arXiv subjects

Delphine Sinoquet

Publications and source records attributed to Delphine Sinoquet.

5 recordsLinked to original sources

arXiv2024

Kernel-based sensitivity analysis for (excursion) sets

In this paper, we aim to perform sensitivity analysis of set-valued models and, in particular, to quantify the impact of uncertain inputs on feasible sets, which are key elements in solving a robust optimization problem under constraints. While most sensitivity analysis methods deal with scalar outputs, this paper introduces a novel approach for performing sensitivity analysis with set-valued outputs. Our innovative methodology is designed for excursion sets, but is versatile enough to be applied to set-valued simulators, including those found in viability fields, or when working with maps like pollutant concentration maps or flood zone maps. We propose to use the Hilbert-Schmidt Independence Criterion (HSIC) with a kernel designed for set-valued outputs. After proposing a probabilistic framework for random sets, a first contribution is the proof that this kernel is characteristic, an essential property in a kernel-based sensitivity analysis context. To measure the contribution of each input, we then propose to use HSIC-ANOVA indices. With these indices, we can identify which inputs should be neglected (screening) and we can rank the others according to their influence (ranking). The estimation of these indices is also adapted to the set-valued outputs. Finally, we test the proposed method on three test cases of excursion sets.

math.ST↗

arXiv2023

Sensitivity analysis for sets : application to pollutant concentration maps

In the context of air quality control, our objective is to quantify the impact of uncertain inputs such as meteorological conditions and traffic parameters on pollutant dispersion maps. It is worth noting that the majority of sensitivity analysis methods are designed to deal with scalar or vector outputs and are ill suited to a map-valued output space. To address this, we propose two classes of methods. The first technique focuses on pointwise indices. Sobol indices are calculated for each position on the map to obtain Sobol index maps. Additionally, aggregated Sobol indices are calculated. Another approach treats the maps as sets and proposes a sensitivity analysis of a set-valued output with three different types of sensitivity indices. The first ones are inspired by Sobol indices but are adapted to sets based on the theory of random sets. The second ones adapt universal indices defined for a general metric output space. The last set indices use kernel-based sensitivity indices adapted to sets. The proposed methodologies are implemented to carry out an uncertainty analysis for time-averaged concentration maps of pollutants in an urban environment in the Greater Paris area. This entails taking into account uncertain meteorological aspects, such as incoming wind speed and direction, and uncertain traffic factors, such as injected traffic volume, percentage of diesel vehicles, and speed limits on the road network.

math.OC↗

arXiv2023

Study on the impact of uncertain design parameters on the perfomances of a permanent magnet assisted synchronous reluctance motor

In this paper, deterministic and robust design optimizations of a permanent magnet assisted synchronous reluctance machine were performed to study the impact of different uncertain input parameters on the design. These optimizations were carried out using a surrogate model based on 2-D finite element simulations. Different robust optimizations considering geometric and magnetic uncertain parameters were compared to the deterministic optimization. It was noticed that both geometrical and magnetic properties tolerances greatly impact the machines' performances, where the magnetic properties had a more significant impact on the mean torque. In such a case, robust optimization is essential to find optimal and robust electric motors designs.

math.OC↗

arXiv2023

M{é}thodologie de dimensionnement par optimisation bay{é}sienne d'une machine synchro-r{é}luctante assist{é}e d'aimants permanents

In this article, three optimization approaches are exploited to improve the performance of a permanent magnet-assisted synchronous reluctance machine: a first optimization using fixed substitution models and two Bayesian optimization approaches based on adaptive substitution models. The results show that Bayesian approaches lead to machines with better performance using the same computation time (same number of finite element simulations). Unlike optimization methodologies based on fixed substitution models, Bayesian approaches provide solutions directly based on finite element simulations and, therefore, do not require verification.

math.OC↗

arXiv2022

Robust design optimization taking into account manufacturing uncertainties of a permanent magnet assisted synchronous reluctance motor

In this paper, deterministic and robust design optimizations of a permanent magnet assisted synchronous reluctance machine were performed to increase its mean torque while reducing torque ripple. These optimizations were carried out using a surrogate model based on 2-D finite element simulations. The results of the robust optimizations, which considered manufacturing uncertainties, were compared to the deterministic optimization. The robust designs have shown not only good mean torque and torque ripple performances, but they have also shown improved robustness against design parameters uncertainties.

math.OC↗