Passage Problem Research Articles

Reliability analysis of multi-degree-of-freedom nonlinear random structure vibration systems with correlation failure modes

Based on the generalized probabilistic finite element method, this paper presents an approximate solution technique for general multi-degree-of-freedom nonlinear random vibration systems with random parameters. The fourth-moment technique, maximum entropy theory and incomplete probability information theory are employed to systematically develop a reliability analysis method for dynamic random structural systems with correlation failure modes under unavailable joint probability density functions of basic random variables. The first passage problem of multi-degree-of-freedom nonlinear random vibration systems is solved.

RELIABILITY EVALUATIONS OF 3-D FRAME SUBJECTED TO NON-STATIONARY EARTHQUAKE

The objective of the present work is to evaluate the integrated reliability of multistoried space frame subjected to random earthquake. The stochastic ground motion is described by fully non-stationary sigma-oscillatory model. The stochastic dynamic analysis is performed in the frequency domain to obtain the power spectral density function of random response. Finally, the reliability formulations are developed based on computed random response through the solution of first passage problem. A building frame idealized as a space frame in finite element modelling is considered for reliability analysis. Simple modal analysis is also performed for comparison of results.

Nonlinear stochastic dynamics: A survey of recent developments

This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.

Process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions.

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.

On the Dependence Structure of Certain Multi-dimensional Ito Processes and Corresponding Hitting Times

A direct approach to derive dependence properties among components of multi-dimensional stochastic processes has been discussed by N. Ebrahimi (1994, J. Multivariate Anal.50, 55–67). Dependence properties among hitting times involving multi-dimensional stochastic processes has been initiated by N. Ebrahimi (1987, J. Appl. Probab.24, 115–122) and explored further by N. Ebrahimi and T. Ramalingham (1988, J. Appl. Probab.25, 355–362; 1989, J. Appl. Probab.26, 287–295). Let X(t)=(X1(t), …, Xk(t)) be an Ito process assuming values in Rk. In this article, under certain conditions, we show that the process X(t) has a certain dependence structure. We also consider the first passage problem involving X(t) and discuss the dependence structure among hitting times of X1(t), …, and Xk(t).

Printing Anglo-Saxon in Holland and John Selden's Mare Clausum seu de Dominio Maris

[Provision of the special sorts needed to print Anglo-Saxon required drawing on the skill of a punchcutter. For John Selden's Mare Clausum (London, John Stansby 1635) the special sorts used were sixteenth-century ones inherited by Stansby ultimately from those made for Archbishop Parker (†1575)- Selden's book, on the dominion as opposed to the freedom of the seas, caused such a political stir that three Dutch editions were produced somewhat hastily in 1636. This article considers how the printers of these editions, who had no access to the exclusively English tradition of printing Anglo-Saxon, coped with the problem of printing passages in that language. Two of the printers, the Elzeviers and the Maires in Leiden, apparently used the same punchcutter, who may have been Arent Corsz[oon] van Hoogenacker. It was the first attempt to cut a set of Anglo-Saxon special sorts in the seventeenth century., Provision of the special sorts needed to print Anglo-Saxon required drawing on the skill of a punchcutter. For John Selden's Mare Clausum (London, John Stansby 1635) the special sorts used were sixteenth-century ones inherited by Stansby ultimately from those made for Archbishop Parker (†1575)- Selden's book, on the dominion as opposed to the freedom of the seas, caused such a political stir that three Dutch editions were produced somewhat hastily in 1636. This article considers how the printers of these editions, who had no access to the exclusively English tradition of printing Anglo-Saxon, coped with the problem of printing passages in that language. Two of the printers, the Elzeviers and the Maires in Leiden, apparently used the same punchcutter, who may have been Arent Corsz[oon] van Hoogenacker. It was the first attempt to cut a set of Anglo-Saxon special sorts in the seventeenth century.]

