Identification of nonlinear systems in the frequency domain using two-dimensional Volterra series

This paper presents the identification of second-order two-dimensional kernels using the Volterra series model in the frequency domain. The study focuses on nonlinear systems where the input varies over both time and spatial dimensions. The Volterra series, known for its effectiveness in modeling complex nonlinear systems, is extended to two dimensions. The kernels are computed using the least squares method, with the input defined as a product of cosine functions. By simplifying the expressions and applying the Fourier transform, accurate kernel identification is achieved. The results demonstrate the efficacy of this approach in precisely matching the estimated system with the actual system, as evidenced by the minimal identification error. This work contributes to the development of advanced techniques for nonlinear system identification in industrial and scientific applications.