Efficient Estimation of Synthetic Indicators for the Assessment of Nonlinear Systems Quality

The availability of synthetic indicators of the degree and type of nonlinearity in systems is used in various fields to assess system quality or to highlight possible malfunctions. Different distortion or damage indexes are synthetic measures designed (and standardized) to evaluate the frequency trend of specific aspects resulting from the nonlinear behavior of the system under consideration. The different measures of deviation from linear behavior quantitatively consider the system and its nonlinearity characteristics; they were defined according to practically feasible measurement methodologies and the various aspects of the system’s nonlinearity that needed to be highlighted. In parallel, techniques for representing and modeling nonlinear systems have been defined, capable of describing the system in a more general way, attempting to capture its input–output characteristics by varying the level of stress to which the system is subjected. Numerous modeling techniques have been proposed, aimed at representing the nonlinear behavior of physical devices. In this paper, after an extensive description of the Hammerstein model identification technique based on swept sinusoidal signals, we show how the nonlinear model of the system can be used to obtain accurate estimates of the parameter aimed at describing the nonlinearity characteristics of the system. This extensive description makes it possible to point out that the same Hammerstein model can be obtained not only from a single type of excitation, but it is shown that the identification technique can be extended to input signals of different types. The description of the method also makes clear the motivation behind the introduction of the proposed original technique for estimating, from a single measurement, the model parameters of the nonlinear system—and from these the synthetic estimators—relative to multiple values of the input signal amplitude, thus enabling a considerable increase in the estimation efficiency of these parameters. The proposed technique is verified with both synthetic and laboratory experiments, demonstrating the effectiveness of the method in evaluating nonlinear system parameters, distortion estimates, and parameters defined for an early detection of defects of the structure.