Dimensionality reduction for surrogate model construction for global sensitivity analysis: Comparison between active subspace and local sensitivity analysis

Global sensitivity analysis of combustion kinetic models is time consuming, because numerous samples generated by kinetic model simulations within the uncertainty space of the input parameters are needed. To alleviate this problem, surrogate models are often adopted to replace the kinetic model to generate samples. Directly constructing surrogate models is difficult in high-dimensional systems, therefore, local sensitivity analysis is usually first performed to exclude unimportant parameters. However, local sensitivity analysis may cause inaccurate screening when the model is nonlinear and the uncertainties of the input parameters are large. To overcome this difficulty, we propose herein the active subspace-based surrogate model (ASSM) method, which uses the active subspace to transform the high-dimensional input to low-dimensional features and then maps these features to the model target. The entire parameters are included in the ASSM while the mapping relationship is fitted with low-dimensional features. The accuracy and the computational cost of the ASSM are compared with those of the local sensitivity-based surrogate model (LSSM) in the hydrogen and methanol combustion systems. The results show that the ASSM can improve the data utilization and lead to a lower computational cost compared to the LSSM when several targets are considered, because one kinetic model simulation can yield original samples for many model targets simultaneously for the ASSM. The global sensitivity analysis with the ASSM and the LSSM is compared in the hydrogen, methanol and n-decane combustion systems, and the results show that the ASSM could lead to more reliable sensitivity indices than the LSSM because the active subspace-based dimensionality reduction can prevent the possibility of missing important parameters by transforming the entire parameters to new features instead of excluding some parameters.