Constraint-Based Off-Nominal Behavior Modeling for Europa Clipper

The risk assessment for the Europa Clipper mission evaluates the probability of mission failure based on the failure rates of individual components and dependencies among them. The probabilities are calculated by integrating the failure probability density functions over the intervals of time within which a fault may occur. The response of the spacecraft to different faults can result in different schedules of activities, changing both the failure probability density functions and the time intervals of integration. This paper describes an approach to generating the schedules for the different fault cases and determining the associated time intervals. In order to represent the behavior of the spacecraft using a simple, declarative syntax, we employ a language based on ontologies of behavior and scenarios. A constraint-based analysis engine uses the declarative specification to identify bounds on system parameters and fill in details of behavior. These bounds include the time windows within which certain faults can occur, which are also the bounds for integration in the calculation of failure probability. Determining these time windows is a constraint optimization problem. For an individual fault in Clipper's propulsion subsystem, the engine is able to solve for values of the time window, but it cannot directly solve for the windows when they are functions of the times of previous faults. We used Mathematica to solve for these functions, and for more complicated scenarios, the functions are nearly too large to manage. We discuss this challenge of maintaining a closed-form calculation for more detailed fault models, and present the model of propulsion fault response behavior that illustrates the challenge. We also discuss some advantages of the behavior modeling language, comparing to a mixed integer-linear program model. Time windows are given for some of the many scenarios of interest.