Dept. of Aerospace Engineering
http://hdl.handle.net/2142/14799
Sun, 05 Jul 2020 01:39:04 GMT2020-07-05T01:39:04ZEfficient solution of the Fokker-Planck Equation via smooth particle hydrodynamics for nonlinear estimation
http://hdl.handle.net/2142/106319
Efficient solution of the Fokker-Planck Equation via smooth particle hydrodynamics for nonlinear estimation
Duffy, Michael
Modeling and predicting the transient behavior of higher dimensional nonlinear dynamical systems subject to Gaussian white noise excitation remains an open problem with broad application to nonlinear estimation, uncertainty quantification, and reliability to name but a few. These problems remain open in large part due to the Curse of Dimensionality, where computational costs tend to increase exponentially, in time and/or memory, with the number of states of the system. This is especially true for sampling based methods that, while robust and often very simple to implement, quickly become computationally cost ineffective in many applications. Parametric models are usually able to scale far more efficiently as state dimension increases, but they are often limited to specific classes of systems due to not being as robust as sampling based methods.
Another method to analyze the uncertainty in those dynamical systems is to solve the system's corresponding Fokker-Planck equation. The Fokker-Planck Equation (FPE) is the degenerate parabolic partial differential continuity equation that fully defines the evolution of the states' transition probability density function (PDF) over time. This also makes the transient solution to the FPE an option for estimation purposes. Since any dynamical system that is subject to Gaussian white noise excitation, either additive and/or multiplicative, and satisfies the Markov assumption has a corresponding FPE; this represents an extremely large class of systems of engineering interest. However, finding solutions to the transient Fokker-Planck equation remains difficult for the same reasons mentioned previously; solving partial differential equations in high dimensional state spaces also runs up against the Curse of Dimensionality. Analytical solutions only exist for linear systems and a handful of low dimension nonlinear systems to make evaluating simulation efficacy even more difficult.
This work extensively modifies the Smooth Particle Hydrodynamics (SPH) meshfree method in order to rigorously assess its accuracy in simulating up to four state Fokker-Planck equations and explore its suitability for scaling further into higher dimensions. Due to the different potential applications of transient FPE solutions, SPH algorithm performance is analyzed from both an accuracy focused, runtime agnostic standpoint (relevant to reliability analysis) and a runtime focused, accuracy sacrificing standpoint more suited to nonlinear estimation. Rigorous analysis of the convergence characteristics of the algorithm as particle spatial resolution changes is given, as well as the performance impacts of the various accuracy and runtime modifications. The SPH algorithm turns out to be capable of simulating the transient FPE even at extremely low spatial resolution in a stable and robust manner across a variety of systems. However, the mathematical properties of the SPH algorithm make it unable to achieve an arbitrary accuracy concomitant with increasing particle spatial density, especially once one gets to four dimensions. Steep diminishing returns on increased accuracy for computational effort expended are also observed as particle count and state dimension increase.
While not very suitable for applications where accuracy is essential far out into the tails of the time-dependent PDF, the SPH algorithm's ability to reliably approximate the probability evolution over time even at very low spatial resolution makes it a good candidate for use in nonlinear estimation. A novel Bayesian Filter based on the SPH simulated FPE is presented in detail, along with a resampling methodology developed to efficiently perform measurement likelihood updates without degeneracy of the SPH particle field occurring. This new FPE-SPH Filter is compared directly to the Extended Kalman Filter and Particle Filter with importance resampling for each system. The FPE-SPH Filter is able to accurately and robustly estimate a variety of two and four state dynamical systems with long times between state measurements, including the bi-modal Duffing oscillator that renders approaches such as the Extended Kalman Filter inconsistent.
Lastly, a new method of visualizing the error of high dimensional PDFs is presented, referred to as Sub-Field Signatures (SFSs). These signatures make it easier to analyze at a glance both the distribution and balance of the field error to assess simulation performance at a given time regardless of state dimension. This provides a more information dense way to analyze error than traditional RMS error values, but one that is not nearly as involved as the collections of marginal distributions typically used to examine higher dimensional PDFs.
