KLE-(V)AR: A new identification technique for reduced order disturbance models with application to sheet forming processes

A new identification technique that combines the Karhunen–Loève expansion (KLE) with the use of Vector AutoRegressive processes (VAR) is presented in this paper. Given measurements, collected over a period of time, of a set of correlated random variables the method generates a reduced order state-space dynamic model describing the spatial and temporal relationship among the variables. Some of the advantages of the new method are the fewer number of parameters needed to be estimated compared with traditional subspace methods, and its ability to efficiently track nonstationary random processes. Simulation examples from high dimensional sheet forming processes are included for illustration.