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ERROR IN MEASUREMENTS

ERROR IN MEASUREMENTS. P M V Subbarao Professor 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.

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ERROR IN MEASUREMENTS

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  1. ERROR IN MEASUREMENTS P M V Subbarao Professor Mechanical Engineering Department How Truthful are Our Observations?

  2. 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.

  3. The First Law of Measurements A good measuring strategy is reliable and, because it is reliable, it has a small amount of error in its observations.

  4. 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.

  5. 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.

  6. 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

  7. Role of Physical Phenomenon on Estimation For convection the appropriate area-weighting is For radiation the appropriate area-weighting is So even the same apparatus could require two (or more) true values to define the same concept.

  8. 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 • A claim of numerical Accuracy establishes an upper bound on the error.

  9. Study of Errors • Classify errors. • Identify sources of errors. • Remove errors we can correct. • Develop a procedure for computing the estimate of errors (uncertainty). • Demonstrate how to apply these methods to a measurement.

  10. Measurement Chain System Disturbance System/sensor Interaction

  11. Measurement Chain Calibration Error

  12. Measurement Chain

  13. Fuel injected at TC A I R Air Combustion Products Actual Cycle Intake Stroke Compression Stroke Power Stroke Exhaust Stroke Verification of Diesel Theorem

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