Дисертації з теми "Multi-fidelity Analysi"

The Ph.D. program has been focused on the development of a multidisciplinary integrated environment for the design of wing for which large changes in shape are expected to be allowed during the flight in order to be better adapted for the different flight segments. The first phase of study has been dedicated to the investigation of the proper Multidisciplinary Design Optimization (MDO) architecture for the integrated management of the design process and a multilevel solution has been proposed and implemented. Such framework involves several disciplinary analysis and optimization loops: in particular aerodynamic analysis, structural analysis, material optimization and mission and performance evaluation are the main components considered for the preliminary design development for such a “morphing” wing. This stage addressed basically the multidisciplinarity and interdisciplinarity issues. The second phase has been dedicated to the investigation of possible techniques for the reduction of the computational burden that characterizes typically this kind of integrated design processes. For this purpose multi-fidelity analysis techniques have been considered involving the use of surrogate models. In particular the attention has been focused on the study of a proper methodology to build an approximated model for the estimation of aerodynamic coefficients to be used for performance evaluation in the mission optimization stage. In this case a procedure involving variables screening phase, data-fit surrogate models evaluation and assessment phase and a final crucial global correction phase of the best surrogate model has been proposed.

This work is on Gaussian-process based approximation of a code which can be run at different levels of accuracy. The goal is to improve the predictions of a surrogate model of a complex computer code using fast approximations of it. A new formulation of a co-kriging based method has been proposed. In particular this formulation allows for fast implementation and for closed-form expressions for the predictive mean and variance for universal co-kriging in the multi-fidelity framework, which is a breakthrough as it really allows for the practical application of such a method in real cases. Furthermore, fast cross validation, sequential experimental design and sensitivity analysis methods have been extended to the multi-fidelity co-kriging framework. This thesis also deals with a conjecture about the dependence of the learning curve (ie the decay rate of the mean square error) with respect to the smoothness of the underlying function. A proof in a fairly general situation (which includes the classical models of Gaussian-process based metamodels with stationary covariance functions) has been obtained while the previous proofs hold only for degenerate kernels (ie when the process is in fact finite-dimensional). This result allows for addressing rigorously practical questions such as the optimal allocation of the budget between different levels of codes in the multi-fidelity framework.

Computer Aided Engineering driven analysis is gaining grounds in automotive industry. Prediction of brake noise using CAE techniques has become populardue to its overall low cost as compared to physical testing. However, the presence of several uncertain parameters which affect brake noise and also the lack of basic understanding about brake noise, makes it difficult to make reliable decisions based on CAE analysis. Therefore, the confidence level in CAE techniques has to be increased to ensure reliability and robustness in the CAE solutions which support design work. One such way to achieve reliability in the CAE analysis isinvestigated in this thesis by incorporating the effects of different sources of uncertainty and variability in the analysis and estimating the probability of designfailure (probability of brake noise above a certain threshold). While incorporating the uncertainties in the CAE analysis ensures robustness, it is computationally intensive. This thesis work aims to gain an understanding about a brakenoise - creep groan, and to bring robustness into the CAE analysis along with reduction in computational time. A probabilistic analysis technique called hierarchical multi-fidelity statistical approachis explored in this thesis work, to estimate the probability of design failure or design robustness at a faster rate. It incorporates the stochasticity in the input parameters while running simulations. The method involves application of a hierarchy of approximations to the system response computed with variations in mesh resolution or variations in number of modes or changing solver time step,etc. And finally it uses the probability theory, to relate the information provided by approximate solutions to get the target failure estimation.Through this method, reliable data regarding the probability of design failure was approximated for every simulation and at a reduced computational time.Additionally, it provided information about critical parameters that influenced brake noise which was meritorious for design management. Estimation of probability of design failure by this method has been proved to be reliable in the case of brake noise according to the simulation results and the method can be considered robust.
Computer Aided Engineering (cae) driven analysis is gaining grounds in automotive industry. Brake noise is one such place where cae simulations are gaining more attention. The presence of several uncertain parameters which affect brake noises and also the lack of basic understanding about brake noise, makes it difficult to make reliable decisions based on cae deterministic analyses alone.Therefore, the confidence level in cae analyses has to be increased to ensure cae analysis robustness. One way to achieve this is by incorporating the effects of different sources of uncertainty and variability in the cae analysis and estimating the probability of design failure. Such a reliability measure (i.e. probability of noise event occurrence or exceedance of noise level than a threshold) can provide car manufacturers with an idea about the costs of warranty claims due to brake noise and can be used as a metric to evaluate different design solutions, before the final design goes to the production stage.  On one hand, using the high-fidelity models of brake/chassis system is generally computationally intensive, and thus, often only limited number of simula-tion runs are feasible for uncertainty analysis and design failure risk assessment. On the other hand, analyses on low-fidelity models, typically based on simplified assumptions during the development phase are fast but not always accu-rate. Striking for a good balance between efficiency and accuracy/robustness is an important task, when dealing with uncertainty/risk analysis of such complex dynamical systems To address these issues, a hierarchical multi-fidelity statistical approach has been adopted in this study, in order to estimate the probability of design failure. It employs a hierarchy of approximations to the system response computed with different fidelity by surrogate modelling, coarse spatial/temporal model mesh resolution variation, changing solver time step, etc., using probability theory, to relate information provided by approximate solu-tions to the target failure estimation. Using this approach opens up the possi-bility to use a low-fidelity models to accelerate the uncertainty quantification of complex brake/chassis systems, while granting unbiased estimation of system design failure risk/reliability. It also enables management of design changes, during fast iterations of the design process. This approach is used for studying one of the brake noise issue called creep groan, understand the root cause and providedesign proposals.

