| dc.description.abstract | Multi-Scale Analysis (MSA) is a powerful tool used in process systems engineering and has been utilized in many applications such as fault detection and filtering. In this paper, the extension of MSA for interval data is studied. Unlike single-valued data, interval data use bounds to denote the uncertainties within data points. Data aggregation can be used to convert a set of single-valued data into a smaller set of interval data. The literature on MSA of interval data is sparse and its use in process engineering has not been documented. Therefore, in this paper, three methods of handling interval data are studied: an interval arithmetic (IA) method, a center and radii (CR) method, and an upper and lower (UL) bound method. The main drawback identified when working with intervals is interval inflation/over-estimation. In this paper, interval inflation caused when applying MSA on interval data is described in detail. New algorithms to correct for the over-estimations have been proposed. The overestimations in interval data were corrected, and all three methods performed equally well in decomposing and reconstructing the signals. The Interval MSA algorithms developed were utilized to filter noisy interval data. The CIMSA-CR (the center and radii method) performed the best amongst the three methods for the filtering application. The optimum depth of decomposition, the shape of features in the input signal were also studied to understand how it affects the filtering performance. | en |
