Identification of distributed-parameter systems from sparse measurements

Abstract

• A system identification methodology for distributed-parameter systems is proposed. • The methodology only requires measurements from sparse sensor locations. • The methodology extends the standard lumped-parameter system identification methods. • The methodology is suitable for modeling and model-based indoor climate control. • Results are presented for simulated as well as real systems. In this paper, a method for the identification of distributed-parameter systems is proposed, based on finite-difference discretization on a grid in space and time. The method is suitable for the case when the partial differential equation describing the system is not known. The sensor locations are given and fixed, but not all grid points contain sensors. Per grid point, a model is constructed by means of lumped-parameter system identification, using measurements at neighboring grid points as inputs. As the resulting model might become overly complex due to the involvement of neighboring measurements along with their time lags, the Lasso method is used to select the most relevant measurements and so to simplify the model. Two examples are reported to illustrate the effectiveness of the method, a simulated two-dimensional heat conduction process and the construction of a greenhouse climate model from real measurements.