Uncertainty Evaluation via Polynomial Chaos Expansion

Uncertainty evaluation is an important task in almost all activities in the field of calibration and standard conformity assessment. Evaluation of uncertainty is a process in which the statistical characteristics (mainly the first and second moments; i.e. the average and the standard deviation) of the result of a measurement are estimated based on those of contributing factors. The result of this process is used to determine how appropriate a measurement is for a specific application. The measurement uncertainty influences the result of binary decisions made on conformity assessment, calibration and many other applications in the fields of jurisdiction, commerce, law enforcement or healthcare. Another important application of uncertainty evaluation, is to evaluate and validate mathematical or computer models simulating real world phenomena. For example, an uncertainty evaluation process can be utilized to quantify the error characteristics of a simulation software. Many techniques have been introduced and practiced for uncertainty evaluation. The applicability of each method relies upon the measurement model, possibility of performing repeated simulations and availability of statistical data. In this paper, we examine a celebrated uncertainty propagation method, namely; the Polynomial Chaos Expansion in the uncertainty evaluation of measurements described by a rigorous mathematical model. These measurement processes have been conventionally studied using sensitivity coefficients which can be calculated via partial derivatives. The two approaches are compared in an illustrative example.

Keywords:

Uncertainty evaluation , Measurement uncertainty , Polynomial Chaos Expansion