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PurposeThe purpose of this work is to investigate the similarity requirements for the application of multifidelity modeling (MFM) for the prediction of airfoil dynamic stall using computational fluid dynamics (CFD) simulations.Design/methodology/approachDynamic stall is modeled using the unsteady Reynolds-averaged Navier–Stokes equations and Menter's shear stress transport turbulence model. Multifidelity models are created by varying the spatial and temporal discretizations. The effectiveness of the MFM method depends on the similarity between the high- (HF) and low-fidelity (LF) models. Their similarity is tested by computing the prediction error with respect to the HF model evaluations. The proposed approach is demonstrated on three airfoil shapes under deep dynamic stall at a Mach number 0.1 and Reynolds number 135,000.FindingsThe results show that varying the trust-region (TR) radius (λ) significantly affects the prediction accuracy of the MFM. The HF and LF simulation models hold similarity within small (λ ≤ 0.12) to medium (0.12 ≤ λ ≤ 0.23) TR radii producing a prediction error less than 5%, whereas for large TR radii (0.23 ≤ λ ≤ 0.41), the similarity is strongly affected by the time discretization and minimally by the spatial discretization.Originality/valueThe findings of this work present new knowledge for the construction of accurate MFMs for dynamic stall performance prediction using LF model spatial- and temporal discretization setup and the TR radius size. The approach used in this work is general and can be used for other unsteady applications involving CFD-based MFM and optimization.

In this paper, a computationally efficient multifidelity local search algorithm for aerodynamic design optimization is presented. In this paper’s approach, direct optimization of a computationally ...

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.

Exploration of design tradeoffs for aerodynamic surfaces requires solving of multi-objective optimization (MOO) problems. The major bottleneck here is the time-consuming evaluations of the computat...

In this paper, an additional filler wire with opposite polarity was inserted in tandem flux cored arc welding process to increase the welding speed and deposition rate. In this hybrid welding, the ...

Purpose The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration. Design/methodology/approach The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead. Findings The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm. Originality/value The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

Purpose Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models. Design/methodology/approach In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels. Findings To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent. Originality/value The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

Aerodynamic inverse design is proposed using multifidelity models and the manifold mapping (MM) technique. Aerodynamic inverse design aims at achieving a target performance characteristic, such as a pressure coefficient distribution of an airfoil or local lift distribution of a wing. Due to the high computational cost of accurate aerodynamic models and the large number of design variables, the overall cost of inverse design can be prohibitive. The MM-based optimization algorithm leverages the speed of the low-fidelity model to accelerate the optimization process, but refers back to the high-fidelity model to ensure an accurate solution. In this work, the MM technique is applied to the characteristic distribution under consideration in each application. In particular, the pressure coefficient distribution is modeled with the MM technique in the case of airfoil inverse design, and the sectional lift distribution in the case of wing design. The proposed method is tested and evaluated on six airfoil inverse design cases and one rectangular wing inverse design case. In the two-dimensional cases, parameterized with eight design variables, direct aerodynamic inverse design using pattern search required 700 to 1200 high-fidelity model evaluations, which took 300 to 700 hours in total. The MM-based design algorithm required less than 20 high-fidelity simulations and 1000 to 2000 low-fidelity evaluations, which took 30 to 90 hours. In the three-dimensional case, parameterized with three design variables, direct aerodynamic inverse design took around 50 hours, whereas the MM-based design needed around six hours.

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.

This work proposes the use of model-based sensitivity analysis to determine important internal factors that affect the cost of a large-scale complex engineered systems (LSCES), such as geo-stationary communication satellites. A physics-based satellite simulation model and a parametric cost model are combined to model a real-world satellite program whose data is extracted from selected acquisitions reports. A variance-based global sensitivity analysis using Sobol’ indices computationally aids in establishing internal factors. The internal factors in this work are associated with requirements of the program, operations and support, launch, ground equipment, personnel required to support and maintain the program. The results show that internal factors such as the system based requirements affect the cost of the program significantly. These important internal factors will be utilized to create a simulation-based framework that will aid in the design and development of future LSCES.

Numerical optimization procedures have been widely used in the design of microwave components and systems. Most often, optimization algorithms are applied at the later stages of the design process to tune the geometry and/or material parameter values. To ensure sufficient accuracy, parameter adjustment is realized at the level of full-wave electromagnetic (EM) analysis, which creates perhaps the most important bottleneck due to the entailed computational expenses. The cost issue hinders utilization of global search procedures, whereas local routines often fail when the initial design is of insufficient quality, especially in terms of the relationships between the current and the target operating frequencies. This paper proposes a procedure for automated adaptation of the performance requirements, which aims at improving the reliability of the parameter tuning process in the challenging situations as described above. The procedure temporarily relaxes the requirements to ensure that the existing solution can be improved, and gradually tightens them when close to terminating the optimization process. The amount and the timing of specification adjustment is governed by evaluating the design quality at the current design, and the convergence status of the algorithm. The proposed framework is validated using two examples of microstrip components (a coupler and a power divider), and shown to well handle design scenarios that turn infeasible for conventional approaches, in particular, when decent starting points are unavailable.

