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This work proposes a multifidelity modeling approach for predicting aeroelastic flutter of airfoils and wings. Using aerodynamic models based on the doublet-lattice method and time-accurate Euler e...

In this article, a structure and design procedure of a novel compact dual-polarized corrugated horn antenna with high gain and a stable phase center for satellite communication is presented. The antenna incorporates an ortho-mode transducer (OMT), a mode converter, and a corrugated structure. The compact OMT section is designed to be fed by standard WR-75 waveguides. The proposed compact design utilizes only ten corrugated slots to yield a symmetric radiation pattern. The antenna impedance bandwidth (VSWR < 1.5) is 10.2 to 15 GHz. Furthermore, the antenna exhibits 14–17 dBi gain, a constant 30° half-power beamwidth (HPBW) radiation pattern, and less than 9 mm phase center variation over the operating frequency range. The aperture diameter is 7 cm and the total antenna length is 15 cm. Due to the aforementioned features, the proposed antenna is suitable as the feed reflector for both uplink and downlink satellite communications. The design is numerically and experimentally validated.

The objective of this work is to reduce the cost of performing model-based sensitivity analysis for ultrasonic nondestructive testing systems by replacing the accurate physics-based model with machine learning (ML) algorithms and quickly compute Sobol’ indices. The ML algorithms considered in this work are neural networks (NNs), convolutional NN (CNNs), and deep Gaussian processes (DGPs). The performance of these algorithms is measured by the root mean-squared error on a fixed number of testing points and by the number of high-fidelity samples required to reach a target accuracy. The algorithms are compared on three ultrasonic testing benchmark cases with three uncertainty parameters, namely, spherically void defect under a focused and a planar transducer and spherical-inclusion defect under a focused transducer. The results show that NNs required 35, 100, and 35 samples for the three cases, respectively. CNNs required 35, 100, and 56, respectively, while DGPs required 84, 84, and 56, respectively.

Global sensitivity analysis (GSA) is a method to quantify the effect of the input parameters on outputs of physics-based systems. Performing GSA can be challenging due to the combined effect of the high computational cost of each individual physics-based model, a large number of input parameters, and the need to perform repetitive model evaluations. To reduce this cost, neural networks (NNs) are used to replace the expensive physics-based model in this work. This introduces the additional challenge of finding the minimum number of training data samples required to train the NNs accurately. In this work, a new method is introduced to accurately quantify the GSA values by iterating over both the number of samples required to train the NNs, terminated using an outer-loop sensitivity convergence criteria, and the number of model responses required to calculate the GSA, terminated with an inner-loop sensitivity convergence criteria. The iterative surrogate-based GSA guarantees converged values for the Sobol’ indices and, at the same time, alleviates the specification of arbitrary accuracy metrics for the surrogate model. The proposed method is demonstrated in two cases, namely, an eight-variable borehole function and a three-variable nondestructive testing (NDT) case. For the borehole function, both the first- and total-order Sobol’ indices required 200 and \(10^5\) data points to terminate on the outer- and inner-loop sensitivity convergence criteria, respectively. For the NDT case, these values were 100 for both first- and total-order indices for the outer-loop sensitivity convergence, and \(10^6\) and \(10^3\) for the inner-loop sensitivity convergence, respectively, for the first- and total-order indices, on the inner-loop sensitivity convergence. The differences of the proposed method with GSA on the true functions are less than 3% in the analytical case and less than 10% in the physics-based case (where the large error comes from small Sobol’ indices).

The Midwest state of Iowa in the US is one of the major producers of corn, soybean, ethanol, and animal products, and has long been known as a significant contributor of nitrogen loads to the Mississippi river basin, supplying the nutrient-rich water to the Gulf of Mexico. Nitrogen is the principal contributor to the formation of the hypoxic zone in the northern Gulf of Mexico with a significant detrimental environmental impact. Agriculture, animal agriculture, and ethanol production are deeply connected to Iowa’s economy. Thus, with increasing ethanol production, high yield agriculture practices, growing animal agriculture, and the related economy, there is a need to understand the interrelationship of Iowa’s food-energy-water system to alleviate its impact on the environment and economy through improved policy and decision making. In this work, the Iowa food-energy-water (IFEW) system model is proposed that describes its interrelationship. Further, a macro-scale nitrogen export model of the agriculture and animal agriculture systems is developed. Global sensitivity analysis of the nitrogen export model reveals that the commercial nitrogen-based fertilizer application rate for corn production and corn yield are the two most influential factors affecting the surplus nitrogen in the soil.

Purpose Dual-rotor wind turbines (DRWTs) are a novel type of wind turbines that can capture more power than their single-rotor counterparts. Because their surrounding flow fields are complex, evaluating a DRWT design requires accurate predictive simulations, which incur high computational costs. Currently, there does not exist a design optimization framework for DRWTs. Since the design optimization of DRWTs requires numerous model evaluations, the purpose of this paper is to identify computationally efficient design approaches. Design/methodology/approach Several algorithms are compared for the design optimization of DRWTs. The algorithms vary widely in approaches and include a direct derivative-free method, as well as three surrogate-based optimization methods, two approximation-based approaches and one variable-fidelity approach with coarse discretization low-fidelity models. Findings The proposed variable-fidelity method required significantly lower computational cost than the derivative-free and approximation-based methods. Large computational savings come from using the time-consuming high-fidelity simulations sparingly and performing the majority of the design space search using the fast variable-fidelity models. Originality/value Due the complex simulations and the large number of designable parameters, the design of DRWTs require the use of numerical optimization algorithms. This work presents a novel and efficient design optimization framework for DRWTs using computationally intensive simulations and variable-fidelity optimization techniques.

