Noise Spectral Density of Hysteretic Systems

Abstract

This chapter presents the analysis of output spectral density for hysteretic systems driven by noisy inputs. Closed form analytical solutions for output spectra are derived for bistable hysteretic systems, as well as for complex hysteretic systems that can be described through Preisach model as weighted superposition of symmetric rectangular operators. The mathematical machinery of diffusion processes on graphs is used to circumvent the difficulties related to the non-Markovian property of the output of hysteretic systems. The calculations are appreciably simplified by the introduction of the “effective” distribution function. The implementation of the method for the case of Ornstein-Uhlenbeck process is presented in details and general qualitative features of these spectral densities are examined. Due to the universality of the Preisach model, this approach can be used to describe hysteresis nonlinearities of various physical origins. In the last part of this chapter, the spectral density analysis is extended to other models of hysteresis, such as the energetic model, the Jiles-Atherton model, the Coleman-Hodgdon model, the Bouc-Wen and model, and the Preisach model. The statistical technique to compute the output spectra is based on Monte-Carlo simulations and Fast Fourier Transforms. The intrinsic differences between the algebraic, differential, and integral modeling of hysteresis are well exposed when the systems are driven by noisy inputs and their stochastic behaviors are compared against each other.KeywordsHysteretic SystemsOutput Spectral DensityPreisach ModelJiles-Atherton ModelPreisach DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.