Metrology in Energy and Environmental Engineering

Metrology Applied to Energy and Environmental Engineering

• Metrology is the science of measurement, applied to energy and environmental engineering.
• Error and uncertainty are crucial concepts in metrology.
• Measurements rarely equal the true value, the difference is the error.
• True value (X) or μ
• Measured (best) value (Xbest)
• Absolute error δx = |Xbest − X|
• Relative error εx = |Xbest − X| / Xbest

Types of Errors

• Measurement blunders (big mistakes)
• Systematic (bias) errors
• Dynamic errors
• Random errors

Measurement Blunders (Big Mistakes)

• These errors come from inadequacies in calibration, data acquisition system or loss of information.
• They occur due to issues with sensor placement or miscalibration.
• Data from blunders should be disregarded.

Systematic Errors - Bias

• Bias error is a consistent offset between the average indicated value and the true value.
• Repetition of measurements does not remove bias error.
• Bias error can be estimated by calibration, by concomitant methodology, or by inter-laboratory comparisons.
• Corrections for bias error must be incorporated into data.
• Example of Defects of the Instrument: uncalibrated instruments, wrong working conditions, and instrument-surveyor interaction (parallax error).
• Example of Instrument-Medium of Interest Interaction: using an immersed sensor and protection tubes (thermowells) for temperature measurements.
• Example of Cylindrical Fin: a conduction path between the support and the transducer affecting temperature measurement.

Estimation of Systematic Errors

• The level of bias error can only be estimated by comparison.
• Corrections for bias error should be incorporated into the data
• If there’s a 0.5°C overestimation in calibration for example, all results should be adjusted accordingly.
• The uncertainty associated with the calibration remains and propagates to the uncertainty in the result.

Dynamic Errors

• Dynamic error is the difference between the true value and the reading of the device, when the measured quantity is changing

• Also, response time: the speed the measurement system reacts to changes in the measured variable.

• Lag Error: the time delay between input changes and the system’s response.

• Overshoot and Undershoot: when a system initially exceeds or falls short of its final value

• Hysteresis Error: output depends on both current and past inputs.

Statistical Background – Average Value

• An average provides an estimate of the true value

Statistical Background - Quantify the Spread of Data

• One way to quantify spread is the range: the difference between the highest and lowest values
• The standard deviation (s or σ) indicates how much the readings typically differ from the average.

Statistical Background - Data Distribution

• Data distribution or the frequency distribution curve shows the number of occurrences of data with the same value.
• The Curve shows the spread of data or the frequency distribution.

Normal Distribution (Gaussian Distribution)

• For normally distributed data, the probability density function is used to determine the frequency of a specific range of values.

Standard Deviation in Metrology

• In metrology, the standard deviation is important for quantifying spread in data, and defining confidence intervals for measurements.
• A low standard deviation means consistent results.
• A high standard deviation indicates inconsistency and systematic errors, or other influences.
• Standard deviation is directly proportional to the width of the variation, and therefore used to characterize the uncertainty of a measurement.

Independent Uncorrelated Variables

• A function of several independent and uncorrelated variables. Examples are temperature sensor on either side to measure a flow meter.

Statistical Mean and Standard Deviation of a Function

• The uncertainty in the outcome of function that depends on multiple variables can be evaluated by total differential calculations.

Numerical Examples

• Provide example calculations to demonstrate the methods. These demonstrate error propagation and different scenarios.

Conclusion

• A variety of methods are available for quantifying measurement errors and uncertainties for metrology.