Aerodynamic design is inherently a multi-objective optimization (MOO) problem. Determining the best possible trade-offs between conflicting aerodynamic objectives can be computationally challenging when carried out directly at the level of high-fidelity computational fluid dynamics simulations. This paper presents a computationally cheap methodology for exploration of aerodynamic design trade-offs. In particular, point-by-point identification of a set of Pareto-optimal designs is executed starting in the neighborhood of a single-objective optimal design, and using a trust-region-based, multi-fidelity optimization algorithm as well as locally constructed response surface approximations (RSAs). In this work, the RSAs are constructed using second-order polynomials without mixed terms, multi-fidelity models, and adaptive corrections. The application of the point-by-point MOO algorithm is demonstrated through MOO of transonic airfoil shapes using the Reynold–Averaged Navier Stokes equations and the Spalart–Allmaras turbulence model. The results demonstrate that the Pareto front in the neighborhood of an initial design can be obtained at a low cost when considering up to 12 design variables. The results also indicate that the computational cost of the optimization process grows slowly with the number of the design variables, and the repeatability of the algorithm is very good when starting the search from different initial points.

Purpose An improvement in the energy efficiency of wind turbines can be achieved using dual rotors. Because of complex flow physics, the design of dual-rotor wind turbines (DRWTs) requires repetitive evaluations of computationally expensive partial differential equation (PDE) simulation models. Approaches for solving design optimization of DRWTs constrained by PDE simulations are investigated. The purpose of this study is to determine design optimization algorithms which can find optimal designs at a low computational cost. Design/methodology/approach Several optimization approaches and algorithms are compared and contrasted for the design of DRWTs. More specifically, parametric sweeps, direct optimization using pattern search, surrogate-based optimization (SBO) using approximation-based models and SBO using kriging interpolation models with infill criteria are investigated for the DRWT design problem. Findings The approaches are applied to two example design cases where the DRWT fluid flow is simulated using the Reynolds-averaged Navier−Stokes (RANS) equations with a two-equation turbulence model on an axisymmetric computational grid. The main rotor geometry is kept fixed and the secondary rotor characteristics, using up to three variables, are optimized. The results show that the automated numerical optimization techniques were able to accurately find the optimal designs at a low cost. In particular, SBO algorithm with infill criteria configured for design space exploitation required the least computational cost. The widely adopted parametric sweep approach required more model evaluations than the optimization algorithms, as well as not being able to accurately find the optimal designs. Originality/value For low-dimensional PDE-constrained design of DRWTs, automated optimization algorithms are essential to find accurately and efficiently the optimal designs. More specifically, surrogate-based approaches seem to offer a computationally efficient way of solving such problems.

Purpose The purpose of this paper is to reduce the overall computational time of aerodynamic shape optimization that involves accurate high-fidelity simulation models. Design/methodology/approach The proposed approach is based on the surrogate-based optimization paradigm. In particular, multi-fidelity surrogate models are used in the optimization process in place of the computationally expensive high-fidelity model. The multi-fidelity surrogate is constructed using physics-based low-fidelity models and a proper correction. This work introduces a novel correction methodology – referred to as the adaptive response prediction (ARP). The ARP technique corrects the low-fidelity model response, represented by the airfoil pressure distribution, through suitable horizontal and vertical adjustments. Findings Numerical investigations show the feasibility of solving real-world problems involving optimization of transonic airfoil shapes and accurate computational fluid dynamics simulation models of such surfaces. The results show that the proposed approach outperforms traditional surrogate-based approaches. Originality/value The proposed aerodynamic design optimization algorithm is novel and holistic. In particular, the ARP correction technique is original. The algorithm is useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces, which is challenging using conventional methods because of excessive computational costs.

Model-based sensitivity analysis is crucial in quantifying which input variability parameter is important for nondestructive testing (NDT) systems. In this work, neural networks (NN) and convolutional NN (CNN) are shown to be computationally efficient at making model prediction for NDT systems, when compared to models such as polynomial chaos expansions, Kriging and polynomial chaos Kriging (PC-Kriging). Three different ultrasonic benchmark cases are considered. NN outperform these three models for all the cases, while CNN outperformed these three models for two of the three cases. For the third case, it performed as well as PC-Kriging. NN required 48, 56 and 35 high-fidelity model evaluations, respectively, for the three cases to reach within \(1\%\) accuracy of the physics model. CNN required 35, 56 and 56 high-fidelity model evaluations, respectively, for the same three cases.

The phenomenon of dynamic stall produce adverse aerodynamic loading which can adversely affect the structural strength and life of aerodynamic systems. Aerodynamic shape optimization (ASO) provides an effective approach for delaying and mitigating dynamic stall characteristics without the addition of auxiliary system. ASO, however, requires multiple evaluations time-consuming computational fluid dynamics models. Metamodel-based optimization (MBO) provides an efficient approach to alleviate the computational burden. In this study, the MBO approach is utilized for the mitigation of dynamic stall characteristics while delaying dynamic stall angle of the flow past wind turbine airfoils. The regression Kriging metamodeling technique is used to approximate the objective and constrained functions. The airfoil shape design variables are described with six PARSEC parameters. A total of 60 initial samples are used to construct the metamodel, which is further refined with 20 infill points using expected improvement. The metamodel is validated with the normalized root mean square error based on 20 test data samples. The refined metamodel is used to search for the optimal design using a multi-start gradient-based method. The results show that an optimal design with a \(3^\circ \) delay in dynamic stall angle as well a reduction in the severity of pitching moment coefficients can be obtained.

The state of Iowa has long been recognized as a significant contributor of nitrogen loads to the Mississippi river basin. The nitrogen loads are mainly in the form of nitrates arising from high yield agriculture and animal agriculture. With excessive water flowing through the water system of Iowa, the surplus nitrogen in the soil gets carried into the Mississippi river basin and ultimately to the Gulf of Mexico, resulting in the generation of a hypoxic zone having a detrimental impact on the environment. Iowa is a leading producer of corn, soybean, animal products, and ethanol; hence, agriculture and animal agriculture are well rooted in its economy. With increasing ethanol demands, high yield agricultural practices, growing animal agriculture, and a connected economy, there is a need to understand the interdependencies of the Iowa food-energy-water (IFEW) nexus. In this work, a model of the IFEW system interdependencies is proposed and used as the basis for a computational system model, which can be used to guide decision-makers for improved policy formation to mitigate adverse impacts of the nitrogen export on the environment and economy. Global sensitivity analysis of the proposed IFEW system model reveals that the commercial nitrogen application rate for corn and corn yield are the critical parameters affecting nitrogen surplus in soil.

