17,860 research outputs found
An Interpretation of the Dual Problem of the THREE-like Approaches
Spectral estimation can be preformed using the so called THREE-like approach.
Such method leads to a convex optimization problem whose solution is
characterized through its dual problem. In this paper, we show that the dual
problem can be seen as a new parametric spectral estimation problem. This
interpretation implies that the THREE-like solution is optimal in terms of
closeness to the correlogram over a certain parametric class of spectral
densities, enriching in this way its meaningfulness
Well posedness and Maximum Entropy Approximation for the Dynamics of Quantitative Traits
We study the Fokker-Planck equation derived in the large system limit of the
Markovian process describing the dynamics of quantitative traits. The
Fokker-Planck equation is posed on a bounded domain and its transport and
diffusion coefficients vanish on the domain's boundary. We first argue that,
despite this degeneracy, the standard no-flux boundary condition is valid. We
derive the weak formulation of the problem and prove the existence and
uniqueness of its solutions by constructing the corresponding contraction
semigroup on a suitable function space. Then, we prove that for the parameter
regime with high enough mutation rate the problem exhibits a positive spectral
gap, which implies exponential convergence to equilibrium.
Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy
(DynMaxEnt) method for approximation of moments of the Fokker-Planck solution,
which can be interpreted as a nonlinear Galerkin approximation. The limited
applicability of the DynMaxEnt method inspires us to introduce its modified
version that is valid for the whole range of admissible parameters. Finally, we
present several numerical experiments to demonstrate the performance of both
the original and modified DynMaxEnt methods. We observe that in the parameter
regimes where both methods are valid, the modified one exhibits slightly better
approximation properties compared to the original one.Comment: 28 pages, 4 tables, 5 figure
Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering
This report presents a new methodology, called moment matching, of propagating the uncertainties in estimating repair costs of a building due to future earthquake excitation, which is required, for example, when assessing a design in performance-based earthquake engineering. Besides excitation uncertainties, other uncertain model variables are considered, including uncertainties in the structural model parameters and in the capacity and repair costs of structural and non-structural components. Using the first few moments of these uncertain variables, moment matching requires only a few well-chosen point estimates to propagate the uncertainties to estimate the first few moments of the repair costs with high accuracy. Furthermore, the use of moment matching to estimate the exceedance probability of the repair costs is also addressed. These examples illustrate that the moment-matching approach is quite general; for example, it can be applied to any decision variable in performance-based earthquake engineering.
Two buildings are chosen as illustrative examples to demonstrate the use of moment matching, a hypothetical three-story shear building and a real seven-story hotel building. For these two examples, the assembly-based vulnerability approach is employed when calculating repair costs. It is shown that the moment-matching technique is much more accurate than the well-known First-Order-Second-Moment approach when propagating the first two moments, while the resulting computational cost is of the same order. The repair-cost moments and exceedance probability estimated by the moment-matching technique are also compared with those by Monte Carlo simulation. It is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Furthermore, the amount of computation for moment matching scales only linearly with the number of uncertain input variables.
Last but not least, a procedure for feature selection is presented and illustrated for the second example. The conclusion is that the most important uncertain input variables among the many influencing the uncertainty in future repair costs are, in order of importance, ground-motion spectral acceleration, component capacity, ground-motion details and unit repair costs
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