Multivariate Autoregressive Analysis in Locating the Origin of Fluctuation in Continuous Industrial Processes

Thesis for the degree of Doctor of Technology to be presented with due permission for public examination and criticism in Auditorium K1702, Abstract Continuous industrial processes are prone to fluctuate. Process fluctuations arise when the control equipment fails to fully compensate for, e.g. variations in the quality of raw materials and wear in valve actuators. When fluctuation becomes powerful enough, it reduces process efficiency, product quality and the lifetime of process components. Often a large number of measurements throughout the whole plant display the same fluctuation symptoms, which complicates locating the origin of the fluctuation and eventually identifying the cause. Multivariate autoregressive (MAR) modelling has provided good results in solving fluctuation problems in actual process plants. However, the theory behind this technique makes several assumptions, which are not valid when analysing actual industrial plants. These assumptions include the linearity and the stationarity of the process, the normal distribution and the whiteness of the disturbances and the infinite length of the data available for analysis. This work makes a contribution to narrowing this gap between theory and practice. In this work a new analysis procedure is developed. This procedure automates several steps in analysing process fluctuations with MAR modelling. The analysis procedure includes confidence analysis of the results calculated from MAR models, and it makes MAR analysis a more practical tool for solving fluctuation problems in industrial processes. The analysis procedure is applied in case studies in separate branches of process industry. ii iii Acknowledgements The ideas for this work have evolved over several years, while I have developed and applied techniques for process analysis as part of my work at introduced me to multivariate autoregressive modelling when I was a student and who has always found the time for valuable discussions on (and off) the subject. Several of his ideas are embedded in this work. I would also like to thank my colleagues for their understanding while I have been absent from work, concentrating on the thesis. A(l) The coefficient matrix) (m m × of an MAR model for each delay e The vector) 1 (× m of the noise sources in an MAR model. e(k) The vector) 1 (× m of values of the noise source time series at sample index k. e j The jth noise source in an MAR model. f Frequency in Hertz. H(f) The transfer function matrix) (m m × from the noise sources to …