Aircraft Safety Analysis Using Generalized Polynomial Chaos

In this paper we investigate the application of generalized polynomial chaos (gPC) for optimal control based aircraft safety assessment with parameter uncertainties. The approach is based on the formulation of an appropriate optimal control problem to obtain worst case inputs. The criterion to be assessed is introduced in the cost function and the numerical solution is obtained using direct optimal control methods. In this context, we consider the case where the parameter distribution is unknown and assume a truncated uniform distribution with truncation values to be determined. The approach can be summarized as follows: First an optimization assisted bisection search algorithm is performed. This algorithm yields regions of a defined size in which a violation of the criterion occurs. In order to obtain a local explicit representation of the worst-case solution, we approximate this solution in the parameter space using a spectral representation based on gPC. This representation is then used to determine the worst case truncation limits of the uniform distribution and to estimate the exceedance probability for the criterion under investigation. The application is illustrated using a F-16 short period model with model reference adaptive controller. In this example, we estimate the exceedance probability for the maximum tracking error in the angle of attack for worst case reference command inputs and plant uncertainties in pitch damping, pitch stiffness, and control effectiveness.