Data-driven reduced-order models for transient temperature fields using dynamic mode decomposition

Dynamic mode decomposition (DMD) is used to obtain a reduced-order model that describes evolution of states in a thermal system—no knowledge of the material properties, thermal loads, boundary conditions, or underlying physics is required. Temperature fields in a system with a curved surface and complex heat transfer boundary conditions, and a system with multiple thermal properties are obtained using a thermal imaging camera. For both of the systems, experiments yield temperature matrices, each of which is a snapshot in time. Time-shifted data matrices serve as inputs to the DMD algorithm, which obtains the dominant spatial and temporal modes of the systems, which in turn can be used to construct reduced-order models that can be used for state estimation and/or prediction. Error in reconstruction of the transient thermal fields is within 5%. Additionally, the DMD modes can be scaled to produce results for change in the boundary condition. The algorithm can be implemented with a few lines of code and is computationally inexpensive.