Direct Monte Carlo Simulation Technique Research Articles

Seismic Reliability Analysis of Structures by an Adaptive Support Vector Regression-Based Metamodel

ABSTRACT The dual metamodeling approach is usually adopted to tackle the stochastic nature of earthquakes in seismic reliability analysis relying on the lognormal response assumption. Alternatively, a direct response approximation approach where separate metamodels are constructed for each earthquake is attempted here avoiding prior distribution assumption. Further, an adaptive support vector regression-based metamodeling is proposed that selects new training samples near the failure boundary with due consideration to accuracy and efficiency. The effectiveness of the approach is elucidated by comparing it with the results obtained by the direct Monte Carlo simulation technique and a state-of-the-art active learning-based Kriging approach.

Seismic fragility of non-ductile RC frames for pounding risk assessment

Building structures subjected to seismic excitation tend to vibrate with a unique set of dynamic characteristics, such as natural frequencies, fundamental mode shapes etc. In series-configured structural systems, a difference in such characteristics induces a phase difference between the structures’ oscillations, leading to structural collisions or pounding. Pounding often becomes a cause of catastrophic failures, hence an accurate estimation of structural integrity with respect to pounding is of paramount importance. This study aims to examine different fragility curve development methodologies available in the literature to assess the seismic performance of adjacent Reinforced Concrete (RC) structures subjected to structural pounding. The study primarily focuses on displacement-based fragility curves for the highly critical floor-to-column interactions of an eight-storey non-ductile RC frame, non-eccentrically adjacent to a three-storey rigid RC frame having different storey heights. Nonlinear time–history analyses have been performed to simulate pounding, and fragility curves have been generated using five methodologies. The direct Monte-Carlo Simulation technique has been used to benchmark against the obtained results to identify the suitability of each fragility assessment technique. Results indicate that even though there is no effect of the choice of assessment methodology on the estimated risk at low performance levels and intensity measures, the disparity becomes clearly visible at higher levels. The study presents alternate ways of developing accurate fragility curves by keeping in mind the need for computational efficiency without compromising the accuracy of results. The High Dimensional Model Representation meta-model is found to efficiently represent target pounding fragilities while incurring minimal computational costs.

Stochastic Stability Analysis of Coupled Viscoelastic Systems with Nonviscously Damping Driven by White Noise

Nonviscously damped structural system has been raised in many engineering fields, in which the damping forces depend on the past time history of velocities via convolution integrals over some kernel functions. This paper investigates stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents. Using the coordinate transformation, the coupled Itô stochastic differential equations of the norm of the response and angles process are obtained. Then the problem of the moment Lyapunov exponent is transformed to the eigenvalue problem, and then the second-perturbation method is used to derive the moment Lyapunov exponent of coupled stochastic system. Lyapunov exponent also can be obtained according to the relationship between moment Lyapunov exponent and Lyapunov exponent. Finally, the effects of various physical quantities of stochastic coupled system on the stochastic stability are discussed in detail. These results are validated by the direct Monte Carlo simulation technique.

Seismic reliability analysis of reinforced concrete bridge pier using efficient response surface method–based simulation

Seismic reliability analysis of bridge structures during and succeeding an earthquake event is of significant importance. The more accurate and robust approach of seismic reliability analysis is based on direct Monte Carlo simulation technique. But it is computationally challenging due to the requirement of large number of nonlinear time history analyses. The response surface method–based metamodeling approach is a viable alternative in such situation. This study explores the advantage of moving least squares method–based adaptive response surface method compared to the usually applied least squares method–based response surface method for improved seismic reliability analysis of multi-span bridge pier. The nonlinear time history analyses of the bridge pier are performed in the OpenSees with fibre sections considering a ground motion bin corresponding to the specified hazard level of the bridge site. The seismic reliability analysis results obtained by the usual least squares method and the proposed moving least squares method–based response surface method are compared with that of obtained by more accurate direct Monte Carlo simulation technique to elucidate the effectiveness of the proposed approach.

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.

