Uncertainty-wise Test Case Generation and Minimization for Cyber-Physical Systems

Abstract

Cyber-Physical Systems (CPSs) typically operate in highly indeterminateenvironmental conditions, which require the development of testing methods that must explicitly consider uncertainty in test design, test generation, and test optimization. Towards this direction, we propose a set of uncertainty-wise test case generation and test case minimizationstrategies that rely on test ready models explicitly specifying subjective uncertainty. We propose two test case generation strategies and four test case minimizationstrategies based on the Uncertainty Theory and multi-objectivesearch. These strategies include a novel methodology for designing and introducing indeterminacy sources in the environment during test execution and a novel set of uncertainty-wise test verdicts. We performed an extensive empirical study to select the bestalgorithm out of eight commonly used multi-objective search algorithms, for each of the four minimizationstrategies, with five use cases of two industrial CPS case studies. The minimizedset of test cases obtained with the best algorithm for each minimizationstrategy were executedon the two real CPSs. The results showed that our best test strategy managed to observe 51% more uncertainties due to unknown indeterminate behaviorsof the physical environmentsof the CPSs as compared to the other test strategies. Also, the same test strategy managed to observe 118% more unknown uncertainties as compared to the unique number of known uncertainties.