TY - GEN

T1 - Aircraft Safety Analysis Using Generalized Polynomial Chaos

AU - Diepolder, J.

AU - Piprek, P.

AU - Grüter, B.

AU - Akman, T.

AU - Holzapfel, F.

N1 - Publisher Copyright:
© 2019, Springer Nature Singapore Pte Ltd.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Generalized polynomial chaos

KW - Optimal control

KW - Safety analysis

UR - http://www.scopus.com/inward/record.url?scp=85068622944&partnerID=8YFLogxK

U2 - 10.1007/978-981-13-7086-1_5

DO - 10.1007/978-981-13-7086-1_5

M3 - Conference contribution

AN - SCOPUS:85068622944

SN - 9789811370854

T3 - Lecture Notes in Electrical Engineering

SP - 67

EP - 81

BT - Air Traffic Management and Systems III - Selected Papers of the 5th ENRI International Workshop on ATM/CNS, EIWAC 2017

A2 - Koga, Tadashi

PB - Springer Verlag

T2 - 5th ENRI International Workshop on ATM/CNS, EIWAC 2017

Y2 - 14 November 2017 through 16 November 2017

ER -