Quasi-probability Approach for Modelling Local Extinction and Counter-gradient in Turbulent Premixed Combustion
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In this work, we present a probabilistic analysis of a detailed one-dimensional biofilm model that explicitly accounts for planktonic bacterial invasion in a multi-species biofilm. The objective is (1) to quantify and understand how the uncertainty in the parameters of the invasion submodel impacts the biofilm model predictions (here the microbial species volume fractions); and (2) to spot which parameters are the most important factors enhancing the biofilm model response. An emulator (or “surrogate”) of the biofilm model is trained using a limited experimental design of size N=216 and corresponding to a Halton’s low-discrepancy sequence in order to optimally cover the uncertain space of dimension d=3 (corresponding to the three scalar parameters newly introduced in the invasion submodel). A comparison of different types of emulator (generalized Polynomial Chaos expansion – gPC, Gaussian process model – GP) is carried out; results show that the best performance (measured in terms of the Q2 predictive coefficient) is obtained using a Least-Angle Regression (LAR) gPC-type expansion, where a sparse polynomial basis is constructed to reduce the problem size and where the basis coordinates are computed using a regularized least-square minimization. The resulting LAR gPC-expansion is found to capture the growth in complexity of the biofilm structure due to niche formation. Sobol’ sensitivity indices show the relative prevalence of the maximum colonization rate of autotrophic bacteria on biofilm composition in the invasion submodel. They provide guidelines for orienting future sensitivity analysis including more sources of variability, as well as further biofilm model developments.