To improve the stealthiness, and the efficiency of military aircraft, engineers moved carried weapons from external hand points, to weapons bays. However, the flow inside bays is turbulent, and characterised by strong broadband, and tonal noise. The open bay flow leads to variability in the released store trajectory, excites the missile, and bay structures, and reduces the aircraft stealthiness. This thesis aims to improve our understanding of real weapon bay flow, and suggests a method for quantifying the store trajectory variability. The main spatio-temporal characteristics of cavity flows are described using post-processing methods, like, SPL, OASPL, and wavelet transform. Also, the code HMB3 is validated for simulation of cavity flows, comparing Scale Adaptive (SAS) results with experiments. To further improve the understanding of the physics driving this flow, a simple model is presented, and compared to experiments. The results are promising, and the model is able to reproduce the cavity flow fluctuations both in space and time. To support measurements of the noise field around a cavity flow, beamforming is applied to the CFD results. This method was able of capturing the main sources of noise around the cavity, using a microphone array, and the mean flow to simulate the propagation of acoustic waves. Also, recommendations for future use of this technique are given. Developments were carried out for this thesis, and for the first time, a CFD code is reported to simulate the complete weapon bay operation, including door operation, store release, and store aeroelasticity. The different parts of the code are strongly coupled, and work together. Thanks to new capabilities of HMB3, this thesis shows more insight on the physics behind realistic weapon bay operation. The flow establishment during door opening is described, and appears to be important for store design, only if the doors are moving very fast. Store releases are simulated, and statistical analysis of the data is performed. A statistical metric was proposed to identify the minimum number of simulations necessary for capturing the mean and standard deviation of the trajectories. Using averaged, and filtered flow data, the trajectory phases were identified and the role of the pressure field inside the cavity was clarified. In addition, the aeroelasticity of the store was computed during carriage, door opening, and release phases, showing small deformations that may lead to structural fatigue. Thanks to the efficiency of the SAS method, a large number of simulations were performed, and more than 1800 cavity travel times were simulated. Simulation of the flow around a store in a supersonic flow, and at high attitude is described in an appendix of the thesis. Like a cavity, this flow has complex features that require advanced turbulence modelling to be simulated. In addition, novel cavity flow controls are investigated, and described in a restricted appendix of the thesis.

