Abstract

The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic action and mechanical properties of its elements. In this article, the seismic performance of high-rise, mid-rise and low-rise of steel buildings, subjected to long duration seismic actions like those of Mexico City, is analyzed. The analysis is conducted by using a probabilistic approach. The seismic actions are selected to be compatible with the design spectra of the Mexican seismic code for soft soils and long duration earthquakes, characteristic for this region. The dynamic analyses are performed by using Monte Carlo simulations. The strength and ductility of the beams and columns are considered random variables; the seismic actions are also modelled in a probabilistic way. The damage index of Park and Ang is used. The results show that the uncertainties expected in the response are significant, being the randomness of the seismic action the main cause. From the comparison between the mean values of the probabilistic approach and those corresponding to the deterministic case, a good consistency of the result obtained for low-rise and mid-rise buildings is observed. Nevertheless, the consistency is lower in the case of high-rise buildings. The analyzed low-rise and mid-rise buildings show a good seismic performance to seismic actions, but the high-rise buildings show slight or moderate damage. It is concluded that the probabilistic approach provides a more complete information on the structural response.

Abstract

A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the
paper is to review some of the di erent methods available for analysing the effects of randomness of models
and data in structural analysis. While most of these techniques can be grouped under the general name of
Monte Carlo methods, the several published algorithms are more suitable to some objectives of analysis than
to others in each case. These objectives have been classiffed into the following cathegories: (1), The Statistical
Description of the structural scattering, a primary analysis in which the uncertain parameters are treated as
random variables; (2) The consideration of the spatial variability of the random parameters, that must then
be modelled as Random Fields (Stochastic Finite Elements); (3) The advanced Monte Carlo methods for
calculating the usually very low failure probabilities (Reliability Analysis) and, (4), a deterministic technique
that depart from the random nature of the above methods, but which can be linked with them in some cases,
known as the Response Surface Method. All of these techniques are critically examined and discussed. The
concluding remarks point out some research needs in the field from the authors' point of view.

Abstract

Recently proposed capacity-based damage indices and parametric models for capacity curves are applied to frame steel buildings located in soft soils of the Mexico City. To do that, the seismic performance of 2D models of low-, mid- and high-rise buildings is
assessed. Deterministic and probabilistic nonlinear static and incremental dynamic analyses are implemented. Monte Carlo simulations and the Latin Hypercube sampling technique are used. Seismic actions are selected among accelerograms recorded in the study area. Spectral matching techniques are applied, so that the acceleration time histories have a predefined mean response spectrum and controlled error. The design spectrum of the Mexican seismic code for the zone is used as target spectrum. The well-known Park and Ang damage index allows calibrating the capacity-based damage index. Both damage indices take into account the contribution to damage of the stiffness degradation and of the energy dissipation. Damage states and fragility curves are also obtained and discussed in detail. The results reveal the versatility, robustness and reliability of the parametric model for capacity curves, which allow modelling the nonlinear part of the capacity curves by the cumulative integral of a cumulative lognormal function. However, these new capacitybased damage index and capacity models have been tested for and applied to 2D frame buildings only; they have not been applied to 3D building models yet. The Park and Ang and the capacity-based damage indices show that for the analysed buildings, the contribution to damage of the stiffness degradation is in the range 66–77% and that of energy loss is in the range 29–34%. The lowest contribution of energy dissipation (29%) is found for the low-rise, more rigid, building. The energy contribution would raise with the ductility of the building and with the duration of the strong ground motion. High-rise frame buildings in soft soils of Mexico City show the worst performance so that the use of adequate braced frames to control the displacements could be recommended.

Abstract

The Urban Seismic Risk index (USRi) published in a previous article (Carreño et al., Nat Hazards 40:137–172, 2007) is a composite indicator that measures risk from an integrated perspective and guides decision-making for identifying the main interdisciplinary
factors of vulnerability to be reduced or intervened. The first step of the method is the evaluation of the potential physical damage (hard approach) as a result of the convolution of the seismic hazard with the physical vulnerability of buildings and infrastructure.
Subsequently, a set of social context conditions that aggravate the physical effects is also considered (soft approach). According to this procedure, the physical risk index is evaluated for each unit of analysis from existing loss scenarios, whereas the total risk index is obtained by multiplying the former index by an impact factor using an aggravating coefficient, based on variables associated with the socio-economic conditions of each unit of analysis. The USRi has been developed using the underlying holistic and multi-hazard approach of the Urban Risk Index framework proposed for the evaluation of disaster risk in different megacities worldwide. This article presents the sensitivity analysis of the index to different parameters such as input data, weights and transformation functions used for the scaling or normalization of variables. This analysis has been performed using the Monte Carlo simulation to validate the robustness of this composite indicator, understanding as robustness how the cities maintain the ranking as well as predefined risk
level ranges, when compared with the deterministic results of risk. Results are shown for different cities of the world.

