Global sensitivity analysis is used to quantify the influence of input variables on a numerical model output. Sobol' indices are now classical sensitivity measures. However their estimation requires a large number of model evaluations, especially when interaction effects are of interest. Derivative-based global sensitivity measures (DGSM) have recently shown their efficiency for the identification of non-influential inputs. In this paper, we define crossed DGSM, based on second-order derivatives of model output. By using a L 2-Poincaré inequality, we provide a crossed-DGSM based maximal bound for the superset importance (i.e. total Sobol' indices of an interaction between two inputs). In order to apply this result, we discuss how to estimate the Poincaré constant for various probability distributions. Several analytical and numerical tests show the performance of the bound and allow to develop a generic strategy for interaction screening.
International audienceA framework for designing and analyzing computer experiments is presented, which is constructed for dealing with functional and scalar inputs and scalar outputs. For designing experiments with both functional and scalar inputs, a two-stage approach is suggested. The first stage consists of constructing a candidate set for each functional input. During the second stage, an optimal combination of the found candidate sets and a Latin hypercube for the scalar inputs is sought. The resulting designs can be considered to be generalizations of Latin hypercubes. Gaussian process models are explored as metamodel. The functional inputs are incorporated into the Kriging model by applying norms in order to define distances between two functional inputs. We propose the use of B-splines to make the calculation of these norms computationally feasible
In this article we illustrate an approach of a security threat analysis of the quadrocopter AR.Drone, a toy for augmented reality (AR) games. The technical properties of the drone can be misused for attacks, which may relate security and/or privacy aspects. Our aim is to sensitize for the possibility of misuses and the motivation for an implementation of improved security mechanisms of the quadrocopter. We focus primarily on obvious security vulnerabilities (e.g. communication over unencrypted WLAN, usage of UDP, live video streaming via unencrypted WLAN to the control device) of this quadrocopter. We could practically verify in three exemplary scenarios that this can be misused by unauthorized persons for several attacks: high-jacking of the drone, eavesdropping of the AR.Drones unprotected video streams, and the tracking of persons. Amongst other aspects, our current research focuses on the realization of the attack of tracking persons and objects with the drone. Besides the realization of attacks, we want to evaluate the potential of this particular drone for a "safe-landing" function, as well as potential security enhancements. Additionally, in future we plan to investigate an automatic tracking of persons or objects without the need of human interactions.
Sensitivity analysis aims at exploring which of a number of variables have an impact on a certain response. Not only are the individual variables of interest but also whether they interact or not. By analogy with the total sensitivity index, used to detect the most influential variables, a screening of interactions can be done efficiently with the so-called total interaction index (TII), defined as the superset importance of a pair of variables. Our aim is to investigate the TII, with a focus on statistical inference. At the theoretical level, we derive its connection to total and closed sensitivity indices. We present several estimation methods and prove the asymptotical efficiency of the Liu and Owen estimator. We also address the question of estimating the full set of TIIs, with a given budget of function evaluations. We observe that with the pick-and-freeze method the full set of TIIs can be estimated at a linear cost with respect to the problem dimension. The different estimators are then compared empirically. Finally, an application is given aiming at discovering a block-additive structure of a function, where no prior knowledge either about the interaction structure or about the blocks is available.
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