Static Performance Characteristics objectives:

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ATMS 320 Meteorological Instrumentation

• Static Performance Characteristics objectives
• Define some basic terms related to the
  performance of an instrument
• Appreciate the requirements for making a
  meaningful static calibration
• Learn the types of statistics applied in static
  sensor calibration
• Be able to apply the rules of significant digits

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ATMS 320 Static Performance Characteristics

• Sensor performance characteristics
• Static
• Dynamic
• Drift
• Exposure

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ATMS 320 Static Performance Characteristics

• Sensor performance characteristics
• Static
• Dynamic
• Drift
• Exposure

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ATMS 320 Static Performance Characteristics

• See formal definition of terms, Analog signal
  Transducer in Section 3.1 of the text

Instrument An instrument is a sensor plus other
transducers as required, and a data display
element.
Sensor An element that receives energy from the
measurand and produces an output signal related
in some way to the measurand.
Transducer A device that converts energy from
one form to another.
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ATMS 320 Static Performance Characteristics

• Static calibration
• Performed by varying one input, usually in a
  stepwise fashion, over the possible range of
  values while holding other inputs, if any,
  constant.

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Ultimate objective of calibration to define
instrument accuracy.
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ATMS 320 Static Performance Characteristics

• Static calibration example
• At each measurement step, the output is observed
  in steady-state conditions (when the input has
  been held steady long enough for the output to
  stabilize).

one period of calibration
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ATMS 320 Static Performance Characteristics

• Transfer plot a plot of sensor raw output
  versus the measurand over the design range of the
  sensor.

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ATMS 320 Static Performance Characteristics

• Range measurand interval over which a sensor is
  designed to respond

range
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ATMS 320 Static Performance Characteristics

• Span algebraic difference between the upper and
  lower range values

? span
100 0 100
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ATMS 320 Static Performance Characteristics

• Static sensitivity slope of the transfer curve.

Example
static sensitivity
d raw output / d input
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ATMS 320 Static Performance Characteristics

• Input/output fit
• Linear v. non-linear
• Random error
• Cannot be individually eliminated because the
  errors are not predictable ? causes uncertainty
  in the measurement

Random error non-systematic error that can only
be described statistically and cannot be
corrected.
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ATMS 320 Static Performance Characteristics

• Hysteresis when the sensor output for a given
  input depends upon whether the input was
  increasing or decreasing
• Threshold special case of hysteresis that
  occurs when the output remains zero while the
  input slowly increases.

See Section 3.2 for other definitions resolution,
linearity, stability,
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ATMS 320 Static Performance Characteristics

• Cookbook for calibration (how to derive the
  calibration equation)

Note
because of random errors
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ATMS 320 Static Performance Characteristics
Xi is the measurand (primary input) a is a
coefficient of the statistical fit
In order to be able to determine the coefficients
of the calibration equation, there must be at
least N measurements of input/output to match
the N coefficients (number of equations number
of unknowns).
Most likely, we will have more data pairs
(input/output) than number of coefficients that
we desire for our equation, so we use
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ATMS 320 Static Performance Characteristics
The Method of Least-Squares (Section 3.2.2)
Let us use the chalkboard to show an example
(Section 3.3)
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ATMS 320 Static Performance Characteristics
The Method of Least-Squares notes from
chalkboard
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ATMS 320 Static Performance Characteristics
The Method of Least-Squares notes from
chalkboard
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ATMS 320 Static Performance Characteristics
is the raw sensor output (w/ error) c is a
coefficient of the calibration eqtn. X1 is the
best estimate of the true but unknowable
input (subscript 1 refers to the sensor
output as designated in Fig. 1-1 of the
textbook).
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ATMS 320 Static Performance Characteristics
Actual measurand amount
Instrument error
Best estimate of measurand (from calibration
eqtn.)
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ATMS 320 Static Performance Characteristics
Gaussian distribution
standard deviation
mean
bias, imprecision, inaccuracy definitions are
found in Section 3.2.2.1 of the textbook
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ATMS 320 Static Performance Characteristics
The purpose of static calibration is to remove
the bias and to numerically define the
imprecision.
Problems -drift since last calibration -secondary
inputs not accounted for in calibration
e.g. aneroid barometer is sensitive to
changes in air temperature
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ATMS 320 Static Performance Characteristics

• Examples of sensors with bias and imprecision
• Bias 0, imprecision is large
• Bias large, imprecision small
• Bias 0, small imprecision

input
(input is the constant value shown)
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ATMS 320 Static Performance Characteristics

• In the previous examples, we have treated
  instrument error as if it originated from a
  single source
• In reality there are multiple sources of error

If each error is independent of the other
then the errors can be combined using
the root-sum-square (RSS)
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ATMS 320 Static Performance Characteristics

• Rules for applying significant digits
• Nonzero digits are significant
• Zeros between nonzero digits are significant
• Zeros to the left of the first nonzero digit in a
  number are not significant
• Zeros to the right of the decimal point are
  significant
• Some ambiguity when a number ends in zeros that
  are not to the right of the decimal point

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