PASSAGE THROUGH RESONANCE OF ROLLING FINNED PROJECTILES WITH CENTER-OF-MASS OFFSET

Finned projectiles that are meant to be unspun could acquire small roll rates in flight due to slight configurational asymmetries. If the roll rate matches the natural yawing frequency of the projectile, a resonance phenomenon takes place resulting in yaw amplification, and possible loss of stability. To avoid this, finned projectiles are deliberately spun to a roll rate well beyond the resonance value. This gives rise to a passage-through-resonance phenomenon in the flight of finned projectiles. Finned projectiles passing through resonance are known to exhibit the phenomena of roll lock-in, transient resonance, and catastrophic yaw. Projectiles locked in at the resonance condition experience large yaw and are likely to lose the desired flight path. On the other hand, transient resonance is a milder phenomenon where the projectile locks in at resonance briefly before continuing to build-up to the design value. However, the yaw amplification during the brief period of resonance may be sufficient to destabilize the projectile. The problem of passage through resonance of finned projectiles with a center-of-mass offset is considered in this paper. Roll lock-in and transient resonance at normal and reverse resonance is shown. It is observed that the yaw amplification at transient resonance is much lower than that at lock-in. The lack of yaw amplification can be understood based on the bifurcation analysis and numerical simulations reported in this paper.

To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations

A weighted Sobolev space is constructed in which smooth functions are not dense and their closure is of codimension one. With the help of this weighted space, counterexamples are constructed to natural hypotheses on the passage to the limit in non-uniformly-elliptic equations and on the structure of the limit equation.

Rare events probabilities estimation by “ Russian Roulette and Splitting ” simulation technique

An advanced Monte Carlo Simulation (MCS) technique—namely, “Russian Roulette and Splitting” (RR & S) technique is applied for the reliability assessment of mechanical systems under stochastic excitations. The basic features of the algorithm are described and discussed. As a numerical example the technique is used for the numerical solution of the first passage problem in the low probability range. Results are compared with available solutions, obtained by another variance reduction technique—“Double and Clump”(D & C) procedure.

Breaching of a Small Irrigation Dam in Oregon: A Case History

Abstract Dam removal or breaching (partial removal) is an increasingly common remedy for fish passage, habitat degradation, water quality, and other problems caused by dams in the United States. The Jackson Street Dam, built in 1960 on Bear Creek in Medford, Oregon, resulted in a barrier to migration of Pacific salmon Oncorhynchus spp. and steelhead O. mykiss, loss of stream habitat, eutrophication, and an algae-choked impoundment in downtown Medford. The 11-ft-high concrete and wooden structure was owned and operated by the Rogue River Valley Irrigation District as one of its primary diversions. The dam was breached in 1998, culminating a 13-year, US$1.2 million effort led by the Rogue Valley Council of Governments and the Medford Urban Renewal Agency in collaboration with the irrigation district, other government agencies, and local citizens. Breaching reduced the dam to a series of three concrete steps dropping 1 ft each, thereby providing fish passage and restoring a free-flowing stream within the for...

Numerical Solution of First Passage Problems in Random Vibrations Using Finite Difference Method.

The finite difference method is applied to estimate the reliability of the single degree of freedom system subjected to white noise excitation. In this paper, the probability that the system response stays within a safe region is used as the system reliability. It is difficult to obtain the accurate reliability from the probability density of the system response. Then the boundary condition of the finite difference scheme which we presented in the previous paper for the probability density of the system response is modified to obtain reliability directly from the Fokker-Planck equation, which governs the probability density. The reliability of the Duffing oscillator is calculated in the illustrated examples. The validity of the present method is demonstrated by comparison with the results of the Monte Carlo simulation.

Statius' Thebaid 4.165-72 and Euripides' Phoenissae 1113-18

The description of Capaneus' shield in Stat. Theb. 4 contaminates aspects of Adrastus' shield (the emblem) and of Hippomedon's (the decorative schema) as they are pictured in the second heroic catalogue of Euripides' Phoenissae. This paper helps explain on literary grounds some textual and linguistic problems of the Statian passage.

