Direct Monte Carlo Technique Research Articles

Reliability sensitivity analysis using axis orthogonal importance Latin hypercube sampling method

In this article, a combined use of Latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is equivalently solved by reliability sensitivity analysis of a series of hyperplanes through each sampling point parallel to the tangent hyperplane of limit state surface around the design point. The analytical expressions of these hyperplanes are given, and the formulas for reliability sensitivity estimators and variances with the samples are derived according to the first-order reliability theory and difference method when non-normal random variables are involved and not involved, respectively. A procedure is established for the reliability sensitivity analysis with two versions: (1) axis orthogonal Latin hypercube importance sampling and (2) axis orthogonal quasi-random importance sampling with the Halton sequence. Four numerical examples are presented. The results are discussed and demonstrate that the proposed procedure is more efficient than the one based on the Latin hypercube sampling and the direct Monte Carlo technique with an acceptable accuracy in sensitivity estimation of the failure probability.

Diffusion correlation effects of molybdenum and silicon in molybdenum disilicide

Diffusion data for both principal directions of silicon and molybdenum as well as germanium are briefly summarised. Analysis is performed of the defect formation energies (available from previous ab initio calculations and experimental measurements) for diffusion mechanisms via home and foreign sublattices. The home sublattice mechanism is shown to be the preferred one for both silicon and molybdenum. Tracer correlation factors for silicon and molybdenum diffusion via sublattice vacancies in the respective sublattices of the tetragonal C11b structure of molybdenum disilicide are calculated by a direct Monte Carlo simulation technique. Correlation factors for Si diffusion on its sublattice are compared with literature values that were calculated using a more complicated Monte Carlo method based on the matrix approach. It is shown that there is no need for this complicated approach and that the direct Monte Carlo simulation technique gives highly accurate correlation factors. Correlation factors and anisotropy ratios of vacancy-mediated diffusion in both sublattices are deduced and compared with experimental data. Tracer correlation in the tetragonal direction is shown to contribute 0.40 eV (i.e. over 55%) of the migration energy of the corresponding Si diffusivity. Two possible jump rates for Si diffusion are separately estimated. Mo diffusion correlation factors are calculated using the direct Monte Carlo technique. A comparison with experiment is made and the ratio of two possible jump rates is also estimated.

Time-dependent analysis of cable trusses -Part II. Simulation-based reliability assessment

One of the possible alternatives of simulation-based time-dependent reliability assessment of pre-stressed biconcave and biconvex cable trusses, the Monte Carlo method, is applied in this paper. The influence of an excessive deflection of cable truss (caused by creep of cables and rheologic changes) on its time-dependent serviceability is investigated. Attention is given to the definition of the basic random variables and their statistical functions (basic, mutually dependent random variables such as the pre-stressing forces of the bottom and top cable, structural geometry, the Young's modulus of elasticity of the cables, and the independent variables, such as permanent load, wind, snow and thermal actions). Then, the determination of the response of the cable truss to the loading effects, and the definition of the limiting values considering serviceability of the structure are performed. The potential of the method, using direct Monte Carlo technique for simulation-based time-dependent reliability assessment as a powerful tool, is emphasized. Results obtained by the First order reliability method (FORM) are compared with those obtained by the Monte Carlo simulation technique.

Monte Carlo based geometrical model for efficiency calculation of an n-type HPGe detector

A procedure to optimize the geometrical model of an n-type detector is described. Sixteen lines from seven point sources ((241)Am, (133)Ba, (22)Na, (60)Co, (57)Co, (137)Cs and (152)Eu) placed at three different source-to-detector distances (10, 20 and 30 cm) were used to calibrate a low-background gamma spectrometer between 26 and 1408 keV. Direct Monte Carlo techniques using the MCNPX 2.6 and GEANT 4 9.2 codes, and a semi-empirical procedure were performed to obtain theoretical efficiency curves. Since discrepancies were found between experimental and calculated data using the manufacturer parameters of the detector, a detail study of the crystal dimensions and the geometrical configuration is carried out. The relative deviation with experimental data decreases from a mean value of 18-4%, after the parameters were optimized.

Probing local non-Gaussianities within a Bayesian framework

Aims: We outline the Bayesian approach to inferring f_NL, the level of non-Gaussianity of local type. Phrasing f_NL inference in a Bayesian framework takes advantage of existing techniques to account for instrumental effects and foreground contamination in CMB data and takes into account uncertainties in the cosmological parameters in an unambiguous way. Methods: We derive closed form expressions for the joint posterior of f_NL and the reconstructed underlying curvature perturbation, Phi, and deduce the conditional probability densities for f_NL and Phi. Completing the inference problem amounts to finding the marginal density for f_NL. For realistic data sets the necessary integrations are intractable. We propose an exact Hamiltonian sampling algorithm to generate correlated samples from the f_NL posterior. For sufficiently high signal-to-noise ratios, we can exploit the assumption of weak non-Gaussianity to find a direct Monte Carlo technique to generate independent samples from the posterior distribution for f_NL. We illustrate our approach using a simplified toy model of CMB data for the simple case of a 1-D sky. Results: When applied to our toy problem, we find that, in the limit of high signal-to-noise, the sampling efficiency of the approximate algorithm outperforms that of Hamiltonian sampling by two orders of magnitude. When f_NL is not significantly constrained by the data, the more efficient, approximate algorithm biases the posterior density towards f_NL = 0.

