Tackling random fields non-linearities with unsupervised clustering of polynomial chaos expansion in latent space: application to global sensitivity analysis of river flooding

AbstractA surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the $$Q_2$$ Q 2 metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake.

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A Global Sensitivity Analysis Framework for Hybrid Simulation

10.31224/osf.io/wnqgb ◽

2021 ◽

Author(s):

Giuseppe Abbiati ◽

Stefano Marelli ◽

Nikolaos Tsokanas ◽

Bruno Sudret ◽

Bozidar Stojadinovic

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Polynomial Chaos Expansion ◽

Chaos Expansion ◽

Analysis Framework ◽

Global Sensitivity ◽

Sensitivity Indices

Hybrid Simulation is a dynamic response simulation paradigm that merges physical experiments and computational models into a hybrid model. In earthquake engineering, it is used to investigate the response of structures to earthquake excitation. In the context of response to extreme loads, the structure, its boundary conditions, damping, and the ground motion excitation itself are all subjected to large parameter variability. However, in current seismic response testing practice, Hybrid Simulation campaigns rely on a few prototype structures with fixed parameters subjected to one or two ground motions of different intensity. While this approach effectively reveals structural weaknesses, it does not reveal the sensitivity of structure's response. This thus far missing information could support the planning of further experiments as well as drive modeling choices in subsequent analysis and evaluation phases of the structural design process.This paper describes a Global Sensitivity Analysis framework for Hybrid Simulation. This framework, based on Sobol' sensitivity indices, is used to quantify the sensitivity of the response of a structure tested using the Hybrid Simulation approach due to the variability of the prototype structure and the excitation parameters. Polynomial Chaos Expansion is used to surrogate the hybrid model response. Thereafter, Sobol' sensitivity indices are obtained as a by-product of polynomial coefficients, entailing a reduced number of Hybrid Simulations compared to a crude Monte Carlo approach. An experimental verification example highlights the excellent performance of Polynomial Chaos Expansion surrogates in terms of stable estimates of Sobol' sensitivity indices in the presence of noise caused by random experimental errors.

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