Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: application to urban drainage simulation

TL;DR

This paper introduces a surrogate modeling approach combining PCA and sparse polynomial chaos for efficient global sensitivity analysis and Bayesian calibration of an urban drainage model, significantly reducing computational costs.

Contribution

The novel integration of PCA and sparse polynomial chaos expansions enables fast uncertainty quantification and model calibration in hydrological simulations.

Findings

Reduced computational cost for sensitivity analysis

Accurate estimation of Sobol' indices from polynomial chaos

Accelerated Bayesian inference using the surrogate model

Abstract

This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge from a catchment area during a precipitation event is considered. The goal of the case study is to perform a global sensitivity analysis and to identify the unknown model parameters as well as the measurement and prediction errors. These objectives can only be achieved by cheapening the incurred computational costs, that is, lowering the number of necessary model runs. With this in mind, a regularity-exploiting metamodeling technique is proposed that enables fast uncertainty quantification. Principal component analysis is used for output dimensionality reduction and sparse polynomial chaos expansions are used for the emulation of the reduced outputs. Sobol' sensitivity indices are obtained directly from the expansion coefficients by a mere post-processing. Bayesian inference via Markov chain Monte Carlo posterior sampling is drastically accelerated.