Fokker-Planck Equation; smooth particle hydrodynamics (SPH); meshfree methods; nonlinear filtering; state estimation; Bayesian filter; high-dimensional analysis; stochastic processes
Mon, 30 Sep 2019 00:00:00 GMThttp://hdl.handle.net/2142/1063192019-09-30T00:00:00ZDuffy, MichaelMicroscale strain accumulation during fatigue and fracture of additively manufactured Ti-6Al-4V
http://hdl.handle.net/2142/106305
Microscale strain accumulation during fatigue and fracture of additively manufactured Ti-6Al-4V
VanSickle, Raeann
The goal of this thesis is to relate the different microstructural features in additively manufactured and conventionally manufactured Ti-6Al-4V alloys to the observed fatigue and fracture behaviors. Additively manufactured Direct Metal Laser Melted (DMLM) Ti-6Al-4V samples with two different build orientations and build layer thicknesses were compared to conventionally manufactured annealed Ti-6Al-4V samples. Optical images of the microstructure were recorded after these samples had been heat tinted in a laboratory oven. Using a modified single edge notch tension geometry, the samples were fatigue precracked then subjected to monotonic loading, followed by unloading and reloading. The Digital Image Correlation (DIC) measured plastic strain from fatigue precracking (i.e. plastic wake) was compared to the optical microstructural images. While the plastic wake was observed to be relatively uniform and symmetric about the crack line in the conventional samples, the prior β grain boundaries were seen to influence the size and shape of the plastic wake in the additively manufactured samples. Unlike the relatively straight precrack in the conventional Ti-6Al-4V, the fatigue crack in the additively manufactured samples was observed to periodically propagate parallel to the α’ laths and deflect at prior β grain boundaries. The fatigue crack also propagated towards voids observed on the surface of additively manufactured samples. Voids and other defects observed within the additively manufactured alloy could be responsible for the premature failure of the samples in several experiments. Needle-like regions of high strain that correlated to the α’ laths were observed in the additively manufactured samples, suggesting significant influence of the microstructure on the plastic zone. In one experiment, cracks nucleated at these regions of localized strain after subsequent reloading in additively manufactured Ti-6Al-4V.
Additive Manufacturing; Direct Metal Laser Melting; Titanium; Digital Image Correlation; Fracture; Fatigue
Tue, 13 Aug 2019 00:00:00 GMThttp://hdl.handle.net/2142/1063052019-08-13T00:00:00ZVanSickle, RaeannA model of quadrotor UAV power consumption and its performance across a range of flight conditions
http://hdl.handle.net/2142/106288
A model of quadrotor UAV power consumption and its performance across a range of flight conditions
Faustino, Alexander B.
This thesis presents a parametric model of quadrotor power consumption and characterizes the performance of this model in hardware experiments. Like other existing power models that have been used both for quadrotors and general rotorcraft, it can be expressed as the sum of four terms---induced, parasitic, profile, and climb power---that depend on estimates of the aerodynamic forces and moments acting on the quadrotor. The model's accuracy was measured across a wide range of flight conditions. The results of an ablation study to show the relative contribution of each term are presented, concluding that the contribution strongly depends on the ground velocity of the quadrotor. Both the dataset and code are freely available as a benchmark to facilitate future work in this area.
Quadrotor UAVs; UAV power modeling
Thu, 12 Dec 2019 00:00:00 GMThttp://hdl.handle.net/2142/1062882019-12-12T00:00:00ZFaustino, Alexander B.First steps in development of a translational non equilibrium model using maximum entropy principle
http://hdl.handle.net/2142/106286
First steps in development of a translational non equilibrium model using maximum entropy principle
Jayaraman, Vegnesh
This thesis elaborates the steps taken in the development of a model for flows that are in translational non-equilibrium. The backbone of the model relies on Boltzmann equation for gases as a starting point. Three mathematical tools - domain decomposition, moment methods similar to method of weighted residuals and maximum entropy principle are used for defining the model and developing the underlying governing equations. The underlying modeling goal was to serve as a bridge in terms of computational cost and accuracy, between high fidelity Boltzmann equations and empirically driven Navier Stokes equations. The model effectiveness is studied by solving numerically discretized model equations for one dimensional setting . The problem studied is that of a normal shock occurring in a monoatomic gas. The various assumptions, validation tools used and problems associated with model development are elaborated.
