15,148 research outputs found
Meta-models for structural reliability and uncertainty quantification
A meta-model (or a surrogate model) is the modern name for what was
traditionally called a response surface. It is intended to mimic the behaviour
of a computational model M (e.g. a finite element model in mechanics) while
being inexpensive to evaluate, in contrast to the original model which may take
hours or even days of computer processing time. In this paper various types of
meta-models that have been used in the last decade in the context of structural
reliability are reviewed. More specifically classical polynomial response
surfaces, polynomial chaos expansions and kriging are addressed. It is shown
how the need for error estimates and adaptivity in their construction has
brought this type of approaches to a high level of efficiency. A new technique
that solves the problem of the potential biasedness in the estimation of a
probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural
Reliability and its Applications (5th APSSRA) May 2012, Singapor
Sequential design of computer experiments for the estimation of a probability of failure
This paper deals with the problem of estimating the volume of the excursion
set of a function above a given threshold,
under a probability measure on that is assumed to be known. In
the industrial world, this corresponds to the problem of estimating a
probability of failure of a system. When only an expensive-to-simulate model of
the system is available, the budget for simulations is usually severely limited
and therefore classical Monte Carlo methods ought to be avoided. One of the
main contributions of this article is to derive SUR (stepwise uncertainty
reduction) strategies from a Bayesian-theoretic formulation of the problem of
estimating a probability of failure. These sequential strategies use a Gaussian
process model of and aim at performing evaluations of as efficiently as
possible to infer the value of the probability of failure. We compare these
strategies to other strategies also based on a Gaussian process model for
estimating a probability of failure.Comment: This is an author-generated postprint version. The published version
is available at http://www.springerlink.co
Simultaneous Extrema in the Entropy Production for Steady-State Fluid Flow in Parallel Pipes
Steady-state flow of an incompressible fluid in parallel pipes can
simultaneously satisfy two contradictory extremum principles in the entropy
production, depending on the flow conditions. For a constant total flow rate,
the flow can satisfy (i) a pipe network minimum entropy production (MinEP)
principle with respect to the flow rates, and (ii) the maximum entropy
production (MaxEP) principle of Ziegler and Paltridge with respect to the
choice of flow regime. The first principle - different to but allied to that of
Prigogine - arises from the stability of the steady state compared to
non-steady-state flows; it is proven for isothermal laminar and turbulent flows
in parallel pipes with a constant power law exponent, but is otherwise invalid.
The second principle appears to be more fundamental, driving the formation of
turbulent flow in single and parallel pipes at higher Reynolds numbers. For
constant head conditions, the flow can satisfy (i) a modified maximum entropy
production (MaxEPMod) principle of \v{Z}upanovi\'c and co-workers with respect
to the flow rates, and (ii) an inversion of the Ziegler-Paltridge MaxEP
principle with respect to the flow regime. The interplay between these
principles is demonstrated by examples.Comment: Revised version 2; 5 figure
Empirical models, rules, and optimization
This paper considers supply decisions by firms in a dynamic setting with adjustment costs and compares the behavior of an optimal control model to that of a rule-based system which relaxes the assumption that agents are explicit optimizers. In our approach, the economic agent uses believably simple rules in coping with complex situations. We estimate rules using an artificially generated sample obtained by running repeated simulations of a dynamic optimal control model of a firm's hiring/firing decisions. We show that (i) agents using heuristics can behave as if they were seeking rationally to maximize their dynamic returns; (ii) the approach requires fewer behavioral assumptions relative to dynamic optimization and the assumptions made are based on economically intuitive theoretical results linking rule adoption to uncertainty; (iii) the approach delineates the domain of applicability of maximization hypotheses and describes the behavior of agents in situations of economic disequilibrium. The approach adopted uses concepts from fuzzy control theory. An agent, instead of optimizing, follows Fuzzy Associative Memory (FAM) rules which, given input and output data, can be estimated and used to approximate any non-linear dynamic process. Empirical results indicate that the fuzzy rule-based system performs extremely well in approximating optimal dynamic behavior in situations with limited noise.Decision-making. ,econometric models ,TMD ,
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