.kukuca
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Meranie nie je:
izolovaná činnosť (meranie ako také)
len rutinná technická činnosť (pri ktorej nemusím rozmýšľať)
niečo, čo sa ma netýka (lebo sa s tým nestretnem)
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Meranie je:
jedna z najčastejších ľudských činností
súčasť väčšiny ľudských činností
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Meranie je:
zistenie kvantitatívnej charakteristiky predmetu alebo javu,
najčastejšie zistenie hodnoty fyzikálnej veličiny
odpovedanie na otázky
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Lord Kelvin:
When you can measure what you are speaking about, and can express it in numbers, you know something about it;
but when you cannot measure it, when you cannot express it in numbers, then your knowledge is of a meagre and unsatisfactory kind.
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George Miller:
In truth, a good case could be made that if your knowledge is meagre and unsatisfactory, the last thing in the world you should do is make measurements.
The chance is negligible that you will measure the right things accidentally.
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Meranie poskytuje:
informácie o výsledku nejakej práce - konštatovanie stavu
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Meranie poskytuje:
priebežné informácie počas vývoja a výroby - ovplyvnenie výsledku
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Meranie poskytuje:
informácie o stave a prevádzke systémov - zabezpečenie funkcie
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Meranie podporuje:
uľahčenie práce
vyššiu kvalitu výrobkov
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Meranie podporuje:
nové metódy diagnostiky
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Meranie limituje:
dosiahnuteľné parametre výrobkov
„spravodlivosť“ v obchode
medzinárodnú spoluprácu a obchod
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Medzinárodná spolupráca
legislatíva a normalizácia
dôležitosť medzinárodných metrologických organizácií (medzinárodné porovnania)
presun „kvantových“ etalónov do výroby a prevádzky
vyššie nároky na prístrojové a personálne vybavenie organizácií
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Meranie vyžaduje:
znalosti objektu merania - v prvom rade treba byť odborníkom vo svojom odbore
znalosti z teórie merania - spracovanie a vyhodnotenie výsledku merania
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Meranie vyžaduje:
znalosti reálnych možností meracej techniky - vedieť rozlíšiť „šľahačku na torte“ od skutočne zásadných vlastností meracieho prístroja
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Meranie vyžaduje:
získať informácie – samotné meranie
namerané údaje spracovať
správne interpretovať výsledok merania
nameraná hodnota
meracia jednotka
odhad chyby merania
podmienky merania
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Úlohy pre „používateľov“:
vedieť si vybrať vhodný (správny) merací prístroj
vedieť navrhnúť zloženie meracieho systému
naprogramovať splnenie požadovanej úlohy
vybrať „tie správne“ merané veličiny
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Chyby merania
Hrubé chyby (omyly)
vylúčiť
Systematické chyby (deterministické)
korigovať
Náhodné chyby (stochastické)
zmenšovať
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Absolútna chyba ΔX
ΔX = Xm - Xs
K = Xs - Xm
Xm – nameraná hodnota
Xs – skutočná hodnota
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Relatívna chyba δX
δX = ΔX / Xs
δX = ΔX / Xs
δX = ΔX / Xm
δXp= ΔX / XN
δX = ΔX/X .100 %
δX = ΔX/X . 106 ppm
Xs – skutočná hodnota
Xs – správna hodnota
Xm – nameraná hodnota
XN – nominálna hodnota (rozsah)
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Chyby merania
„Skutočné“ hodnoty chýb
zistené porovnaním s presnejším meradlom
Hranice chýb
zaručované výrobcom
max. chyby s pravdepodobnosťou 100 %
Neistoty
interval chýb s pravdepodobnosťou < 100 %
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Hranice chýb
