Model order reduction using overcomplete damped sinusoid dictionary and sparse coding

Model order reduction (MOR) is an approximation approach where a high order complex system is modeled by a low order parametric system. Power system transients, RLC interconnects in deep submicron technology, and large scale dynamical systems are just a few examples of MOR practical applications. In this paper, the focus is on approximating the impulse response of high order RLC-like systems. In the proposed approach an overcomplete dictionary of damped sinusoids is constructed and the sparse coding paradigm is used to find the sparsest solution to the given impulse response. Two modifications of the basic dictionary with added random atoms are used. A particle swarm optimization with constraints algorithm is employed to refine the sparse coding model, and finally, the best model is chosen adaptively. A system of order 24 is simulated and reduced models of orders 4, 6 and 8 are tested for different dictionary sizes.