The dynamic stall phenomenon is characterized by the formation of a leading-edge vortex, which is responsible for adverse aerodynamic forces and moments adversely impacting the structural strength and life of a system. Aerodynamic shape optimization (ASO) provides a cost-effective approach to delay or mitigate the dynamic stall characteristics. Unfortunately, ASO requires multiple evaluations of accurate but time-consuming computational fluid dynamics (CFD) simulations to produce optimum designs rendering the optimization process computationally costly. The current work proposes a surrogate-based optimization (SBO) technique to alleviate the computational burden of ASO to delay and mitigate the deep dynamic stall characteristics of airfoils. In particular, the Kriging regression surrogate model is used for approximating the objective and constraint functions. The airfoil geometry is parametrized using six PARSEC parameters. The objective and constraint functions are evaluated with the unsteady Reynolds-averaged Navier-Stokes equations with a C-grid mesh topology and Menter's shear stress transport turbulence model. The approach is demonstrated on a vertical axis wind turbine airfoil at a Reynolds number of 135,000 and a Mach number of 0.1 undergoing a sinusoidal oscillation with a reduced frequency of 0.05. The surrogate model is constructed with 60 initial samples and further refined with 20 infill samples using expected improvement. The generated surrogate model is validated with the normalized root mean square error based on 20 test data samples. The refined surrogate model is utilized for finding the optimal design using multi-start gradient-based search. The optimal airfoil has a higher thickness, larger leading-edge radius, and an aft camber compared to the baseline. These geometric shape changes delay the dynamic stall angle by over 3 ∘ and reduces the severity of the pitching moment coefficient fluctuation. Finally, global sensitivity analysis is conducted on the optimal design using Sobol' indices revealing the most influential shape variables and their interaction effects impacting the airfoil dynamic stall characteristics.

Purpose Strategies for accelerated multi-objective optimization of aerodynamic surfaces are investigated, including the possibility of exploiting surrogate modeling techniques for computational fluid dynamic (CFD)-driven design speedup of such surfaces. The purpose of this paper is to reduce the overall optimization time. Design/methodology/approach An algorithmic framework is described that is composed of: a search space reduction, fast surrogate models constructed using variable-fidelity CFD models and co-Kriging, and Pareto front refinement. Numerical case studies are provided demonstrating the feasibility of solving real-world problems involving multi-objective optimization of transonic airfoil shapes and accurate CFD simulation models of such surfaces. Findings It is possible, through appropriate combination of surrogate modeling techniques and variable-fidelity models, to identify a set of alternative designs representing the best possible trade-offs between conflicting design objectives in a realistic time frame corresponding to a few dozen of high-fidelity CFD simulations of the respective surfaces. Originality/value The proposed aerodynamic design optimization algorithmic framework is novel and holistic. It proved useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search space, which is extremely challenging when using conventional methods due to the excessive computational cost.

In the paper, computationally efficient constrained multi-objective design optimization of transonic airfoil profiles is considered. Our methodology focuses on fixed-lift design aimed at finding the best possible trade-offs between the two objectives: minimization of the drag coefficient and maximization of the pitching moment. The algorithm presented here exploits the surrogate-based optimization principle, variable-fidelity computational fluid dynamics (CFD) models, as well as auxiliary data-driven surrogates (here, using Kriging). In order to permit computationally feasible construction of the Kriging models, initial design space reduction is also utilized. The design process has three major stages: (i) identification of the extreme points of the Pareto front through single-objective optimization (one objective at a time), (ii) construction of the Kriging model and initial Pareto front generation using multi-objective evolutionary algorithm (MOEA), and (iii) Pareto front refinement using response correction techniques and local response surface approximation (RSA) models. For the sake of computational efficiency, stages (i) and (ii) are realized at the level of coarse-discretization CFD model. The RSA models are also utilized to predict the angle of attack necessary to achieve the target lift coefficient, which considerably reduces the CFD simulation effort involved in the design process. Two design case studies are considered involving B-spline-parameterized airfoil shapes with 8 and 12 design variables. The 10-element Pareto front representations are obtained at the cost corresponding to just over two hundred of high-fidelity CFD model evaluations. This cost is not only considerably lower (up to two orders of magnitude) than the cost of direct high-fidelity model optimization using metaheuristics but, more importantly, renders multi-objective optimization of aerodynamic components computationally tractable even at the level of accurate CFD models.

Multifidelity methods are introduced to the nondestructive evaluation (NDE) of measurement systems. In particular, Cokriging interpolation metamodels of physics-based ultrasonic testing (UT) simulation responses are utilized to accelerate the uncertainty propagation in model-assisted NDE. The proposed approach is applied to a benchmark test case of UT simulations and compared with the current state-of-the-art techniques. The results show that Cokriging captures the physics of the problem well and is able to reduce the computational burden by over one order of magnitude compared to the state of the art. To the best of the author’s knowledge, this the first time multifidelity methods are applied to model-assisted NDE problems.

Supersonic vehicles are an important type of potential transports. Analysis of these vehicles requires the use of accurate models, which are also computationally expensive, to capture the highly nonlinear physics. This paper presents results of numerical investigations of using physics-based surrogate models to design supersonic airfoil shapes. Variable-fidelity models are generated using inviscid computational fluid dynamics simulations and analytical models. By using response correction techniques, in particular, the manifold mapping technique, fast surrogate models are constructed. The effectiveness of the approach is investigated using lift-constrained drag minimization problems of supersonic airfoil shapes. Compared with direct optimization, the results show that an order of magnitude speed up can be obtained. Furthermore, we investigate the effectiveness of the variable-fidelity technique in terms of speed and design quality using several combinations of medium-fidelity and low-fidelity models.