Hypersonic, Boltzmann, Translation, BGK, non equilibrium, maximum entropy
Wed, 11 Dec 2019 00:00:00 GMThttp://hdl.handle.net/2142/1062862019-12-11T00:00:00ZJayaraman, VegneshLinear burn rate of green ionic liquid multimode monopropellant
http://hdl.handle.net/2142/106277
Linear burn rate of green ionic liquid multimode monopropellant
Rasmont, Nicolas Gerard Emmanuel
green monopropellant; hydroxylammonium nitrate; energetic ionic liquid; linear burn
rate; multimode propulsion
Wed, 11 Dec 2019 00:00:00 GMThttp://hdl.handle.net/2142/1062772019-12-11T00:00:00ZRasmont, Nicolas Gerard EmmanuelReduced order extended kalman filter incorporating dynamics of an autonomous underwater vehicle for motion prediction
http://hdl.handle.net/2142/106250
Reduced order extended kalman filter incorporating dynamics of an autonomous underwater vehicle for motion prediction
Hascaryo, Rodra Wikan
Autonomous Underwater Vehicles (AUVs) and Remotely Operated Vehicles (ROVs) are used for a wide variety of missions such as exploration and scientific research. One key challenge for these autonomous vehicles is the creation of a reliable motion prediction. Kinematic Extended Kalman Filters (EKF) have been applied for AUV motion prediction in the context of Simultaneous Localization and Mapping (SLAM) [1]. It has been suggested that a dynamics based EKF would produce more accurate predictions as it considers forces acting on the AUV. Presented in this thesis is an motion prediction EKF for AUVs using a simplified dynamic model. First, the dynamic model is presented and then the simplification process is shown. The filter was implemented with a simulator vehicle in an open-source marine vehicle simulator called UUV Simulator and the results were tested against those obtained through dead reckoning. Results show good predictions, although there are improvements needed before the EKF could be used on manned operational system.
Extended Kalman Filter; Vehicle Dynamics; Autonomous Underwater Vehicle; Unmanned Underwater Vehicle; Marine Vehicle Dynamics; Kalman Filter
Mon, 09 Dec 2019 00:00:00 GMThttp://hdl.handle.net/2142/1062502019-12-09T00:00:00ZHascaryo, Rodra WikanAn energy-conservative cut-cell method and advanced B-spline-based filtering method for flow simulation
http://hdl.handle.net/2142/106215
An energy-conservative cut-cell method and advanced B-spline-based filtering method for flow simulation
Bay, Yong Yi
This dissertation develops two computational methods to improve the accuracy and stability of numerical simulations of turbulent flows. The first method develops an energy stable cut-cell approach to the spatial discretization of domains for simulating incompressible flows. The second method develops a B-spline-based dissipative filter that dynamically adjusts to local under-resolution and is applied to compressible flow simulations. Each method is demonstrated on a series of relevant and increasingly complex problems.
The cut-cell method addresses the challenge of stable and accurate discretization of complex geometries in the simulation of an incompressible flow. The method uses a staggered variable arrangement on regular Cartesian grids combined with computational geometry to achieve discrete conservation and a summation-by-parts (SBP) property to enable provable energy stability in the presence of arbitrary geometries. The development emphasizes the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. The accuracy and robustness of the method is demonstrated with Taylor-Couette flow, Taylor-Green vortex, lid-driven cavity and flows past a circular cylinder.