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Mavris, Dimitri; Committee Member: Beeson, Don; Committee Member: Duncan, Scott; Committee Member: German, Brian; Committee Member: Kumar, Viren. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This thesis demonstrates that a parametrically-modifiable Advanced Marine Vehicle Structural (AMVS) module (that can be integrated into a larger framework of marine vehicle analysis modules) enables stakeholders, as a group, to complete structurally feasible ship designs using the Set-Based Design (SBD) method. The SBD method allows stakeholders to identify and explore multiple solutions to stakeholder requirements and only eliminating the infeasible poorer solutions after all solutions are completely explored. SBD offers the and advantage over traditional design methods such as Waterfall and Spiral because traditional methods do not adequately explore the design space to determine if they are eliminating more optimal solutions in terms of cost, risk and performance. The fundamental focus for this thesis was on the development of a parametrically modifiable AMVS module using a low-fidelity structural analysis method implemented using a numerical 2D Finite Element Analysis (FEA) applied to the HY2-SWATH. To verify the AMVS module accuracy, a high-fidelity structural analysis was implemented in MAESTRO to analyze the reference marine vehicle model and provide a comparison baseline. To explore the design space, the AMVS module is written to be parametrically modified through input variables, effectively generating a new vessel structure when an input is changed. AMVS module is used to analyze an advanced marine vessel in its two operating modes: displacement and foil-borne. AMVS demonstrates the capability to explore the design space and evaluate the structural feasibility of the advance marine vehicle designs through consideration of the material, stiffener/girder dimensions, stiffener/girder arrangement, and machinery/equipment weights onboard.
Master of Science

A multidisciplinary approach for the modeling and analysis of the performance of Olympic rowing boats is presented. The goal is to establish methodologies and tools that would determine the effects of variations in applied forces and rowers motions and weights on mean surge speed and oscillatory boat motions. The coupling between the rowers motions with the hull and water forces is modeled with a system of equations. The water forces are computed using several fluid dynamic models that have different levels of accuracy and computational cost. These models include a solution of the Reynolds Averaged Navier--Stokes equations complemented by a Volume of Fluid method, a linearized 3D potential flow simulation and a 2D potential flow simulation that is based on the strip theory approximation. These results show that due to the elongated shape of the boat, the use of Sommerfeld truncation boundary condition does not yield the correct frequency dependence of the radiative coefficients. Thus, the radiative forces are not computed in the time-domain problem by means of a convolution integral, accounting for flow memory effects, but were computed assuming constant damping and added mass matrices. The results also show that accounting for memory effects significantly improves the agreement between the strip theory and the RANS predictions. Further improvements could be obtained by introducing corrections to account for longitudinal radiative forces, which are completely neglected in the strip theory. The coupled dynamical system and the multi-fidelity fluid models of the water forces were then used to perform a sensitivity analysis of boat motions to variations in rowers weights, exerted forces and cadence of motion. The sensitivity analysis is based on the polynomial chaos expansion. The coefficients of each random basis in the polynomial chaos expansion are computed using a non-intrusive strategy. Sampling, quadrature, and linear regression methods have been used to obtain the these coefficients from the outputs generated by the system at each sampling point. The results show that the linear regression method provides a very good approximation of the PCE coefficients. In addition, the number of samples needed for the expansion, does not grow exponentially with the number of varying input parameters. For this reason, this method has been selected for performing the sensitivity analysis. The sensitivity of output parameters to variations in selected input parameters of the system are obtained by taking the derivatives of the expansion with respect to each input parameter. Three test cases are considered: a light-weight female single scull, a male quad scull, and a male coxless four. For all of these cases, results that relate the effects of variations in rowers weights, amplitudes of exerted forces and cadence of rowing on mean boat speed and energy ratio, defined as the ratio of kinetic energy of the forward motion to that of the oscillatory motions, are presented. These results should be useful in the design of rowing boats as well as in the training of rowers.
Ph. D.

The work presented in this thesis is dedicated to the study of vehicle rollover and the tyre and suspension characteristics influencing it. Recent data shows that 35.4% of recorded fatal crashes in Sports Utility Vehicles (SUVs) included vehicle rollover. The effect of rollover on an SUV tends to be more severe than for other types of passenger vehicle. Additionally, the number of SUVs on the roads is rising. Therefore, a thorough understanding of factors affecting the rollover resistance of SUVs is needed. The majority of previous research work on rollover dynamics has been based on low fidelity models. However, vehicle rollover is a highly non-linear event due to the large angles in vehicle body motion, extreme suspension travel, tyre non-linearities and large forces acting on the wheel, resulting in suspension spring-aids, rebound stops and bushings operating in the non-linear region. This work investigates vehicle rollover using a complex and highly non-linear multi-body validated model with 165 degrees of freedom. The vehicle model is complemented by a Magic Formula tyre model. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to systematically identify the sensitivity of rollover propensity to suspension kinematic and compliance characteristics. In this process, several rollover metrics are examined together with stability considerations and an appropriate rollover metric is devised. Research so far reveals that the tyre properties having the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness, and tyre vertical stiffness. Key kinematic and compliance characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force. The study of suspension and tyre parameters affecting rollover is supplemented by an investigation of a novel anti-rollover control scheme based on a reaction wheel actuator. The simulations performed so far show promising results. Even with a very simple and conservative control scheme the reaction wheel, with actuator torque limited to 100Nm, power limited to 5kW and total energy consumption of less than 3kJ, increases the critical manoeuvre velocity by over 9%. The main advantage of the proposed control scheme, as opposed to other known anti-rollover control schemes, is that it prevents rollover whilst allowing the driver to maintain the desired vehicle path.