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).

This paper demonstrates the use of the polynomial chaos-based Cokriging (PC-Cokriging) on various simulation-based problems, namely an analytical borehole function, an ultrasonic testing (UT) case and a robust design optimization of an airfoil case. This metamodel is compared to Kriging, polynomial chaos expansion (PCE), polynomial chaos-based Kriging (PC-Kriging) and Cokriging. The PC-Cokriging model is a multi-variate variant of PC-Kriging and its construction is similar to Cokriging. For the borehole function, the PC-Cokriging requires only three high-fidelity samples to accurately capture the global accuracy of the function. For the UT case, it requires 20 points. Sensitivity analysis is performed for the UT case showing that the F-number has negligible effect on the output response. For the robust design case, a 75 and 31 drag count reduction is reported on the mean and standard deviation of the drag coefficient, respectively, when compared to the baseline shape.

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.

The state of Iowa is known for its high-yield agriculture, supporting rising demands for food and fuel production. But this productivity is also a significant contributor of nitrogen loading to the Mississippi River basin causing the hypoxic zone in the Gulf of Mexico. The delivery of nutrients, especially nitrogen, from the upper Mississippi River basin, is a function, not only of agricultural activity, but also of hydrology. Thus, it is important to consider extreme weather conditions, such as drought and flooding, and understand the effects of weather variability on Iowa’s food-energy-water (IFEW) system and nitrogen loading to the Mississippi River from Iowa. In this work, the simulation decomposition approach is implemented using the extended IFEW model with a crop-weather model to better understand the cause-and-effect relationships of weather parameters on the nitrogen export from the state of Iowa. July temperature and precipitation are used as varying input weather parameters with normal and log normal distributions, respectively, and subdivided to generate regular and dry weather conditions. It is observed that most variation in the soil nitrogen surplus lies in the regular condition, while the dry condition produces the highest soil nitrogen surplus for the state of Iowa.

Purpose This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level. Design/methodology/approach Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate. Findings Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day. Originality/value The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

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.

Model-assisted probability of detection (MAPOD) and sensitivity analysis (SA) are important for quantifying the inspection capability of nondestructive testing (NDT) systems. To improve the computational efficiency, this work proposes the use of polynomial chaos expansions (PCEs), integrated with least-angle regression (LARS), a basis-adaptive technique, and a hyperbolic truncation scheme, in lieu of the direct use of the physics-based measurement model in the MAPOD and SA calculations. The proposed method is demonstrated on three ultrasonic testing cases and compared with Monte Carlo sampling (MCS) of the physics model, MCS-based kriging, and the ordinary least-squares (OLS)-based PCE method. The results show that the probability of detection (POD) metrics of interests can be controlled within 1% accuracy relative to using the physics model directly. Comparison with metamodels shows that the LARS-based PCE method can provide up to an order of magnitude improvement in the computational efficiency.

The PC-Kriging metamodeling method is proposed for yield estimation of multi-band patch antennas. PC-Kriging is a combination of polynomial chaos expansion (PCE) and Kriging metamodeling, where PCE is used as a trend function for the Kriging interpolation metamodel. The method is demonstrated on the Ishigami analytical function and a dual-band patch antenna. The PC-Kriging is shown to reach the prescribed accuracy limit with significantly fewer training points than both PCE and Kriging. This translates into considerable computational savings of yield estimation over alternative metamodel-based procedures and direct EM-driven Monte Carlo simulation. The saving are obtained without compromising evaluation reliability.

Recent advances in sensing are empowering the deployment of inexpensive dense sensor networks (DSNs) to conduct structural health monitoring (SHM) on large-scale structural and mechanical systems. There is a need to develop methodologies to facilitate the validation of these DSNs. Such methodologies could yield better designs of DSNs, enabling faster and more accurate monitoring of states for enhancing SHM. This paper investigates a model-assisted approach to validate a DSN of strain gauges under uncertainty. First, an approximate physical representation of the system, termed the physics-driven surrogate, is created based on the sensor network configuration. The representation consists of a state-space model, coupled with an adaptive mechanism based on sliding mode theory, to update the stiffness matrix to best match the measured responses, assuming knowledge of the mass matrix and damping parameters. Second, the physics-driven surrogate model is used to conduct a series of numerical simulations to map damages of interest to relevant features extracted from the synthetic signals that integrate uncertainties propagating through the physical representation. The capacity of the algorithm at detecting and localizing damages is quantified through probability of detection (POD) maps. It follows that such POD maps provide a direct quantification of the DSNs’ capability at conducting its SHM task. The proposed approach is demonstrated using numerical simulations on a cantilevered plate elastically restrained at the root equipped with strain gauges, where the damage of interest is a change in the root’s bending rigidity.

