Uncertainty and Sensitivity Analysis in Aircraft Operating Costs in Structural Design Optimization

The paper focuses on the development of an aircraft design optimization methodology that models uncertainty and sensitivity analysis in the tradeoff between manufacturing cost, structural requirements, andaircraft direct operating cost.Specifically,ratherthanonlylooking atmanufacturingcost, direct operatingcost is also consideredintermsof the impact of weight on fuel burn, in addition to the acquisition cost to be borne by the operator. Ultimately, there is a tradeoff between driving design according to minimal weight and driving it according to reduced manufacturing cost. Theanalysis of cost is facilitated withagenetic-causal cost-modeling methodology,andthe structural analysis is driven by numerical expressions of appropriate failure modes that use ESDU International reference data. However, a key contribution of the paper is to investigate the modeling of uncertainty and to perform a sensitivity analysis to investigate the robustness of the optimization methodology. Stochastic distributions are used to characterize manufacturing cost distributions, andMonteCarlo analysis is performed in modeling the impact of uncertainty on the cost modeling. The results are then used in a sensitivity analysis that incorporates the optimization methodology. In addition to investigating manufacturing cost variance, the sensitivity of the optimization to fuel burn cost and structural loading are also investigated. It is found that the consideration of manufacturing cost does make an impact and results in a different optimal design configuration from that delivered by the minimal-weight method. However, it was shown that at lower applied loads there is a threshold fuel burn cost at which the optimization process needs to reduce weight, and this threshold decreases with increasing load. The new optimal solution results in lower direct operating cost with a predicted savings of 640=m2 of fuselage skin over the life, relating to a rough order-of-magnitude direct operating cost savings of $500,000 for the fuselage alone of a small regional jet. Moreover, it was found through the uncertainty analysis that the principle was not sensitive to cost variance, although the margins do change.

The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Analysis of Transonic Limit Cycle Oscillations under Uncertainty

For the computation of limit cycle oscillations (LCO) at transonic speeds, CFD is required to capture the nonlinear flow features present. The Harmonic Balance method provides an effective means for the computation of LCOs and this paper exploits its efficiency to investigate the impact of variability (both structural a nd aerodynamic) on the aeroelastic behaviour of a 2 dof aerofoil. A Harmonic Balance inviscid CFD solver is coupled with the structural equations and is validated against time marching analyses. Polynomial chaos expansions are employed for the stochastic investiga tion as a faster alternative to Monte Carlo analysis. Adaptive sampling is employed when discontinuities are present. Uncertainties in aerodynamic parameters are looked at first followed by the inclusion of structural variability. Results show the nonlinear effect of Mach number and it’s interaction with the structural parameters on supercritical LCOs. The bifurcation boundaries are well captured by the polynomial chaos.

Prediction of Limit Cycle Oscillations Using an Implicit Aeroelastic-Harmonic Balance Method

This work proposes a extends a novel approach to compute tran sonic Limit Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a methodology to determine the unknown frequency of oscillations using an implicit for- mulation of the HB method to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and respective linear structural models is used to exercise the new method. Results show consistent agreement between the proposed and time-marching methods for both LCO amplitude and frequency.

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

This work proposes a novel approach to compute transonic limit-cycle oscillations using high-fidelity analysis. Computational-Fluid-Dynamics based harmonic balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling harmonic balance methods to accurately capture limit-cycle oscillations; this is achieved by defining a frequency-updating procedure based on a coupled computational-fluid-dynamics/computational-structural-dynamics harmonic balance formulation to find the limit-cycle oscillation condition. A pitch/plunge airfoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional time-domain simulations. Results show consistent agreement between the proposed and time-marching methods for both limit-cycle oscillation amplitude and frequency while producing at least a one-order-of-magnitude reduction in computational time.

Reducing Parametric Uncertainty in Limit Cycle Oscillations

The assimilation of discrete higher fidelity data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance method (HDHB). The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on both a pitch/plunge aerofoil and Goland wing configuration. In both cases significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their
true deterministic values.