Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review.

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas, contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs. It ends with topics for future research.

/pdf/kriging-metamodeling-in-simulation-a-review-2hj4mjqeb7.pdf

Kriging Metamodeling in Simulation: A Review

Kriging metamodeling in simulation : A review

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

http://www2.mae.ufl.edu/haftka/eoed/protected/ASME04.kriging.pdf

Use of Kriging Models to Approximate Deterministic Computer Models

Many optimization methods for simulation-based design rely on the sequential use of metamodels to reduce the associated computational burden. In particular, kriging models are frequently used in variable fidelity optimization. Nevertheless, such methods may become computationally inefficient when solving problems with large numbers of design variables and/or sampled data points due to the expensive process of optimizing the kriging model parameters in each iteration. One solution to this problem would be to replace the kriging models with traditional Taylor series response surface models. Kriging models, however, were shown to provide good approximations of computer simulations that incorporate larger amounts of data, resulting in better global accuracy. In this paper, a metamodel update management scheme (MUMS) is proposed to reduce the cost of using kriging models sequentially by updating the kriging model parameters only when they produce a poor approximation. The scheme uses the trust region ratio (TR-MUMS), which is a ratio that compares the approximation to the true model. Two demonstration problems are used to evaluate the proposed method: an internal combustion engine sizing problem and a control-augmented structural design problem. The results indicate that the TR-MUMS approach is very effective; on the demonstration problems, it reduced the number of likelihood evaluations by three orders of magnitude compared to using a global optimizer to find the kriging parameters in every iteration. It was also found that in trust region-based method, the kriging model parameters need not be updated using a global optimizer—local methods perform just as well in terms of providing a good approximation without affecting the overall convergence rate, which, in turn, results in a faster execution time.

https://www.gano.name/shawn/papers/SDM_2005_MUMS_GANO.pdf

Update strategies for kriging models used in variable fidelity optimization

Solving design problems that rely on very complex and computationally expensive calculations using standard optimization methods might not be feasible given design cycle time constraints. Variable fidelity methods address this issue by using lower-fidelity models and a scaling function to approximate the higher-fidelity models in a provably convergent framework. In the past, scaling functions have mainly been either first-order multiplicative or additive corrections. These are being extended to second order. In this investigation variable metric approaches for calculating second-order scaling information are developed. A kriging-based scaling function is introduced to better approximate the high-fidelity response on a more global level. An adaptive hybrid method is also developed in this investigation. The adaptive hybrid method combines the additive and multiplicative approaches so that the designer does not have to determine which is more suitable prior to optimization. The methodologies developed in this research are compared to existing methods using two demonstration problems. The first problem is analytic, whereas the second involves the design of a supercritical high-lift airfoil. The results demonstrate that the krigingbased scaling methods improve computational expense by lowering the number of high-fidelity function calls required for convergence. The results also indicate the hybrid method is both robust and effective.

Hybrid Variable Fidelity Optimization by Using a Kriging-Based Scaling Function

Solving design problems that rely on very complex and computationally expensive calculations using standard optimization methods may not be feasible given design cycle time constraints. Variable fldelity methods address this issue by using lower fldelity models and a scaling function to approximate the higher fldelity models in a provably convergent framework. In the past, scaling functions have mainly been either flrst order multiplicative or additive corrections; recently these have been extended to second order. In this work a kriging based scaling function is introduced to better approximate the high fldelity response on a more global level. An adaptive hybrid method is also studied. It combines the additive and multiplicative approaches so that the designer doesn’t have to determine which is better before optimization. The difierent methods are theoretically described and then compared using two demonstration problems. The flrst problem is analytic, while the other is a design of a supercritical high-lift airfoil. The results show that the warm-started kriging based scaling methods have the potential to improve computational expense by lowering the number of high fldelity function calls required for convergence. The results also indicate the hybrid method is efiective.

/pdf/variable-fidelity-optimization-using-a-kriging-based-scaling-uiielul3h5.pdf

Variable Fidelity Optimization Using a Kriging Based Scaling Function

Due to their current successes, unmanned aerial vehicles (UAVs) are becoming a standard means of collecting information. However, as their missions become more complex and require them to fly farther, UAVs can become large and expensive due to fuel needs. Sidestepping the paradigm of a fixed static wing, the variform concept developed in this paper allows for greater fuel efficiency. Bulky wings could morph into sleeker profiles, reducing drag, as they burn fuel. The development of such wings will rely heavily on computational design exploiting state of the art optimization techniques that account for uncertainty and insure reliability.

http://www.gano.name/shawn/papers/mdo02.pdf

Optimized unmanned aerial vehicle with wing morphing for extended range and endurance

Research in unmanned aerial vehicles (UAVs) has grown in interest over the past couple decades. Historically, UAVs were designed to maximize endurance and range, but demands for UAV designs have changed in recent years. In addition to the traditional demands for endurance and range, today customer demands include maneuverability. Therefore, UAVs are being designed to morph, to change their geometrical shape during flight, for enhanced maneuvering capability. In this investigation the morphing UAV concept under study is referred to as the buckle wing. The design of the buckle-wing airfoil geometries is posed as a multilevel, multiobjective optimization problem. This buckle-wing design problem includes two competing objectives of maneuverability and long range/endurance. Multiobjective problems have many optimal solutions each depicting a dierent compromise scenario. Each optimal solution is a Pareto point, and the set of all these points represents the Pareto curve. This is a powerful means of showing the global picture of the solution eld. The goal of this paper is to explore and compare the Pareto curves of the buckle-wing UAV to that of a conventional non-morphing UAV. In order to make this performance comparison, Compromise Programming is used as the optimizing method, and the VortexPanel Method is used in calculating the aerodynamics. The buckle-wing UAV’s enhanced capabilities are demonstrated both quantitatively and graphically.

/pdf/morphing-uav-pareto-curve-shift-for-enhanced-performance-5e8616joee.pdf

Shawn E. Gano

Papers

Update strategies for kriging models used in variable fidelity optimization

Hybrid Variable Fidelity Optimization by Using a Kriging-Based Scaling Function

Variable Fidelity Optimization Using a Kriging Based Scaling Function

Optimized unmanned aerial vehicle with wing morphing for extended range and endurance

Morphing UAV Pareto Curve Shift for Enhanced Performance