Shape-preserving Response Prediction Research Articles

Numerical Investigation of Configurations with Optimum Swirl Recovery for Propeller Propulsion Systems

This paper addresses the design of swirl recovery vanes for propeller propulsion in tractor configuration at cruise conditions using numerical tools. A multifidelity optimization framework is formulated for the design purpose, which exploits low-fidelity potential flow-based analysis results as input for high-fidelity Euler equation-based simulations. Furthermore, a model alignment procedure between low- and high-fidelity models is established based on a shape-preserving response prediction algorithm. Two cases of swirl recovery are examined. The first is the swirl recovery by the trailing wing, which leads to a reduction of the lift-induced drag. This is achieved by the optimization of the wing twist distribution. The second case is swirl recovery by a set of stationary vanes, which leads to production of additional thrust. In the latter case, four configurations are evaluated by locating the vanes at different azimuthal and axial positions relative to the wing. An optimum configuration is identified where the vanes are positioned on the blade-downgoing side downstream of the wing. For the configuration and conditions examined, the wing twist optimization reduces the induced drag by 3.9 counts (5.9% of wing-induced drag), whereas the optimized 4-bladed SRVs lead to an induced-drag reduction of 6.1 counts (9.2% of wing-induced drag).

Feature‐based surrogates for low‐cost microwave modelling and optimisation

A simple, reliable, and accurate surrogate modelling technique for microwave structures is presented. A hierarchical surrogate model is constructed using response surface approximations (RSAs) of suitable response features with embedded ‘visible’ knowledge. The authors describe and discuss a novel scanning algorithm for capturing these desired response features. They demonstrate that the dependence of the selected features on the designable parameters is much less non-linear than that of the original responses taken as functions of the design parameters. They illustrate the steps of their algorithm using novel diagrams. They simplify the description of their modelling process by exploiting an operator notation. They discuss relationships between their method and other feature-based approaches such as shape-preserving response prediction (SPRP). They provide a wideband microstrip bandstop filter, a fourth-order ring resonator bandpass filter and a microstrip bandpass filter with open stub inverter examples to demonstrate their approach. Using these examples, they compare their approach with two very different direct RSA methods (kriging and radial basis function) and an SPRP method. The models of all the filter examples are validated using design optimisation.

Surrogate modelling and optimization using shape-preserving response prediction: A review

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 engineering design problems are provided.

Aerodynamic shape optimization by variable-fidelity computational fluid dynamics models: A review of recent progress

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.

Variable-resolution shape optimisation: low-fidelity model selection and scalability

Computationally-efficient aerodynamic shape optimisation can be realised using surrogate-based methods. By shifting the optimisation burden to a cheap and yet reasonably accurate surrogate model, the design cost can be substantially reduced, particularly if the surrogate exploits an underlying physics-based low-fidelity model (e.g., the one obtained by coarse-discretisation computational fluid dynamics (CFD) simulation). The knowledge about the physical system of interest contained in the low-fidelity model allows us to construct an accurate representation of the original, high-fidelity CFD model, using a small amount of high-fidelity data and dramatically reduce the overall design cost. Two fundamental issues in such a process are a proper selection of the quality of the low-fidelity model (e.g., the model 'mesh coarseness' that may affect both the optimisation cost and the reliability of the design process), as well as the scaling properties of the surrogate-based design process with respect to the dimensionality of the design space. Our investigations are carried out for specific variable-resolution optimisation methodologies exploiting two types of correction methods: shape-preserving response prediction and space mapping.

Inverse airfoil design using variable-resolution models and shape-preserving response prediction

The paper presents a computationally efficient surrogate-based optimization algorithm for the inverse design of transonic airfoils. Our approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity airfoil model by an iterative re-optimization of two different surrogate models. Initially, for a few design iterations, a corrected physics-based low-fidelity model is employed, which is subsequently replaced by a response surface approximation model. 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 (SPRP) technique is utilized to predict the high-fidelity model response, here, the airfoil pressure distribution. In this prediction process, SPRP employs the actual changes of the low-fidelity model response (or the surface approximation model) due to the design variable adjustments. The SPRP algorithm is embedded into the trust region framework to ensure good convergence properties of the optimization procedure. Our algorithm is applied to constrained inverse airfoil design in inviscid transonic flow. A comparison with the basic version of the optimization algorithm, exploiting only a physics-based low-fidelity model, is carried out. While the performance of both versions is similar with respect to their ability to match the target pressure distribution, the improved algorithm offers substantial design cost savings, from 25 to 72 percent, depending on the test case.

Rapid electromagnetic‐based microwave design optimisation exploiting shape‐preserving response prediction and adjoint sensitivities

A new development of the shape-preserving response prediction (SPRP) technique for microwave design optimisation is presented here. The original SPRP method is enhanced by employing low-cost derivative information obtained through adjoint sensitivities. The authors propose using operator notation to simplify the SPRP surrogate description. The enhancement through sensitivity data is twofold: to ensure first-order consistency between the SPRP surrogate and the high-fidelity electromagnetic (EM) model under optimisation and to speed up the surrogate optimisation process. Fast surrogate optimisation allows us to use coarse-discretisation EM simulations as an underlying low-fidelity model and, therefore, efficiently apply SPRP to cases where reliable circuit models are not available (e.g. design of antenna structures). The proposed approach is demonstrated using a dielectric resonator filter and an ultra-wideband monopole antenna. Comparison with three benchmark techniques, including the original SPRP methods, space mapping with sensitivity and direct optimisation of the high-fidelity model, is also provided.