Reliability sensitivity method by line sampling

Reliability sensitivity refers to the derivative of the failure probability with respect to the distribution parameter of basic random variable. Conventionally, this requires repetitive evaluations of the failure probability for different distribution parameters, which is a direct but computationally expensive task. An efficient simulation algorithm is presented to perform reliability sensitivity analysis using the line sampling technique, which gives a good failure probability evaluation for high-dimensional problems and still presents a comparative one for low-dimensional problems. On the basis of the line sampling procedure for failure probability analysis, the concept and implementation are presented for reliability sensitivity. It is shown that the desired information about reliability sensitivity can be obtained by a very limited increase of computation effort based on the failure probability analysis by the line sampling technique. The presented reliability sensitivity algorithm is more efficient than the one based on the direct Monte Carlo technique, especially for cases where the failure probability is low and the number of random variables is large, which is illustrated by several examples. Additionally, limitations of the line sampling based reliability sensitivity method are demonstrated by a numerical example as well.

Time-dependent analysis and simulation-based reliability assessment of suspended cables with rheological properties

The intention of the paper is to illustrate the ability of the probabilistic time-dependent reliability assessment procedure applied to non-linear suspended cable structure with rheological properties, when a rope made from the high strength synthetic fibres is used in order to demonstrate the new qualitatively different concept. Attention is turned to the individual main steps in the assessment procedure, i.e. to the selection of an appropriate method of structural analysis and to derivation of an appropriate closed-form and discrete analytical models, analysis of random variables representing individual actions (four basic random variables, such as structural geometry, cable’s modulus of elasticity and creep strain increments and loading, are considered), evaluation of the structural response with respect to the interaction of the random variables considering a history of the time-dependent action effects and to the definition of the limiting values considering serviceability of cable structure. The potential of the method using direct Monte Carlo technique as one of the possible alternatives for simulation-based time-dependent reliability assessment as a powerful tool is emphasized. The influence of an excessive deflection of suspended cable (caused by creep of cable and rheologic changes) on its serviceability in required time is investigated and illustrative examples are performed.

Probabilistic methods for drug dissolution. Part 2. Modelling a soluble binary drug delivery system dissolving in vitro

The objective of this work is to use direct Monte Carlo techniques in simulating drug delivery from compacts of complex composition, taking into consideration the special features of the in vitro dissolution environment. The paper focuses on simulating a binary system, consisting of poorly soluble drug, dispersed in a matrix of highly soluble acid excipient. At dissolution, the acid excipient develops certain mechanisms, based on local pH modifications of the medium, which strongly influence drug release. Our model directly accounts for such effects as local interactions of the dissolving components, development of wall roughness at the solid–liquid interface, moving concentration boundary layer and mass transport by advection. Results agree with experimental data and have demonstrated that when modelling dissolution in vitro, special attention must be paid to including the particular conditions of the dissolution environment.

New method to minimize the preventive maintenance cost of series–parallel systems

General preventive maintenance model for input components of a system, which improves the reliability to ‘as good as new,’ was used to optimize the maintenance cost. The cost function of a maintenance policy was minimized under given availability constraint. An algorithm for first inspection vector of times was described and used on selected system example. A special ratio-criterion, based on the time dependent Birnbaum importance factor, was used to generate the ordered sequence of first inspection times. Basic system availability calculations of the paper were done by using simulation approach with parallel simulation algorithm for availability analysis. These calculations, based on direct Monte Carlo technique, were applied within the programming tool Matlab. A genetic algorithm optimization technique was used and briefly described to create the Matlab's algorithm to solve the problem of finding the best maintenance policy with a given restriction. Adjacent problem, which we called ‘reliability assurance,’ was also theoretically solved, concerning the increase of the cost when asymptotic availability value conforms to a given availability constraint.

