Optimal Sensor Placement and Online Spatiotemporal Modeling for Parabolic Distributed Parameter System under Sparse Sensing

Restrictions on the number and placement of sensors are common in the modeling of parabolic distributed parameter systems (DPSs). Since the information from measurements is incomplete, developing an accurate approximation model and capturing their dynamic behavior for time-varying DPSs under sparse sensing is a challenge. In this paper a novel online spatiotemporal modeling framework includ data completion and optimal sensor placement is developed. Firstly, in the offline initialization phase, a set of offline data collected under a full sensing environment is used to learn the initial full spatial basis functions (BFs) and establish an initial temporal model. Then, a completion algorithm is developed to reconstruct the sparse data into full data, and the optimal sensor position is selected by the offline data based on the underlying algebraic structure of the recovery error. Finally, in the online learning phase with few sensors, by utilizing incremental learning techniques, an online learning strategy is designed in which both spatial BFs and the temporal model can be recursively updated from new data. The performance and effectiveness of the proposed method are verified through an experimental study of a flat-plate lithium-ion battery thermal process. Precise temperature distribution of the battery is modeled through only 3 sensors. The model accuracy is very close to that achieved with full sensing data, and the processing speed is significantly faster.