A B-spline-based dissipative filter is developed that is provable dissipative for bounded domain simulations. The spectral regularization algorithm can be described using the singular values of the filter operator with the amount of filtering set by a scalar- or vector-valued penalty parameter. The penalty parameter can also be chosen to minimize the generalized cross validation (GCV) function that measures fit between the pre-filtered discrete solution and the filtered solution. Efficient algorithms for the GCV optimization are developed for both the scalar and vector penalty parameters. The scheme is demonstrated for shock-like solutions of the Burgers' equation, decaying Burgers' turbulence and compressible turbulent channel flow, revealing the filter scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions.
cut-cell; B-spline
Tue, 26 Nov 2019 00:00:00 GMThttp://hdl.handle.net/2142/1062152019-11-26T00:00:00ZBay, Yong YiReduced-order modeling of non-Boltzmann thermochemistry and radiation for hypersonic flows
http://hdl.handle.net/2142/106155
Reduced-order modeling of non-Boltzmann thermochemistry and radiation for hypersonic flows
Sahai, Amal
The non-equilibrium aerothermal environment during hypersonic flows is determined by the interaction between a multitude of disparate physical phenomena with varying characteristic time scales. The multi-physics nature of this flight regime renders the task of accurately estimating vehicular characteristics both theoretically and computationally challenging. The rapid dissipation of flow velocity into thermal energy in the post-shock region drives collisional-radiative processes that alter the chemical and energy composition of the flowfield. Traditional thermochemical and radiative models often introduce ad-hoc simplifications and rely on model parameters calibrated for a limited range of experimental conditions. Recent advances in computing power have allowed non-equilibrium internal state population distributions of gaseous species to be precisely determined using ab-initio quantum-chemistry calculations, referred to as the state-to-state (StS) approach. Similarly, first-principles based databases for different chemical species are now available that can characterize radiative behavior by accounting for millions of individual radiative transitions, referred to as line-by-line (LBL) modeling. Although exceedingly accurate, both StS and LBL approaches are computationally expensive and cannot be viably applied for solving practical physical problems. This thesis is aimed at developing a unified reduced-order framework for describing non-equilibrium thermochemistry and radiative heating which retains the physical fidelity of the aforementioned approaches but at dramatically lowered computational costs.
A computationally tractable description of non-Boltzmann thermochemistry is obtained using the multi-group maximum-entropy (MGME) framework. This involves dividing individual internal states into bins and then reconstructing the state population distribution using the maximum entropy principle. The current work introduces an adaptive grouping methodology that incorporates state-specific kinetics for further improving the MGME method. Two strategies are considered —Modified Island Algorithm and Spectral Clustering Method — for identifying clusters of states that are likely to equilibrate faster with respect to each other and then lumping them together into bins. The efficacy of MGME-based model reduction is assessed by studying non-equilibrium characteristics of two chemical systems, molecular nitrogen and carbon-dioxide, in a homogeneous chemical reactor. The introduction of adaptive binning which correctly accounts for localized thermalization due to preferential transition pathways allows the complex dynamics of about 9,000 internal states to be modeled using only 10-30 bins.
The multi-variate nature of radiative transfer is tackled by breaking it down into two components: geometric transfer and spectral modeling. A combination of discrete-ordinate method and finite-volume discretization with mesh sweeping is used to resolve generalized three-dimensional radiation fields in the angular and spatial domains. A reduced-order representation of the spectral variation in absorption/emission behavior is obtained through multi-group Planck-averaging. A formal interpretation for Planck-averaging is obtained based on maximum entropy closure in frequency space which allows a direct equivalence to be drawn with the MGME framework. Furthermore, a new generalized grouping strategy for non-equilibrium radiation is proposed that considers both absorption and emission coefficients while defining reduced-order groups. A detailed line-of-sight analysis for various Earth and Jovian entry problems indicates that Planck-averaging combined with the new grouping procedure allows reliable predictions while achieving a two orders-of-magnitude speed-up with respect to narrow-band methods (and three to four orders with respect to full LBL modeling).
