Global sensitivity analysis for the boundary control of an open channel

The goal of this paper is to solve the global sensitivity analysis for a particular control problem. More precisely, the boundary control problem of an open-water channel is considered, where the boundary conditions are defined by the position of a down stream overflow gate and an upper stream underflow gate. The dynamics of the water depth and of the water velocity are described by the Shallow Water equations, taking into account the bottom and friction slopes. Since some physical parameters are unknown, a stabilizing boundary control is first computed for their nominal values, and then a sensitivity anal-ysis is performed to measure the impact of the uncertainty in the parameters on a given to-be-controlled output. The unknown physical parameters are de-scribed by some probability distribution functions. Numerical simulations are performed to measure the first-order and total sensitivity indices

Adaptive estimation of linear functionals by model selection

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with respect to the $\mathbb{L}_p$ loss. An application to the problem of estimating a signal or its $r^{th}$ derivative at a given point is developed and minimax rates are proved to hold uniformly over Besov balls. We also apply our non asymptotic oracle inequality to the estimation of the mean of the signal on an interval with length depending on the noise level. Simulations are included to illustrate the performances of the procedure for the estimation of a function at a given point. Our method provides a pointwise adaptive estimator.Comment: Published in at http://dx.doi.org/10.1214/07-EJS127 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices

L2 Boosting on generalized Hoeffding decomposition for dependent variables. Application to Sensitivity Analysis

This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional settings. Then, we apply a greedy algorithm with these previous estimators to Sensitivity Analysis. We also establish the consistency of this $\mathbb L_2$-boosting up to sparsity assumptions on the signal to analyse. We end the paper with numerical experiments, which demonstrates the low computational cost of our method as well as its efficiency on standard benchmark of Sensitivity Analysis.Comment: 48 pages, 7 Figure

Bayesian Multiple Hypothesis Tracking of Merging and Splitting Targets

International audienceThis paper presents a Bayesian model for the multiple target tracking problem that handles a varying number of splitting and merging targets applied to convective cloud tracking. The model decomposes the tracking solution into events and targets state. The events include target births, deaths, splits, and merges. The target state contains both the target positions and attributes. By updating the target attributes and conditioning the events on their updated values we can include high level domain knowledge into the system. This strategy improves the tracking accuracy and the computational efficiency since we focus only on likely events for each situation. A two-step multiple hypothesis tracking algorithm has been developed to estimate the model state. The proposed approach is tested by both simulation and real data for mesoscale convective systems tracking