Variable Selection Methods as a Tool To Find Sensor Locations for Distributed Parameter Systems

Abstract

The problem of finding suitable sensor locations for distributed parameter systems (DPS) is tackled as a variable selection problem. Two existing variable selection methods are used: one is based on principal component analysis (PCA) and the other on the principal variable (PV) method. A new PCA-based variable selection method, called “orthogonal variables in loading space” (OVL) is introduced. The best sensor location for DPS is dependent on sensor characteristics and also on the time interval of interest. This is illustrated in a case study where the best point in time to replace a packed bed filter is studied. Sensor positions are determined for different time intervals and different types of measurement errors. The resulting sensor positions characterize the overall time behavior of the DPS in the selected time interval. As a test, the specific problem of predicting the exit concentration of the packed bed filter is considered. Lagged PLS models are built and a full search is done to determine the best possible sensor locations. These “benchmark” sensor positions are compared to the sensor locations found by the variable selection methods. The OVL method and the PV method both perform well, but the OVL method is additionally computationally less demanding.