Random Walk Model for First-Passage Probability

by Richard H. Toland, Sr. Development Engr.; Hercules Incorporated/ABL, Cumberland, MD,
Cheng Y. Yang, (M.ASCE), Assoc. Prof. of Civ. Engrg.; Univ. of Delaware, Newark, DE,

Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 3, Pg. 791-807

Document Type: Journal Paper


A numerical method is developed for the calculation of first-passage time probability of single degree-of-freedom, linear and nonlinear, dynamic oscillators excited by Gaussian white noise. The random walk model is a difference equation which governs the diffusion of the oscillators response probability in the phase plane and is a discrete analog to the continuous theory Fokker-Planck equation. First-passage is examined by considering the diffusion process when absorbing barriers are superimposed upon the phase plane. Two linear systems are studied for first-passage and compared to results from another numerical approach with good correlation. First-passage is also examined for several nonlinear systems to demonstrate its applicability. It is the study of the latter for which the technique has particular value.

Subject Headings: Numerical methods | Probability | Linear functions | Nonlinear response | Oscillations | Degrees of freedom | Nonlinear analysis | Gaussian process

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