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Finally, the reliability formulations are developed based on computed random response through the solution of first passage problem.
The first passage problem for linear and non-linear oscillators excited by white and coloured noise are considered.
Directly planning to the grasps associated with the first element is a narrow passage problem [33, 34] and should be avoided.
This work aims at an accurate reference solution, providing a basis for the comparison with Monte Carlo based procedures for the first passage problem of non-linear systems.
A recent review of this approach for the simple γ = 0 case in neuronal modeling can be found in [21], wherein the first passage problem is discussed at great lengths in the context of spiking neurons.
The random process approach leads to a first passage problem involving crossings of a random barrier level, which is solved by means of the ensemble up-crossing rate approximation.
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Critical excitations play an important role in first passage problems because they are the most probable point in the first passage failure region of the standard Normal stochastic load space.
The latter may be predicted as a solution to the relevant first-passage problem.
The theory has been applied to a first-passage problem using a Gaussian process with stationary start and a single constant barrier.
The determination of the peak factor is quite cumbersome in the case of a non-stationary process, due to the necessity of calculating the non-geometric spectral moments of the process and obtaining the threshold level of the first-passage problem corresponding to a certain non-exceedance probability value.
SubSim/Splitting is a variant of Subset Simulation applicable to first-passage problems involving deterministic dynamical systems.
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