Stability and reliability analysis of nonlinear stochastic system using data-driven dimensional analysis method

Stability and reliability are two critical aspects in the qualitative analysis of dynamic systems. In this paper, a data -driven dimensional analysis methodology is proposed to analyze the stability and reliability of nonlinear stochastic dynamical systems. The analytical solutions for the largest Lyapunov exponent and the conditional reliability function with minimal arguments are identified. Beginning with random state data, it first discovers the unique and relevant set of dimensionless groups through the Buckingham Pi theorem and sensitivity analysis. The expressions for the quantities of interest (the largest Lyapunov exponent for stability analysis, and the conditional reliability function for reliability assessment) are determined using Gaussian process regression. Subsequently, the dimensionality of these expressions is reduced based on the relative importance of the dimensionless parameter cluster within the unique dimensionless set. The effectiveness and accuracy of this data -driven method for analyzing stochastic stability and reliability are illustrated by two representative numerical examples, i.e., a 2-DOF nonlinear system subjected to purely parametrical Gaussian white noises, and a 2-DOF system subjected to both parametrical and external noises, respectively. Furthermore, the extensionality of the analytical expressions is also validated. The data -driven dimensional analysis methodology specified here overcomes the limitations of classical dimensional analysis and offers more accurate expressions with fewer arguments compared to other data -driven methods found in the existing literature.