Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs

An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith

Constrained H̳₂ design via convex optimization with applications

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.In title on t.p., double-underscored "H" appears in script.Includes bibliographical references (p. 133-138).A convex optimization controller design method is presented which minimizes the closed-loop H2 norm, subject to constraints on the magnitude of closed-loop transfer functions and transient responses due to specified inputs. This method uses direct parameter optimization of the closed-loop Youla or Q-parameter where the variables are the coefficients of a stable orthogonal basis. The basis is constructed using the recently rediscovered Generalized Orthonormal Basis Functions (GOBF) that have found application in system identification. It is proposed that many typical control specifications including robustness to modeling error and gain and phase margins can be posed with two simple constraints in the frequency and time domain. With some approximation, this formulation allows the controller design problem to be cast as a quadratic program. Two example applications demonstrate the practical utility of this method for real systems. First this method is applied to the roll axis of the EOS-AM1 spacecraft attitude control system, with a set of performance and robustness specifications. The constrained H2 controller simultaneously meets the specifications where previous model-based control studies failed. Then a constrained H2 controller is designed for an active vibration isolation system for a spaceborne optical technology demonstration test stand. Mixed specifications are successfully incorporated into the design and the results are verified with experimental frequency data.by Beau V. Lintereur.S.M

Reconfigurable autopilot design for a high performance aircraft using model predictive control

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Page 136 blank.Includes bibliographical references (p. 135).The losses of military and civilian aircraft due to control surface failures have prompted research into controllers with a degree of reconfiguration. This thesis will describe a design approach incorporating Model Predictive Control (MPC) with a self updating model to achieve a level of reconfiguration in a generic high performance aircraft. MPC has the advantage of explicitly taking a model of the failed system and incorporating it into a receding horizon optimization problem. MPC also has the added benefits of allowing constraints on the inputs, outputs, and states of the system as well as tuning flexibility. This thesis describes the development of four types of MPC autopilots. A description of the controller implementation and failure implementation is also included. Each autopilot is subject to a surface failure during certain times in a sample maneuver and the resulting controller adaptation is analyzed. All MPC controllers are found to maintain good performance in the event of certain failures with an updated internal model. It is when the internal model is not updated that full performance is not recovered and in some cases, loss of the aircraft results.by Jose Pedro Ruiz.S.M

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide

Modelação comportamental e pré-distorção digital de transmissores de rádio-frequência

Doutoramento em Engenharia ElectrotécnicaNos atuais sistemas de telecomunicações, os transmissores de rádio-frequência são desenvolvidos tendo maioritariamente em conta a eficiência da conversão da potência fornecida da fonte em potência de rádio-frequência. Este tipo de desenho resulta em amplificadores de potência com características de transmissão não-lineares, que distorcem severamente o envelope de informação no processo de amplificação, gerando distorção fora da banda. Para corrigir este problema utiliza-se um processo de compensação não linear, sendo que a pré-distorção digital se tem favorecido pela sua flexibilidade e precisão. Este método é tipicamente aplicado de uma forma cega, por força bruta até se obter a compensação desejada. No entanto, quando o método se mostra ineficaz, como se verificou em amplificadores de potência baseados em transístores de nitreto de gálio, é difícil saber o que modificar nos sistemas para os tornar de novo úteis. De forma a compreender e desenhar sistemas de pré-distorção digital robustos é necessário, por um lado, perceber o comportamento dos amplificadores de rádio-frequência, por outro, perceber as limitações e relações entre os modelos digitais e o comportamento real do amplificador. Nesse sentido, esta tese explora e descreve estas relações de forma a suportar a escolha de modelos de pré-distorção, desenvolve novos modelos baseados no comportamento dos transístores, e propõe métodos de caracterização para os amplificadores de RF.In current telecommunication systems, the main concern when developing the radio frequency transmitter is power efficiency. This type of design generally leads to a highly nonlinear transmission characteristic, mainly due to the radio frequency power amplifier. This nonlinear transmission severely distorts the information envelope, leading to spectral regrowth, out-of-band distortion. To correct this problem a nonlinear compensation process is employed. For this application, digital predistortion is generally favored for its flexibility and accuracy. Digital predistortion is mostly applied in a blind manner, using brute force until the desired compensation is achieved. Because of this, when the method fails, as it has in gallium nitride based power amplifiers, it is difficult to modify the system to achieve the desired results. To understand and design robust predistortion systems, it is both necessary to have knowledge of the power amplifiers’ behavior, on one hand, and understand the limitations and relations between the digital models and these behaviors, on the other. To do this, this thesis explores and describes these relationships, granting support to the digital predistortion model choice, it further develops new predistortion models based on the physics of the transistors’ behaviors, and it proposes methods for the characterization of radio frequency power amplifiers

