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Instrumentation Lecture Overview - Statistical Analysis and Calibration Techniques

This lecture by Professor Miles Greiner on January 27, 2014, covers essential topics in instrumentation, focusing on statistical analysis as applied to lab experiments and measurement accuracy. Key announcements include homework deadlines, lab location, and instructions for Lab 2, which investigates statistical analysis of UNR Quad Measurements. Important concepts discussed include transfer functions, instrument sensitivity, repeatability, and calibration methods for reducing measurement imprecision. Students must work in pairs and adhere to lab guidelines to ensure professionalism and thorough understanding.

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Instrumentation Lecture Overview - Statistical Analysis and Calibration Techniques

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  1. ME 322: InstrumentationLecture 4 January 27, 2014 Professor Miles Greiner

  2. Announcements • Turn in HW 1 now (use ME 322 student number, not name) • HW 2 due Monday 2/3/2014 (assignment and reading on Web) • Go to PE 113 for lab this week • Lab 2 - Statistical Analysis of UNR Quad Measurements • Download and read instructions Lab 2 Instructions and Lab Guidelines

  3. In Lab • Please • Work in 2-person lab groups (assigned in lab) • Be on time (responsibility to lab partner) • Be prepared (read lab instructions) • Be professional and patient (treat the TA’s well) • Lab Participation Points are assigned by Lab TA

  4. Pressure • Can’t see it • Need gages (gauges) to • Qualitatively know when it changes • Quantitativelymeasure it • Units • [Pa] = [N/m2]; [kPa] = [1000 Pa]; [MPa] = [106 Pa] • [psi] = [lbf/in2] • Gage Pressure • Amount a vessel’s pressure is above its surrounding’s • PGAGE = P – PATM P PATM

  5. Some Gages • Bourdon Tube • Diaphragm • Manometers • Vertical • Inclined • Water Head, h

  6. Instrument Transfer Function • Relationship between the instrument reading R and its measurand M (quantity being measured) • May not be linear

  7. U-Tube Manometer • The reading can be given in units of inches or cm of water column [in WC] or [cm WC] • Or inches or cm of mercury or alcohol • What is the transfer function (Reading versus Measurand)? Measurand Reading DP = 0 Fluid Air (1 ATM, 27°C) Water (30°C) Hg (27°C) 1.774 995.7 13,565

  8. Transfer Function Low rm (alcohol) High rm (mercury)

  9. Inclined-Well Manometer AW P1 P2 AT h1 q h2 DP = 0 R

  10. Transfer Function R If And

  11. Transfer Function Small q Large q

  12. General “Linear” Instrument Characteristics RMAX DRMIN MMAX DMMIN (smallest change in reading that can be detected, i.e. tick mark, digit) )

  13. Sensitivity affects both Resolution and Range • In general, it is not hard to change sensitivity • Increasing S improves resolution • but decreases range • Resolution as a fraction of Range

  14. Instrument Repeatability • Will an instrument give the same reading every time it is exposed to the same Measurand? • Why not? • Transfer function may drift with time. So at a later time the readings may shift to consistently higher (or lower) values than before. • Referred to as Systematic or Calibration Error • Random variations of uncontrolled inputs (such as RF (radio frequency) noise, orientation of instrument, humidity, may lead to Random variations of the Reading. • Referred to as Random Errors or Imprecision

  15. General Instrument Desired Input (Measurand M) i.e. length, pressure temperature Instrument Output Reading R (deflection, number of steps, needle angle) Controlled (i.e. temperature, orientation) Uncontrolled (i.e. RF frequency, walking stride length Undesired Inputs x1, x2, x3, x4, x5,…

  16. General Transfer Function • Reading R = fn(M, x1, x2,…, xn) • How to find the Transfer Function? • Theory: • good for simple device (manometer) • Done in other classes • Only includes the effects you model (at best)! • Calibration: • controlled measurement process • Measure reading (R) while exposing instrument to a range of measurands (M) that are being measured by a reliable standard (used to determine M).

  17. Calibration Correlation Instrument Under Test Standard • Correlate Reading R with Measurand M (least squares fit) • May not be linear • Uncontrolled inputs can cause R to have undesired variations of the same M! • The sized of the variation is a measure of the instrument impression (random, inconsistent output) • Systematic errors can be removed using calibration, but random errors cannot!

  18. How to reduce Measurement Imprecision? • Improve the control of undesired inputs, and/or • Use a different instrument that is less sensitive to uncontrolled inputs

  19. Calibration Transfer Function Data Correlate Scatter – Uncontrolled inputs instrument

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