On optimizing sensor placement for spatio-temporal temperature estimation in large battery packs

This paper optimizes the number of sensors and their locations for estimating the 2-D spatio-temporal temperature dynamics in large battery packs. Monitoring temperature in battery packs is crucial for safety, efficiency, and longterm endurance. The temperature dynamics in large battery packs evolve in space and time, whereas sensors only provide pointwise data. Moreover, the number of sensors should be minimized to reduce costs. The temperature dynamics are modeled by a system of linear two-dimensional heat partial differential equations (PDEs). In this paper we perform eigende-composition of the PDEs to produce a finite-dimensional model. Modal observability is defined from the magnitude of these eigenmodes. The process of optimizing the number and location of sensors involves two steps: First, a binary optimization minimizes the number of sensors. Second, a constrained nonlinear programming problem is solved to optimize the previously found sets with respect to a min-max-type objective function. The optimization procedure is independent of the estimator design.