Improving parameter estimation with an efficient sequential probabilistic collocation-based optimal design method

Abstract

Accurate estimation of soil hydraulic parameters is essential for modeling of water flow and solute transport in unsaturated soil. Ensemble-based methods have been proposed to provide the optimal monitoring (data-collection) strategy to improve hydraulic parameter estimation. To guarantee the performance, however, these methods usually require relatively large ensemble sizes, leading to high computational cost. To this end, we develop an efficient sequential probabilistic collocation-based optimal design (SPCOD) method, which integrates the adaptive ANOVA (analysis of variance)-based probabilistic collocation-based Kalman filter with the sequential optimal design. At the forecast step, the probabilistic collocation method is used to construct a reduced-order surrogate for system model with the adaptive ANOVA-based polynomial chaos expansion (PCE). At the design step, an information metric in the PCE form is derived to evaluate candidate monitoring strategies. The one with the maximum expected information metric value is chosen as the optimal. At the analysis step, the PCE coefficients are sequentially updated by a square-root Kalman filter with the real-time measurements obtained from the optimal monitoring strategy. Two synthetic numerical cases involving water flow and solute transport in the vadose zone are employed to illustrate the performance of the proposed method. The results show that: (1) compared with conventional fixed monitoring strategies, the optimal monitoring strategy designed by SPCOD provides more accurate parameter estimation and state prediction; (2) compared with our previously developed sequential ensemble-based optimal design method (Man et al., 2016b), the new approach provides a more robust and accurate optimal monitoring design with nearly the same computational cost.