58905 - Sensitivity Analysis of an Aircraft Engine Model Under Consideration of Dependent Variables 

Complex systems, such as aircraft gas turbines, are of paramount importance for both, the private mobility as well as the industrial transport sector of modern societies. For economic and safety-related reasons, it is crucial that such systems are as reliable and resilient as possible. To ensure this in an efficient and sustainable manner, the Collaborative Research Center ''Regeneration of Complex Capital Goods'' (CRC 871) conducts research on scientific principles for the maintenance, repair and overhaul (MRO) of these complex capital goods, especially in the domain of civil aviation.

A major task of the CRC 871 is the development of a digital performance twin of a V2500-A1 turbofan engine by International Aero Engines (IAE), Spuhler et al. (2019). This model is intended for simulating virtual regeneration processes and thus to provide support for decision-makers in MRO-processes. The steady state performance of the V2500-A1 jet engine is calculated with an iteration matching model based on Newton Raphson method.

In MRO-processes, a fundamental basis for decision-makers is knowledge about the effects of deterioration of individual components on the overall engine performance. Sensitivity analyses are a proven tool in this context. In numerous engineering fields, the knowledge about a model’s sensitivity, i.e. about the influences of model input variables on the model output variables, provides an essential basis for the understanding of underlying system processes and system modeling in general, Saltelli et al. (2008). In MRO-processes, this knowledge provides a valuable foundation for decision-makers, e.g. in the prioritization of regeneration measures.

As stated in Saltelli et al. (2008), scatter plots serve as a first optical and solid basis for a sensitivity analysis, allowing the sensitivity of individual inputs to be easily represented. However, since they are unsuitable for representing interaction effects between input variables, the so-called Sobol indices (Sobol, 2001) are typically utilized. These variance-based indices can display the effect of a single input variable on the output variables, as well as interaction effects with other input variables on the output variables. The Sobol indices, as well as most other sensitivity analysis tools, are based on the assumption that all input variables are independent of each other. However, this assumption rarely applies in reality, i.e., input variables are indeed often dependent on each other. Therefore, in this paper, a sensitivity analysis of the above mentioned performance model for an aircraft engine is conducted, first, optical by means of scatter plots, and second by applying Kucherenko indices (Kucherenko et al., 2012), a generalized form of the Sobol indices. These indices are capable of taking into account dependencies between input variables and are therefore suitable for addressing real world problems. As input variables, the efficiencies of the V2500-A1’s five turbomachines are considered, the exhaust gas temperature (EGT), performance parameter of the aircraft engine, as the output. First results show that the variance in the efficiencies of the high-pressure system, for example due to deterioration, generates a greater variance in the EGT and thus has a greater impact than variations in the efficiencies of the low-pressure system.

References

Spuhler, T., Kellersmann, A., Bode, C., Friedrichs, J., Reitz, G., Kotulla, M., Kappei, F. and Michaelis, T. (2019): The V2500-A1 as a Test Rig towards Digital Twin Modeling. International Gas Turbine Congress 2019 Tokyo

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S. (2008): Global sensitivity analysis: the primer. John Wiley & Sons.

Sobol,I.M. (2001): Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. MATH COMPUT SIMULAT, 55(1–3), 271-280

Kucherenko, S., Tarantola, S., and Annoni, P. (2012): Estimation of global sensitivity indices for models with dependent variables. Computer physics communications, 183(4), 937-946.