Loïc Brevault

Decoupled Multidisciplinary Design Optimization Formulation for Interdisciplinary Coupling Satisfaction Under Uncertainty

At early design phases, taking into account uncertainty in the optimization of a multidisciplinary system is essential to assess the optimal characteristics and performance. Uncertainty multidisciplinary design optimization methods aim at efficiently organizing not only the different disciplinary analyses, the uncertainty propagation, and the optimization but also the handling of interdisciplinary couplings under uncertainty. A new decoupled uncertainty multidisciplinary design optimization formulation (named Individual Discipline Feasible/Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the realizations of the uncertain variables is presented in this paper. Coupling satisfaction in realizations is necessary to maintain the equivalence between the coupled and decoupled uncertainty multidisciplinary design optimization formulations, and therefore to ensure the physical relevance of the obtained designs. The proposed approach relies on the iterative construction of Polynomial Chaos Expansions in order to represent, at the convergence of the optimization problem, the functional couplings between the disciplines. The proposed formulation is tested on an analytic problem and on the design of a two-stage launch vehicle.

Efficient Global Optimization Using Deep Gaussian Processes

Efficient Global Optimization (EGO) is widely used for the optimization of computationally expensive black-box functions. It uses a surrogate modeling technique based on Gaussian Processes (Kriging). However, due to the use of a stationary covariance, Kriging is not well suited for approximating non stationary functions. This paper explores the integration of Deep Gaussian processes (DGP) in EGO framework to deal with the non-stationary issues and investigates the induced challenges and opportunities. Numerical experimentations are performed on analytical problems to highlight the different aspects of DGP and EGO.

How to Deal with Mixed-Variable Optimization Problems: An Overview of Algorithms and Formulations

Real world engineering optimization problems often involve discrete variables (e.g., categorical variables) characterizing choices such as the type of material to be used or the presence of certain system components. From an analytical perspective, these particular variables determine the definition of the objective and constraint functions, as well as the number and type of parameters that characterize the problem. Furthermore, due to the inherent discrete and potentially non-numerical nature of these variables, the concept of metrics is usually not definable within their domain, thus resulting in an unordered set of possible choices. Most modern optimization algorithms were developed with the purpose of solving design problems essentially characterized by integer and continuous variables and by consequence the introduction of these discrete variables raises a number of new challenges. For instance, in case an order can not be defined within the variables domain, it is unfeasible to use optimization algorithms relying on measures of distances, such as Particle Swarm Optimization. Furthermore, their presence results in non-differentiable objective and constraint functions, thus limiting the use of gradient-based optimization techniques. Finally, as previously mentioned, the search space of the problem and the definition of the objective and constraint functions vary dynamically during the optimization process as a function of the discrete variables values.

Preliminary study on launch vehicle design: Applications of multidisciplinary design optimization methodologies

The design of complex systems such as launch vehicles involves different fields of expertise that are interconnected. To perform multidisciplinary studies, concurrent engineering aims at providing a collaborative environment which often relies on data set exchange. In order to efficiently achieve system-level analyses (uncertainty propagation, sensitivity analysis, optimization, etc.), it is necessary to go beyond data set exchange which limits the capabilities of performance assessments. Multidisciplinary design optimization methodologies is a collection of engineering methodologies to optimize systems modelled as a set of coupled disciplinary analyses and is a key enabler to extend concurrent engineering capabilities. This article is focused on several examples of recent developments of multidisciplinary design optimization methodologies (e.g. multidisciplinary design optimization with transversal decomposition of the design process, multidisciplinary design optimization under uncertainty) with applications to launch vehicle design to illustrate the benefices of taking into account the coupling effects between the different physics all along the design process. These methods enable to manage the complexity of the involved physical phenomena and their interactions in order to generate innovative concepts such as reusable launch vehicles beyond existing solutions.

Advanced Space Vehicle Design Taking into Account Multidisciplinary Couplings and Mixed Epistemic/Aleatory Uncertainties

Space vehicle design is a complex process involving numerous disciplines such as aerodynamics, structure, propulsion and trajectory. These disciplines are tightly coupled and may involve antagonistic objectives that require the use of specific methodologies in order to assess trade-offs between the disciplines and to obtain the global optimal configuration. Generally, there are two ways to handle the system design. On the one hand, the design may be considered from a disciplinary point of view (a.k.a. Disciplinary Design Optimization): the designer of each discipline has to design its subsystem (e.g. engine) taking the interactions between its discipline and the others (interdisciplinary couplings) into account. On the other hand, the design may also be considered as a whole: the design team addresses the global architecture of the space vehicle, taking all the disciplinary design variables and constraints into account at the same time. This methodology is known as Multidisciplinary Design Optimization (MDO) and requires specific mathematical tools to handle the interdisciplinary coupling consistency.