ERROR IN MEASUREMENTS

P M V SubbaraoProfessor

Mechanical Engineering Department

How Truthful are Our Observations?

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.

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

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.

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.

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

For convection the appropriate area-weighting is

TdAA1

For radiation the appropriate area-weighting is

dATA

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So even the same apparatus could require two (or more) true values to define the same concept.

Role of Physical Phenomenon on Estimation

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.

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.

Measurement Chain

System Disturbance System/sensor

Interaction

Calibration Error

Measurement Chain

Measurement Chain

Verification of Diesel Theorem

A I R

CombustionProducts

Fuel injectedat TC

IntakeStroke

Air

CompressionStroke

PowerStroke

ExhaustStroke

ActualCycle