Decoupled UMDO formulation for interdisciplinary coupling satisfaction under uncertainty

International audienceAt early design phases, taking into account uncertainty for the optimization of a multidisciplinary system is essential to establish the optimal system characteristics and performances. Uncertainty Multidisciplinary Design Optimization (UMDO) formulations have to eciently organize the dierent disciplinary analyses, the uncertainty propagation, the optimization, but also the handling of interdisciplinary couplings under uncertainty. A decoupled UMDO formulation (Individual Discipline Feasible - Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the instantiations of the uncertain variables is presented in this paper. Ensuring coupling satisfaction in instantiations is essential to ensure the equivalence between the coupled and decoupled UMDO problem formulations. The proposed approach relies on the iterative construction of surrogate models based on Polynomial Chaos Expansion in order to represent at the convergence of the optimization problem, the coupling functional relations as a coupled approach under uncertainty does. The performances of the proposed formulation is assessed on an analytic test case and on the design of a new Vega launch vehicle upper stage

Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities, application to aerospace systems

International audienceThe design process of complex systems such as new configurations of aircraft or launch vehicles is usually decomposed in different phases which are characterized by the depth of the analyses in terms of number of design variables and fidelity of the physical models. At each phase, the designers have to deal with accurate but computationally intensive models as well as cheap but inaccurate models. Multi-fidelity modeling is a way to merge different fidelity models to provide engineers with accurate results with a limited computational cost. Within the context of multi-fidelity modeling, approaches based on Gaussian Processes emerge as popular techniques to fuse information between the different fidelity models. The relationship between the fidelity models is a key aspect in multi-fidelity modeling. This paper provides an overview of Gaussian process-based multi-fidelity modeling techniques for variable relationship between the fidelity models (e.g., linearity, non-linearity, variable correlation). Each technique is described within a unified framework and the links between the different techniques are highlighted. All approaches are numerically compared on a series of analytical test cases and four aerospace related engineering problems in order to assess their benefits and disadvantages with respect to the problem characteristics

Surrogate model-based multi-objective MDO approach for partially Reusable Launch Vehicle design

International audienceReusability of the first stage of launch vehicles may offer new perspectives to lower the cost of payload injection into orbit if sufficient reliability and low refurbishment costs can be achieved. One possible option that may be explored is to design the launch vehicle first stage for both reusable and expendable uses, in order to increase the flexibility and adaptability to different target missions. This paper proposes a multi-level MDO approach to design aerospace vehicles addressing multi-mission problems. The proposed approach is focused on the design of a family of launchers for different missions sharing commonalities using multi-objective Bayesian Optimization to account for the computational cost associated with the discipline simulations. The multi-mission problem addressed in this paper considers two missions: a reusable configuration for a SSO orbit with a medium payload range and recovery of the first stage using a glider strategy; and an expendable configuration for a medium payload injected into a Geostationary Transfer Orbit (GTO). A dedicated MDO formulation introducing couplings between the missions is proposed in order to efficiently solve the multi-objective MDO problem while limiting the number of calls to the exact MDA thanks to the use of Gaussian Processes and multi-objective Efficient Global Optimization

Efficient Global Optimization using Deep Gaussian Processes

International audienceEfficient 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

Sequential calibration of material constitutive model using mixed-effects calibration

