An Uncertainty Quantification Method Based on Generalized Interval

Abstract

The need to quantify aleatory and epistemic uncertainties has been widely recognized in the engineering applications. Aleatory uncertainty arises from inherent randomness, whereas epistemic uncertainty is due to the lack of knowledge. Traditionally uncertainty has been quantified by probability measures and the two uncertainty components are not readily differentiated. Intervals naturally capture the systematic error during data acquisition. We develop a new feature extraction and back propagation neural network in the context of generalized interval theory, where all parameters are in the form of a generalized interval. Calculation of generalized interval based on the Kaucher arithmetic is greatly simplified in this application. To demonstrate the new framework, this paper provides a case study of recognizing the cutting states in the manufacturing process. The stable, transition, and chatter state states are recognized by the generalized back propagation neural network (GBPNN) model. The results show that the proposed method has a good recognition performance.