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.

Multiple cutout optimization in composite plates using evolutionary structural optimization

The optimization of cutouts in composite plates was investigated by implementing a procedure known as Evolutionary Structural Optimization. Perforations were introduced into a finite element mesh of the plate from which one or more cutouts of a predetermined size were evolved. In the examples presented, plates were rejected from around each evolving cutout based on a predefined rejection criterion. The Limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure criterion. Finite element plates with values below the product of the average Tsai-Hill number and a rejection criterion were subsequently removed. This process was iterated until a steady state was reached and the rejection criterion was then incremented by an evolutionary rate and the above steps repeated until the desired cutout area was achieved. Various plates with differing lay-up and loading parameters were investigated to demonstrate the generality and robustness of this optimization procedure.

Shape optimization of interior cutouts in composite panels

This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO). An initial small cutout was introduced into each finite element model and elements were removed from around this cutout based on a predefined rejection criterion. In the examples presented, the limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure index. Plates with values below the product of the average Tsai-Hill number and a rejection ratio (RR) were subsequently removed. This process was iterated until a steady state was reached and the RR was then incremented by an evolutionary rate (ER). The above steps were repeated until a cutout of a desired area was achieved.

Optimization of image quality and dose for Varian aS500 electronic portal imaging devices (EPIDs)

This study was carried out to investigate whether the electronic portal imaging (EPI) acquisition process could be optimized, and as a result tolerance and action levels be set for the PIPSPro QC-3V phantom image quality assessment. The aim of the optimization process was to reduce the dose delivered to the patient while maintaining a clinically acceptable image quality. This is of interest when images are acquired in addition to the planned patient treatment, rather than images being acquired using the treatment field during a patient's treatment. A series of phantoms were used to assess image quality for different acquisition settings relative to the baseline values obtained following acceptance testing. Eight Varian aS500 EPID systems on four matched Varian 600C/D linacs and four matched Varian 2100C/D linacs were compared for consistency of performance and images were acquired at the four main orthogonal gantry angles. Images were acquired using a 6 MV beam operating at 100 MU min(-1) and the low-dose acquisition mode. Doses used in the comparison were measured using a Farmer ionization chamber placed at d(max) in solid water. The results demonstrated that the number of reset frames did not have any influence on the image contrast, but the number of frame averages did. The expected increase in noise with corresponding decrease in contrast was also observed when reducing the number of frame averages. The optimal settings for the low-dose acquisition mode with respect to image quality and dose were found to be one reset frame and three frame averages. All patients at the Northern Ireland Cancer Centre are now imaged using one reset frame and three frame averages in the 6 MV 100 MU min(-1) low-dose acquisition mode. Routine EPID QC contrast tolerance (+/-10) and action (+/-20) levels using the PIPSPro phantom based around expected values of 190 (Varian 600C/D) and 225 (Varian 2100C/D) have been introduced. The dose at dmax from electronic portal imaging has been reduced by approximately 28%, and while the image quality has been reduced, the images produced are still clinically acceptable.

Directional Modulation Transmitter Synthesis using Particle Swarm Optimization

Phased DM transmitter array synthesis using particle swarm optimization (PSO) is presented in this paper. The PSO algorithm is described in details with key parameters provided for 1-D four-element half-wavelength spaced QPSK DM array synthesis. A DM transmitter array for boresight and 30º direction secure communications are taken as examples to validate the proposed synthesis approach. The optimization process exhibits good convergence performance and solution quality.

Effects of process parameters upon the shape memory and pseudo-elastic behaviors of laser-welded NiTi thin foil

This article discusses the effects of laser welding parameters such as power, welding speed, and focus position on the weld bead profile, microstructure, pseudo-elasticity (PE), and shape memory effect (SME) of NiTi foil with thickness of 250 um using 100W CW fiber laser. The parameter settings to produce the NiTi welds for analysis in this article were chosen from a fractional factorial design to ensure the welds produced were free of any apparent defect. The welds obtained were mainly of cellular dendrites with grain sizes ranging from 2.5 to 4.8 um at the weld centerline. A small amount of Ni3Ti was found in the welds. The onset of transformation temperatures (As and Ms) of the NiTi welds shifted to the negative side as compared to the as-received NiTi alloy. Ultimate tensile stress of the NiTi welds was comparable to the as received NiTi alloy, but a little reduction in the pseudo-elastic property was noted. Full penetration welds with desirable weld bead profiles and mechanical properties were successfully obtained in this study.