Abstract

The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described in this paper. The proposed method considers fully three-dimensional finite element models in order to take into account the effect of the most significant structural characteristics (presence of three buttresses, penetrations, additional reinforcement around the penetrations, etc.), the lack of symmetry of the forces generated by the prestressing system, as well as the nonlinear behaviour of the materials and the sensitivity of the results to uncertainties associated with several parameters. The computational model is completely described, including the constitutive equations for the concrete, the reinforcing steel and prestressing tendons, the spatial discretization—isoparametric elements including the reinforcement are used. The structural models and the analyses performed for their calibration are also described. The influence on the failure pressure of incorporating the foundation slab in the structural model, and the influence of the thermal effects, are discussed. One of the conclusions of the numerical study is that the failure process can be appropriately simulated by means of a structural model which does not include either the foundation slab or the thermal effects. Finally, results of a probabilistic simulation of the failure pressure are given.

Abstract

The main objective of this article is to propose a simplified methodology to assess the expected seismic damage in reinforced concrete buildings from a probabilistic point of view by using Monte Carlo simulation. In order to do so, the seismic behaviour of the building was studied by using random capacity obtained by considering the mechanical properties of the materials as random variables. From the capacity curves, the damage states and fragility curves can be obtained, and curves describing the expected seismic damage to the structure as a function of a seismic hazard characteristic can be developed. The latter can be calculated using the capacity spectrum and the demand spectrum according to the methodology proposed by the Risk-UE project. In order to define the seismic demand as a random variable, a set of real accelerograms were obtained from European and Spanish databases in such a way that the mean of their elastic response spectra was similar to an elastic response spectrum selected from Eurocode 8. In order to combine the uncertainties associated with the seismic action and the mechanical properties of materials, two procedures are considered to obtain functions relating the peak ground acceleration to the maximum spectral displacements. The first method is based on a series of non-linear dynamic analyses, while the second is based on the well-known ATC-40 procedure called equal displacement approximation. After applying both procedures, the probability density functions of the maximum displacement at the roof of the building are gathered and compared. The expected structural damage is finally obtained by replacing the spectral displacement calculated using ATC-40
and the incremental dynamic procedure. In the damage functions, the results obtained from incremental static and dynamic analyses are compared and discussed from a probabilistic point of view.

Abstract

Monte Carlo simulation is increasingly being used in the analysis of large and complex structural systems for the assessment of the uncertainty spread and the reliability. A major handicap for the popularization of this technology is the large number of deterministic evaluations needed to such purposes, inasmuch as linear or nonlinear finite element solvers are required for each output sample
calculation. In order to simplify this task neural networks are evaluated in this paper as a partial surrogate of the deterministic solver. The neural networks are trained with the input/output pairs resulting from a few number of finite element simulations, and are henceforth used in a Monte Carlo context. It is shown that when employed in this way, neural networks constitute a promising tool for a drastic reduction of the computational cost needed by a Monte Carlo simulation in this field of application. Three types of networks have been selected for the study, two of which correspond to supervised and the other one to hybrid learning procedures. The paper compares the network designs in their more relevant aspects, which are the training speed and accuracy, the extrapolation ability and the accuracy of the estimated probabilities.
 

Abstract

This document presents an analysis in the development of a new mathematical formulation with which it will be possible to determine, through probabilistic approaches, the cost that can be generated if a diversified electricity market existed, in which the demand is able to actively participate. For this, it is considered that the electrical demand in a moment of time has associated a probability distribution and a system that makes it controllable. The cost of uncertainty of demand is mathematically developed by calculating the expected cost of supplying the most convenient demand value for the power system. The validation of the analytical formula is done through the Monte Carlo method, which allows us to compare the penalty costs in the case of underestimating or overestimating the demand for electrical energy. 

Abstract

Faced with the problem of wind speed in generation and the difficulty that this entails in the economic future of electric power, mathematical formulations (functions), called uncertainty costs, have been developed. The term is used in a model composed of two parts, an implication of penalization costs for overestimation and the other due to the underestimation of a programmed power. Through analytical mathematics and Monte Carlo simulations, we have found the expected value of the costs of uncertainty, the stability of primary resources through the distribution of probability. However, the results can not be evaluated accurately from an analytical point of view, without taking into account the variability around the average value. In this article we calculate the analytical function of the variance, we understand as a measure of dispersion of the expected values of uncertainty costs for the specific case of wind operators; Likewise, this formulation has been validated through Monte Carlo simulations. The function found is used to observe the dispersion of the data around its expected average value, by applying the standard deviation.

Abstract

An important concern in sheet stamping is the risk of obtaining brittle final products that can be affected by fracture. Monte Carlo simulations presented herein show that this is governed by two main factors, namely static and dynamic friction coefficients. Whereas the latter correlates in a non-linear manner with minimum and maximum end thickness, the relationship of these design parameters to the former exhibits a bifurcation that is typical of highly non-linear phenomena, in which there is a sensitivity to small perturbations of the input values (chaos). In order to estimate the reliability of the process (i.e., the probability of obtaining brittle products due to low minimum and maximum thicknesses) with a reduced number of Monte Carlo runs, it is proposed to assimilate the problem to a pattern recognition task, due to the existence of two classes, namely robust and brittle. Among many pattern recognition algorithms that are useful to this end, use is made of support vector machines, as this incorporates the powerful tool of class margins that allow a drastic reduction of the number of simulations.