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A modified variable complexity modeling for efficient multidisciplinary aircraft conceptual design

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Abstract

This paper describes a modified variable complexity modeling (MVCM) framework that uses a neural network to replace the Taylor series after several warm-up iterations. The MVCM framework with an additive scaling function is most efficient in terms of high-fidelity function evaluation savings compared with traditional variable complexity modeling (VCM) among multiplicative and hybrid scaling functions. The MVCM framework achieves 59.1 and 68.6 % savings in high-fidelity function evaluations for one-dimensionally and two-dimensionally constrained problems, respectively, compared with the VCM method. The MVCM framework provides a larger trust region than the VCM due to the global behavior of neural networks. The MVCM solution also converges closely to the high-fidelity function. The MVCM framework is integrated with an in-house low-fidelity aircraft design synthesis program and a high-fidelity analysis (AADL3D) for the conceptual design of multidisciplinary regional jet aircraft (RJA) to enhance the optimal RJA configuration compared with low-fidelity analysis results. The optimal RJA wing configuration using the MVCM framework provides more realistic and reasonable configurations compared to the results of low-fidelity analysis with a short turnaround time.

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Abbreviations

f :

Objective function

g :

Inequality constraint

x :

Design vector

x L :

Lower bound of design space

x U :

Upper bound of design space

β :

Multiplicative scaling factor

γ :

Additive scaling factor

\( \Delta \) :

Trust region size

ɛ f :

Objective function convergence tolerance

ɛ x :

Design variable convergence tolerance

ɛ g :

Constraint convergence tolerance

ρ :

Trust region ratio

ω :

Hybrid scaling weight factor

\( \lambda \) :

Taper ratio

\( \varLambda_{LE} \) :

Leading sweep angle

\( \Delta C_{dflap} \) :

Drag increment due to flap

AR :

Aspect ratio

C L :

Lift coefficient

C D :

Total drag coefficient

C Lmax :

Maximum lift coefficient

C nβ :

Directional stability derivative

C mα :

Pitching moment coefficient

C Do :

Parasitic drag

M :

Mach number

P avail :

Power available

SFC :

Fuel specified consumption

(X, Y, Z) cg :

Aircraft center of gravity

W e :

Empty weight

W fuel :

Fuel weight

W o :

Takeoff gross weight

W odesign :

Design gross weight

X LND :

Landing distance

X TO :

Takeoff distance

V avail :

Available speed

I xx , I yy , I zz :

Moment of inertia

high :

High-fidelity model

low :

Low-fidelity model

n :

Current iteration

scaled :

Scaled low-fidelity value

w :

Wing

0 :

Initial value

* :

Optimum value

−:

Approximate function

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Acknowledgments

The authors would like to acknowledge that this research was supported by Konkuk University in 2014.

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  1. Konkuk University, Seoul, 143-701, South Korea

    Nhu Van Nguyen, Maxim Tyan & Jae-Woo Lee

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  1. Nhu Van Nguyen
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  2. Maxim Tyan
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  3. Jae-Woo Lee
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Correspondence to Jae-Woo Lee.

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Nguyen, N.V., Tyan, M. & Lee, JW. A modified variable complexity modeling for efficient multidisciplinary aircraft conceptual design. Optim Eng 16, 483–505 (2015). https://doi.org/10.1007/s11081-014-9273-7

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