Propulsion-Airframe Integration Using Statistical Surrogates from Computer Simulations

A unique perspective of system integration is presented in terms of statistical design and analysis. Advanced statistical concepts are employed to quantify the variance of the statistical models as well as to specify model truncation error. Three models are developed for this study: 1) a supersonic wing section; 2) a supersonic turbojet system and; 3) an integrated supersonic wing section and supersonic turbojet. The three models are analyzed and separately and surrogate models are developed for each model independently using Design of Experiments and advanced statistical analyses. The individual surrogate models are statistically validated compared to their respective models. The individual wing and turbojet surrogate models are then used to estimate the performance of the combined wing and turbojet system surrogate model performance. Conversely, the combined wing and turbojet system surrogate is used to estimate the individual performance of the wing section and turbojet surrogate models' results. It must be noted that the system interactions in the simpler models presented in this study were minimal but if disparate systems are considered for integration the same concepts will apply. If strong interactions are likely to be present, than the integrated model must be developed accordingly.

Statistical surrogates are developed from turbojet and wing section models and used to demonstrate integration of major system components using statistical superposition principles. Fourth-order optimal response surfaces were developed for a supersonic turbojet model as well as a supersonic wing section model. Independent parameters of Mach number, compressor pressure ratio, and maximum turbine inlet temperature were used for the Design of Experiments inputs for the turbojet model. For the wing section model, independent parameters of Mach number, wedge half-angle, and angle of attack were used for the Design of Experiments inputs. The common parameter of Mach number was used along with fixed altitude to provide the system integration environment. The statistical surrogate models were developed for the wing and turbojet system individually as well as for the overall combined system of wing plus turbojet. The combined system of turbojet and wing section used the independent input parameters of Mach number, compressor pressure ratio, maximum turbine inlet temperature, wedge half-angle, and angle of attack. All models maintained the same truncation error and level of variance, providing minimal propagation of uncertainty throughout the process.

The lift-to-drag ratio of the wing is used to demonstrate the statistical integration process. First, the surrogate model for lift-to-drag ratio for the wing is statistically developed and corroborated for uncertainty in model prediction. Second, the surrogate model for lift- to-drag ratio of the combined wing plus turbojet is statistically developed and corroborated for uncertainty in model prediction. Lastly, the lift-to-drag predictions of both surrogates are statistically compared to determine if the integrated model maintains the same level of precision as the individual models. All models are interchangeable in terms of statistical prediction intervals to within prescribed uncertainty and precision levels.