Direct Monte-Carlo simulation of developing detonation in gas

The research on gaseous detonation has recently become a very important issue, mainly due to safety reasons in connection with increasing use of gaseous fuels. To simulate detonation, the direct Monte-Carlo simulation technique has been proposed, together with simple model of molecular collisions, making it possible to heat the gas in a way similar to the processes in the flame. Such model is capable of producing waves, having the features characteristic for detonation (Dremin in Towards detonation theory. Springer, 1999). In the present work the influence of finite reaction time and the inverse reaction upon formation and extinguishing detonation, in the framework of this model, has been investigated.

Reliability analysis of concrete structures with neural networks and response surfaces

PurposeTo research the feasibility in using artificial neural networks (ANN) and response surfaces (RS) techniques for reliability analysis of concrete structures.Design/methodology/approachThe evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. RS and the ANN techniques have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparisons are carried out using the well‐known first‐order reliability method (FORM), with non‐linear limit state functions. The reliability analysis of reinforced concrete structure problems is specially considered taking into account the spatial variability of the material properties using random fields and the inherent non‐linearity.FindingsIt was observed that direct Monte Carlo simulation technique has a low performance in complex problems. FORM, RS and neural networks techniques are suitable alternatives, despite the loss of accuracy due to approximations characterizing these methods.Research limitations/implicationsThe examples tested are limited to moderated large non‐linear reinforced concrete finite element models. Conclusions are drawn based on the examples.Practical implicationsSome remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (computing failure probability and safety levels) is high, these two techniques could improve the performance of the structural reliability analysis through simulation techniques.Originality/valueThis paper is important in the field of reliability analysis of concrete structures specially when neural networks or RS techniques are used.

Buckling analysis of cylindrical shells with random geometric imperfections

In this paper the effect of random geometric imperfections on the limit loads of isotropic, thin-walled, cylindrical shells under deterministic axial compression is presented. Therefore, a concept for the numerical prediction of the large scatter in the limit load observed in experiments using direct Monte Carlo simulation technique in context with the Finite Element method is introduced. Geometric imperfections are modeled as a two dimensional, Gaussian stochastic process with prescribed second moment characteristics based on a data bank of measured imperfections. (The initial imperfection data bank at the Delft University of Technology, Part 1. Technical Report LR-290, Department of Aerospace Engineering, Delft University of Technology). In order to generate realizations of geometric imperfections, the estimated covariance kernel is decomposed into an orthogonal series in terms of eigenfunctions with corresponding uncorrelated Gaussian random variables, known as the Karhunen–Loéve expansion. For the determination of the limit load a geometrically non-linear static analysis is carried out using the general purpose code STAGS (STructural Analysis of General Shells, user manual, LMSC P032594, version 3.0, Lockheed Martin Missiles and Space Co., Inc., Palo Alto, CA, USA). As a result of the direct Monte Carlo simulation, second moment characteristics of the limit load are presented. The numerically predicted statistics of the limit load coincide reasonably well with the actual observations, particularly in view of the limited data available, which is reflected in the statistical estimators.

Stochastic finite element method for spatial distribution of material properties and external loading

In this paper, a stochastic finite element method is presented for the analysis of structures having statistical uncertainities in both material properties and externally applied loads, which are modelled as a homogeneous Gaussian stochastic process. The Neumann expansion technique has been used for the inversion of a stochastic stiffness matrix. The digital simulation technique was adopted to generate the deviatoric part of the stiffness matrix and load vector. A beam problem was taken up for comparison of results obtained by Neumann expansion and the direct Monte Carlo simulation technique. The comparison of the results shows that the values approach those obtained by direct Monte Carlo solutions as the order of expansion of the Neumann series is increased. An excellent agreement was achieved for cases when the coefficient of variation is comparatively small.

Surface tension and universality in the three-dimensional Ising model

The amplitudeτ0 of the interfacial free energy per unit area (or surface tension) of the body-centered-cubic Ising model is found using a direct monte carlo simulation technique. The combinationτξ2/kBTc, whereξ is the correlation length, is shown to agree within the precision of the simulations with a previously reported estimate for the simple cubic lattice. Evidence is also presented for the universality of the finite-size scaling amplitude for the surface tension.