Correlation-Induced Steady-State Shift in Nonlinear Systems Under Correlated Poisson Pulses

Abstract

Abstract. Stochastic analysis traditionally assumes excitations to be independent. However, correlations among excitations are prevalent in engineering systems and often disregarded for analytical simplicity. Such neglect introduces fundamental errors in response predictions. For instance, correlated excitations can induce an asymmetric response probability density function (PDF) and a nonzero-mean response—phenomena that an independence assumption would fail to capture, leading to substantial predictive error. This study investigates the response of nonlinear systems driven by Poisson white noise with correlated pulse amplitudes. To account for this correlation, additional terms are incorporated into the generalized Fokker–Planck (FP) equation. The modified FP equation is solved using the exponential-polynomial closure (EPC) method, yielding an approximate PDF for the system response. The accuracy of this solution is validated by comparing its predictions with Monte Carlo simulations. Analyses of linear, Duffing, and Dimentberg oscillators quantitatively reveal how the sign and magnitude of the pulse correlation shape the response statistics. These findings confirm that excitation correlation significantly influences the system response and must be explicitly included for accurate analysis.