One-stage Bayesian experimental design optimization for measuring soil-water characteristic curve

The direct measurements of soil-water characteristic curve (SWCC) are often costly and time-consuming. Therefore, only a limited number of test data can be obtained from a single SWCC test, based on which the estimated SWCC inevitably produces uncertainty. It is reasonable to select the experimental scheme (i.e., specify the values of the control variables at measuring points) in order to improve the expected value of information of the measurement data for reducing the uncertainty in the estimated SWCC. A one-stage Bayesian experimental design optimization (OBEDO) approach is developed for SWCC testing exploiting prior knowledge and information of testing apparatus. Discretization of control variables (e.g., matric suction) is used to generate the design space of the candidate experimental scheme, which is specified by the initial measuring points and the additional measuring points to control the general trajectory of SWCC and further reduce the uncertainty in SWCC, respectively. The value of data corresponding to the experimental scheme is quantified by the expected utility. The candidate experimental scheme with the maximum expected utility is identified using the subset simulation optimization (SSO) and treated as the optimal experimental design scheme. The proposed approach is illustrated using an experimental design example. The results show that it provides a rational tool to determine the optimal experiment scheme for SWCC testing considering the uncertainty of soil.