Computational methods for probability of instability calculations

This paper summarizes the development of the methods and a computer program to compute the probability of instability of a dynamic system that can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the roots of the characteristic equation or Routh-Hurwitz test functions are investigated. Computational methods based on system reliability analysis methods and importance sampling concepts are proposed to perform efficient probabilistic analysis. Numerical examples are provided to demonstrate the methods.