We introduce a novel approach to solving PDE-constrained optimization problems, specifically rela... more We introduce a novel approach to solving PDE-constrained optimization problems, specifically related to aircraft design. These optimization problems require running expensive computational fluid dynamics (CFD) simulations which have previously been approximated with a reduced order model (ROM) to lower the computational cost. Instead of using a single global ROM as is traditionally done, we propose using multiple piecewise ROMs, constructed and used with the aid of machine learning techniques. Our approach consists of clustering a set of precomputed non linear partial differential equations (PDE) solutions from which we build our piecewise ROMs. Then during the optimization problem, when we need to run a simulation for a given optimization parameter, we select the optimal piecewise ROM to use. Initial results on our test dataset are promising. We were able to achieve the same or better accuracy by using piecewise ROMs rather than a global ROM, while further reducing the computationa...
A novel approach to solving highly parameterized optimization problems is introduced specifically... more A novel approach to solving highly parameterized optimization problems is introduced specifically related to problems involving running expensive computer simulations such as aircraft design. These optimization problems require running expensive computational fluid dynamics (CFD) simulations in order to evaluate objective function and constraints. In particular, very often, the number of computer simulation increases when the optimization parameter space is highdimensional making the problem computationally intensive. Various approaches have been proposed in literature to reduce the dimensionality of the problem, such as the method of active subspace which consist in a linear approximation of the subspace. This method is not suitable when the subspace is nonlinear. The approach proposed consists of using an autoencoder in order to have a nonlinear approximation of the subspace. Different autoencoder architectures are compared in performances and accuracy. Finally, the proposed appro...
A computational framework is proposed for efficiently solving multidisciplinary analysis and opti... more A computational framework is proposed for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in a relatively high-dimensional design parameter space. It relies on proje...
International Journal for Numerical Methods in Engineering, 2020
SummaryIn this paper, a new take on the concept of an active subspace for reducing the dimension ... more SummaryIn this paper, a new take on the concept of an active subspace for reducing the dimension of the design parameter space in a multidisciplinary analysis and optimization (MDAO) problem is proposed. The new approach is intertwined with the concepts of adaptive parameter sampling, projection‐based model order reduction, and a database of linear, projection‐based reduced‐order models equipped with interpolation on matrix manifolds, in order to construct an efficient computational framework for MDAO. The framework is fully developed for MDAO problems with linearized fluid‐structure interaction constraints. It is applied to the aeroelastic tailoring, under flutter constraints, of two different flight systems: a flexible configuration of NASA's Common Research Model; and NASA's Aeroelastic Research Wing #2 (ARW‐2). The obtained results illustrate the feasibility of the computational framework for realistic MDAO problems and highlight the benefits of the new approach for cons...
We introduce a novel approach to solving PDE-constrained optimization problems, specifically rela... more We introduce a novel approach to solving PDE-constrained optimization problems, specifically related to aircraft design. These optimization problems require running expensive computational fluid dynamics (CFD) simulations which have previously been approximated with a reduced order model (ROM) to lower the computational cost. Instead of using a single global ROM as is traditionally done, we propose using multiple piecewise ROMs, constructed and used with the aid of machine learning techniques. Our approach consists of clustering a set of precomputed non linear partial differential equations (PDE) solutions from which we build our piecewise ROMs. Then during the optimization problem, when we need to run a simulation for a given optimization parameter, we select the optimal piecewise ROM to use. Initial results on our test dataset are promising. We were able to achieve the same or better accuracy by using piecewise ROMs rather than a global ROM, while further reducing the computationa...
A novel approach to solving highly parameterized optimization problems is introduced specifically... more A novel approach to solving highly parameterized optimization problems is introduced specifically related to problems involving running expensive computer simulations such as aircraft design. These optimization problems require running expensive computational fluid dynamics (CFD) simulations in order to evaluate objective function and constraints. In particular, very often, the number of computer simulation increases when the optimization parameter space is highdimensional making the problem computationally intensive. Various approaches have been proposed in literature to reduce the dimensionality of the problem, such as the method of active subspace which consist in a linear approximation of the subspace. This method is not suitable when the subspace is nonlinear. The approach proposed consists of using an autoencoder in order to have a nonlinear approximation of the subspace. Different autoencoder architectures are compared in performances and accuracy. Finally, the proposed appro...
A computational framework is proposed for efficiently solving multidisciplinary analysis and opti... more A computational framework is proposed for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in a relatively high-dimensional design parameter space. It relies on proje...
International Journal for Numerical Methods in Engineering, 2020
SummaryIn this paper, a new take on the concept of an active subspace for reducing the dimension ... more SummaryIn this paper, a new take on the concept of an active subspace for reducing the dimension of the design parameter space in a multidisciplinary analysis and optimization (MDAO) problem is proposed. The new approach is intertwined with the concepts of adaptive parameter sampling, projection‐based model order reduction, and a database of linear, projection‐based reduced‐order models equipped with interpolation on matrix manifolds, in order to construct an efficient computational framework for MDAO. The framework is fully developed for MDAO problems with linearized fluid‐structure interaction constraints. It is applied to the aeroelastic tailoring, under flutter constraints, of two different flight systems: a flexible configuration of NASA's Common Research Model; and NASA's Aeroelastic Research Wing #2 (ARW‐2). The obtained results illustrate the feasibility of the computational framework for realistic MDAO problems and highlight the benefits of the new approach for cons...
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Papers by Gabriele Boncoraglio