Bayesian Experimental Design for Finding Reliable Level Set under Input Uncertainty
This addresses a practical manufacturing challenge of ensuring machine performance despite input variations, but it is incremental as it builds on existing level set estimation methods by incorporating input uncertainty.
The paper tackles the problem of identifying input conditions for reliable machine operation under input uncertainty, formulating it as an Input Uncertain Reliable Level Set Estimation (IU-rLSE) problem and proposing an efficient active learning algorithm with theoretical and empirical validation.
In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately control the input conditions during the actual usage of the machine, there is a need to guarantee the performance of the machine after properly incorporating the possible variation in input conditions. In this paper, we formulate this practical manufacturing scenario as an Input Uncertain Reliable Level Set Estimation (IU-rLSE) problem, and provide an efficient algorithm for solving it. The goal of IU-rLSE is to identify the input range in which the outputs smaller/greater than a desired threshold can be obtained with high probability when the input uncertainty is properly taken into consideration. We propose an active learning method to solve the IU-rLSE problem efficiently, theoretically analyze its accuracy and convergence, and illustrate its empirical performance through numerical experiments on artificial and real data.