### ME 322: Instrumentation Lecture 6

January 30, 2015 Professor Miles Greiner Review Calibration, Lab 3 Calculations, Plots and Tables

### Announcements/Reminders

• • • HW 2 due Monday – L3PP – Lab 3 preparation problem • Create an Excel Spreadsheet to complete the tables, plots and question in the Lab 3 instructions, using the sample data on the Lab 3 website.

• Bring that spreadsheet to lab next week and use it for your data. You can sign up for Extra credit Science Olympiad until Wed, Feb 4, 2015 HW 1 Comments – – Plot using Excel (not by hand) Hint: Do some summation calculations by hand to be sure you know how it is done

### Instrument Calibration (review)

• • • • Measure instrument output (R) for a range of known measurands (M, as measured by a reliable standard) Perform measurements for at least one cycle of ascending and descending measurands Fit an algebraic equation to the R vs M data to get instrument transfer function: – – Linear:

R = aM + b

Other: i.e.

R = aM 2 + bM + c

, or … Find standard error of the estimate of R given M, s R,M – 𝑠 𝑦,𝑥 = 𝑛 𝑖=1 (𝑦 𝑖 −𝑎𝑥 𝑖 −𝑏) 2 𝑛−2 – This assumes the deviations are the same for all values of M

### How to Use the Calibration

• Invert transfer function – If linear:

M = (R-b)/a

• • Find standard error of the estimate of M given R –

s M,R = s R,M /a

For a given reading – The best estimate of the measurand is • – The best statements of the confidence interval are • •

M = M = + s M,R

units (68%), or

+ 2s M,R

units (95%), or …

### What does Calibration do?

• • • Removes systematic bias (calibration) error Quantifies random errors – imprecision, non-repeatability errors – But does not remove them Quantifies user’s level of confidence in the instrument

### Manufacturers often state “accuracy”

• May include both imprecision and calibration drift – Often not clearly defined • This is one of the objectives of Lab 3

## Table 1 Equipment Specifications

Transmitter Full Scale Range Relative Accuracy Absolute Accuracy Manufacturer's Inverted Transfer Function Pressure Standard Full Scale Range Relative Accuracy Absolute Accuracy Model 616-1 3 inch-WC ±0.25% FS ±0.0075 inch-H 2 O h = (3 inch-H2O)(I T -4mA)/16mA Model 616-5 40 inch-WC ±0.25% FS ±0.1 inch-H 2 O h = (40 inch-H2O)(I T -4mA)/16mA 25 mBar (10 in-WC) 350 mBar (141 in-WC) ±0.1% FS ±0.035% FS ±0.01 inch-H 2 O ±0.05 inch-H 2 O • In your report you will use the first column, and only one from the second and third columns • The confidence levels for the transmitter accuracy is not given by the manufacturer – We will determine it in this experiment.

Standard Reading, h S [in WC]

0 0.5328

1.0597

1.5617

2.0863

2.5295

1.9637

1.5483

0.9211

0.5216

0 0.5619

0.9595

1.4562

1.9927

2.6214

2.1092

1.6423

1.0696

0.5315

0

Transmitter Output, I T [mA]

4 6.88

9.72

12.48

15.34

17.83

14.66

12.35

9.03

6.83

4.01

7.09

9.18

11.92

14.84

18.3

15.43

12.89

9.86

6.88

4.02

### Table 2 Calibration Data

• • This table shows two cycles of ascending and descending pressure calibration data. The transmitter current did not return to 4.00 mA at the end of the descending cycles.

Fig. 1 Measured Transfer Function • • For the sample data – The measured transmitter current is consistently higher than that predicted by the manufacturer specified transfer function. – Standard errors of the estimates for the transmitter current for a given pressure heat is S I,h mA, and S h,I = 0.0065 in-WC. = 0.035 – The manufacturer-stated accuracy (0.0075 in-WC) for the transmitter is 1.15 times larger than S h,I , corresponding to a 75% confidence level. Your data may be different!

Fig. 2 Error in Manufacturer’s Transfer Function • • Error in the manufacturer-specified transfer function increases with pressure Maximum error magnitude is 0.35 mA.

### Fig. 3 Deviation from Linear Fit

• • • S I,h characterizes the deviations over the full range of h S Neither the ascending nor the deviations are generally positive or negative, which suggests that hysteresis does not play a strong role in these measurements. There are no systematic deviations form the fit correlation, indicating the instrument response is essentially linear.

### This lecture demonstrates how to

• • • • Format plot labels, borders, fonts,..

– Different symbols for ascending and descending data Calculate standard error of estimate, confidence level Write abstract last: Objective, methods, results Sample Data • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH3 22Instrumentation/Labs/Lab%2003%20PressureCalibration /Lab%20Index.htm

### Confidence Level of Manufacture-Stated Uncertainty

• • • Find the probability a measurement is within 1.15 standard deviations of the mean Identify: Symmetric problem z 1 = -1.15, z 2 = 1.15

𝑃 −1.15 < 𝑧 < 1.15

= 𝐼 1.15 − 𝐼 −1.15

= 𝐼 1.15 − −𝐼 1.15

= 2𝐼 1.15 = 2 0.3749 = 75% • Your confidence level may be different

Interpretation of Measurement Question Transmitter Output, I T Inverted Measured Transfer Function Standard Error of the Estimate of Pressure Head for a Given Current, S h,I 68% Confidence Interval Inverted Manufacturer's Transfer Function Confidence Interval if not Calibrated (Unknown confidence Level) 10.73 mA h = (0.1838 inWC/mA)I T - 0.7342 inWC 0.0065 in WC 1.2380 ± 0.0065 in WC h = (0.1875 inWC/mA)I T - 0.75 inWC 1.2619 ± 0.0075 inWC

### Abstract

• • • In this lab, a 3-inch-WC pressure transmitter was calibrated using a pressure standard.

– The transmitter current I T was measured for a range of pressure heads h, as measured by a pressure standard. The measured inverted-transfer-function was – h = (0.1838 in-WC/mA)I T – (0.7335 in-WC), – The 68%-confidence-level confidence-interval for this function is ± 0.0064 in-WC The manufacturer’s stated uncertainty is 0.0075 in-WC – This is 1.15 time larger than the 68%-confidence-level interval, which corresponds to a 75%-confidence-level

Lab 3 Static Calibration of Electronic Pressure Transmitters February 3, 2014 Group 0 Miles Greiner Lab Instructors: Josh McGuire, Şevki Çeşmeci, and Roberto Bejarano

xy

S yx S xy