Identification of switched dynamic system for electric multiple unit train modeling

A new iterative algorithm is proposed to identify the high-speed train model which is described as a switched dynamic system including a fast switched nonlinear static subsystem followed by a non-switched linear dynamic subsystem. The non-switched property of the linear part leads to a more complex dynamics of the whole system, compared to the switched Hammerstein system which linear part switches synchronously with its nonlinear part. The proposed iterative algorithm alternates between identifying the switched nonlinear static subsystem and the linear dynamic subsystem. The switched nonlinear subsystem identification incorporates a quadratic error bound constraint with respect to nominal values of model parameters, and is formulated as a second-order cone program. Properties of convergence and asymptotic unbiasedness of the obtained estimates are proved under some necessary assumptions. With real data and simulation examples, the proposed iterative algorithm produces convergent and asymptotically unbiased estimates. In the simulation results, incorporating the quadratic error bounds results in a fast convergence rate in the presence of a small noise variance, and also produces a smaller identification error in the presence of colored noises with a non-zero mean and a large variance.