Inlet distortion is an important consideration in fan performance. Distortion can be caused through flight conditions and airframe-engine interfaces. The focus of this paper is a series of high-fidelity time accurate Computational Fluid Dynamics (CFD) simulations of a multistage fan. These investigate distortion transfer and generation as well as the underlying flow physics of these phenomena under different operating conditions. The simulations are performed on the full annulus of a 3 stage fan. The code used to carry out these simulations is a modified version of OVERFLOW 2.2 developed as part of the Computational Research and Engineering Acquisition Tools and Environment (CREATE) program. Several modifications made to the code are described within this thesis. The inlet boundary condition is specified as a 1/rev total pressure distortion. Simulations at choke, design, and near stall points are analyzed and compared to experimental data. Analysis includes the phase and amplitude of total temperature and pressure distortion through each stage of the fan and blade loading plots. An understanding of the flow physics associated with distorted flows will help designers account for unsteady flow physics at design and off-design operating conditions and build more robust fans with a greater stability margin.

En ingénierie, la conception de systèmes complexes, tels que les lanceurs aérospatiaux, implique l'analyse et l'optimisation de problèmes présentant diverses problématiques. En effet, le concepteur doit prendre en compte différents aspects dans la conception de systèmes complexes, tels que la présence de fonctions coûteuses en temps de calcul et en boîte noire , la non-stationnarité des performances optimisées, les multiples objectifs et contraintes impliqués, le traitement de multiples sources d’information dans le cadre de la multi-fidélité, et les incertitudes épistémiques et aléatoires affectant les modèles physiques. Un large éventail de méthodes d'apprentissage automatique est utilisé pour relever ces différents défis. Dans le cadre de ces approches, les processus Gaussiens, bénéficiant de leur formulation Bayésienne et non paramétrique, sont populaires dans la littérature et divers algorithmes d'état de l'art pour la conception de systèmes complexes sont basés sur ces modèles.Les processus Gaussiens, bien qu'ils soient largement utilisés pour l'analyse et l'optimisation de systèmes complexes, présentent encore certaines limites. Pour l'optimisation de fonctions coûteuses en temps de calcul et en boite noire, les processus Gaussiens sont utilisés dans le cadre de l'optimisation Bayésienne comme modèles de régression. Cependant, pour l'optimisation de problèmes non stationnaires, les processus Gaussiens ne sont pas adaptés en raison de l'utilisation d'une fonction de covariance stationnaire. En outre, dans l'optimisation Bayésienne multi-objectif, un processus Gaussien est utilisé pour chaque objectif indépendamment des autres objectifs, ce qui empêche de prendre en considération une corrélation potentielle entre les objectifs. Une autre limitation existe dans l'analyse multi-fidélité où des modèles basés sur les processus Gaussiens sont utilisés pour améliorer les modèles haute fidélité en utilisant l'information basse fidélité, cependant, ces modèles supposent généralement que les différents espaces d'entrée de fidélité sont définis de manière identique, ce qui n'est pas le cas dans certains problèmes de conception.Dans cette thèse, des approches sont développées pour dépasser les limites des processus Gaussiens dans l'analyse et l'optimisation de systèmes complexes. Ces approches sont basées sur les processus Gaussiens profonds, la généralisation hiérarchique des processus Gaussiens.Pour gérer la non-stationnarité dans l'optimisation bayésienne, un algorithme est développé qui couple l'optimisation bayésienne avec les processus Gaussiens profonds. Les couches internes permettent une projection Bayésienne non paramétrique de l'espace d'entrée pour mieux représenter les fonctions non stationnaires. Pour l'optimisation Bayésienne