A Response-Adaptive Method for Design of Validation Experiments in Computational Mechanics

Abstract

For model verification and validation (V & V) in computational mechanics, a hypothesis test for the validity check (HTVC) is useful, in particular, with a limited number of experimental data. However, HTVC does not address how type I and II errors can be reduced when additional resources for sampling become available. For the validation of computational models of safety-related and mission-critical systems, it is challenging to design experiments so that type II error is reduced while maintaining type I error at an acceptable level. To address the challenge, this paper proposes a new method to design validation experiments, response-adaptive experiment design (RAED). The RAED method adaptively selects the next experimental condition from among candidates of various operating conditions (experimental settings). RAED consists of six key steps: (1) define experimental conditions, (2) obtain experimental data, (3) calculate u-values, (4) compute the area metric, (5) select the next experimental condition, and (6) obtain additional experimental datum. To demonstrate the effectiveness of the RAED method, a case study of a numerical example is shown. It is demonstrated that additional experimental data obtained through the RAED method can reduce type II error in hypothesis testing and increase the probability of rejecting an invalid computational model.