The new simulation framework, with its focus on minimizing computational outlays, is ideally suited for realizing flow-radiation coupled simulations on large computational meshes. This is demonstrated by investigating, in conjunction with the US3D flow solver, the impact of vibrational non-equilibrium on carbon dioxide wake flows and resultant infrared radiation around NASA's Mars 2020 vehicle. Predictions for flowfield properties and radiative transfer are obtained using the conventional two-temperature model, bin-based StS model, and for decoupled/coupled flow-radiation calculations. Conventional two-temperature models overestimate the rate of thermal equilibration in the near-wake region resulting in the population of mid-lying and upper carbon dioxide vibrational levels being underpredicted by multiple orders of magnitude. Additionally, the two-temperature approach (in comparison to bin-based StS) overpredicts the rate of carbon dioxide dissociation thereby leading to erroneous estimates for flow properties in the post-shock region (primary source of afterbody radiative emission). This results in inflated values for surface radiative heat flux with conventional two-temperature modeling, although overall differences in radiative behavior are moderated by factors such as fast characteristic relaxation times for ground vibrational levels.
Reduced-order Thermochemistry, Radiative Transfer, Non-Boltzmann Distribution, Hypersonic Flow, Carbon Dioxide IR Radiation
Thu, 19 Sep 2019 00:00:00 GMThttp://hdl.handle.net/2142/1061552019-09-19T00:00:00ZSahai, AmalOn the role of signaling in mitigation of road-traffic congestion: The price of anarchy of signaling-based strategies in stochastic networks
http://hdl.handle.net/2142/106130
On the role of signaling in mitigation of road-traffic congestion: The price of anarchy of signaling-based strategies in stochastic networks
Massicot, Olivier
We study the influence of information design on routing in the presence of vagaries, following the canonical congestion game approach. We allow a central controller to observe nature's state and make exploit the information gap between her and the drivers, to cater information to drivers in a most social manner. In addition to the extreme cases of full and no information, she can also use randomized public signaling and personal recommendations.
We revisit these programs and raise algorithmic concerns, but most importantly, we revisit Roughgarden's celebrated Price of Anarchy (PoA) in uncertain networks. Unexpectedly, no upper bound on the PoA holds if drivers are kept uninformed in the presence of vagaries, while fully informed drivers perform regularly. On the other hand, uninformed drivers might outperform informed drivers by a factor equal to the price of anarchy. Comparing pairwise all information provisions, we establish a table of competitive ratios, which turn out to only take vales one, the PoA, and infinity.
Road-traffic; congestion; signaling games; signal; information design; game theory; price of anarchy; Wardrop equilibrium; Bayesian game
Mon, 22 Jul 2019 00:00:00 GMThttp://hdl.handle.net/2142/1061302019-07-22T00:00:00ZMassicot, OlivierAutonomous robotic system for high throughput plant phenotyping (width estimation) in agricultural fields
http://hdl.handle.net/2142/105844
Autonomous robotic system for high throughput plant phenotyping (width estimation) in agricultural fields
Choudhuri, Anwesa
We present an autonomous robotic system for the estimation of crop stem width in highly cluttered and variable agricultural fields. Stem width is an important phenotype (observable trait) needed by breeders and plant-biologists to measure plant growth. However, its manual measurement is cumbersome, inaccurate, and inefficient. There is an immense need to automate such a task in order to increase the productivity of plants in future. The presented system aims to achieve this goal. It navigates autonomously through every row of an agricultural field under the plant canopy. This navigation is based on deep optical flow on videos collected by the robot and lane estimates from a low cost LiDAR sensor. The phenotyping is performed using deep learning or a sequence of image processing steps to eliminate background. Width is estimated based on the robot velocity from wheel encoders, and validated by the lane estimates from the LiDAR. This system has been tested and exhaustively validated against available hand-measurements on biomass sorghum (Sorghum bicolor) in real experimental fields. Experiments indicate that this system is also effective for other kinds of crops, like corn. The width estimation match on sorghum is 93.5% (using optical flow) and 92.38% (using LiDAR lane estimates) when compared against manual measurements by trained agronomists. Thus, our results clearly establish the feasibility of using small robots for stem-width estimation under the canopy in realistic field settings. Furthermore, the techniques presented here can be utilized for automating other important phenotypic measurements.
Robotics, Deep Learning, Computer Vision, Agriculture
Fri, 19 Jul 2019 00:00:00 GMThttp://hdl.handle.net/2142/1058442019-07-19T00:00:00ZChoudhuri, Anwesa