Trawl-doors are a large part of the fluid flow resistance of trawlers fishing gear and has considerable effect on the fuel consumption. A key factor in reducing that consumption is by implementing computational models in the design process. This study presents a robust two dimensional computational fluid dynamics models that is able to capture the nonlinear flow past multi-element hydrofoils. Efficient optimization algorithms are applied to the design of trawl-doors using problem formulation that captures true characteristics of the design space where lift-to-drag ratio is maximized. Four design variables are used in the optimization process to control the fluid flow angle of attack, as well as position and orientation of a leading-edge slat. The optimization process involves both multi-point space mapping, and mixed modeling techniques that utilize space mapping to create a physics-based surrogate model. The results demonstrate that lift-to-drag maximization is more appropriate than lift-constraint drag minimization in this case and that local search using multi-point space mapping can yield satisfactory design at low computational cost. By using global search with mixed modeling a solution with higher quality is obtained, but at a higher computational cost than local search.

Ultrasonic testing (UT) is used to detect internal flaws in materials or to characterize material properties. Computational simulations are an important part of the UT process. Fast models are essential for UT applications such as inverse design or model-assisted probability of detection. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to use data-driven surrogate modeling techniques (kriging interpolation), and physics-based surrogate modeling techniques (space mapping), as well a mixture of the two approaches. These techniques are investigated for two cases involving UT simulations of metal components immersed in a water bath during the inspection process.

Trawl-doors have a large influence on the fuel consumption of fishing vessels. Design and optimization of trawl-doors using computational models are a key factor in minimizing the fuel consumption. This paper presents an optimization algorithm for the shape design of trawl-door shapes using computational fluid dynamic (CFD) models. Accurate CFD models are computationally expensive. Therefore, the direct use of traditional optimization algorithms, which often require a large number of evaluations, may be prohibitive. The proposed approach is iterative and uses low-order local response surface approximation models of the expensive CFD model, constructed in each iteration, to reduce the number of evaluations. The algorithm is applied to the design of a multi-element trawl-doors, involving up to four design variables controlling the angle of attack and the slat and flap position and orientation. The results show that a satisfactory design can be obtained at the cost of a few iterations of the algorithm.

A brief review of some recent variable-fidelity aerodynamic shape optimization methods is presented. We discuss three techniques that—by exploiting information embedded in low-fidelity computational fluid dynamics (CFD) models—are able to yield a satisfactory design at a low computational cost, usually corresponding to a few evaluations of the original, high-fidelity CFD model to be optimized. The specific techniques considered here include multi-level design optimization, space mapping, and shape-preserving response prediction. All of them use the same prediction–correction scheme, however, they differ in the way the low-fidelity model information it utilized to construct the surrogate model. The presented techniques are illustrated using three specific cases of transonic airfoil design involving lift maximization and drag minimization.

Computer simulation models are ubiquitous in modern engineering design. In many cases, they are the only way to evaluate a given design with sufficient fidelity. Unfortunately, an added computational expense is associated with higher fidelity models. Moreover, the systems being considered are often highly nonlinear and may feature a large number of designable parameters. Therefore, it may be impractical to solve the design problem with conventional optimization algorithms. A promising approach to alleviate these difficulties is surrogate-based optimization (SBO). Among proven SBO techniques, the methods utilizing surrogates constructed from corrected physics-based low-fidelity models are, in many cases, the most efficient. This article reviews a particular technique of this type, namely, shape-preserving response prediction (SPRP), which works on the level of the model responses to correct the underlying low-fidelity models. The formulation and limitations of SPRP are discussed. Applications to several en...

A low-speed wind tunnel is developed for conducting research on the flow past micro air vehicles. The tunnel is of open suction type and is composed of a square inlet with a honeycomb and turbulence screens, settling chamber, contraction, experimental section housing, diffuser, and axial fan. In this paper, we describe the details of the design optimization procedure of the contraction, which is key to getting a high quality flow in the experimental section. A high-fidelity computational fluid dynamic (CFD) flow solver is used to capture the nonlinear flow physics. Due to the high computational expense of the CFD simulations, surrogate-based optimization (SBO) is used to accelerate the design process. The SBO approach replaces direct optimization of the high-fidelity (accurate but computationally expensive) model by iterative optimization of a properly corrected low-fidelity model. Here, we exploit variable–fidelity CFD simulations, as well as a simple multiplicative response correction technique to construct the surrogate model of the wind tunnel contraction, allowing us to optimize its shape at a low computational cost. To our knowledge, it is the first application of variable–fidelity surrogate modeling to wind tunnel contraction design. The optimum nozzle design is verified using a high-fidelity CFD simulation, as well as by experimental measurements of the fabricated wind tunnel. Experimental validation confirms the correctness of the numerical optimization procedures utilized to design the contraction.

The paper presents a computational framework for assessing quantitatively the detection capability of structural health monitoring (SHM) systems for flat plates. The detection capability is quantified using the probability of detection (POD) metric, developed within the area of nondestructive testing, which accounts for the variability of the uncertain system parameters and describes the detection accuracy using confidence bounds. SHM provides the capability of continuously monitoring the structural integrity using multiple sensors placed sensibly on the structure. It is important that the SHM can reliably and accurately detect damage when it occurs. The proposed computational framework models the structural behavior of flat plate using a spring-mass system with a lumped mass at each sensor location. The quantity of interest is the degree of damage of the plate, which is defined in this work as the difference in the strain field of a damaged plate with respect to the strain field of the healthy plate. The computational framework determines the POD based on the degree of damage of the plate for a given loading condition. The proposed approach is demonstrated on a numerical example of a flat plate with two sides fixed and a load acting normal to the surface. The POD is estimated for two uncertain parameters, the plate thickness and the modulus of elasticity of the material, and a damage located in one spot of the plate. The results show that the POD is close to zero for small loads, but increases quickly with increasing loads.