multiobjectif, un modèle de processus Gaussien profond multiobjectif est développé. Chaque couche de ce modèle correspond à un objectif et les différentes couches sont reliées par des arrêtes non orientés pour coder la corrélation potentielle entre objectifs. De plus, une approche de calcul de l'expected hyper-volume improvement est proposée pour prendre également en compte cette corrélation au niveau du critère d'ajout de point. Enfin, pour aborder l'analyse multi-fidélité pour différentes définitions d'espace d'entrée, un modèle de processus gaussien profond à deux niveaux est développé. Ce modèle permet une optimisation conjointe du modèle multi-fidélité et du mapping entre les espaces d'entrée des différentes fidélités.Les différentes approches développées sont évaluées sur des problèmes analytiques ainsi que sur des problèmes de conception de véhicules aérospatiaux et comparées aux approches de l'état de l'art
In engineering, the design of complex systems, such as aerospace launch vehicles, involves the analysis and optimization of problems presenting diverse challenges. Actually, the designer has to take into account different aspects in the design of complex systems, such as the presence of black-box computationally expensive functions, the complex behavior of the optimized performance (e.g., abrupt change of a physical property here referred as non-stationarity), the multiple objectives and constraints involved, the multi-source information handling in a multi-fidelity framework, and the epistemic and aleatory uncertainties affecting the physical models. A wide range of machine learning methods are used to address these various challenges. Among these approaches, Gaussian Processes (GPs), benefiting from their Bayesian and non-parametric formulation, are popular in the literature and diverse state-of-the-art algorithms for the design of complex systems are based on these models.Despite being widely used for the analysis and optimization of complex systems, GPs, still present some limitations. For the optimization of computationally expensive functions, GPs are used within the Bayesian optimization framework as regression models. However, for the optimization of non-stationary problems, they are not suitable due to the use of a prior stationary covariance function. Furthermore, in Bayesian optimization of multiple objectives, a GP is used for each involved objective independently, which prevents the exhibition of a potential correlation between the objectives. Another limitation occurs in multi-fidelity analysis where GP-based models are used to improve high-fidelity models using low-fidelity information. However, these models usually assume that the different fidelity input spaces are identically defined, which is not the case in some design problems.In this thesis, approaches are developed to overcome the limits of GPs in the analysis and optimization of complex systems. These approaches are based on Deep Gaussian Processes (DGPs), the hierarchical generalization of Gaussian processes.To handle non-stationarity in Bayesian optimization, a framework is developed that couples Bayesian optimization with DGPs. The inner layers allow a non-parametric Bayesian mapping of the input space to better represent non-stationary functions. For multi-objective Bayesian optimization, a multi-objective DGP model is developed. Each layer of this model corresponds to an objective and the different layers are connected with undirected edges to encode the potential correlation between objectives. Moreover, a computational approach for the expected hyper-volume improvement is proposed to take into account this correlation at the infill criterion level as well. Finally, to address multi-fidelity analysis for different input space definitions, a two-level DGP model is developed. This model allows a joint optimization of the multi-fidelity model and the input space mapping between fidelities.The different approaches developed are assessed on analytical problems as well as on representative aerospace vehicle design problems with respect to state-of-the-art approaches