Investigation of Machining Parameters for Multiple Response Optimization in Microelectrodischarge Milling

This paper investigated the influence of three micro electrodischarge milling process parameters, which were feed rate, capacitance, and voltage. The response variables were average surface roughness (R a ), maximum peak-to-valley roughness height (R y ), tool wear ratio (TWR), and material removal rate (MRR). Statistical models of these output responses were developed using three-level full factorial design of experiment. The developed models were used for multiple-response optimization by desirability function approach to obtain minimum R a , R y , TWR, and maximum MRR. Maximum desirability was found to be 88%. The optimized values of R a , R y , TWR, and MRR were 0.04, 0.34 μm, 0.044, and 0.08 mg min−1, respectively for 4.79 μm s−1 feed rate, 0.1 nF capacitance, and 80 V voltage. Optimized machining parameters were used in verification experiments, where the responses were found very close to the predicted values.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

Experimental design and batch experiments for optimization of Cr(VI) removal from aqueous solutions by hydrous cerium oxide nanoparticles

Hydrous cerium oxide (HCO) was synthesized by intercalation of solutions of cerium(III) nitrate and sodium hydroxide and evaluated as an adsorbent for the removal of hexavalent chromium from aqueous solutions. Simple batch experiments and a 2⁵ factorial experimental design were employed to screen the variables affecting Cr(VI) removal efficiency. The effects of the process variables; solution pH, initial Cr(VI) concentration, temperature, adsorbent dose and ionic strength were examined. Using the experimental results, a linear mathematical model representing the influence of the different variables and their interactions was obtained. Analysis of variance (ANOVA) demonstrated that Cr(VI) adsorption significantly increases with decreased solution pH, initial concentration and amount of adsorbent used (dose), but slightly decreased with an increase in temperature and ionic strength. The optimization study indicates 99% as the maximum removal at pH 2, 20 °C, 1.923 mM of metal concentration and a sorbent dose of 4 g/dm³. At these optimal conditions, Langmuir, Freundlich and Redlich–Peterson isotherm models were obtained. The maximum adsorption capacity of Cr(VI) adsorbed by HCO was 0.828 mmol/g, calculated by the Langmuir isotherm model. Desorption of chromium indicated that the HCO adsorbent can be regenerated using NaOH solution 0.1 M (up to 85%). The adsorption interactions between the surface sites of HCO and the Cr(VI) ions were found to be a combined effect of both anion exchange and surface complexation with the formation of an inner-sphere complex.

OPTIMIZATION OF THE SLOW-MODE PLASMON POLARITON IN LIGHT-EMITTING TUNNEL-JUNCTIONS

Light emitted from metal/oxide/metal tunnel junctions can originate from the slow-mode surface plasmon polariton supported in the oxide interface region. The effective radiative decay of this mode is constrained by competition with heavy intrinsic damping and by the need to scatter from very small scale surface roughness; the latter requirement arises from the mode's low phase velocity and the usual momentum conservation condition in the scattering process. Computational analysis of conventional devices shows that the desirable goals of decreased intrinsic damping and increased phase velocity are influenced, in order of priority, by the thickness and dielectric function of the oxide layer, the type of metal chosen for each conducting electrode, and temperature. Realizable devices supporting an optimized slow-mode plasmon polariton are suggested. Essentially these consist of thin metal electrodes separated by a dielectric layer which acts as a very thin (a few nm) electron tunneling barrier but a relatively thick (several 10's of nm) optically lossless region. (C) 1995 American Institute of Physics.