Compressive Sensing-based Pruning of Frequency-Domain Volterra Models

The Volterra approach is a powerful tool for the behavioral modeling of dynamic systems, but the resulting complexity grows more than exponentially with the considered degree of nonlinearity. A frequency-domain Volterra representation is favorable when the target is predicting the steady-state response to periodic signals, and pruning methods to reduce the number of coefficients have been proposed by exploiting a priori knowledge about the expected amplitude distribution of the input spectrum. However, in principle, a further and complementary simplification can be attained according to the behavior of the system, which is reflected in the input-output signals used for the identification. In this context, the present paper proposes a data-driven pruning method for frequency-domain Volterra models, based on compressive sensing theory. In particular, ℓ1-norm optimization paired with accuracy-oriented sparsification of the estimated coefficients is proposed in order to prune the model while keeping performance under control. The designed technique is applied to identify the simplified Volterra representation under quasi-sinusoidal conditions of a Wiener-Hammerstein system, considering two different classes of input signals. Results highlight the potentiality of the approach, which is able to effectively prune the models according to a predetermined accuracy target.