Generating automated and online test oracles for Simulink models with continuous and uncertain behaviors

Test automation requires automated oracles to assess test outputs. For cyber physical systems (CPS), oracles, in addition to be automated, should ensure some key objectives: (i) they should check test outputs in an online manner to stop expensive test executions as soon as a failure is detected; (ii) they should handle time- and magnitude-continuous CPS behaviors; (iii) they should provide a quantitative degree of satisfaction or failure measure instead of binary pass/fail outputs; and (iv) they should be able to handle uncertainties due to CPS interactions with the environment. We propose an automated approach to translate CPS requirements specified in a logic-based language into test oracles specified in Simulink - a widely-used development and simulation language for CPS. Our approach achieves the objectives noted above through the identification of a fragment of Signal First Order logic (SFOL) to specify requirements, the definition of a quantitative semantics for this fragment and a sound translation of the fragment into Simulink. The results from applying our approach on 11 industrial case studies show that: (i) our requirements language can express all the 98 requirements of our case studies; (ii) the time and effort required by our approach are acceptable, showing potentials for the adoption of our work in practice, and (iii) for large models, our approach can dramatically reduce the test execution time compared to when test outputs are checked in an offline manner.