### Abstract

- Top of page
- Abstract
- Introduction
- Issues in Process Trend Identification
- An Interval-Halving Algorithm for Trend Extraction
- Performance Metrics
- Case Studies
- Conclusions
- Notation
- Literature Cited
- Appendix

Qualitative process trend representation is an useful approach to model the temporal evolution of sensor data and has been applied in areas such as process monitoring, data compression, and fault diagnosis. However, the sheer volume of real-time sensor data that needs to be processed necessitates an automated approach for trend extraction. The step of recovering important temporal features is a difficult procedure to automate because of the absence of a priori knowledge about the sensor trend characteristics such as noise and varying scales of evolution. A novel approach is proposed to automatically identify the qualitative shapes of sensor trends using a polynomial-fit based interval-halving technique. To estimate the significance of fit-error, an estimate of the noise obtained from wavelet-based denoising is used. The procedure identifies the qualitative trend as a sequence of piecewise unimodals or quadratic segments. The least-order (among constant, first-order and quadratic) polynomial with fit-error statistically insignificant compared to noise (as dictated by F-test) is used to represent the segment. If the fit-error is large even for the quadratic polynomial, then the length is halved and the process is repeated on the first half segment until fit-error is acceptable. A constrained polynomial fit is used to ensure the continuity of the fitted data and an outlier detection methodology is used to detect any jump (step) changes in the signal. The whole procedure is recursively applied to the remaining data until the entire data record is covered. Finally, a unique assignment of qualitative shape is made to each of the identified segments. The application of the interval-halving technique for trend extraction is illustrated on a variety of both simulated and industrial data. © 2004 American Institute of Chemical Engineers *AIChE J*, 50: 149–162, 2004