Abstract
Every measurement has the purpose of obtaining the numerical value of a physical quantity. There are, however, several factors that hinder the accomplishment of this objective, causing measurement uncertainty. In this chapter, after a clarification of concepts such as measurement method, measurement procedure and measurement model, uncertainty is defined statistically and an analytic method is introduced for its calculation. Uncertainty due to additive, multiplicative and non-linear systematic errors is also analyzed in detail. Finally, several examples of uncertainty analysis in acoustical measurements are provided.
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Notes
- 1.
The measuring instrument itself introduces reflection and diffraction phenomena that may change the sound field, which in turn changes the measurand. The same is true for the operator conducting the measurement.
- 2.
According to the GUM, there may be more than one true values. This is because when the specification of the measurand is not exhaustive, there are many different values that agree with the definition.
- 3.
Identical conditions means to control as far as possible all possible variables; for instance, the same physical system, the same instrument, the same operator, the same environmental conditions, and the minimum reasonable time between measurements to prevent drifts in the instrument’s characteristics as well as those of the physical system where the measurand manifests itself.
- 4.
We say “that is a function of” instead of “equal to” because the instrument could be uncalibrated or have some nonlinearity that should be corrected.
- 5.
The resonance curve is not exactly parabolic, but in the neighborhood of its maximum it can be approximated by a parabola. The approximation will be better if the frequencies where the response is measured are close to the resonant frequency.
- 6.
An example where there are explicit solutions but numerical methods are preferred is the solution of linear equation systems of high order.
- 7.
Appendix 2 introduces basic statistical concepts. In the Glossary of Appendix 1, there is a summary of definitions of common use in metrology.
- 8.
The term “population” is used in Statistics to refer to all of the homogeneous elements to which some given statistical parameters apply.
- 9.
Equivalently, it can be defined as the mean of the difference between the measured value and the true value.
- 10.
It is interesting to note that in this case, we are interested in measurements of sound pressure instead of sound pressure level.
- 11.
Note that only the conventional values are known, not the real ones. However, the conventional values have less dispersion and do not have any known systematic effect.
References
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Miyara, F. (2017). Uncertainty. In: Software-Based Acoustical Measurements. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-55871-4_2
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DOI: https://doi.org/10.1007/978-3-319-55871-4_2
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