Leifur Leifsson

Surrogate-Based Methods

Objective functions that appear in engineering practice may come from measurements of physical systems and, more often, from computer simulations. In many cases, optimization of such objectives in a straightforward way, i.e., by applying optimization routines directly to these functions, is impractical. One reason is that simulation-based objective functions are often analytically intractable (discontinuous, non-differentiable, and inherently noisy). Also, sensitivity information is usually unavailable, or too expensive to compute. Another, and in many cases even more important, reason is the high computational cost of measurement/simulations. Simulation times of several hours, days or even weeks per objective function evaluation are not uncommon in contemporary engineering, despite the increase of available computing power. Feasible handling of these unmanageable functions can be accomplished using surrogate models: the optimization of the original objective is replaced by iterative re-optimization and updating of the analytically tractable and computationally cheap surrogate. This chapter briefly describes the basics of surrogate-based optimization, various ways of creating surrogate models, as well as several examples of surrogate-based optimization techniques.

Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction

Abstract A computationally efficient design methodology for transonic airfoil optimization has been developed. In the optimization process, a numerically cheap physics-based low-fidelity surrogate (the transonic small-disturbance equation) is used in lieu of an accurate, but computationally expensive, high-fidelity (the compressible Euler equations) simulation model. Correction of the low-fidelity model is achieved by aligning its corresponding airfoil surface pressure distribution with that of the high-fidelity model using a shape-preserving response prediction technique. The resulting method requires only a single high-fidelity simulation per iteration of the design process. The method is applied to airfoil lift maximization in two-dimensional inviscid transonic flow, subject to constraints on shock-induced pressure drag and airfoil cross-sectional area. The results showed that more than a 90% reduction in high-fidelity function calls was achieved when compared to direct high-fidelity model optimization using a pattern-search algorithm.

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 reg...

Knowledge-Based Airfoil Shape Optimization Using Space Mapping

A computationally efficient optimization methodology for transonic airfoil design is presented. A direct optimization of the expensive high-fidelity computational fluid dynamics (CFD) airfoil model is replaced by an iterative updating and re-optimization of a cheap surrogate model. The surrogate is constructed using the low-fidelity model which is based on the same governing fluid flow equations as the high-fidelity model, but uses coarser mesh resolution and relaxed convergence criteria. The low-fidelity model undergoes suitable corrections to become a reliable representation of the high-fidelity one so that it can be subsequently used to find an approximate optimum design of the latter. The corrections are implemented using space mapping. To our knowledge, it is one of the first applications of space mapping to aerodynamic shape optimization. Our method is applied to constrained airfoil lift maximization and drag minimization in two-dimensional inviscid transonic flow. The optimized designs are obtained at substantially lower computational cost when compared to the direct high-fidelity model optimization.

Simulation-Driven Aerodynamic Design Using Variable-Fidelity Models

Computer simulations is a fundamental tool of the design process in many engineering disciplines including aerospace engineering. However, although high-fidelity numerical models are accurate, they can be computationally expensive with evaluation time for a single design as long as hours, days or even weeks. Simulation-driven design using conventional optimization techniques may be therefore prohibitive.This book explores the alternative: performing computationally efficient design using surrogate-based optimization, where the high-fidelity model is replaced by its computationally cheap but still reasonably accurate representation: a surrogate. The emphasis is on physics-based surrogates. Application-wise, the focus is on aerodynamics and the methods and techniques described in the book are demonstrated using aerodynamic shape optimization cases. Applications in other engineering fields are also demonstrated.State-of-the-art techniques and a depth of coverage never published before make this a unique and essential book for all researchers working in aerospace and other engineering areas and dealing with optimization, computationally expensive design problems, and simulation-driven design.

Grey-box modeling of an ocean vessel for operational optimization

Abstract 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.

Rapid EM-Driven Antenna Dimension Scaling Through Inverse Modeling

In this letter, a computationally feasible technique for dimension scaling of antenna structures is introduced. The proposed methodology is based on inverse surrogate modeling where the geometry parameters of the antenna structure of interest are explicitly related to the operating frequency. The surrogate model is identified based on a few antenna designs optimized for selected reference frequencies. For the sake of computational efficiency, the reference designs are obtained at the level of the coarse-discretization electromagnetic (EM) simulation antenna model. An appropriate correction allows us to elevate the inverse surrogate to the level of the high-fidelity EM model and, thus, utilize it for determining the dimensions of the scaled design. Having the inverse model established, the dimension scaling process requires just a single evaluation of the antenna at a fine discretization (carried out at the correction stage). Our approach is demonstrated using two examples: a dielectric resonator antenna, and an enhanced-bandwidth patch antenna.

Multi-Level Surrogate-Based Airfoil Shape Optimization

Robust and computationally efficient airfoil shape optimization algorithm is presented. Our technique exploits a set of computational fluid dynamics (CFD) models of increasing discretization density that are sequentially optimized with the optimal design of the “coarser” model being the initial design for the “finer” one. The final design is refined using a response surface approximation model constructed from the coarse-discretization CFDsimulation data and corrected using single high-fidelity evaluation. The presented technique is easy to implement. Operation of our algorithm is demonstrated using several test cases of transonic airfoils. In all instances, an optimized design is obtained at a low computational cost corresponding to a few high-fidelity CFD simulations. Our results are compared to other optimization techniques, both conventional and surrogate-based ones.

Computational Optimization, Modelling and Simulation: Recent Trends and Challenges

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.

Adaptive Response Correction for Surrogate-Based Airfoil Shape Optimization

An adaptive response correction (ARC) technique for computationally efficient surrogate-based optimization (SBO) of transonic airfoils is developed. SBO replaces a direct optimization of the high-fidelity (accurate but computationally expensive) airfoil model by an iterative optimization of a properly corrected low-fidelity one. Here, both models are based on the same governing fluid flow equations, however, the low-fidelity one uses a coarser discretization and relaxed convergence criteria. The ARC technique exploits the knowledge contained in the low-fidelity model to construct a fast and yet an accurate prediction tool (surrogate) that is used to find the high-fidelity model optimum. The optimization algorithm is embedded in the trust-region framework to ensure convergence. Examples demonstrate that the optimized airfoil design can be obtained at a substantially lower computational cost when compared to the direct high-fidelity model optimization.