1. ME 322: Instrumentation Lecture 5 January 28, 2015 Professor Miles Greiner Lab 3, transmitter characteristics, least-squares, standard error of the estimate

2. Announcements HW 2 due Monday 2/2/2015 – assignment and reading on Web – L3PP = Lab 3 preparation problem Process sample data Bring spreadsheet to lab (part of lab participation) 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 Download Extra-Credit Opportunity, Help at Science Olympiad – See Letter with instructions here See Letter with instructions here – Saturday, February 7, 2015, 9:00am to 3:00pm – ~1% course grade extra credit, equal to ~One homework or lab assignment ~4 points on a test – Sign up by Wednesday, January 28, 2015

3. Lab 3 Pressure Transmitter Calibration Dwyer Series 616 Pressure Transmitter Measurand: Pressure difference between HI and LO ports, –  P = P HI – P LO – Power must be supplied to pins 1 and 2 (10-35 VDC) Sensor: diaphragm with a strain or proximity gage – Output may be affected by orientation due to gravity (undesired) The Output or “Reading” is current, I T [mA], measured by a Digital Multimeter (DMM) I T P HI P LO Proximity Sensor or

4. Transmitter Characteristics See Lab 3 website, ~$150 See Lab 3 website Use different diaphragm thickness or flexibilities to get different sensitivities to vary Full Scale (FS) range and resolution Output Signal: 4 to 20 mA (h = 0 to FS, linear) Accuracy: 616: ±0.25% F.S. Stability: ±1% F.S./yr. Two models in lab: – 616-1: FS = 3 in WC; Accuracy = 0.0025*3 = ±0.0075 in WC – 616-4: FS = 40in WC; Accuracy = 0.0025*40 = ±0.1 in WC – What does this accuracy mean (what is its confidence level)?

5. Manufacturer’s Inverted Transfer Function

6. Pressure Standard Characteristics Martel BetaGage Model 321A, ~$2000 More stable (less calibration drift) than Dwyer 616’s (More expensive) Each devise has two pressure gages – FS = 25 mBar (10 in WC); ±0.1% FS: Accuracy = 10*0.001= 0.01 in WC Use this to calibrate 3 in WC transmitter – ±0.0075 in WC – FS = 350 mBar (141 in WC), ±0.035% FS Accuracy = 141*0.00035=0.05 in WC Use this to calibrate 40 in WC transmitter – ±0.1 in WC In Lab 3, one gage will be shared by two stations

7. Gage Characteristics High pressure transmitters will be connected to high pressure calibrator port Low pressure transmitters to low calibrator port One calibrator will be shared by two groups Accuracy of the transmitter and Standard are roughly the same, but Standard drifts less

8. Lab 3 Set-up and Procedure Transmitter LO port open to atmosphere Bulb, standard, HI transmitter port, and manometer high pressure port to “high” pressure tube Open valve to allow high pressure tube to reach atmospheric – Set I T = 4.00 mA, and “zero” the Pressure Standard At each pressure level record h S (from Standard) and I T (from DMM) Record data from two ascending and descending pressure cycles, with at least 6 measurements in each direction

9. Plot Manufacturer’s and Measured Transfer Functions Fit a line I T,F = ah S + b to the data – Measured transfer function (Use least-squares find a & b) The data does not all fall along one thin line due to gage imprecision (more like a “cloud” than a line) The measured current for this gage is systematically larger than predicted by the Manufacturer

10. Error of Manufacturer’s Transfer Function Plotting e = I T – I M makes it easier to see error – I T = transmitter, I M = manufacturer Increases with h S reaches ~0.35 mV (out of 20 mV)

11. Deviation of Data form Fit Line Deviation plot d= I T – I T,F (above the fit) makes it easier to see ~Equally scatter above and below Same for ascending and descending data (no hysteresis) No systematic deviations (linear response)

12. How to use the calibrated pressure transmitter? Measure gage current, I Algebraically invert the transfer function (I = ah + b) to find h – h = (I – b)/a If we did not calibrate, then we would assume the dotted line, which systematically give higher pressures than actually applied How to find a and b and the uncertainty in h? Manufacturer Prediction Measured

13. Least Squares Linear Fit y or R x or M y F = ax + b d i = y i – y F,i

14. Find a & b that minimize E

15. Summary Hint: You may use your calculator to find a & b – unless told otherwise. Learn how.

16. How well does Best-Fit Line fit the data?

17. Standard Error of the Estimate of y given x Characterizes the vertical spread of the data 68% of all y i will be within ±s x,y of y F (x) 95% is within ±2s x,y Assuming the error is the same for all x s y,x y x

18. Standard Error of the Estimate of x given y Characterizes the horizontal spread that contains 68% of the data s x,y = s y,x /a, a = slope of best fit line s y,x s x,y y x

20. Transfer Function Plot Best fit line R = a*h T + b