Juan J. Alonso

Bio: Juan J. Alonso is an academic researcher from Stanford University. The author has contributed to research in topics: Adjoint equation & Aerodynamics. The author has an hindex of 51, co-authored 290 publications receiving 9987 citations. Previous affiliations of Juan J. Alonso include Princeton University & Center for Turbulence Research.

The complex-step derivative approximation

Abstract: The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.

SU2: An Open-Source Suite for Multiphysics Simulation and Design

Abstract: This paper presents the main objectives and a description of the SU2 suite, including the novel software architecture and open-source software engineering strategy. SU2 is a computational analysis and design package that has been developed to solve multiphysics analysis and optimization tasks using unstructured mesh topologies. Its unique architecture is well suited for extensibility to treat partial-differential-equation-based problems not initially envisioned. The common framework adopted enables the rapid implementation of new physics packages that can be tightly coupled to form a powerful ensemble of analysis tools to address complex problems facing many engineering communities. The framework is demonstrated on a number, solving both the flow and adjoint systems of equations to provide a high-fidelity predictive capability and sensitivity information that can be used for optimal shape design using a gradient-based framework, goal-oriented adaptive mesh refinement, or uncertainty quantification.

CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences

Abstract: This report documents the results of a study to address the long range, strategic planning required by NASA's Revolutionary Computational Aerosciences (RCA) program in the area of computational fluid dynamics (CFD), including future software and hardware requirements for High Performance Computing (HPC). Specifically, the "Vision 2030" CFD study is to provide a knowledge-based forecast of the future computational capabilities required for turbulent, transitional, and reacting flow simulations across a broad Mach number regime, and to lay the foundation for the development of a future framework and/or environment where physics-based, accurate predictions of complex turbulent flows, including flow separation, can be accomplished routinely and efficiently in cooperation with other physics-based simulations to enable multi-physics analysis and design. Specific technical requirements from the aerospace industrial and scientific communities were obtained to determine critical capability gaps, anticipated technical challenges, and impediments to achieving the target CFD capability in 2030. A preliminary development plan and roadmap were created to help focus investments in technology development to help achieve the CFD vision in 2030.

Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design

Abstract: This paper describes the history, objectives, structure, and current capabilities of the Stanford University Unstructured (SU 2 ) tool suite. This computational analysis and design software collection is being developed to solve complex, multi-physics analysis and optimization tasks using arbitrary unstructured meshes, and it has been designed so that it is easily extensible for the solution of Partial Differential Equation-based (PDE) problems not directly envisioned by the authors. At its core, SU 2 is an open-source collection of C++ software tools to discretize and solve problems described by PDEs and is able to solve PDE-constrained optimization problems, including optimal shape design. Although the toolset has been designed with Computational Fluid Dynamics (CFD) and aerodynamic shape optimization in mind, it has also been extended to treat other sets of governing equations including potential flow, electrodynamics, chemically reacting flows, and several others. In our experience, capabilities for computational analysis and optimization have improved considerably over the past two decades. However, the ability to integrate the resulting software packages into coupled multi-physics analysis and design optimization solvers has remained a challenge: the variety of approaches chosen for the independent components of the overall problem (flow solvers, adjoint solvers, optimizers, shape parameterization, shape deformation, mesh adaption, mesh deformation, etc) make it difficult to (a) expand the range of applicability to situations not originally envisioned, and (b) to reduce the overall burden of creating integrated applications. By leveraging well-established object-oriented software architectures (using C++) and by enabling a common interface for all the necessary components, SU 2 is able to remove these barriers for both the beginner and the seasoned analyst. In this paper we attempt to describe our efforts to develop SU 2 as an integrated platform. In some senses, the paper can also be used as a software reference manual for those who might be interested in modifying it to suit their own needs. We carefully describe the C++ framework and object hierarchy, the sets of equations that can be currently modeled by SU 2 , the available choices for numerical discretization, and conclude with a set of relevant validation and verification test cases that are included with the SU 2 distribution. We intend for SU 2 to remain open source and to serve as a starting point for new capabilities not included in SU 2 today, that will hopefully be contributed by users in both academic and industrial environments.

