Unscented Kalman Filter for Operating Mode Change Detection

Real-life processes are mostly characterized by several operating regimes or modes. Each operating mode corresponds to particular operating conditions and may require the use of a specific control strategy. Therefore, the task of identifying or determining continuously the current operating mode of the process is of a great value as it allows to implement the control strategy that is in accordance with the current operating mode of the process. The use of an unscented Kalman filter is considered here for the purpose of tracking the active operating mode of the process at every time instant and consequently detecting when a change occurs in the process operating mode. Introduction The modelling of processes or systems exhibiting several operating regimes or modes has always been a subject of interest in various research areas like economics [3], finances [5], climatology [10], and engineering sciences [2]. The development of such models comes from the extension of the underlying principles of the classical linear regression theory, leading to the birth of different generalizations known as switched regression models or switched models. The work of [1], among others, has paved the way to the first principles of this appealing modelling technique. Since then, many major contributions [6] has specified and strengthened this formalism which has the potential to be of a practical use as soon a process or system displays several operating modes and can eventually “switch”, in a forced or natural manner, between these operating modes. The determination of the active operating mode for a process exhibiting several operating modes is a crucial task for the implementation of the appropriate control strategy in regard to the current operating mode. It is also a key to achieve safety and profitability objectives for the process by the means of appropriate control actions. When the changes in the process operating modes are triggered by known variables or conditions (for example a process operator pushing a button), the active operating mode determination is facilitated. In the other situation where the reason why the process switches from one operating mode to another is not well mastered, it has to be inferred by using the measured process variables. In this scenario, there is a need to provide a way to estimate at each time instant the active operating mode of the process so that a change in the operating modes can be easily detected when it occurs. In [4], the proposed procedure is based on the generation of analytical redundancy equations between the process input and output variables. The feasibility of the method is conditioned by the existence of the analytical redundancy equations. In the rest of this paper, the focus is on a particular class of multiple operating regime processes or systems known as PWA (Piece-Wise Affine) systems [13] and their extension to dynamic systems PWARX (Piece-Wise Auto-Regressive eXogeneous). The presented problem is the task of determining at each time instant the active operating mode by using the measurements of the system’s input and output variables. The problem is investigated in a supervised detection framework, i.e. assuming that the different operating modes have been previously listed and ha l-0 03 36 11 4, v er si on 1 3 N ov 2 00 8 Author manuscript, published in "1st International Workshop on Systems Engineering Design & Applications, SENDA 2008, Monastir : Tunisia (2008)"