Mathieu Balesdent

Stagewise Multidisciplinary Design Optimization Formulation for Optimal Design of Expendable Launch Vehicles

DOI: 10.2514/1.52507 Optimal design of launch vehicles is a complex process that gathers a series of disciplines. The classical method used to solve such problems consists in decomposing the problem into the different disciplines and in associating a global optimizer and disciplinary analyzers (multidiscipline feasible method, most used in launch vehicle design). Thispaper presents a new multidisciplinary design optimization method basedon atransverse decomposition of the design process adapted to the multistage launch vehicle architecture. The proposed bilevel method splits up the optimizationprocessintodifferent flightphasesandperformsthedifferentstageoptimizationseithersequentiallyor concurrently. Thus, the proposed approach transforms the global multidisciplinary design optimization problem into the coordination of elementary multidisciplinary design optimization problems and moves the problem complexity from the system level to the subsystem level. Three formulations of this method are proposed and compared with the multidiscipline feasible method on a multistage launch vehicle design problem. The proposed methodallowsthedimensionofthesearchdomainandthenumberofconstraintsatthesystemleveltobereduced.In thatway,thisapproachmakestheuseofheuristicmethodssuchasthegeneticalgorithmsmoreefficientinsolvingthe large-scale highly nonlinear launch vehicle design problem.

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.

New multidisciplinary design optimization approaches for launch vehicle design

Launch vehicle design is a complex problem involving a series of disciplines. These disciplines present conflicting objectives and require multidisciplinary design optimization methods in order to handle the couplings and to make the search of compromises easier. Launch vehicle design problem is a specific multidisciplinary design optimization problem because it combines the optimizations of design and trajectory variables. In this article, we present a new multidisciplinary design optimization approach, called the StageWise decomposition for Optimal Rocket Design (SWORD). This method splits up the multidisciplinary design optimization process into different stages and transforms the initial multidisciplinary design optimization problem into the coordination of elementary ones. This method is compared to the standard multidisciplinary design optimization method (multidiscipline feasible method). In this article, we propose a new formulation of the SWORD method and a new dedicated optimization strategy. Results show that using a global search algorithm, the stagewise decomposition for optimal rocket design method allows to find a better optimum than multidiscipline feasible method. Furthermore, with the new proposed optimization strategy, the SWORD method does not require any initialization from the user, allows to quickly find feasible solutions and converge to an optimum in a limited computation time.

Deciding Degree of Conservativeness in Initial Design Considering Risk of Future Redesign

Early in the design process, there is often mixed epistemic model uncertainty and aleatory parameter uncertainty. Later in the design process, the results of high-fidelity simulations or experiments will reduce epistemic model uncertainty and may trigger a redesign process. Redesign is undesirable because it is associated with costs and delays; however, it is also an opportunity to correct a dangerous design or possibly improve design performance. In this study, we propose a margin-based design/redesign method where the design is optimized deterministically, but the margins are selected probabilistically. The final design is an epistemic random variable (i.e., it is unknown at the initial design stage) and the margins are optimized to control the epistemic uncertainty in the final design, design performance, and probability of failure. The method allows for the tradeoff between expected final design performance and probability of redesign while ensuring reliability with respect to mixed uncertainties. The method is demonstrated on a simple bar problem and then on an engine design problem. The examples are used to investigate the dilemma of whether to start with a higher margin and redesign if the test later in the design process reveals the design to be too conservative, or to start with a lower margin and redesign if the test reveals the design to be unsafe. In the examples in this study, it is found that this decision is related to the variance of the uncertainty in the high-fidelity model relative to the variance of the uncertainty in the low-fidelity model.

Simulating future test and redesign considering epistemic model uncertainty

At the initial design stage engineers oft.en rely onlow-fldelity models that have high epistemic uncertainty. Taditional safety-margin-based deterministic design resorts to testing to reduce epistemic uncertainty and achieve targeted levels of safety. Testing is used to calibrate models and prescribe redesign when tests are not passed. After calibration, reduced epistemic model uncertainty can be leveraged through redesign to restore safety or improve design per for mance; howevet·, redesign may be associated with substantial costs or delays. In this paper, a methodology is described for optimizing the safety-margin-based design, testing, and redesign process to allow the designer· to tradeoff between the risk of future redesign and the possible performance and reliability beneflts. The proposed methodology represents the epistemic model uncertainty with a Kriging sunogate and is applicable in a wide range o f design problems. The method is illustrated on a cantilever bearn design problem where there is mixed epistemic model error and aleatory parameter uncertainty.

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.

Analysis of extreme aircraft wake vortex circulations

Because of its take-off, an aircraft generates a wake essentially made of a pair of counter-rotating vortices notably characterized by their total circulation. In this test case, we analyze the evolution of wake vortex total circulation with the extreme value theory. It consists in estimating the probability that a wake vortex circulation exceeds a given threshold for a fixed set of CMC samples