Generalized linear-in-parameter models : theory and audio signal processing applications

This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.reviewe

Advances in Trans-dimensional Geophysical Inference

This research presents a series of novel Bayesian trans-dimensional methods for geophysical inversion. A first example illustrates how Bayesian prior information obtained from theory and numerical experiments can be used to better inform a difficult multi-modal inversion of dispersion information from empirical Greens functions obtained from ambient noise cross-correlation. This approach is an extension of existing partition modeling schemes. An entirely new class of trans-dimensional algorithm, called the trans-dimensional tree method is introduced. This new method is shown to be more efficient at coupling to a forward model, more efficient at convergence, and more adaptable to different dimensions and geometries than existing approaches. The efficiency and flexibility of the trans-dimensional tree method is demonstrated in two different examples: (1) airborne electromagnetic tomography (AEM) in a 2D transect inversion, and (2) a fully non-linear inversion of ambient noise tomography. In this latter example the resolution at depth has been significantly improved by inverting a contiguous band of frequencies jointly rather than as independent phase velocity maps, allowing new insights into crustal architecture beneath Iceland. In a first test case for even larger scale problems, an application of the trans-dimensional tree approach to large global data set is presented. A global database of nearly 5 million multi-model path average Rayleigh wave phase velocity observations has been used to construct global phase velocity maps. Results are comparable to existing published phase velocity maps, however, as the trans-dimensional approach adapts the resolution appropriate to the data, rather than imposing damping or smoothing constraints to stabilize the inversion, the recovered anomaly magnitudes are generally higher with low uncertainties. While further investigation is needed, this early test case shows that trans-dimensional sampling can be applied to global scale seismology problems and that previous analyses may, in some locales, under estimate the heterogeneity of the Earth. Finally, in a further advancement of partition modelling with variable order polynomials, a new method has been developed called trans-dimensional spectral elements. Previous applications involving variable order polynomials have used polynomials that are both difficult to work with in a Bayesian framework and unstable at higher orders. By using the orthogonal polynomials typically used in modern full-waveform solvers, the useful properties of this type of polynomial and its application in trans-dimensional inversion are demonstrated. Additionally, these polynomials can be directly used in complex differential solvers and an example of this for 1D inversion of surface wave dispersion curves is given

Optical angular momentum in air core fibers

As data consumption continues to grow, the backbone of the internet, comprising single mode fiber (SMF)-based infrastructure, is fundamentally limited by nonlinear optical effects. One strategy to address this bottleneck, space division multiplexing (SDM), utilizes multiple modes in a single fiber as independent data channels. Orbital Angular Momentum (OAM) carrying modes, which have twisting phase fronts tracing out helices as the beams propagate, have recently received tremendous attention as a means of achieving low-crosstalk, digital signal processing (DSP)-free transmission with enhanced capacity. Terabit-scale transmission using 4 OAM modes over 1.1km has been demonstrated, but questions remain – how many OAM modes can fibers support, and how stable is propagation over longer lengths? In this thesis, we investigate angular momentum carrying modes in a novel class of fibers featuring an air core. We find that high-order OAM states, although arising in degenerate pairs, counterintuitively resist mode coupling due to OAM conservation, pointing to a unique stability inherent to OAM modes in fibers. We achieve OAM propagation up to 13.4km lengths, and achieve mode purities greater than 15dB at data-center length-scales. We use these fibers to transmit wavelength-division multiplexed data with 25 GHz channel spacing, 10 GBaud rates and quadrature-phase-shift keyed modulation formats in 12 modes simultaneously, over 1.2km, and over a large number of wavelengths across the C-band (1530-1565nm). However, transmission over every mode in every channel of the C-band was prevented by the accidental degeneracy of OAM states with undesired modes. To achieve a larger ensemble of stable modes over a larger wavelength range, we study new fiber designs that avoid this accidental degeneracy problem. We find that the most scalable modal eigenbasis is a set of states that carry non-integer amounts of average OAM, also called spin-orbit coupled modes in analogy with similar effects observed in atomic physics. We demonstrate excitation and transmission of 24 such modes over device lengths (10m). The achievement of a record number of uncoupled modes in fibers confirms the viability of angular momentum states as data carriers, and potential applications include links in data centers, high capacity optical amplifiers, and quantum communications links.2017-09-09T00:00:00