Probability of detection (POD) is used for reliability analysis in nondestructive testing (NDT) area. Traditionally, it is determined by experimental tests, while it can be enhanced by physics-based simulation models, which is called model-assisted probability of detection (MAPOD). However, accurate physics-based models are usually expensive in time. In this paper, we implement a type of stochastic polynomial chaos expansions (PCE), as alternative of actual physics-based model for the MAPOD calculation. State-of-the-art least-angle regression method and hyperbolic sparse technique are integrated within PCE construction. The proposed method is tested on a spherically-void-defect benchmark problem, developed by the World Federal Nondestructive Evaluation Center. The benchmark problem is added with two uncertainty parameters, where the PCE model usually requires about 100 sample points for the convergence on statistical moments, while direct Monte Carlo method needs more than 10000 samples, and Kriging based Monte Carlo method is oscillating. With about 100 sample points, PCE model can reduce root mean square error to be within 1% standard deviation of test points, while Kriging model cannot reach that level of accuracy even with 200 sample points.

A methodology for a rapid design optimization of integrated photonic couplers is presented. The proposed technique exploits variable-fidelity electromagnetic (EM) simulation models, additive response correction for accommodating the discrepancies between the EM models of various fidelities, and local response surface approximations for a fine tuning of the final design. A specific example of a 1,555 nm coupler is considered with an optimum design obtained at a computational cost corresponding to about 24 high-fidelity EM simulations of the structure.

Trawl-doors have a large influence on the fuel consumption of fishing vessels. Design and optimization of trawl-doors using computational models are key factors in minimizing the fuel consumption. This paper presents an efficient optimization algorithm for the design of trawl-door shapes using computational fluid dynamic models. The approach is iterative and uses variable-fidelity models and space mapping. The algorithm is applied to the design of a multi-element trawl-door, involving four design variables controlling the angle of attack and the slat position and orientation. The results demonstrate that a satisfactory design can be obtained at a cost of a few iterations of the algorithm. Compared with direct optimization of the high-fidelity model and local response surface surrogate models, the proposed approach requires 79% less computational time while, at the same time, improving the design significantly (over 12% increase in the lift-to-drag ratio).

This work introduces multifidelity metamodeling for reliability analysis of nondestructive testing (NDT) systems. Specifically, the Cokriging metamodel is utilized to accelerate the uncertainty propagation within model-assisted probability of detection (MAPOD) analysis of ultrasonic testing (UT) systems. The Cokriging multifidelity metamodel fuses a limited amount of data obtained from high-fidelity (HF) physics-based UT models, which are accurate but time-consuming to evaluate, with a conservative to large amount of data from low-fidelity (LF) physics-based UT models, which are less accurate but faster to evaluate. The resulting Cokriging metamodel is fast to evaluate and yields an accurate estimate of the output of the HF model. The proposed approach is demonstrated on three benchmark UT MAPOD cases involving spherically-void and pill-box shaped defects in flat aluminum plates using planar and focused transducers. The results show that a two-level Cokriging metamodel is capable of yielding estimations of the HF model that are globally accurate within 1% of the standard deviation of the testing points. Furthermore, the result show that the Cokriging metamodeling approach needs around one order of magnitude fewer training data points when compared to the current state-of-the-art approaches that rely on metamodels constructed with Kriging.

Variable-fidelity optimization (VFO) can be efficient in terms of the computational cost when compared with traditional approaches, such as gradient-based methods with adjoint sensitivity information. In variable-fidelity methods, the direct optimization of the expensive high-fidelity model is replaced by iterative re-optimization of a physics-based surrogate model, which is constructed from a corrected low-fidelity model. The success of VFO is dependent on the reliability and accuracy of the low-fidelity model. In this paper, we present a way to develop a fast and reliable low-fidelity model suitable for aerodynamic shape of transonic wings. The low-fidelity model is component based and accounts for the zero-lift drag, induced drag, and wave drag. The induced drag can be calculated by a proper method, such lifting line theory or a panel method. The zero-lift drag and the wave drag can be calculated by two-dimensional flow model and strip theory. Sweep effects are accounted for by simple sweep theory. The approach is illustrated by a numerical example where the induced drag is calculated by a vortex lattice method, and the zero-lift drag and wave drag are calculated by MSES (a viscous-inviscid method). The low-fidelity model is roughly 320 times faster than a high-fidelity computational fluid dynamics models which solves the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. The responses of the high-and low-fidelity models compare favorably and, most importantly, show the same trends with respect to changes in the operational conditions (Mach number, angle of attack) and the geometry (the airfoil shapes).

The idea of using distributed propulsion has been suggested with the objective of reducing aircraft noise. This paper investigates the effects of such a system on aircraft performance and weight. The distributed propulsion concept considered here involves replacing a small number of large engines with a moderate number of small engines and ducting part of the engine exhaust to exit out along the trailing edge of the wing. Models to describe the effects of this distributed propulsion concept were formulated and integrated into a multidisciplinary design optimization formulation. The most important effect modeled is the impact on the propulsive efficiency when there is blowing out of the trailing edge of a wing. An increase in propulsive efficiency is attainable with this arrangement as the trailing edge jet ‘fills in’ the wake behind the body, improving the overall aerodynamic/propulsion system, resulting in an increased propulsive efficiency. Other models formulated include the effect of the trailing edge jet on the induced drag, longitudinal control through thrust vectoring of the trailing edge jet, increased weight due to the ducts, and thrust losses within the ducts. The Blended-Wing-Body (BWB) aircraft was used as a testbed in this study. Two different BWB configurations were optimized, a conventional propulsion BWB with four pylon mounted engines and a distributed propulsion BWB with eight boundary layer ingestion inlet engines, for a mission of 7750 nm at Mach 0.85 carrying 478 passengers. The results show that the optimum BWB designs have comparable planform shapes and TOGW of approximately 860,000 lb, but have different weight distributions. The distributed propulsion BWB has a heavier propulsion system ( + 17.5 % ) and a lighter wing ( − 11.5 % ) than the conventional propulsion BWB. Although the distributed propulsion BWB has a 1.6% higher lift-to-drag ratio than the conventional propulsion BWB, the fuel weight is still 1.2% higher, mainly due to 3.8% higher specific fuel consumption associated with smaller turbofan engines. The results furthermore show that more than two-thirds of the possible savings due to filling in the wake will be required to obtain this optimum design. Achieving such high savings by filling in the wake will be challenging. However, by developing more efficient small turbofan engines and reducing the distributed propulsion system weight, the necessary savings by filling in the wake will be achieved.

