Controlled Monte Carlo simulation method

Over the last two decades, there has been increasing interest in probabilistic, or stochastic, robust control theory. Monte Carlo simulation methods have been used to synthesize and analyze controllers for uncertain systems [170,255], First- and second-order reliability methods were incorporated to compute the probable performance of linear-quadratic-regulator... 

The selection of the importance descriptor, C t), based on the notion of distance between samples led to the development of a method called distance-controlled Monte Carlo simulation (Pradlwarter and Schueller 1999). Here the trajectories are further manipulated using the Russian roulette with splitting strategy so as to make the realizations to be uniformly distributed in space. 

Grand Canonical Monte Carlo simulation is used to investigate the properties of water (fluid of most importance) confined in mesoporous Controled Porous Glass (Vycor-like) numerically obtained by the off-lattice method developed by P. Levitz [Adv. Coll. Int. Sci. 76-77 (1998), 71]. We first outline the interaction model and give the adsorption isotherm obtained at 300 K. Good agreement is found with available experimental results. 

The simple approach discussed above is valid for steady-state Monte Carlo simulations, but dynamic simulations are also possible. In this case, the model probabilities must be updated frequently, generally after every iteration. A detailed discussion of these methods would be too lengthy to be included herein the most common algorithm for dynamic Monte Carlo simulation follows the approach proposed by Gillespie, which requires the discretization of the polymerization reactor with small control volumes and the conversion of the polymerization kinetic rates into molecular collision frequencies [97, 98],... 

ABSTRACT This paper addresses Time-Lunited Dispatch (TLD), the application of which allows aircraft to dispatch for limited periods of time with faults present in their engine control systems. TLD attributes and certification requirements are discussed, and a Monte Carlo simulation algorithm for modelling TLD is presented. When attempting to improve the design of systems to which TLD is applied, a measure of the contribution made by individual components to the system failure would allow areas of weakness within the system to be identified. System modifications could then be focussed on these areas. This paper presents a method of calculating component importance measures for systems to which TLD is applied. Potential areas of use for the importance measures are identified and discussed. 

Beyond the above computation, and with the help of a Monte Carlo simulation (see, also, Section 3), the degree to which the individual component contributes to a system failure was determined. The above method also permits taking into account specific maintenance strategies. The life histories of the individual components are created over a period of time from 5 x 10 h and thereby it is also determined whether the system failure can be traced to corresponding component failures at any specific point in time. Here the failure-prone components are recorded in connection with each individual failure. Results demonstrate that position transmission (2) is involved in 100% of all system failures, which is natural because of the system s logical structure (Figure 5.23). The mechanical system of the valve is involved in 12%, the hydraulic control element in 29%, and the control pulse in 59% of all cases of system failure. 

In addition to the statistical response, the effectiveness of the active control system is further demonstrated using the method of Monte Carlo simulation. Sample functions of the components of the buffeting loads in the normal coordinates are simulated using the Fast Fourier transform (FFT) technique [25]. Then, a system of simultaneous coupled differential equations is solved using a 4 order Runge-Kutta numerical integration method to obtain the sample function of bridge response quantities [11]. 

Central force models represent an alternative approach to representing the interactions of water molecules. Here each atom interacts with all other atoms, even on the same molecule, via pairwise additive, central potentials. i83-i85 This is clearly a flexible model because stretch and bend motions are controlled by the potentials. The interactions contain a local minimum for intramolecular interactions this minimum maintains the geometry of the molecule. One advantage of the central force model is that integral equation methods can be applied to the determination of liquid state properties. This is computationally much less demanding than molecular dynamics or Monte Carlo simulations, although the integral equation methods are restricted in practice to central force models. 

Exact solutions to the problem of determining Pf are not available for most cases of practical interest. One takes recourse to approximate analytical solutions or to Monte Carlo simulation-based methods. The analytical methods can be broadly classified into those based on level crossing statistics and those based oti Markovian property of system responses. The simulation-based methods typically employ suitable strategies to control the sampling variance. A discussion of these topics forms the subject of the following sections. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

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