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Chapter 5 Notes

# Chapter 5 Notes - Chapter 5 Uncertainty Analysis Figures...

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1 Chapter 5 Uncertainty Analysis Figures from Theory and Design for Mechanical Measurements; Figliola, Third Edition Uncertainty Analysis ± Error = difference between true value and observed ± Uncertainty = we are estimating the probable error, giving us an interval about the measured value in which we believe the true value must fall. ± Uncertainty Analysis = process of identifying and qualifying errors. Measurement Errors ± Two General Groups 1.Bias Error- shifts away from true mean 2.Precision Error- creates scatter

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2 Figure 5.1 ± Best estimate of true value: ± Assumption: 1. Test objective known 2. Measurement is clearly defined, where all bias errors have been compensated through calibration 3. Data obtained under fixed operating conditions 4. Engineers have experience with system components xx x ' µ Figliola, 2000 Design-Stage Uncertainty Analysis Feasibility Assessment Figliola, 2000 Two Basic Types of Error Considered ± Zero-Order Uncertainty –“ µ 0 ” is an estimate of the expected uncertainty caused by reading the data (interpretation error or quantization error). It is assumed that this error is less than the instrumentation error. – Arbitrary Rule –set µ 0 equal to ½ instrument resolution with 95% probability. µ 0 = ± ½ resolution (95%) – At 95%, only 1 in 20 measurements would fall outside the interval defined by µ 0.
3 Two Basic Types of Error Considered ± Instrument Error - “ µ c ”, is a combination of all component errors and gives an estimate of the instrument bias error. Errors are combined by the root-sum- squares (RSS) method. – Elemental errors combine to give an increase in uncertainty µ xk ee e + + + 1 22 2 ... µ xj j k e = 2 1 -must maintain consistency in units of error -should use the same probability level in all cases (95% preferred) ± Assume that the combined errors follow a Gausion distribution. By using RSS, we can get a statistical estimate of error, which assumes that the worst case element errors will not all add up to the highest error at any one time. Design Stage Uncertainty ± Combine zero order and instrumental error - Estimates minimum uncertainty - Assumes perfect control over test conditions and measurement procedures - Can be used to chain sensors and instruments to predict overall measurement system error Figliola, 2000

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4 Figliola, 2000 Error Sources ± Calibration Errors ± Data-acquisition errors ± Data-reduction errors ± Within each category, there are elemental error sources. It is not critical to have each elemental error listed in the right place. It is simply a way to organize your thinking. The final uncertainty will come out the same. Calibration Error ± Sources: 1. Bias and precision error in standard used 2. Manner in which standard is applied Calibration does not eliminate error; it reduces it to a more acceptable level.
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Chapter 5 Notes - Chapter 5 Uncertainty Analysis Figures...

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