Diego A. Alvarez

Neural-network-based reliability analysis: a comparative study

Abstract A study on the applicability of different kinds of neural networks for the probabilistic analysis of structures, when the sources of randomness can be modeled as random variables, is summarized. The networks are employed as numerical devices for substituting the finite element code needed by Monte Carlo simulation. The comparison comprehends two network types (multi-layer perceptrons and radial basis functions classifiers), cost functions (sum of square errors and cross-entropy), optimization algorithms (back-propagation, Gauss–Newton, Newton–Raphson), sampling methods for generating the training population (using uniform and actual distributions of the variables) and purposes of neural network use (as functional approximators and data classifiers). The comparative study is performed over four examples, corresponding to different types of the limit state function and structural behaviors. The analysis indicates some recommended ways of employing neural networks in this field.

Estimation of the lower and upper probabilities of failure using random sets and subset simulation

The focus of the present paper is the determination of the lower and upper bounds of the probability of failure under uncertain inputs by means of random set theory. Under this general framework, it is possible to model uncertainty in the form of probability boxes, fuzzy sets, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition the dependence between the input variables can be expressed using copulas. In order to speed up the calculation, a very efficient probability-based reliability method known as “subset simulation” will be used. This method is specially suited for finding small probabilities of failure in both low- and high-dimensional spaces, disjoint failure regions and nonlinear limit state functions. The proposed method represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. A numerical example shows the usefulness of the proposed approach.

Prediction of modified Mercalli intensity from PGA, PGV, moment magnitude, and epicentral distance using several nonlinear statistical algorithms

Despite technological advances in seismic instrumentation, the assessment of the intensity of an earthquake using an observational scale as given, for example, by the modified Mercalli intensity scale is highly useful for practical purposes. In order to link the qualitative numbers extracted from the acceleration record of an earthquake and other instrumental data such as peak ground velocity, epicentral distance, and moment magnitude on the one hand and the modified Mercalli intensity scale on the other, simple statistical regression has been generally employed. In this paper, we will employ three methods of nonlinear regression, namely support vector regression, multilayer perceptrons, and genetic programming in order to find a functional dependence between the instrumental records and the modified Mercalli intensity scale. The proposed methods predict the intensity of an earthquake while dealing with nonlinearity and the noise inherent to the data. The nonlinear regressions with good estimation results have been performed using the “Did You Feel It?” database of the US Geological Survey and the database of the Center for Engineering Strong Motion Data for the California region.