methods for correction
TRANSCRIPT
1/15/07 BAE 5413 1
Compensation for Interfering and Modifying Inputs
• Methods of compensation– Inherent insensitivity
• eg. Shielding instrument from EMI
• Construction of strain gauges from invar
– High Gain feedback– Calculated output corrections– Filtering– Opposing inputs
1/15/07 BAE 5413 2
Method of inherent insensitivity
• Minimize Fi, Fmi, Fmd
• Selectivity - ability to of an instrument to select the input of interest and reject interference signals
Fd
Fmi
FiIi
Im
Id
O
Fmd
Interfering input
Modifying input
Desired input
Output
ModifiedInterfering
Output
ModifiedDesiredOutput
1/15/07 BAE 5413 3
Method of high gain feedback
• System with modifying input
Fd
Im
Id O
Fmd
Modifying input
Desired input
Output
ModifiedDesiredOutput
)( mdd IFIO =
1/15/07 BAE 5413 4
Method of high gain feedback
• Feedback loop added
• Kfb >>1
• O is no longer a function of Fd(Im)
dmdfb
fbmdd
mdfb
fbmdd IIFK
KIFI
IFK
KIFIO =≅
+=
)(
)(
)(1
)(
1/15/07 BAE 5413 5
Method of calculated output correction
• Computer based systems allow correction to be made easily
• Requires that Ii be measured also
Ii
Id
Interfering input
Desired input
OOutput
Fi
Fd
-Fi
Calculation
Instrument
sum
sum
1/15/07 BAE 5413 6
Method of Opposing Inputs
• Input information is used in some manner to form a correcting signal within the instrument
Ii
Id
Interfering input
Desired input
OOutput
Fi
Fd
-Fi
Instrument
sum
1/15/07 BAE 5413 7
Method of filtering
• Removes interfering signal– Frequency of desired signal must be different from frequency
of interference
Fd
Fmi
FiIi
Im
Id
Fmd
Interfering inputat Frequency fi
Modifying input
Desired input
ModifiedInterfering
Output
ModifiedDesiredOutput
OOutput
Band reject filterrejecting fi
1/15/07 BAE 5413 8
Reporting Instrument Error
• NIST 1297– Standardizes the reporting of uncertainty– Coordinated with CIPM/ISO– Based on representing each component of uncertainty (ui) in
a measurement by an estimated standard deviation associated with that component. ui = standard uncertainty
– Divides types of uncertainty into two categories• Type A - can be evaluated directly as a standard deviation• Type B - must be estimated in non-statistical fashion, but is
expressed as a standard deviation
– Assumes a correction factor is applied to remove systematic error (bias is removed by calibration)
– Defines combined uncertainty (uc) as the RMS of the component uncertainties: ( )∑=
iic uu 2
1/15/07 BAE 5413 9
NIST 1297 -cont-
– Note:
and
–– Defines expanded uncertainty, U, as the range within which
the “value of the measurand”(Y) can confidently be expected to lie. And expanded uncertainty can be calculated as a product of coverage factor (k), and combined uncertainty (uc)
– Y- measurand, y - measurement result
ii
i xx
uu
∂∂=
∑
∂∂=
ii
i
ic x
x
uu
2
ckuU =
ckuyUyY ±=±=
1/15/07 BAE 5413 10
NIST 1297 -cont-
– Recommends use of a coverage factor of 2 (This is equivalent to ±2 standard deviations or 95% if normal) or an explanation why.
1/15/07 BAE 5413 11
Traceability of measurand and uncertainty
• A traceable measurand is not needed for determination of uncertainty.– Correction of systematic error or bias is assumed– Standard deviation of y given a single Y allows u(y) to be
determined
InstrumentY y
ExemplaryInstrument