In aircraft design, ground/flight vibration tests are conducted to extract aircraft's modal parameters (natural frequencies, damping ratios and mode shapes) also known as the modal basis. The main problem in aircraft modal identification is the large number of sensors needed, which increases operational time and costs. The goal of this paper is to minimize the number of sensors by optimizing their locations in order to reconstruct a truncated modal basis of N mode shapes with a high level of accuracy in the reconstruction. There are several methods to solve sensors placement optimization (SPO) problems, but for this case an original approach has been established based on an iterative process for mode shapes reconstruction through an adaptive Kriging metamodeling approach so called efficient global optimization (EGO)-SPO. The main idea in this publication is to solve an optimization problem where the sensors locations are variables and the objective function is defined by maximizing the trace of criteria so called AutoMAC. The results on a 2D wing demonstrate a reduction of sensors by 30% using our EGO-SPO strategy.

The interaction between inertial, elastic and aerodynamic forces for structures subjected to a fluid flow may cause unstable coupled vibrations that can endanger the structure itself. Predicting these interactions is a time consuming but crucial task in an aircraft design process. In order to reduce the computational time surrogate reduced order models can be used in both structural and aerodynamic models. More over it is possible to avoid launching CFD computations at every time step. A database of aerodynamic pressure distribution on the structural component can be created conveniently sampling the space of the structural model DoF. Starting from the knowledge of the pre-computed data-set a Gaussian Process can be applied to predict the pressure distribution on an unexplored point of the space of DoF. The knowledge of the standard deviation can be used to give indications on where to launch further CFD computations to enrich the database. This technique will be first applied to a database of pressures obtained using the software Xfoil®, later it will be applied to CFD simulations of type RANS launched with elsA® on one Flap track Fairing of an Airbus aircraft.

In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a prior known relation between outputs, joint auto-and cross-covariance functions can be constructed. Realizations from these joint-covariance functions give outputs that are consistent with the prior relation. One issue with gaussian process regression is efficient inference when scaling upto large datasets. In this paper we use approximate inference techniques upon multi-output kernels enforcing relationships between outputs. Results of the proposed methodology for theoretical data and real world applications are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of real aircraft flight tests, while imposing knowledge of aircraft physics into the model.

Operational Modal Analysis is widely gaining popularity as a means to perform system identification of a structure. Instead of using a detailed experimental setup Operational Modal Analysis relies on measurement of ambient displacements to identify the system. Due to the random nature of ambient excitations and their output responses, various statistical methods have been developed throughout the literature both in the time-domain and the frequency-domain. The most popular of these algorithms rely on the assumption that the structure can be modelled as a multi degree of freedom second order differential system. In this paper we drop the second order differential assumption and treat the identification problem as a curve-fitting problem, by fitting a Gaussian Mixture Model in the frequency domain. We further derive equivalent models for the covariance-driven and the data-driven algorithms. Moreover, we introduce a model comparison criterion to automatically choose the optimum number of Gaussian's. Later the algorithm is used to predict modal frequencies on a simulated problem.

Engineering design is a costly exercise, primarily because gathering data for various design cases requires constructing and experimenting on that design point. Hence engineers learn basic principles of the system and construct more detailed models based on the initial principles and simplifying assumptions. Eg. FEM in structural design or CFD in fluid simulations. We estimate the physical parameters, experimental data for tensile test of AL6061 and lift diagrams for XFLR5 airfoil using change-point kernels.

In this paper a sparse approximation of inference for multi-output Gaussian Process models based on a Variational Inference approach is presented.In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs.Using a general framework for constructing auto-and cross-covariance functions that are consistent with the physical laws, physical relationships among several outputs can be imposed.One major issue with Gaussian Processes is efficient inference, when scaling up-to large datasets.The issue of scaling becomes even more important when dealing with multiple outputs, since the cost of inference increases rapidly with the number of outputs.In this paper we combine the use of variational inference for efficient inference with multi-output kernels enforcing relationships between outputs.Results of the proposed methodology for synthetic data and real world applications are presented.The main contribution of this paper is the application and validation of our methodology on a dataset of real aircraft flight tests, while imposing knowledge of aircraft physics into the model.

In this paper analytical methods to formally incorporate knowledge of physics-based equations between multiple outputs in a Gaussian Process (GP) model are presented. In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a general framework for constructing auto- and cross-covariance functions that are consistent with the physical laws, physics-based relationships among several outputs can be imposed. Results of the proposed methodology for simulated data and measurement from flight tests are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of flight tests, while imposing knowledge of flight mechanics into the model.

Structural dynamic testing is concerned with estimation of system properties i.e. modal parameters. Modal parameters are extracted from measured data that are subjected to variability. Therefore these parameters when extracted from different data samples can be assumed to be random variables, which can be represented in terms of mean and standard deviation. These levels of variability can be quite important in areas of study such as damage identification given the relative insensitivity of the modal parameters to many types of system damage. This work aims at investigating how two different statistical techniques can estimate the confidence intervals on global modal parameters (natural frequencies and damping ratios), estimated by two different methods of modal extraction, on simulated data (corrupted by different levels of noise). Bootstrap and jackknifing techniques will be used on both time (LSCE) and frequency (UMPA) domain SIMO estimators. This will lead to a comparison of the capabilities of each technique to estimate the statistical properties of the modal parameters. Finally ongoing works on local modal parameters (i.e. mode shapes) estimation will be presented through the use of virtual FRFs constructed from surrogate modeling of the FRFs sets.

Pratham', is a nano-satellite built by the students of IIT Bombay and is slated for launch by the Indian Space Research Organization (ISRO) in the third quarter of 2011. This paper discusses the work done by the Structures Sub-system of Pratham. The objective of the sub-system is to ensure the robustness of the satellite structure so that it survives launch loads. A finite element model of the satellite structure has been made and representative launch loads have been applied. Various static and dynamic analyses have been performed on the satellite structure to obtain the response. Finite Element Analyses of the printed circuit boards (PCBs) onboard the satellite have also been performed. The FEA results have been validated in 2 stages: the geometry was validated by comparing with theoretical results while the element types were validated by comparing with analyses of isolated individual structural elements. The results suggest that the satellite will maintains its structural integrity during launch and that no component of the satellite will fail during launch.

Intégration d'information a priori dans la régression de processus Gaussiens : Applications à l'ingénierie aéronautique Dans cette thèse, nous proposons de construire de meilleurs modèles Processus Gaussiens (GPs) en intégrant les connaissances antérieures avec des données expérimentales. En raison du coût élevé de l’exécution d’expériences sur les systèmes physiques, les modèles numériques deviennent un moyen évident de concevoir des systèmes physiques. Traditionnellement, ces modèles ont été construits expérimentalement et itérativement; une méthode plus rentable de construction de modèles consiste à utiliser des algorithmes d’apprentissage automatique. Nous démontrons comment créer des modèles en intégrant une connaissance antérieure en modifiant les fonctions de covariance. Nous proposons des modèles GP pour différents phénomènes physiques en mécanique des fluides.De même, les lois physiques entre plusieurs sorties peuvent être appliquées en manipulant les fonctions de covariance. Pour chaque application, nous comparons le modèle proposé avec le modèle de l’état de l’art et démontrons les gains de coût ou de performance obtenus.