Trieda presnosti
maximálna relatívna chyba prístroja
maximálna relatívna chyba údaja
maximálna relatívna chyba z dĺžky stupnice
Dvojčlenný vzorec
aditívna zložka
multiplikatívna zložka
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Trieda presnosti
tr.pr. = max(ΔX / XN) . 100 %
-2
-1
0
1
2
0 10 20 30 40 50 60 70 80 90 100
Ab
solú
tna
ch
yb
a
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Trieda presnosti
δX = ΔX/X . 100 %
δXp = ΔX/XN . 100 %
ΔX = δXp . XN / 100 %
δX = δXp . XN / X
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Trieda presnosti
-15
-10
-5
0
5
10
15
0
10
20
30
40
50
60
70
80
90
100
Rel
atí
vn
a c
hyb
a
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Dvojčlenný vzorec
max(ΔX) = Δa + Δm
max(ΔX) = Δa + δm.X / 100 %
max(ΔX) = δa.XN /100 % + δm.X /100 %
(0,1 % z údaja + 0,05 % z rozsahu)
(50 ppm + 10 digit)
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Dvojčlenný vzorec
max(ΔX) = Δa + δm . X / 100 %
-2
-1
0
1
2
0 10 20 30 40 50 60 70 80 90 100
Ab
solú
tna
ch
yb
a
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Dvojčlenný vzorec
max(δX) = δa . XN / X + δm
-15
-10
-5
0
5
10
15
0
10
20
30
40
50
60
70
80
90
100
Rela
tívn
a c
hyb
a
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Neistoty
Uncertainty u
Interval okolo nameranej hodnoty, v ktorom sa nachádza skutočná hodnota s istou pravdepodobnosťou (~ 60 – 70 %).
Daná hodnotou výberovej smerodajnej odchýlky výberového aritmetického priemeru meranej veličiny.
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Chyby meracích prístrojov
Referenčné podmienky
– teplota
– frekvencia (frekvenčný rozsah)
– časový priebeh striedavej veličiny
– ...
Prídavné chyby
– mimo referenčných podmienok
– vplyv meracieho prístroja (spotreba)
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Korekcia spotreby MP
Neexistuje univerzálny (definičný) vzorec
Individuálna analýza vplyvu MP na výsledok merania
Pozor na zanedbanie vplyvu MP
– MP s malým vstupným odporom
– extrémne podmienky merania, napr. vysoká frekvencia
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Zapojenie MP
Paralelne „ako voltmeter“
veľký vstupný odpor
koľko je dosť?
Sériovo „ako ampérmeter“
malý vstupný odpor
mikroampérmeter
Prispôsobenie impedancii systému
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Korekcia spotreby MP
V
x
R
UI
UR
Rx
A
V
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Korekcia spotreby MP
I
RIUR Ax
.
Rx
A
V
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Korekcia spotreby MP
vwv
vwvw
RR
RR
UPP
.
2
Z
A
V
W
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Meracie metódy
Priame meranie
Nepriame meranie
– výpočtom z iných (priamo) nameraných hodnôt
– kompenzačná metóda
– komparačná metóda
– substitučná metóda
– mostíkové metódy
Výchylkové a nulové metódy
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Kompenzačná metóda
RX
NI
UX
RC UN
c
xNxR
RUU
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Komparačná metóda
RXVX
RNVN
N
XNXU
URR
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Mostíková metóda
3
21R
RRRX
213 .. RRRRXR1
R3
RX
R2
NI
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Mostíková metóda
3
21Z
ZZZ X
Z1
Z3
ZX
Z2
NI
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Zákon prenášania chýb
ΔX
X
ΔY
Y XdX
dYY
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Zákon prenášania chýb
XdX
dYY
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Zákon prenášania chýb
XX
YY
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Zákon prenášania chýb
i
i
i
XX
YY
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Zákon prenášania chýb
i
i
i
XX
YY
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Zákon prenášania chýb
i
i
i
XX
Y
YY
YY
1
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Zákon prenášania chýb
i
ii
i
XXX
Y
YY
1
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Zákon prenášania chýb
i
ii
i
XY
X
X
YY
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Zákon prenášania chýb
21 XXY
21 XXY
21 / XXY
21 XXY