Monte Carlo based Robust MDO applied to Aircraft Conceptual Design: a technical-financial coupling optimization strategy

Abstract

Aircraft Conceptual Design is a challenging task that requires not only the understanding of many different disciplines, but also how they interact with each other, leading to many trade-off analyses. The complexity of these interactions grows fast with the number of variables, disciplines and goals of the problem. Multidisciplinary Analysis and Optimization tools can be very helpful to explore the design space, but it is up to the engineering team to define the objective function: optimal with respect to what? For commercial aircraft segment there are two well defined objectives that mostly represent what costumers of this segment desire: minimization of block fuel or minimization of direct operating costs. The objective function is not so clear for the Executive Jets segment and it is usual to apply minimization of MTOW. This paper proposes an architecture that includes Costs, Market Share and Finances disciplines in the optimization loop, treating the market specifications provided by company's intelligence as constraints and maximizes the financial return to the shareholders. This way, the conceived solution complies with all customer needs and also provides the most attractive investment to the shareholders. A comparison is made with the traditional optimization strategy and the results shows that, although both strategies are not exactly conflicting objectives, to maximize the financial return can lead to a different design with significant improvement in financial return. Another key optimization issue treated in this work is the reliability and robustness of the design. Estimation methods have inherent model uncertainties that can not be mitigated even with in-house data calibration. Uncertainty quantification and Robust Design is held in this work by the use of Monte Carlo simulations using triangular distributions and superposition of effects. Results for the Robust Optimization showed that slight changes in the design can improve robustness in the outcomes of interest. Also, the proposed methodology reduces the computational cost of the Robust Design to almost the level of a deterministic design, presenting a significant improvement to this process. Engine Inoperative RC = Rate of Climb Re = Reynolds number Ri = Range for the i-th mission Sref, Sw = Wing reference area SRi = Specific Range for the i-th mission t/c = Thickness-to-Chord ratio TLR = Top Level Requirements TO = Take-off TOFL = Take-Off Field Length TSFC = Thrust Specific Fuel Consumption TSLS = Engine's Sea-Level Static Thrust V, TAS = True Airspeed Vfuel = Fuel Volume VH = Horizontal Tail Volume coefficient VT = Vertical Tail VV = Vertical Tail Volume coefficient Wresf = Fuel reserves weight α, AoA = Angle of Attack β = Sideslip angle Λ = Sweep angle λ = Taper-Ratio Financial acronyms and symbols DOC = Direct Operating Costs IRR = Internal Rate of Return NPV = Net Present Value Optimization acronyms and symbols MDO = Multidisciplinary Design Optimization VDD = Value-Driven Design MOGA = Multi-Objective Genetic Algorithm φ(.) = Vector of O...

Evaluation of the impacts of the Objective Function definition in Aircraft Conceptual Design

“…Where Price is obtained from Figure 2 and the Market Share can be estimated using the Benefit Index (BI) and Attractiveness Index (AI) defined in reference [11]. The benefit index is a functional intended to measure the perceived value of a collection of performance attributes from the customers point of view.…”

“…: how much of the market forecast the design would be able to capture. In reference [11] a Market Share model based on Personas b methodology 22 was proposed and employed in order to compare optimized designs for the traditional strategy (i.e. min{MTOW}) and the technical-financial coupled strategy (i.e.…”

“…It is the one that is able to provide the maximum financial return, and this airplane is not achieved using only technical objective function, leading to the need of the inclusion of economics model into the design framework. [11][12][13][14] As presented above, the selection of the figure of merit to be used as objective function a during the conceptual design has a great influence in the resulting design, and it seems that some choices give the designer more control over the results.…”

Multidisciplinary Design Optimization of Aerial Vehicles: A Review of Recent Advancements

“…Overall, it has been shown that this approach has the potential to determine the design variables with the highest influence, and therefore, it can reduce the total parameters to a number that is relevant but also manageable for each specific case study [19][20][21][22]. As far as the constraints are concerned, those are usually limited to the critical case-depended features [16,23] or similarly, to common airworthiness aspects like the field performance [13,[24][25][26]. In general, constraints can add further fidelity to the design, and this has been often exemplified through the incorporation of safety regulations in the modeling of fuel systems [27], aircraft controls [28,29], and mission requirements for general aviation [25,30,31].…”

“…The first and most frequently encountered set of models in MDO of aerial vehicles are the calculation of aerodynamics, the estimation of the weight, the computation of the structural response, and lastly, the assessment of the propulsion specifications. In the conceptual design stage, it is common to use simple and fast aerodynamic predictions which can be provided by empirical equations [24,28] or panel methods [33,34]; however, in cases where more detailed insights into the design are required, it is often shown that computational fluid dynamics (CFD) codes can be a more accurate and hence suitable alternative [35,36]. Similarly, in the initial design phases, the weight and balance are estimated by using empirical equations [24,37] as well as statistical data [38,39], while for additional fidelity, it is also possible to augment the calculations by using the results of simplified [40][41][42] or full [33,43] structural analyses.…”