Multi-fidelity Design Optimization Research Articles

Multi-fidelity design optimization of solid oxide fuel cells using a Bayesian feature enhanced stochastic collocation

We develop a multi-fidelity surrogate modelling approach to replace the complex and costly physics-based computer models that are often used in the optimization of solid oxide fuel cell (SOFC) performance, or the simplified models that are used in lieu of complex models. We extend multi-fidelity stochastic collocation through a feature engineering step, and eliminate the requirement for the exact low-fidelity output at the inference stage. In contrast to previous approaches, the surrogate model we develop provides detailed spatial information, rather than one or more scalar outputs. This allows for the incorporation of such information into the objective of the optimization study, with the flexibility to choose from more than one objective, such as a minimum, maximum or average. Furthermore, the detailed spatial information can be used for general design purposes, such as ensuring uniformity in reactant and potential distributions. From the results on a 3-d SOFC model, we demonstrate highly accurate predictions of multiple spatially distributed quantities at up to spatial 250,000 locations. The results are superior to state-of-the-art multi-fidelity approaches, particularly for low numbers of high fidelity training points. We use the surrogate model to optimize the SOFC performance with respect to different objectives (including with nonlinear constraints and multiple objectives), with results that are accurate and are obtained in a fraction of the time required for the full model.

A Sequential Sampling Approach for Multi-Fidelity Surrogate Modeling-Based Robust Design Optimization

Abstract Multi-fidelity surrogate modeling has been extensively used in engineering design to achieve a balance between computational efficiency and prediction accuracy. Sequential sampling strategies have been investigated to improve the computational efficiency of surrogate-assisted design optimization. The existing sequential sampling approaches, however, are dedicated to either deterministic multi-fidelity design optimization or robust design under uncertainty using single-fidelity models. This paper proposes a sequential sampling method for robust design optimization based on multi-fidelity modeling. The proposed method considers both design variable uncertainty and interpolation uncertainty during the sequential sampling. An extended upper confidence boundary (EUCB) function is developed to determine both the sampling locations and the fidelity levels of the sequential samples. In the EUCB function, the cost ratio between high- and low-fidelity models and the sampling density are considered. Moreover, the EUCB function is extended to handle constrained robust design optimization problems by combining the probability of feasibility. The performance of the proposed approach is verified using two analytical examples and an engineering case. Results show that the proposed sequential approach is more efficient than the one-shot sampling method for robust design optimization problems.

Efficient Surrogate Modeling and Design Optimization of Compact Integrated On-Chip Inductors Based on Multi-Fidelity EM Simulation Models

High-performance and small-size on-chip inductors play a critical role in contemporary radio-frequency integrated circuits. This work presents a reliable surrogate modeling technique combining low-fidelity EM simulation models, response surface approximations based on kriging interpolation, and space mapping technology. The reported method is useful for the development of broadband and highly accurate data-driven models of integrated inductors within a practical timeframe, especially in terms of the computational expense of training data acquisition. Application of the constructed surrogate model for rapid design optimization of a compact on-chip inductor is demonstrated. The optimized EM-validated design solution can be reached at a low computational cost, which is a considerable improvement over existing approaches. In addition, this work provides a description and illustrates the usefulness of a multi-fidelity design optimization method incorporating EM computational models of graduated complexity and local polynomial approximations managed by an output space mapping optimization framework. As shown by the application example, the final design solution is obtained at the cost of a few high-fidelity EM simulations of a small-size integrated coil. A supplementary description of variable-fidelity EM computational models and a trade-off between model accuracy and its processing time complements the work.