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.

Fast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated for the design of airfoil shapes under uncertainty. The proposed approach is illustrated on a numerical example of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable. The results show that compared with the standard problem formulation the proposed approach yields more robust designs. In other words, the designs obtained by the proposed approach are less sensitive to variations in the uncertain variables than those obtained with the standard problem formulation.

In this paper, we discuss a computationally efficient approach to expedite design optimization of broadband hybrid couplers occupying a minimized substrate area. Structure size reduction is achieved here by decomposing an original coupler circuit into low- and high-impedance components and replacing them with electrically equivalent slow-wave lines with reduced physical dimensions. The main challenge is reliable design of computationally demanding low-impedance slow-wave structures that feature a quasi-periodic circuit topology for wideband operation. Our goal is to determine an adequate number of recurrent unit elements as well as to adjust their designable parameters so that the coupler footprint area is minimal. The proposed method involves using surrogate-based optimization with a reconfigurable co-simulation coarse model as the key component enabling design process acceleration. The latter model is composed in Keysight ADS circuit simulator from multiple EM-evaluated data blocks of the slow-wave unit element and theory-based feeding line models. The embedded optimization algorithm is a trust-region-based gradient search with coarse model Jacobian estimation. We exploit a penalty function approach to ensure that the electrical conditions for the slow-wave lines are accordingly satisfied, apart from explicitly minimizing the area of the coupler. The effectiveness of the proposed technique is demonstrated through a design example of two-section 3-dB branch-line coupler. For the given example, we obtain nine circuit design solutions that correspond to the compact couplers whose multi-element slow-wave lines are composed of unit cells ranging from two to ten.

A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.

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.

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flo...

Yield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since the Monte Carlo sampling-based real physics simulation model evaluations are computationally intensive, this work proposes the polynomial chaos-Kriging (PC-Kriging) metamodeling technique for fast yield estimation. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel since the PCE is good at capturing the function tendency and Kriging is good at matching the observations at training points. The PC-Kriging is demonstrated with an analytical case and a multi-band patch antenna case and compared with direct PCE and Kriging metamodels. In the analytical case, PC-Kriging reduces the computational cost by around 42% compared with PCE and over 94% compared with Kriging. In the antenna case, PC-Kriging reduces the computational cost by over 60% compared with Kriging and over 90% compared with PCE. In both cases, the savings are obtained without compromising the accuracy.

Electromagnetic (EM) analysis is the primary tool utilized in the design of high-frequency structures. In vast majority of cases, simpler models (e.g., equivalent networks or analytical ones) are either not available or lack accuracy: they can only be used to yield initial designs that need to be further tuned. Consequently, EM-driven adjustment of geometry and/or material parameters of microwave and antenna components is a necessary design stage. This, however, is a computationally expensive process, not only because of a considerable computational cost of high-fidelity EM analysis but also due to a typically large number of parameters that need to be adjusted. In particular, conventional numerical optimization routines (both local and global) may be prohibitively expensive. In this paper, a reduced-cost trust-region-based gradient search algorithm is proposed for the optimization of high-frequency components. Our methodology is based on a smart management of the system Jacobian enhancement which combines: (i) omission of (finite-differentiation-based) sensitivity updates for variables that exhibit small (relative) relocation in the directions of the corresponding coordinate system axes and (ii) selective utilization of a rank-one Broyden updating formula. Parameter selection for Broyden-based updating depends on the alignment between the direction of the latest design relocation and respective search space basis vectors. The proposed technique is demonstrated using a miniaturized coupler and an ultra-wideband antenna. In both cases, significant reduction of the number of EM simulations involved in the optimization process is achieved as compared to the benchmark algorithm (computational speedup of 60% on average). At the same time, degradation of the design quality is minor.

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.

Condition assessment of civil infrastructures is difficult due to technical and economic constraints associated with the scaling of sensing solutions. When scaled appropriately, a large sensor network will collect a vast amount of rich data that is difficult to directly link to the existing condition of the structure along with its remaining useful life. This paper presents a methodology to construct a surrogate model enabling diagnostic of structural components equipped with a dense sensor network collecting strain data. The surrogate model, developed as a matrix of discrete stiffness elements, is used to fuse spatial strain data into useful model parameters. Here, strain data is collected from a sensor network that consists of a novel sensing skin fabricated from large area electronics. The surrogate model is constructed by updating the stiffness matrix to minimize the difference between the model’s response and measured data, yielding a 2D map of stiffness reduction parameters. The proposed method is numerically validated on a plate equipped with 40 large area strain sensors. Results demonstrate the suitability of the proposed surrogate model for the condition assessment of structures using a dense sensor network.