This work introduces a variable-fidelity optimization methodology for simulation-driven design optimization of filters. Our approach is based on electromagnetic (EM) simulations of different accuracy controlled by the mesh density. A Kriging interpolation model (the surrogate) is created using sampled low-fidelity EM data and optimized to approximately locate the optimum of the high-fidelity EM model of the filter. This initial surrogate is subsequently improved by blending in the high-fidelity data accumulated during the optimization process using the co-Kriging technique. The algorithm convergence is ensured by embedding it into the trust region framework. The operation and performance of our method is demonstrated using three filter design cases. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:765–769, 2013; View this article online at wileyonlinelibrary.com. DOI: 10.1002/mop.27447

Computational fluid dynamic (CFD) models are ubiquitous in aerodynamic design. Variable-fidelity optimization algorithms have proven to be computationally efficient and therefore suitable to reduce high CPU-cost related to the design process solely based on accurate CFD models. A convenient way of constructing the variable-fidelity models is by using the high-fidelity solver, but with a varying degree of discretization and reduced number of flow solver iterations. So far, selection of the appropriate parameters has only been guided by the designer experience. In this paper, an automated low- fidelity model selection technique is presented. By defining the problem as a constrained nonlinear optimization problem, suitable grid and flow solver parameters are obtained. Our approach is compared to conventional methods of generating a family of variable-fidelity models. Comparison of the standard and the proposed approaches in the context of aerodynamic design of a transonic airfoil indicates that the automated model generation can yield significant computational savings.

A surrogate-based optimization algorithm for transonic airfoil design is presented. The approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity computational fluid dynamics model by an iterative reoptimization of a physics-based surrogate model. The surrogate model is constructed, during each design iteration, using the low-fidelity model and the data obtained from one high-fidelity model evaluation. The low-fidelity model is based on the same governing fluid flow equations as the high-fidelity one, but uses coarser mesh resolution and relaxed convergence criteria. The shape-preserving response prediction technique is utilized to predict the high-fidelity model response, here, the airfoil pressure distribution. In this prediction process, the shape-preserving response prediction employs the actual changes of the low-fidelity model response due to the design variable adjustments. The shape-preserving response prediction algorithm is embedded into the trust reg...

Modelling, simulation and optimization form an integrated part of modern design practice in engineering and industry. Tremendous progress has been observed for all three components over the last few decades. However, many challenging issues remain unresolved, and the current trends tend to use nature-inspired algorithms and surrogate-based techniques for modelling and optimization. This 4th workshop on Computational Optimization, Modelling and Simulation (COMS 2013) at ICCS 2013 will further summarize the latest developments of optimization and modelling and their applications in science, engineering and industry. In this review paper, we will analyse the recent trends in modelling and optimization, and their associated challenges. We will discuss important topics for further research, including parameter-tuning, large-scale problems, and the gaps between theory and applications.

In this paper, reduced-cost design optimization of dual-band antennas is investigated. The primary challenge here is the necessity of independent yet simultaneous handling of the antenna responses at two frequency bands. In order to alleviate this difficulty, a feature-based optimization approach is adopted where the design objectives are formulated in terms of the coordinates of suitably defined characteristic points (also referred to as response features) of the antenna reflection response. Owing to only slightly nonlinear dependence of the feature points on the structure geometry parameters, antenna optimization can be realized at low computational cost compared to conventional algorithms. Our approach is demonstrated using a dual-band patch antenna with the optimum design obtained in just a few dozen of EM simulations of the structure.

Reliable and robust computational fluid dynamics (CFD) solvers are nowadays commonly utilized in the design and analyses of various engineering systems, such as aircraft, turbomachinery, ships, and automotives. Although this has resulted in a drastic decrease of the number of prototype and experimental testing, the use of CFD in the design automation process is still limited. In practice, the geometry parameters that ensure satisfaction of assumed performance requirements are often obtained by repetitive CFD simulations guided by engineering experience. This is a tedious process which does not guarantee optimal results. On the other hand, straight forward automation attempts by employing the CFD solvers directly in the optimization loop are typically impractical, even when using adjoint sensitivity information, because high-fidelity CFD simulations tend to be computationally very expensive. In this paper, we describe a surrogate-based design optimization methodology that shifts the computational burden from the accurate and expensive high-fidelity CFD model to its fast and yet reasonably accurate surrogate. As the surrogate models are computationally much cheaper than the high-fidelity ones, the cost of the design process is greatly reduced. Here, the surrogates are constructed using low-fidelity CFD models and response correction techniques. Application examples, involving the design of axisymmetric hulls in subsonic flow, and airfoils in both subsonic and transonic flows, are presented.

Computer simulations are ubiquitous in contemporary engineering and science. In numerous fields, including mechanical engineering, civil engineering, electrical engineering, structural and aerospace engineering, automotive industry, oil industry, chemical engineering, ocean science and climate research to name just a few, simulation plays a critical role not only for verification purposes, but, more importantly in the design process itself. The complexity of structures and systems makes it analytically intractable, and it is thus extremely time-consuming and challenging to carry out any realistic design tasks, and in many cases, it is almost impossible to achieve any sensible design solutions under stringent constraints. These challenging tasks can be to optimally adjust the geometry and/or material parameters so that the system meets given performance requirements, or to calibrate the model parameters to make it fit given measurements, or to generate the optimal paths/routes for scheduling and planning tasks. In most cases, the interactions can be highly complex and multifold, and it is not easy or possible to isolate the processes of interest in the simplest, solvable form. For example, in the design of an electronic device, it is not just the isolated device to be designed that needs to be considered but also its – sometimes complex – interactions with the environment that affect the device’s performance. On the other hand, using accurate, realistic simulations allows the engineers to avoid costly prototyping and to realize the design closure with numerical models rather than through physical system measurements and prototype re-building. Furthermore, accurate simulations make it possible to analyze phenomena that could not be captured using simplistic theoretical models or too expensive or too time-consuming to be investigated through physical measurements. While high-fidelity numerical models can be very accurate, they tend to be computationally expensive. Simulation times of several hours, days, or weeks are not uncommon. In many cases, it may be a highly challenging task to just set up the model that takes into account all main, relevant system components and their interactions. One of the consequences is that a direct use of high-fidelity simulations in the optimization process may be prohibitive. The presence of massive computing resources is not always translated into computational speedup in practice, which is due to a growing demand for simulation

