Propagation of dynamic measurement uncertainty

The time-dependent measurement uncertainty has been evaluated in a number of recent publications, starting from a known uncertain dynamic model. This could be defined as the 'downward' propagation of uncertainty from the model to the targeted measurement. The propagation of uncertainty 'upward' from the calibration experiment to a dynamic model traditionally belongs to system identification. The use of different representations (time, frequency, etc) is ubiquitous in dynamic measurement analyses. An expression of uncertainty in dynamic measurements is formulated for the first time in this paper independent of representation, joining upward as well as downward propagation. For applications in metrology, the high quality of the characterization may be prohibitive for any reasonably large and robust model to pass the whiteness test. This test is therefore relaxed by not directly requiring small systematic model errors in comparison to the randomness of the characterization. Instead, the systematic error of the dynamic model is propagated to the uncertainty of the measurand, analogously but differently to how stochastic contributions are propagated. The pass criterion of the model is thereby transferred from the identification to acceptance of the total accumulated uncertainty of the measurand. This increases the relevance of the test of the model as it relates to its final use rather than the quality of the calibration. The propagation of uncertainty hence includes the propagation of systematic model errors. For illustration, the 'upward' propagation of uncertainty is applied to determine if an appliance box is damaged in an earthquake experiment. In this case, relaxation of the whiteness test was required to reach a conclusive result.