Fast EM Modeling Exploiting Shape-Preserving Response Prediction and Space Mapping

We present a low-cost modeling methodology for microwave structures exploiting low/high-fidelity electromagnetic (EM) simulations, shape-preserving response prediction (SPRP)/generalized shape-preserving response prediction (GSPRP), and space mapping (SM). Our approach is a two-step process. In step 1, a coarse model is constructed from low-fidelity (coarse discretization) EM simulation data by means of a recently developed SPRP/GSPRP technique. A comparison between the SPRP and GSPRP methods is described. In step 2, the coarse model is enhanced by SM using a fine model (high-fidelity EM simulations). We summarize the substeps in each step of the proposed algorithm and illustrate them graphically. We compare our proposed method with relevant benchmark techniques. Our approach is demonstrated by using two microstrip filter examples. The results and efficiency of our approach are compared with the benchmark techniques, indicating substantial accuracy improvement for comparable training set size. Applications for design optimization are also discussed.

Shape-Preserving Response Prediction for Engineering Design Optimization

Contemporary engineering design relies heavily on computer simulations. The structures and systems considered in many engineering disciplines are far too complex to be described accurately using simple theoretical models; using simulations is often the only way to adequately assess the performance of the design. Unfortunately, high-fidelity simulations are computationally expensive so that their use in an automated design process based on conventional optimization algorithms is often prohibitive. Despite the availability of faster computers and more efficient simulation software: growing demand for improved accuracy and the need to evaluate larger and larger systems effectively diminishes the benefits of this increase in computing power. One of the most promising ways of alleviating these problems are surrogate-based optimization (SBO) techniques which are capable of reducing the number of expensive objective function evaluations in a simulation-driven design process. In SBO, the direct optimization of the expensive model is replaced by iterative updating and re-optimization of its cheap surrogate model. Among proven SBO techniques, the methods exploiting physics-based low-fidelity models are probably the most efficient. This is because the knowledge about the system of interest embedded in the low-fidelity model allows constructing the surrogate model that has good generalization capability at a cost of just a few evaluations of the original model. In this paper, we review one of the most recent techniques of this kind, the so-called shape-preserving response prediction (SPRP). We discuss the formulation of SPRP, its limitations and generalizations, and, most importantly, demonstrate its applications to solve design problems in various engineering areas, including microwave engineering, antenna design, and aerodynamic shape optimization.

Physics-based Surrogates for Low-cost Modeling of Microwave Structures

High-fidelity electromagnetic (EM) simulation is a very accurate but computationally expensive way of evaluating the performance of microwave structures. In many situations, it has to be done multiple times when conducting various design tasks, such as parametric optimization or statistical analysis. Fast and accurate models, so-called surrogates, are therefore indispensable in contemporary microwave engineering. The most popular way of creating such models is by approximation of sampled EM-simulation data using, for example, low-order polynomials, support vector regression or neural networks. Unfortunately, initial cost of creating such models may be extremely high because of a large number of samples necessary to ensure reasonable accuracy. An alternative approach is to use physics-based models, where the surrogate is created by correcting an auxiliary low-fidelity model, e.g., equivalent circuit. In this paper, we review several modeling techniques exploiting this idea, including some variations of space mapping as well as shape-preserving response prediction. Our considerations are illustrated using examples of typical microwave components such as filters and antennas.

Surrogate-Based Aerodynamic Shape Optimization by Variable-Resolution Models

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 region framework that ensures good convergence properties of the optimization procedure. This method is applied to constrained airfoil lift maximization and drag minimization in two-dimensional inviscid transonic flow. The optimized designs are obtained at lower computational cost than that of two comparators. The robustness and scaling properties of the proposed algorithm are investigated.

Rapid antenna design optimization using shape-preserving response prediction

Rapid antenna design optimization using shape-preserving response prediction An approach to rapid optimization of antennas using the shape-preserving response-prediction (SPRP) technique and coarse-discretization electromagnetic (EM) simulations (as a low-fidelity model) is presented. SPRP allows us to estimate the response of the high-fidelity EM antenna model, e.g., its reflection coefficient versus frequency, using the properly selected set of so-called characteristic points of the low-fidelity model response. The low-fidelity model, corrected by means of SPRP, is subsequently used to predict the optimal design. The design process is cost efficient because most operations are performed on the low-fidelity model. Performance of our technique is demonstrated using a dielectric resonator antenna and two planar wideband antenna examples. In all cases, the optimal design is obtained at a cost corresponding to a few high-fidelity simulations of the antenna under design.

