6533b85ffe1ef96bd12c1db7

RESEARCH PRODUCT

Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise

Christian BucherMario Di Paola

subject

Mathematical optimizationSequenceMarkov chainPoisson proceMechanical EngineeringReliability (computer networking)Monte Carlo methodAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseWhite noiseCondensed Matter PhysicsPath IntegrationNonlinear systemNuclear Energy and EngineeringStructural reliabilityApplied mathematicsFirst passage problemRandom vibrationSettore ICAR/08 - Scienza Delle CostruzioniRandom vibrationCivil and Structural EngineeringMathematics

description

Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.

yearjournalcountryeditionlanguage
2015-07-01Probabilistic Engineering Mechanics
https://doi.org/10.1016/j.probengmech.2015.06.007