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The True Nature of Measurements: Understanding Errors and Estimations

aronlee avatar
aronlee
13 diapositives · 191 Views · Jan 07, 2020

Delve into the paradox of measurements, exploring the essence of true values, errors in measurements, and the art of estimation in scientific observations. Learn how to navigate uncertainties to enhance the reliability of data.

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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