99/03808 Reliability of rechargeable batteries in a photovoltaic power supply system: Urbina, A. et al. J. Power Sources, 1999, 80, (1/2), 30–38

We investigate the reliability If a rechargeable battery acting as the energy storage component in a photovoltaic power supply system. A model system was constructed for this that includes the solar resource, the photovoltaic power supp Iy system, the rechargeable battery and a load. The solar resource and the system load are modeled as SI ochastic processes. The photovoltaic system and the rechargeable battery are modeled deterministically, imd an artificial neural network is incorporated into the model of the rechargeable battery to simulate dartage that occurs during deep discharge cycles. The equations governing system behavior are solved simultaneously in the Monte Carlo framework and a fwst passage problem is solved to assess system reliability.

Reliability of rechargeable batteries in a photovoltaic power supply system

We investigated the reliability of a rechargeable battery acting as the energy storage component in a photovoltaic power supply system. A model system was constructed for this that includes the solar resource, the photovoltaic power supply system, the rechargeable battery and a load. The solar resource and the system load are modelled as stochastic processes. The photovoltaic system and the rechargeable battery are modelled deterministically, and an artificial neural network is incorporated into the model of the rechargeable battery to simulate damage that occurs during deep discharge cycles. The equations governing system behaviour are solved simultaneously in the Monte Carlo framework, and a first passage problem is solved to assess system reliability.

Numerically exact diffusion coefficients for lattice systems with periodic boundary conditions. I. Theory

The standard method to study the diffusion of a particle in a system with immobile obstacles is to use Monte Carlo simulations on finite-size lattices with periodic boundary conditions. For example, the diffusion of proteins on the surface of biomembranes in the presence of fractal and random aggregates of obstacles has been studied extensively by M. J. Saxton. In this article, we derive two algebraically exact methods to calculate the diffusion coefficient D for such systems. The first method reduces the problem to that of a first passage problem. The second one uses the Nernst–Einstein relation to transform the problem into a field-driven drift problem where D is related to the zero-field mobility. Systems with closed volumes and multiple independent pathways are discussed. In the second part [Mercier and Slater, J. Chem. Phys. 110, 6057 (1999), following paper], a numerical implementation will be described and tested, and several examples of applications will be given.

Importance sampling for first passage problems of nonlinear structures

This article deals with reliability assessment of mechanical structures subjected to random excitation. The probability of failure is formulated as first passage probability of a given threshold within the observation period. A solution for arbitrary structures exhibiting nonlinear behaviour can be obtained by the Monte Carlo simulation. In order to reduce the sample size, an importance sampling concept is proposed, which automatically adapts the simulation densities in two subsequent simulation runs. The excitation process is simulated by the so-called spectral representation method, where the random variables are the amplitudes and phase angles of a Fourier series expansion. It is proposed to adapt the simulation densities of the amplitudes with respect to the power spectral density of the observed structural response. An example demonstrates the applicability of the procedure.

Wald's equations, first passage times and moments of ladder variables in Markov random walks

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.

Wald's equations, first passage times and moments of ladder variables in Markov random walks

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.

Numerical solution of first passage problems using an approximate Chapman-Kolmogorov relation

A new deterministic numerical method for solving first passage time problem is described, analyzed and computationally tested. The method is based on recursively solving an integral equation for the reliability function. The integral equation is derived from the Chapman-Kolmogorov relation and involves an approximation to the Green's function for the forward Kolmogorov equation. An error analysis yields estimates of convergence rates. Numerical experiments indicate that the method is stable and can accurately approximate the reliability function and first passage times.

A comparison of methods for the statistics of slow-drift oscillations

A probabilistic model for the slowly varying horizontal motion of a moored floating structure, excited by nonlinear, second order wave forces is derived. The model consists of a coupled system of three white-noise excited stochastic differential equations that govern a continuous vector Markov process. Different methods are applied for the investigation of the first passage time probabilities of the displacement of the marine structure. The methods include time history simulation estimation of the first four moments, time history simulation of the first passage problem, and finite element solution of the backward Kolmogorov equation governing the first passage time distribution. The impact of non-Gaussian aspects of the response on extreme value statistics is demonstrated.