Identification of the quadratic kernel of the Volterra equation for modeling non-linear dynamic systems

In the last two decades, integral models have been used to describe dynamics of stationary nonlinear systems in which terms Volterra series are kernels. The most commonly linear term (the impulse transition function depends on one variable) and quadratic (depending variables). An active experiment a special combination rectangular pulses is fed input system carried out select its components output signal identified - "subsystem" "quadratic" subsystem. After isolating subsystem, identification reduced solving two-dimensional equation first kind. literature, inversion formulas given kernel obtained as result arithmetic operations with second-order derivatives signal. Differentiation functions an incorrectly posed problem, when small errors assignment (measurement noise) cause large (especially derivatives). paper proposes use smoothing cubic splines for stable calculation derivatives. To calculate mixed derivative, spline variables built bicubic spline. main problem that arises practice processing data real selection parameter, value error noisy depends. As rule, variance measurement noise unknown experiment. Therefore, this work, it proposed algorithm based L-curve method parameter constructed one), does not require setting noise. has high computational efficiency. performed showed methodical (about 1%) good resistance measurements signals system. reduce random component error, post-processing local-spatial compound filter.