Knowledge-Based Response Correction and Adaptive Design Specifications for Microwave Design Optimization

Simulation-based optimization has become an important design tool in microwave engineering. Yet, employing electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high-computational cost of an accurate EM simulation. This paper is focused on efficient EM-driven design optimization techniques that utilize physically-based low-fidelity models, normally based on coarse-discretization EM simulations. The presented methods attempt to exploit as much of the knowledge about the system or device of interest embedded in the low-fidelity model as possible, so as to reduce the computational cost of the design process. Unlike many other surrogate-based approaches, the techniques discussed here are non-parametric ones, i.e., they are not based on analytical formulas. The paper presents several specific methods, including those based on correcting the low-fidelity model response (adaptive response correction and shape-preserving response prediction), as well as on suitable modification of the design specifications. Formulations, application examples and the discussion of advantages and disadvantages of these techniques are also included.

Derivative-free microwave design optimisation using shape-preserving response prediction and space mapping

A two-level derivative-free algorithm for electromagnetic-simulation-driven design optimisation is introduced. The technique exploits a fast surrogate model that is created using a modified version of a shape-preserving response prediction (SPRP) methodology and a limited amount of coarse-discretisation electromagnetic (EM) simulation data. The surrogate is subsequently utilised by the space mapping algorithm to find a design satisfying given performance specifications. As demonstrated using two examples of microstrip filters and a planar antenna, the design cost is low and corresponds to a few high-fidelity EM simulations of the optimised structure and it is 30–50% lower than that for the original SPRP technique exploiting coarse-discretisation EM models.

Scaling Properties of Multi-Fidelity Shape Optimization Algorithms

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 Bézier 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.

Generalised shape-preserving response prediction for accurate modelling of microwave structures

A generalised shape-preserving response prediction (generalised SPRP or GSPRP) methodology for low-cost and accurate modelling of microwave structures is discussed. The GSPRP method predicts the response of a high-fidelity electromagnetic-simulated model (e.g. S-parameters against frequency) using sets of characteristic points and translation vectors obtained from underlying low-fidelity model responses. Unlike the original SPRP technique, which uses a limited number of training points at restricted locations, GSPSP can utilise an arbitrary number of training points, which are handled through Kriging interpolation applied to model a set of characteristic points corresponding to the entire training set. This increases the flexibility of SPRP and allows us to improve the modelling accuracy if more training points are available. At the same time, the GSPRP inherits the main advantage of SPRP: good prediction accuracy without using a large amount of data, which is in contrast to conventional approximation techniques. This is ensured as the locations of the characteristic points are easy to model. The proposed technique is demonstrated through a comprehensive numerical study as well as comparison with other modelling techniques. Application examples are also given.

Response correction techniques for surrogate-based design optimization of microwave structures

Simulation-based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high-computational cost of an accurate EM simulation. In this article, we present a review of EM-based design optimization techniques exploiting response-corrected physically based low-fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high-fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape-preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012. © 2012 Wiley Periodicals, Inc.

Accurate low-cost microwave component models using shape-preserving response prediction

A technique for accurate modeling of microwave components is presented. Our methodology exploits a recently introduced shape-preserving response prediction (SPRP) technology, which is adopted here to work directly with electromagnetic simulation data of the device under consideration. Unlike in original SPRP, no low-fidelity model is used, which simplifies implementation and makes our method applicable for a variety of microwave structures. SPRP allows us to create models at a low computational cost of a few electromagnetic simulations, which is convenient when solving various design tasks such as parametric optimization. As demonstrated using several test structures including microstrip filters and a planar antenna, the modeling accuracy is competitive to standard approximation techniques. Application examples for design optimization and statistical analysis are also provided. Copyright © 2011 John Wiley & Sons, Ltd.

Accurate modelling of microwave structures using shape-preserving response prediction

An improved technique for accurate modelling of microwave structures is presented. It is a modification of a recently introduced approach exploiting shape-preserving response prediction (SPRP) procedure that estimated the response of the CPU-intensive EM-simulated microwave structure using an auxiliary and computationally cheap model of the structure and a single reference design. Here, the response is estimated using multiple reference designs, which allows better utilisation of available training data. It is demonstrated that the proposed approach offers excellent modelling accuracy, which is not only better than the accuracy provided by space mapping but also better than the accuracy of the original modelling using SPRP. The authors approach is particularly suitable to build low-cost models useful to perform design tasks such as parametric optimisation and statistical analysis.

Fast microwave design optimisation using shape-preserving response prediction and coarse-discretisation EM models

An efficient technique for fast design optimisation of microwave structures is discussed. The approach is based on the recently introduced shape-preserving response prediction method (SPRP). SPRP allows us to estimate the response of the computationally expensive structure under consideration using the properly selected set of characteristic points of the physically based coarse model response. Here, the coarse model is implemented in the same electromagnetic solver as the one that evaluated the original structure, but coarse discretisation is used. It is demonstrated that the presented technique yields a satisfactory design after two or three evaluations of the original structure. The efficiency of this approach is illustrated through the design optimisation of a double annular ring antenna and two microstrip filters. Comparison with the direct EM-simulation-based optimisation of the fine model is also given.