Computational optimization is becoming a standard tool that is widely used in engineering design and industrial applications. Products and services are often concerned with the maximization of profits and reduction of cost, but also aim at being more energy-efficient, environment-friendly and safety-ensured; at the same time they are limited by resources, time and money. Despite of increasing computer power and availability of better simulation packages, there are a number of challenges remaining when applying numerical optimization methods for real-world engineering problems. Also, new challenges emerge when attempting to attack problems whose solution by means of simulation-based optimization was not even possible in the past. This third workshop on Computational Optimization, Modelling and Simulation (COMS 2012) at ICCS 2012 will further summarize the latest developments of optimization and modelling and their applications in science, engineering and industry.

Multi fidelity optimization can be utilized for efficient design of airfoil shapes. In this paper, we investigate the scaling properties of algorithms exploiting this methodology. In particular, we study the relationship between the computational cost and the size of the design space. We focus on a specific optimization technique where, in order to reduce the design cost, the accurate high fidelity airfoil model is replaced by a cheap surrogate constructed from a low fidelity model and the shape preserving response prediction technique. In this study, we consider the design of transonic airfoils and use the compressible Euler equations in the high fidelity computational fluid dynamic (CFD) model. The low fidelity CFD model is same as the high fidelity one, but with coarser mesh resolution and reduced level of solver converge. The number of design variables varies from 3 to 11 by using NACA 4 digit airfoil shapes as well as airfoils constructed by Bezier curves. The results of the three optimization studies show that total cost increases from about 12 equivalent high fidelity model evaluations to 34. The number of high fidelity evaluations increases from 4 to 9, whereas the number of low fidelity evaluations increases more rapidly, from 600 to 2000. This indicates that, while the overall optimization cost scales more or less linearly with the dimensionality of the design space, further cost reduction can be obtained through more efficient optimization of the surrogate model.

A lowspeed wind tunnel is developed for fluid dynamics research at Reykjavik University. The tunnel is designed for conducting research on the flow past micro air vehicles, as well as fundamental research on turbulence. High flow quality is elemental for both research projects. The tunnel is of open suction type and is composed of a square inlet with a honeycomb and turbulence screens, settling chamber, contraction, experimental section housing, diffuser, and axial fan. Here, we describe the details of the design optimization procedure of the contraction, which is a key to getting a high quality flow in the experimental section. A high fidelity computational fluid dynamic (CFD) flow solver is used to capture the nonlinear flow physics. Due to the high computational cost of the CFD simulations, surrogate based optimization (SBO) is used to accelerate the design process. The SBO approach replaces direct optimization of the high fidelity (accurate but computationally expensive) model by iterative optimization of a properly corrected low fidelity model obtained from low fidelity CFD simulations. The optimum contraction design is verified using high fidelity CFD simulation, as well as by experimental measurements.

Operational optimization of ocean vessels, both off-line and in real-time, is becoming increasingly important due to rising fuel cost and added environmental constraints. Accurate and efficient simulation models are needed to achieve maximum energy efficiency. In this paper a grey-box modeling approach for the simulation of ocean vessels is presented. The modeling approach combines conventional analysis models based on physical principles (a white-box model) with a feed forward neural-network (a black-box model). Two different ways of combining these models are presented, in series and in parallel. The results of simulating several trips of a medium sized container vessel show that the grey-box modeling approach, both serial and parallel approaches, can improve the prediction of the vessel fuel consumption significantly compared to a white-box model. However, a prediction of the vessel speed is only improved slightly. Furthermore, the results give an indication of the potential advantages of grey-box models, which is extrapolation beyond a given training data set and the incorporation of physical phenomena which are not modeled in the white-box models. Finally, included is a discussion on how to enhance the predictability of the grey-box models as well as updating the neural-network in real-time.

Surrogate-based optimization (SBO) is the main focus of this book. We provide a brief introduction to the subject in this chapter. In particular, we recall the SBO concept and the optimization flow, discuss the principles of surrogate modeling and typical approaches to construct surrogate models. We also discuss the distinction between function approximation (or data-driven) surrogates and physics-based surrogates, as well as outline the algorithm of SBO exploiting the two aforementioned classes of models. More detailed information about the selected types of SBO algorithms (especially those involving response correction techniques) as well as illustration and application examples in various fields of engineering are provided in the remaining part of the book.

Majority of practical engineering design problems require simultaneous handling of several criteria. Although many of design tasks can be turned into single-objective problems using sufficient formulations, in some situations, acquiring comprehensive knowledge about possible trade-offs between conflicting objectives may be necessary. This calls for multi-objective optimization that aims at identifying a set of alternative, Pareto-optimal designs. The most popular solution approaches to genuine multi-objective optimization include population-based metaheuristics. Unfortunately, such methods are not practical for problems involving expensive computational models, particularly for antenna engineering, where reliable design requires CPU-intensive electromagnetic (EM) analysis. In this work, we discuss two methodologies for expedited multi-objective design optimization of a six-parameter dielectric resonator antenna (DRA) with respect to three design criteria. The considered solution approaches rely on surrogate-based optimization (SBO) paradigm, where the design speedup is obtained by shifting the optimization burden into a cheap replacement model referred to as a surrogate. The latter is utilized for generating the initial approximation of the Pareto front representation as well as further refinement of the initially obtained Pareto-optimal solutions.

