Uncertainty propagation in multi-agent systems for multidisciplinary optimization problems

International audienceBecause of uncertainties on models and variables, deterministic multidisciplinary optimization may achieve under-sizing (without design margins) or over-sizing (with arbitrary design margins). Thus, it is necessary to implement multidisciplinary optimization methods that take into account the uncertainties in order to design systems that are both robust and reliable. Probabilistic methods such as reliability-based design optimization (RBDO) or robust design methods, provide designers with powerful decision-making tools but may involve very time-consuming calculations. New optimization approaches have been developed to deal with such complex problems. Auto-adaptive Multi-Agent Systems (AMAS) is a new approach developed recently, allowing to take into account the various aspects of a multidisciplinary optimization problem (multi-level, computation burden etc.). This approach was suggested for solving complex deterministic optimization problem. Now, the question of the integration of uncertainties in this multi-agent based optimization arises. The aim of this paper is to propose a new methodology for integrating the treatment of uncertainties in an adaptive multi-agent system for sequential optimization. The developed method employs a single loop process in which cycles of deterministic optimization alternate with evaluations of the system reliability. For each cycle, the optimization and the reliability analysis are decoupled from each other. The reliability analysis is carried out at agent level and only after the resolution of the deterministic optimization, to verify the feasibility of the constraints under uncertainties. Following the probabilistic study, the constraints violated (with low reliability) are shifted to the area of feasibility by integrating adaptive safety coeficients whose calculations are based on the agent-level reliability information. The method developed is applied to a conceptual aircraft design problem

Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moir\'e Interferometry Displacement Fields

The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E 1, E 2, 12, G 12) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moir\'e interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article)

Une approche bayesienne de l'identification des constantes élastiques orthotropes de pli à partir de tests de vibration de flexion sur stratifié = A Bayesian approach to identification of orthotropic elastic constants of the ply from vibration tests on a laminate

National audienceL'identification bayesienne est une des approches permettant de prendre en considération des erreurs de mesure ainsi que de modélisation. De plus, cette méthode identifie une densité de probabilité, permettant ainsi d'avoir des informations aussi bien sur la variance que sur la corrélation des propriétés identifiées. Cette procédure peut cependant être très coûteuse en temps de calcul. Pour réduire ce temps de calcul nous proposons ici une approche bayesienne basée sur la méthode des surfaces de réponse. L'approche est appliquée au problème de l'identification de constantes élastiques orthotropes à partir des mesures des fréquences propres d'une plaque vibrante libre. La procédure développée prend en compte des erreurs de mesures, de l'incertitude sur les autres paramètres d'entrée du modèle (dimensions de la plaque, densité), ainsi que des erreurs systématiques. La densité de probabilité jointe des quatre constantes élastiques du pli est identifiée et caractérisée par ses valeurs moyennes et la matrice de variance covariance. Nous trouvons que certaines paramètres, comme le coefficient de Poisson, sont identifiées avec une bien plus grande incertitude que d'autres et qu'une corrélation significative existe entre les différentes propriétés identifiées

Dimensionality reduction of full fields by the principal components analysis

http://www.iccm-central.org/Proceedings/ICCM17proceedings/Themes/Behaviour/FULL%20FIELD%20MEASU%20METH/F14.7%20Gogu.pdfInternational audienceThe principal components analysis is applied to simulated full field displacement maps of 4569 measurement points thus allowing representation of any field within a certain domain as a linear combination of five basis vectors without losing significant information. A dimensionality reduction from 4569 to only 5 is thus achieved

Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Tying non-matching meshes is needed in many instances of finite element mod- eling. Multiple techniques have been proposed in the literature to accomplish the correct communication between different discretizations. They all seek to achieve some trade-off in terms of accuracy, complexity and computational cost. In this work we review several of the existing techniques and benchmark them on several simple test problems in terms of accuracy and computational cost. We also discuss some of the drawbacks and limitations of the existing methods. We then propose two novel contributions. First, a new approach that imposes the continuity of the displacement field at the interface in a point-wise manner only after an integral weighted averaging procedure over each interface. Second, a procedure for the correction of the interpolation operator based on the balance of internal forces and mo- ments at the interface is proposed, which is applicable to all the reviewed methods, both existing and the new proposed one. All the considered approaches are benchmarked on sev- eral test problems in terms of various error measures for displacements, stresses, interface forces and moments, total work at the interface and computational cost

Comparing structural airframe maintenance strategies based on probabilistic estimates of the remaining useful service life

Structural airframe maintenance is a subset of aircraft maintenance, which is often performed at scheduled intervals to detect and repair cracks that would otherwise affect the safety of the aircraft. With the progress of structural health monitoring (SHM) techniques, which uses on-board sensors and actuators to assess damage status, condition-based maintenance (CBM) is considered as an alternative to traditional scheduled maintenance. By applying SHM techniques, CBM can access damages status as frequently as needed and unscheduled maintenance can be asked once the damage exceeds a particular threshold. Due to the harsh working environment and sensor limitation, the measurement data acquired from SHM is often quite noisy. In this paper, Extended Kalman filter is used to filer the noise to provide an accurate estimation of crack size and crack growth parameters together with their associated uncertainty. This knowledge is used to obtain a probabilistic estimate of the remaining useful service life of the structure. Based on these estimates, two maintenance philosophies are developed and further compared in terms of maintenance stop number or replaced panel number. The results indicate that both these two strategies reduce considerably the maintenance stop number compared to scheduled maintenance

Optimisation multidisciplinaire sous incertitudes en conception préliminaire avion

Les incertitudes sont couramment intégrées dans les méthodes d'optimisation afin d'obtenir des systèmes fiables et/ou robustes. Les systèmes à optimiser de plus en plus complexes font souvent intervenir plusieurs disciplines étroitement couplées : des méthodes spécifiques permettant de propager les incertitudes doivent donc être implémentées. Nous nous intéresserons notamment au problème de conception préliminaire avion dont l'objectif est de minimiser la masse en respectant des contraintes de robustesse et de fiabilité

Engine Pylon Topology Optimization Framework Based on Performance and Stress Criteria

Reducing fuel consumption is a major driver for the design of future aircraft. The engine integration primary structure plays a significant role in the integrated engine thrust-specific fuel consumption. A topology optimization framework was developed to design the primary structure integrating the engine to the aircraft wing considering mass, stress, and engine performance criteria. The proposed approach had to address several challenges associated with the use of nonuniform meshes, the integration of the engine model as a super-element, and the presence of nonconforming mesh interfaces. Analytical adjoint evaluations for all the responses were also derived. The framework was tested on a simplified engine model providing a consistent solution

Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization

Structural topology optimization has seen many methodological advances in the past few decades. In this work we focus on continuum-based structural topology optimization and more specifically on geomet- ric feature based approaches, also known as explicit topology optimization, in which a design is described as the assembly of simple geometric components that can change position, size and orientation in the con- sidered design space. We first review various recent de- velopments in explicit topology optimization. We then describe in details three of the reviewed frameworks, which are the Geometry Projection method, the Moving Morphable Components with Esartz material metho

Faciliter l'identification bayesienne à partir de mesures de champ par la méthode des surfaces de réponse et l'expansion de Karhunen Loeve

http://www-lmdc.insa-toulouse.fr/jfms10/JFMS_PRES/TS1/Gogu_Haftka_Le_Riche.pdfNational audienc