ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

Functional PCA for Marine Submersion Model

3 September 2018, 14:40 – 15:00

Abstract

Submitted by
Tran Vi-vi Elodie PERRIN
Authors
Tran Vi-vi Elodie Perrin (Ecole des Mines de Saint-Etienne)
Abstract
This research is motivated by the estimation of the cost caused by marine submersion problem. We aim at exploiting two computer codes provided by the French State reinsurance company CCR and the BRGM (Bureau de Recherche Géologique et Minière). Their main characteristics are the following :

- Marine submersion model :
-Inputs : sea forcing (waves, water level...), landforms (buildings, drops...), roughness (bitumen, soil...), flooding propagation (along roads, dams, breaches... ) ... ;
-Output : spatial map of the maximum water level reached during the event.

- Damage model :
- Inputs : output map of the marine submersion model and vulnerability data (Geo-tracking properties, buildings characteristics...).
-Output : global cost of the geographical area being studied.

The BRGM model represents at most the complexity of the marine submersion phenomenon at the expense of the computation time (30 minutes for one simulation). At the other hand, the CCR model is faster (5 minutes for one simulation) but overestimates the flooded area. These issues make difficult a direct treatment. Meta-model techniques, such as Gaussian Process regression, have been developed in order to solve computation time issues : an inexpensive mathematical function predicts the computer code output thanks to a few number of simulations. Here we focus on one difficulty : the output of the marine submersion model is a spatial map.

In this frame, a common technique to reduce dimensionality is principal component analysis (PCA). Prediction at unknown inputs is made on the eigen vectors basis with meta-models. However, the output map of the marine submersion model has above 40 000 pixels which makes intractable this standard PCA approach. In addition, PCA does not take into account the functional nature of the data and their features characteristics, such as smoothness. Alternatively, functional Principal Components Analysis (FPCA), which is based on a functional basis decomposition, does not suffer from these drawbacks. FPCA seems less used for spatial data (rather than time series).

In this talk, we compare PCA and functional PCA for spatial outputs. We illustrate on toy examples as well as on the application to marine submersion.
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