ERROR IN MEASUREMENTS P M V Subbarao Professor Mechanical Engineering Department How Truthful are...
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![Page 1: ERROR IN MEASUREMENTS P M V Subbarao Professor Mechanical Engineering Department How Truthful are Our Observations?](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b927f8b9ab0599c2181/html5/thumbnails/1.jpg)
ERROR IN MEASUREMENTS
P M V SubbaraoProfessor
Mechanical Engineering Department
How Truthful are Our Observations?
![Page 2: ERROR IN MEASUREMENTS P M V Subbarao Professor Mechanical Engineering Department How Truthful are Our Observations?](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b927f8b9ab0599c2181/html5/thumbnails/2.jpg)
Paradox of Measurements
• The Merits:• Measurements are essential for development of
science and technology.• It helps innovation and production of new
utilities.• The (self) Contradiction:• It is impossible to obtain true value of a parameter
using measurement.• A reliable measurement can generate reliable
information.
![Page 3: ERROR IN MEASUREMENTS P M V Subbarao Professor Mechanical Engineering Department How Truthful are Our Observations?](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b927f8b9ab0599c2181/html5/thumbnails/3.jpg)
A good measuring strategy is reliable and, because it is reliable,
it has a small amount of error in its observations.
The First Law of Measurements
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Error of Measurement
• Error of measurement refers to the difference between the measurement we obtain and the "true" value of the variable.
• Question: How do you get the "true" measure if all measuring methods produce errors?
• Answer: "True" measures cannot be obtained, but they can be estimated.
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Estimation of the True Value
• What are we trying to measure?• The true value of an object being measured is rarely ever
known.• Identifying the true value needed by an end user is critical. • The true value is often a concept that is very hard (or
impossible) to measure.• Moffat uses the example of average surface temperature
as a true value that is needed for control of a chip.
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Geometrical & Thermal Design Constraints
True measurement of an average surface temperature is impossible because of the huge number of sensors that would be needed.A large number of sensors would cause a large disturbance to the system.True surface temperature must be area-weighted
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For convection the appropriate area-weighting is
TdAA1
For radiation the appropriate area-weighting is
dATA
41
So even the same apparatus could require two (or more) true values to define the same concept.
Role of Physical Phenomenon on Estimation
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Start with the Truth• Goal is to experimentally measure a physical quantity.• The true value of the quantity is a concept. • In almost all cases, the true value cannot be measured.• The error in a measurement is the difference between the true
value and the value reported as a result of a measurement. • If x is the quantity of interest
truemeasured xxError • A claim of numerical Accuracy establishes an upper bound on
the error.
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Study of Errors
1. Classify errors.2. Identify sources of errors.3. Remove errors we can correct.4. Develop a procedure for computing the estimate of
errors (uncertainty).5. Demonstrate how to apply these methods to a
measurement.
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Measurement Chain
System Disturbance System/sensor
Interaction
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Calibration Error
Measurement Chain
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Measurement Chain
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Verification of Diesel Theorem
A I R
CombustionProducts
Fuel injectedat TC
IntakeStroke
Air
CompressionStroke
PowerStroke
ExhaustStroke
ActualCycle