Utilization of adjoint sensitivity techniques allows us to obtain both the response and its derivatives with respect to the geometry and/or material parameters of the structure of interest with a relatively small extra computational cost (El Sabbagh et al. 2006). In electromagnetic simulations, the process of obtaining the derivatives may not require additional simulations to the simulation for obtaining the figures of merit (El Sabbagh et al. 2006). In computational fluid dynamics (CFD), the cost of obtaining the gradients is almost equivalent to one additional flow solution (Jameson 1988). In both cases, the cost of obtaining the derivatives is independent of the number of design variables. Needless to say, the addition of adjoint sensitivities to simulation-based design and optimization has been transformative. In this chapter, we illustrate how surrogate-based modeling and optimization using response correction techniques can be enhanced with adjoint sensitivities. In particular, we start by discussing how to incorporate derivative data into the surrogate modeling and optimization process. Then, we provide the formulations for adjoint-enhanced versions of space mapping (Chap. 6), manifold mapping (Chap. 6), and shape-preserving response prediction (Chap. 7). For each technique, we provide example applications involving simulation-based design of several complex engineering systems including filters, and transonic airfoils.

The trade-offs between the aerodynamic performance and aerodynamic noise signature of two-dimensional airfoil shapes in low-speed, high-lift flow are investigated. The figures of interest are calculated using Reynolds-Averaged Navier-Stokes-based computational fluid dynamics (CFD) simulations. A computationally efficient procedure for obtaining the Pareto front of the figures of interest is presented. The proposed approach utilizes a multi-objective evolutionary algorithm (MOEA) that works with a fast surrogate model of the aerodynamic surface under design, obtained with kriging interpolation of low-fidelity CFD simulations. The surrogate is enhanced by means of space mapping response correction based on a limited number of high-fidelity CFD simulation training points allocated in the design space. The Pareto set generated by the multi-objective optimization of the surrogate using MOEA is iteratively refined by local enhancements of the surrogate model. The proposed method allows us to obtain—at a low computational cost—a set of airfoil geometries representing the trade-offs between the figures of interest. We illustrate the approach using an example of an airfoil at a Mach number of 0.208, lift coefficient of 1.5, and a Reynolds number of 0.665 million.

The size of microwave components has become an important design criterion for contemporary wireless communication engineering. Unfortunately, reduction of geometrical dimensions usually remain in conflict with electrical performance of the circuit, which makes it necessary to look for designs being a compromise between these two types of objectives. In this chapter, we discuss strategies for computationally-efficient multi-objective design optimization of miniaturized microwave structures. More specifically, we consider an optimization methodology based on point-by-point identification of a Pareto-optimal set of designs representing the best possible trade-offs between conflicting objectives, which include electrical performance parameters as well as the size of the structure of interest. Design speedup is achieved by performing most of the operations at the level of suitably corrected equivalent circuit model of the structure under design. Model correction is implemented using a space mapping technique involving, among others, frequency scaling. Operation and performance of our approach is demonstrated using a compact rat-race coupler designed with respect to the following objectives: bandwidth and the layout area. A representation of the Pareto set consisting of ten designs is obtained at the cost corresponding to less than thirty high-fidelity electromagnetic simulations of the structure.

Rising fuel prices and inefficient fishing gear are hampering the fishing industry. Any improvements of the equipment that lead to reduced operating costs of the fishing vessels are highly desirable. This chapter describes an efficient optimization algorithm for the design of trawl-door shapes using accurate high-fidelity computational fluid dynamic models. Usage of the algorithm is demonstrated on the re-design of typical trawl-doors at high- and low-angle of attack.

In this work, a simple yet reliable technique for fast multi-objective design optimization of miniaturized microwave structures is discussed. The proposed methodology is based on point-by-point identification of a Pareto-optimal set of designs representing the best possible trade-offs between conflicting objectives such as electrical performance parameters as well as the size of the structure of interest. For the sake of computational efficiency, most operations are performed on suitably corrected equivalent circuit model of the structure under design. Model correction is implemented using a space mapping technique involving, among others, frequency scaling. Our approach is demonstrated using a compact rat-race coupler. For this specific example, a set of ten designs representing a Pareto set for two objectives (electrical performance and the layout area) is identified at the cost corresponding to less than thirty high-fidelity EM simulations of the structure.

Computational fluid dynamics (CFD) simulations are a fundamental tool in aerodynamic design. Unfortunately, accurate, high-fidelity CFD models may be computationally too expensive to conduct the design using numerical optimization procedures. Recently, variable-fidelity optimization algorithms have attracted attention for their ability to reduce high CPU-cost related to the design process solely based on accurate CFD models. Low-fidelity simulation models are the most critical components of such algorithms. They normally employ the same CFD solver as the high-fidelity model but with reduced discretization density and reduced number of flow solver iterations. Typically, the selection of the appropriate model parameters has only been guided by the designer experience. In this chapter, an automated low-fidelity model selection technique is described. By defining the model setup task as a constrained nonlinear optimization problem, suitable grid and flow solver parameters are obtained. The approach is compared to two conventional methods of generating a family of variable-fidelity models. Comparison of the standard and the proposed approach is carried out in the context of aerodynamic design of transonic airfoils using a multi-level optimization algorithm. The results obtained for several test cases indicate that the automated model generation may lead to significant computational savings of the CFD-based airfoil design process. Illustration of the entire optimization cycle involving automated low-fidelity model preparation and B-spline-parameterized airfoil design using space mapping algorithm is also provided.

Design and optimization of trawl-doors are key factors in minimizing the fuel consumption of fishing vessels. This paper discusses optimization of the trawl-door shapes using high-fidelity 3D computational fluid dynamic (CFD) models. The accurate 3D CFD models are computationally expensive and, therefore, the direct use of traditional optimization algorithms, which often require a large number of evaluations, may be prohibitive. The design approach presented here is a variation of sequential approximate optimization exploiting low-order local response surface models of the expensive 3D CFD simulations. The algorithm is applied to the design of modern and airfoil-shaped trawl-doors.