Models for direct Monte Carlo simulation of coupled vibration–dissociation

Models are developed to permit direct Monte Carlo techniques to simulate coupled vibration–dissociation (CVD) behavior prevalent in high-temperature gases. This transient thermochemical phenomenon leads to dissociation incubation, reduced quasisteady dissociation rates, and non-Boltzmann distributions of vibrational energy during both dissociation and recombination. Essential for simulation of rarefied gas dynamics, Monte Carlo methods employ discrete particles to simulate molecular interactions directly, but have traditionally incorporated simplistic reaction models which failed to capture CVD behavior. To identify thermochemical collisions within the gas, a new dissociation selection probability is developed as a function of the extent by which the collision energy exceeds the gap between the dissociation threshold and the molecular vibrational energy of bounded anharmonic oscillators. A free parameter φ in the probability function controls the extent of vibrational favoring in dissociation selection. The new model is modified for application to the unbounded simple harmonic oscillator. Simulation of dissociation- and recombination-dominated thermochemical relaxation of O2 reservoirs, as well as the dissociation incubation behavior of N2 behind strong shock waves, demonstrates the ability of the new models to capture CVD behavior. Parameter φ is assessed empirically for O2 and N2 dissociation by comparison to experimental data.

Effects of gas-phase collisions in rapid desorption of molecules from surfaces in the presence of coadsorbates

The effects of gas-phase collisions in mixtures of gases rapidly desorbed from surfaces are studied using direct Monte Carlo techniques. The results are compared with the effects observed in the desorption of pure gases under similar conditions. The translational energy distribution of the desorbed particles are found to deviate from the Boltzmann distribution and are found to be well represented by ellipsoidal Boltzmann distributions. In this respect the rapid desorption process is found to have similarities to the expansion of gases in nozzle sources. The influence of mass, internal degrees of freedom, and surface coverage of the adsorbates on the focusing, accelerating, and cooling effects due to gas-phase collisions are analyzed. The presence of molecules with active internal degrees of freedom is found to increase the average number of collisions experienced by the rapidly desorbed molecules. However, the influence of this increased number of collisions on the focusing effects due to gas-phase collisions is less pronounced compared to the focusing effects due to collisions between the desorbed atoms. In a gas mixture containing molecules as the minor constituents (10%) and atoms as the major constituents (90%), atoms are found to be more focused towards the surface normal than the molecules and the mean translational energies of the molecules are found to be less than those calculated in the desorption of pure molecules under similar conditions. The presence of atoms in the desorbed gas mixture is found to increase the most probable speed of the desorbing molecules and this accelerating effect increases with decrease in the mass of the coadsorbed atoms. The light atoms are found to be more efficient than heavy atoms in cooling the internal degrees of freedom.

Epitaxial growth of GexSi

Epitaxial growth of ${\mathrm{Ge}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ alloy films on a Si substrate is simulated employing a direct Monte Carlo technique. In addition to various interlayer and intralayer diffusion processes of Si and Ge atoms, we include a model strain-driven mechanism that gives rise to defects (local out-of-registry regions) in the overgrowth. Our simulation indicates that (i) the overgrowth is defect-free for $x\ensuremath{\le}0.2$, (ii) defect formation is inevitable for $x\ensuremath{\ge}0.5$, and (iii) the transition between the two cases occurs smoothly within $0.2lxl0.5$. On the basis of our simulation, we predict that for a very low Ge fraction $xl0.1$, the critical temperature for the onset of good epitaxial growth will be substantially above the 400\ifmmode^\circ\else\textdegree\fi{}C found for higher $x$ values.

Scanning method as an unbiased simulation technique and its application to the study of self-attracting random walks.

The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ``importance sampling,'' we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight , where p1 is an attractive energy parameter and ${M}_{i}$ is the number of distinct sites visited by walk i.This model, which corresponds to a model of random walks moving in a medium with randomly distributed static traps, has been solved analytically for N\ensuremath{\rightarrow}\ensuremath{\infty} for any dimension d by Donsker and Varadhan (DV) and by others. 〈M〉 and ln\ensuremath{\varphi}, where \ensuremath{\varphi} is the survival probability in the trapping problem, diverge like ${N}^{\ensuremath{\alpha}}$ with \ensuremath{\alpha}=d/(d+2). Most numerical studies, however, have failed to reach the DV regime in which d/(d+2) becomes a good approximation for \ensuremath{\alpha}. On the other hand, our results for \ensuremath{\alpha} (obtained for N\ensuremath{\le}150) are close to the DV values for p\ensuremath{\le}0.7 and p\ensuremath{\le}0.6 for d=2 and 3, respectively.This suggests that the scanning method is more efficient than both the commonly used direct Monte Carlo technique, and the Rosenbluth and Rosenbluth method [J. Chem. Phys. 23, 356 (1954)]. Our results support the conclusion of Havlin et al. [Phys. Rev. Lett. 53, 407 (1984)] that the DV regime exists already for \ensuremath{\varphi}\ensuremath{\le}${10}^{\mathrm{\ensuremath{-}}13}$ for both d=2 and 3. We also find that at the percolation threshold ${p}_{c}$ the exponents for the end-to-end distance are small, but larger than zero, and that the probability of a walk returning to the origin behaves approximately as ${N}^{\mathrm{\ensuremath{-}}1/3}$ for both d=2 and 3.