Identifying model parameters is nowadays intrinsically linked with quantifying the associated uncertainties. While classical methods allow to handle some types of uncertainties such as experimental noise, they are not designed to take into account the variability between the different test specimens, significant in particular for composites materials. The estimation of the impact of this intrinsic variability on the material properties can be achieved using population approaches where this variability is modeled by a probability distribution (e.g., a multivariate Gaussian distribution). The objective is to calibrate this distribution (or equivalently its parameters for a parametric distribution). Among the estimation methods can be found mixed-effects models where the parameters that characterize each replication are decomposed between the population averaged behavior (called fixed-effects) and the impact of material variability (called random-effects). Yet, when the number of model parameters or the computational time of a single run of the simulations increases (for multiaxial models for instance), the simultaneous, global identification of all the material parameters is difficult because of the number of unknown quantities to estimate and because of the required model evaluations. Furthermore, the parameters do not have the same influence on the material constitutive model depending for instance on the nature of the load (e.g., tension, compression). The method proposed in this paper enables to calibrate the model on multiple experiments. It decomposes the overall calibration problem into a sequence of calibrations, each subproblem allowing to calibrate the joint distribution of a subset of the model parameters. The calibration process is eased as the number as the number of unknown parameters is reduced compared to the full problem. The proposed calibration process is applied to an orthotropic elastic model with non linear longitudinal behavior, for a unidirectional composite ply made of carbon fibers and epoxy resin. The ability of the method to sequentially estimate the model parameters distribution is investigated. Its capability to ensure consistency throughout the calibration process is also discussed. Results show that the methodology allows to handle the calibration of complex material constitutive models in the mixed-effects framework

Aerospace system analysis and optimization in uncertainty

Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design

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

International audienceThe 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 (MDO) methodologies is a collection of engineering methodologies to optimize systems modeled as a set of coupled disciplinary analyses and is a key enabler to extend concurrent engineering capabilities. This paper is focused on several examples of recent developments of MDO methodologies (e.g. MDO with transversal decomposition of the design process, MDO 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

On the Primitives of Causality: from the Semantics of Agonist and Antagonist to Models of Accident Causation and System Safety

Controversial discussions on causality have been present in ancient philosophy since the days of Aristotle. Despite the use of this concept in numerous subjects, there is no consensus on the definition of causality and its possible mathematization. Many authors have analyzed the relation between causes and effects; the predominant school of thought reduces causation to a physical relation (either deterministic or probabilistic) between two events. The distinction between causes and consequences is not always clear and meaningful as different “layers of understanding” may be applied to the notion of causality. From this point of view the cause-effect implication relation can be thought of as a first level representation of causation. By “double-clicking” the link between events, the in-depth layers of causality surface, allowing a better comprehension and distinction of the causality nature. It is then important to understand how causality can be incorporated in an accident model. Several accident models have been recently employed to interpret different contributing factors to an adverse event and to help improve our chances on accident prevention. However, accident models do not focus on the nature of the causal relationship. The causal relationship is always limited to “cause(s) imply effect(s)”, but it is never analyzed as to understand the mechanism that lead to such implication. Our language in itself is limited in the ways of describing causal relationships. We will see how the application of the effective metaphor of Agonist and Antagonist actions from the Force Dynamics framework will help analyzing the roles of different actors along the chain of causation. The use of this metaphor, enhanced by the introduction of the Inverse Agonist concept, will provide new insights on the interactions among those actors and will yield the insightful idea of primitives of causality. These primitives will be primal and fundamental notions at the base of a more general concept of causation. We illustrate the use of primitives of causality through an accident example, and we highlight the absence of relevant antagonist and inverse agonist actions that failed to block and de-escalate the accident sequence respectively. We argue that the primitives of causality here introduced allow a deeper understanding of causal mechanisms involved in system accidents and provide a richer basis for conceiving and articulating accident prevention strategies

Active Learning Strategy for Surrogate-Based Quantile Estimation of Field Function

Uncertainty quantification is widely used in engineering domains to provide confidence measures on complex systems. It often requires to accurately estimate extreme statistics on computationally intensive black-box models. In case of spatially or temporally distributed model outputs, one valuable metric results in the estimation of extreme quantile of the output stochastic field. In this paper, a novel active learning surrogate-based method is proposed to determine the quantile of an unidimensional output stochastic process with a confidence measure. This allows to control the error on the estimation of a extreme quantile measure of a stochastic process. The proposed approach combines dimension reduction techniques, Gaussian process and an adaptive refinement strategy to enrich the surrogate model and control the accuracy of the quantile estimation. The proposed methodology is applied on an analytical test case and a realistic aerospace problem for which the estimation of a flight envelop is of prime importance for launch safety reasons in the space industry