Simulation of dynamic systems with uncertain parameters

This dissertation describes numerical methods for representation and simulation of dynamic systems with time invariant uncertain parameters. Simulation is defined as computing a boundary of the system response that contains all the possible behaviors of an uncertain system. This problem features many challenges, especially those associated with minimizing the computational cost due to global optimization. To reduce computational cost, an approximation or surrogate of the original system model is constructed by employing Moving Least Square (MLS) Response Surface Method for non-convex global optimization. For more complicated systems, a gradient enhanced moving least square (GEMLS) response surface is used to construct the surrogate model more accurately and efficiently. This method takes advantage of the fact that parametric sensitivity of an ODE system can be calculated as a by-product with less computational cost when solving the original system. Furthermore, global sensitivity analysis for monotonic testing can be introduced in some cases to further reduce the number of samples. The proposed method has been applied to two engineering applications. The first is hybrid system verification by reachable set computing/approximation. First, the computational burden of using polyhedron for reachable set approximation is reviewed. It is then proven that the boundary of a reachable set is formed only by the trajectories from the boundary of an initial state region. This result reduces the search space from Rn to Rn-1 . Finally, the GEMLS method proposed is integrated with oriented rectangular hull for reachable set representation and an approximation with improved accuracy and efficiency can be achieved. Another engineering application is model-based fault detection. In this case, a fault free system is modeled as a parametric uncertain system whose parameters belong to a given bounded set. The performance boundary of a fault free system can be acquired by using the proposed approach and then employed as an adaptive threshold. A fault is defined when system parameters do not belong to the set due to malfunction or degradation. Once such a fault occurs, the monitored system performance will extend beyond the normal system boundary predicted.