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

Abstract: An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Engineering Design via Surrogate Modelling: A Practical Guide

Abstract: Preface. About the Authors. Foreword. Prologue. Part I: Fundamentals. 1. Sampling Plans. 1.1 The 'Curse of Dimensionality' and How to Avoid It. 1.2 Physical versus Computational Experiments. 1.3 Designing Preliminary Experiments (Screening). 1.3.1 Estimating the Distribution of Elementary Effects. 1.4 Designing a Sampling Plan. 1.4.1 Stratification. 1.4.2 Latin Squares and Random Latin Hypercubes. 1.4.3 Space-filling Latin Hypercubes. 1.4.4 Space-filling Subsets. 1.5 A Note on Harmonic Responses. 1.6 Some Pointers for Further Reading. References. 2. Constructing a Surrogate. 2.1 The Modelling Process. 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach. 2.1.2 Stage Two: Parameter Estimation and Training. 2.1.3 Stage Three: Model Testing. 2.2 Polynomial Models. 2.2.1 Example One: Aerofoil Drag. 2.2.2 Example Two: a Multimodal Testcase. 2.2.3 What About the k -variable Case? 2.3 Radial Basis Function Models. 2.3.1 Fitting Noise-Free Data. 2.3.2 Radial Basis Function Models of Noisy Data. 2.4 Kriging. 2.4.1 Building the Kriging Model. 2.4.2 Kriging Prediction. 2.5 Support Vector Regression. 2.5.1 The Support Vector Predictor. 2.5.2 The Kernel Trick. 2.5.3 Finding the Support Vectors. 2.5.4 Finding . 2.5.5 Choosing C and epsilon. 2.5.6 Computing epsilon : v -SVR 71. 2.6 The Big(ger) Picture. References. 3. Exploring and Exploiting a Surrogate. 3.1 Searching the Surrogate. 3.2 Infill Criteria. 3.2.1 Prediction Based Exploitation. 3.2.2 Error Based Exploration. 3.2.3 Balanced Exploitation and Exploration. 3.2.4 Conditional Likelihood Approaches. 3.2.5 Other Methods. 3.3 Managing a Surrogate Based Optimization Process. 3.3.1 Which Surrogate for What Use? 3.3.2 How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria. 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking. References. Part II: Advanced Concepts. 4. Visualization. 4.1 Matrices of Contour Plots. 4.2 Nested Dimensions. Reference. 5. Constraints. 5.1 Satisfaction of Constraints by Construction. 5.2 Penalty Functions. 5.3 Example Constrained Problem. 5.3.1 Using a Kriging Model of the Constraint Function. 5.3.2 Using a Kriging Model of the Objective Function. 5.4 Expected Improvement Based Approaches. 5.4.1 Expected Improvement With Simple Penalty Function. 5.4.2 Constrained Expected Improvement. 5.5 Missing Data. 5.5.1 Imputing Data for Infeasible Designs. 5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement. 5.7 Summary. References. 6. Infill Criteria With Noisy Data. 6.1 Regressing Kriging. 6.2 Searching the Regression Model. 6.2.1 Re-Interpolation. 6.2.2 Re-Interpolation With Conditional Likelihood Approaches. 6.3 A Note on Matrix Ill-Conditioning. 6.4 Summary. References. 7. Exploiting Gradient Information. 7.1 Obtaining Gradients. 7.1.1 Finite Differencing. 7.1.2 Complex Step Approximation. 7.1.3 Adjoint Methods and Algorithmic Differentiation. 7.2 Gradient-enhanced Modelling. 7.3 Hessian-enhanced Modelling. 7.4 Summary. References. 8. Multi-fidelity Analysis. 8.1 Co-Kriging. 8.2 One-variable Demonstration. 8.3 Choosing X c and X e . 8.4 Summary. References. 9. Multiple Design Objectives. 9.1 Pareto Optimization. 9.2 Multi-objective Expected Improvement. 9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement. 9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement. 9.5 Summary. References. Appendix: Example Problems. A.1 One-Variable Test Function. A.2 Branin Test Function. A.3 Aerofoil Design. A.4 The Nowacki Beam. A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring. A.6 Novel Passive Vibration Isolator Feasibility. References. Index.

Multiobjective evolutionary algorithms: A survey of the state of the art

Abstract: A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.