Design space exploration (DSE) is used to improve and understand engineering designs. Such designs must meet objectives and structural requirements. Design improvement is non-trivial and requires new DSE methods. Turbomachinery manufacturers must continue to improve existing engines to keep up with global demand. Two challenges of turbomachinery DSE are: the time required to evaluate designs, and knowing which designs to evaluate. This research addressed these challenges by developing novel surrogate and principal component analysis (PCA) based DSE methods. Node and PCA-based surrogates were created to allow faster DSE of turbomachinery blades. The surrogates provided static stress estimation within 10% error. Surrogate error was related to the number of sampled finite element (FE) models used to train the surrogate and the variables used to change the designs. Surrogates were able to provide structural evaluations three to five orders of magnitude faster than FEA evaluations. The PCA-based surrogates were then used to create a PCA-based design workflow to help designers know which designs to evaluate. The workflow used either two-point correlation or stress and geometry coupling to relate the design variables to principal component (PC) scores. These scores were projections of the FE models onto the PCs obtained from PCA. Analysis showed that this workflow could be used in DSE to better explore and improve designs. The surrogate methods were then applied to vibratory stress. A computationally simplified analysis workflow was developed to allow for enough fluid and structural analyses to create a surrogate model. The simplified analysis workflow introduced 10% error but decreased the computational cost by 90%. The surrogate methods could not directly be applied to emulation of vibration due to the large spikes which occur near resonance. A novel, indirect emulation method was developed to better estimate vibratory responses Surrogates were used to estimate the inputs to calculate the vibratory responses. During DSE these estimations were used to calculate the vibratory responses. This method reduced the error between the surrogate and FEA from 85% to 17%. Lastly, a PCA-based multi-fidelity surrogate method was developed. This assumed the PCs of the high and low-fidelities were similar. The high-fidelity FE models had tens of thousands of nodes and the low-fidelity FE models had a few hundred nodes. The computational cost to create the surrogate was decreased by 75% for the same errors. For the same computational cost, the error was reduced by 50%. Together, the methods developed in this research were shown to decrease the cost of evaluating the structural responses of turbomachinery blade designs. They also provided a method to help the designer understand which designs to explore. This research paves the way for better, and more thoroughly understood turbomachinery blade designs.

The drivers of fidelity and divorce of pair-bonded individuals, along with their fitness consequences, are of great interest as they influence mating systems, population structure and productivity, and gene flow. Socially monogamous birds offer an ideal opportunity to study divorce since they show great variability in the extent to which pair bonds are maintained. However, there has been little consensus as to whether divorce is a behavioural adaptation to improve a mating situation, or a consequence of other processes. Moreover, the biological and ecological correlates of fidelity are difficult to address because previous work has been based on indirect and potentially biased methods. Finally, in terms of process, the link between the process of mate choice and subsequent mating decisions has been largely inaccessible to study. My doctoral thesis addressed these significant gaps in our understanding of cause, process and consequence in the formation and dissolution of pair bonds in socially monogamous birds. I accomplished this in three principal ways. First, I conducted a robust phylogenetic meta-analysis on 84 studies across 64 species to assess the existing empirical evidence that divorce in socially monogamous birds is adaptive (in terms of breeding success). This analysis revealed that divorce is, in general, adaptive as it is both triggered by relatively low breeding success and leads to improvement in success. Next, I developed a novel probabilistic multievent capture–mark–recapture framework that provides joint estimates of survival and fidelity while explicitly accounting for imperfect detection, capture heterogeneity, and uncertainty in pair status. By applying this model to breeding data on a wild great tit population I showed that birds that remain faithful to their partner exhibit higher survival rates and are more likely to remain faithful in the next breeding season than do birds that change partners. Subsequently, I confirmed the generality of a survival benefit by applying the model to breeding data on other tit populations. Then, by applying the model to data from a population of mute swans, I showed that fidelity decreases the likelihood of skipping breeding and mortality in this long-lived species, and that these effects depended on age, individual quality, and immigration status. Finally, I investigated how the timing of pair formation influences breeding success and divorce probability using five years of data on the over-winter social behaviour of great tits. I showed that early pair formation had a positive effect on fitness components, influencing the likelihood of divorce only indirectly, through breeding success. Further, my work revealed that males, but not females, with higher numbers of the female associates in winter, and males whose future breeding partners were ranked low amongst these, divorced more often. My research makes a significant contribution to our understanding of divorce and fidelity, and generates a number of important implications for future studies. First, my work establishes that divorce is adaptive for breeding success. Second, my results highlight that survival is an important (and likely, widespread) fitness consequence of pairing decisions. Third, I provide a novel statistically rigorous modelling framework for estimating fidelity-rates and testing hypothesis about fidelity that overcomes many of the inherent biases in traditional estimates. Fourth, it provides the first evidence for a selective advantage of early pair formation in wild, thus highlighting that there are benefits to pair familiarity that manifest via social associations of individuals prior to breeding. Finally, my work reveals the selective pressures operating via the social environment can ultimately influence the mating strategies individuals adopt.

Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.

To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.

In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.

The main objectives of this thesis are:

1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver

2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).

3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.

The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.