Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

4GENERAL UNCERTAINTY ANALYSIS USING THE TAYLOR SERIES METHOD (TSM)

As we discussed in Chapter 3, when a result is determined from the values of other variables as in

(4.1)

we must consider how the uncertainties in the X_i's propagate into the result r. If we are considering an experiment, then Eq. (4.1) is a data reduction equation and the X_i's are the measured variables or values found from reference sources (in the case of material properties not measured in the experiment). If we are considering a simulation, then Eq. (4.1) symbolically represents the model that is being solved and the X_i's are the model inputs (geometry, properties, etc.); (4.1) might be a single expression or it might be thousands of lines of computer code.

In Chapter 3, two propagation methods—the MCM and the TSM—were introduced, as were the ideas of general uncertainty analysis and detailed uncertainty analysis. An example of applying both TSM and MCM in a general uncertainty analysis was presented. In this chapter, we consider the application of the TSM in general uncertainty analysis and show the power of this approach with a number of examples/case studies. (The application of detailed uncertainty analysis using both MCM and TSM approaches is presented in Chapters 5, 6 and 7.)

In the planning phase of an experimental program, the general uncertainty analysis approach we use considers only the combined ...