Multi-Fidelity Design Optimization of a Long-Range Blended Wing Body Aircraft with New Airframe Technologies

The German Cluster of Excellence SE²A (Sustainable and Energy Efficient Aviation) is established in order to investigate the influence of game-changing technologies on the energy efficiency of future transport aircraft. In this paper, the preliminary investigation of the four game-changing technologies active flow control, active load alleviation, boundary layer ingestion, and novel materials and structure concepts on the performance of a long-range Blended Wing Body (BWB) aircraft is presented. The BWB that was equipped with the mentioned technologies was designed and optimized using the multi-fidelity aircraft design code SUAVE with a connection to the Computational Fluid Dynamics (CFD) code SU2. The conceptual design of the BWB aircraft is performed within the SUAVE framework, where the influence of the new technologies is investigated. In the second step, the initially designed BWB aircraft is improved by an aerodynamic shape optimization while using the SU2 CFD code. In the third step, the performance of the optimized aircraft is evaluated again using the SUAVE code. The results showed more than 60% reduction in the aircraft fuel burn when compared to the Boeing 777.

Multifidelity design guided by topology optimization

In this study, we present a framework based on the concept of multifidelity design optimization with the purpose of indirectly solving complex—computationally heavy and/or unstable—topology optimization problems. Our primary idea is to divide an original topology optimization problem into two types of subproblems for low-fidelity optimization and high-fidelity evaluation. To realize this idea, artificial design parameters, which we refer to as seeding parameters, are incorporated into the low-fidelity optimization problem for generating various patterns of topology-optimized candidates. The low-fidelity optimization problem is deliberately formulated as an easily solvable one by decreasing the nonlinearity of the original physical phenomena. Notably, selecting valid seeding parameters in the low-fidelity optimization problem is essential for employing the proposed framework. The aim of high-fidelity evaluation is to obtain a satisfactory solution using a high-fidelity analysis model, which considers the nonlinearity of the original physical phenomena, from the data set of the topology-optimized candidates, via the design of experiments. We apply the proposed framework to two case studies of isothermal and thermal turbulent flow problems, and discuss its efficacy as an alternative strategy for solving complex topology optimization problems.

Multidisciplinary and Multifidelity Design Optimization of Electric Vehicle Battery Thermal Management System

Battery thermal management system (BTMS) is a complex and highly integrated system, which is used to control the battery thermal conditions in electric vehicles (EVs). The BTMS consists of many subsystems that belong to different disciplines, which poses challenges to BTMS optimization using conventional methods. This paper develops a general variable fidelity-based multidisciplinary design optimization (MDO) architecture and optimizes the BTMS by considering different systems/disciplines from the systemic perspective. Four subsystems and/or subdisciplines are modeled, including the battery thermodynamics, fluid dynamics, structure, and lifetime model. To perform the variable fidelity-based MDO of the BTMS, two computational fluid dynamics (CFD) models with different levels of fidelity are developed. A low fidelity surrogate model and a tuned low fidelity model are also developed using an automatic surrogate model selection method, the concurrent surrogate model selection (COSMOS). An adaptive model switching (AMS) method is utilized to realize the adaptive switch between variable-fidelity models. The objectives are to maximize the battery lifetime and to minimize the battery volume, the fan's power, and the temperature difference among different cells. The results show that the variable-fidelity MDO can balance the characteristics of the low fidelity mathematical models and the computationally expensive simulations, and find the optimal solutions efficiently and accurately.

Multi-Fidelity Design Optimization: Challenges In Complex Physics-based Computational Mechanics

Engineering systems development is currently pushing the envelope of traditional multidisciplinary design capabilities. Bringing multiple physics into the design loop earlier in the design process has shown promise in handling the strict requirements constantly being placed on various areas of computational mechanics, such as the design of next generation military aircraft. The goal in multi-fidelity design is to aid in this process to expand traditional design capabilities through the implementation of techniques developed to mitigate inadequacies and/or obstacles associated with various levels of complex physics in a single design process. Achieving a desired level of accuracy while maintaining a low computational cost may very well be the greatest obstacle combating computational design. However, other hindrances exist such as determining the appropriate physics (i.e. acoustic, thermal, structural), level of physics (i.e. Potential Flow, Euler, Navier Stokes), and mesh refinement to utilize in any given computational model. This work focuses on leveraging higher fidelity information to correct lower fidelity models so as to take advantage of the speed associated with the latter without compromising accuracy. Corrections are implemented via a custom Hybrid Bridge Function (HBF) while the design aspect is governed through the implementation of a special Trust Region Model Management (TRMM) methodology. Multifidelity design optimization is demonstrated on a thermal plate demonstration problem consisting of four differing levels of fidelity. Results show that employment of the described methodology succeeds in obtaining a design at a lower cost while maintaining a necessary level of accuracy.

Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm

A robust multi-fidelity design optimization methodology has been developed to integrate advantages of high- and low-fidelity analyses, aiming to help designers reach more efficient turbine runners within reasonable computational time and cost. An inexpensive low-fidelity inviscid flow solver handles most of the computational burden by providing data to the optimizer by evaluating objective functions and constraint values in the low-fidelity phase. An open-source derivative-free optimizer, NOMAD, explores the search space, using the multi-objective mesh adaptive direct search optimization algorithm. A versatile filtering algorithm is in charge of connecting low- and high-fidelity phases by selecting among all feasible solutions a few promising solutions which are transferred to the high-fidelity phase. In the high-fidelity phase, a viscous flow solver is used outside the optimization loop to accurately evaluate filtered candidates. High-fidelity analyses results are used to recalibrate the low-fidelity optimization problem. The developed methodology has demonstrated its ability to efficiently redesign a Francis turbine blade for new operating conditions.

Multi-fidelity design optimization of Francis turbine runner blades

A robust multi-fidelity design algorithm has been developed, focusing to efficiently handle industrial hydraulic runner design considerations. The computational task is split between low- and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a derivative-free optimization method employs an inviscid flow solver to obtain the major desired characteristics of a good design in a relatively fast iterative process. A limited number of candidates are selected among feasible optimization solutions by a newly developed filtering process. The main function of the filtering process is to select some promising candidates to be sent into the high-fidelity phase, which have significantly different geometries, and also are dominant in their own territories. The high-fidelity phase aims to accurately evaluate those promising candidates in order to select the one which is closest to design targets. A low-head runner case study has shown the ability of this methodology to identify an optimized blade through a relatively low computational effort, which is significantly different from the base geometry.

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

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.

Multi-fidelity design optimization of transonic airfoils using shape-preserving response prediction

A computationally efficient methodology for transonic airfoil design optimization is presented. Our approach exploits a corrected physics-based low-fidelity surrogate that replaces, in the optimization process, an accurate but computationally expensive highfidelity airfoil model. Correction of the low-fidelity model is achieved by aligning its corresponding airfoil surface pressure distributions with that of the high-fidelity model using a shape-preserving response prediction technique. The presented 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. More than a 90% reduction in high-fidelity function calls is achieved when compared to direct highfidelity model optimization.

Multifidelity Design Optimization of Low-Boom Supersonic Jets

The practical use of high-fidelity multidisciplinary optimization techniques in low-boom supersonic business-jet designs has been limited because of the high computational cost associated with computational fluid dynamics-based evaluations of both the performance and the loudness of the ground boom of the aircraft. This is particularly true of designs that involve the sonic boom loudness as either a cost function or a constraint because gradient-free optimization techniques may become necessary, leading to even larger numbers of function evaluations. If, in addition, the objective of the design method is to account for the performance of the aircraft throughout its full-flight mission while including important multidisciplinary tradeoffs between the relevant disciplines the situation only complicates. To overcome these limitations, we propose a hierarchical multifidelity design approach where high-fidelity models are only used where and when they are needed to correct the shortcomings of the low-fidelity models. Our design approach consists of two basic components: a multidisciplinary aircraft synthesis tool (PASS) that uses highly tuned low-fidelity models of all of the relevant disciplines and computes the complete mission profile of the aircraft, and a hierarchical, multifidelity environment for the creation of response surfaces for aerodynamic performance and sonic boom loudness (BOOM-UA) that attempts to achieve the accuracy of an Euler-based design strategy. This procedure is used to create three design alternatives for a Mach 1.6, 6-8 passenger supersonic business-jet configuration with a range of 4500 n mile and with a takeoff field length that is shorter than 6000 ft. Optimized results are obtained with much lower computational cost than the direct, high-fidelity design alternative. The validation of these design results using the high-fidelity model shows very good agreement for the aircraft performance and highlights the need for improved response surface fitting techniques for the boom loudness approximations.