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Efficient Identification of Hammerstein Systems by Two-Level Optimization with Decomposition

The paper considers popular problem of Hammerstein system identification. It is inspired by the real problem concerning modeling of differential scanning calorimetry for chalcogenide glass properties examination. In spite of variety of identification methods proposed in the literature, none of them can be applied directly, due to specific practical limitations. The most popular approaches, e.g. overparametrization approach, or nonparametric regression estimation, require relatively large number of data or lead to very complicated numerical tasks. The proposed algorithm consists of two steps. Firstly, the impulse response of the linear block is identified by the standard least squares method, assuming i.i.d. input excitation. Next, the coefficients of orthogonal expansion of nonlinear characteristic are estimated independently by iterative optimization, provided that the criterion function is convex. Results of simulation examples give promising results, i.e., satisfactory accuracy and relatively fast computations.