arXiv subjects

Rodrigo B. Platte

Publications and source records attributed to Rodrigo B. Platte.

5 recordsLinked to original sources

arXiv2023

Optimal Control of Transient Flows in Pipeline Networks with Heterogeneous Mixtures of Hydrogen and Natural Gas

We formulate a control system model for the distributed flow of mixtures of highly heterogeneous gases through large-scale pipeline networks with time-varying injections of constituents, withdrawals, and control actions of compressors. This study is motivated by the proposed blending of clean hydrogen into natural gas pipelines as an interim means to reducing end use carbon emissions while utilizing existing infrastructure for its planned lifetime. We reformulate the partial differential equations for gas dynamics on pipelines and balance conditions at junctions using lumped elements to a sparse nonlinear differential algebraic equation system. Our key advance is modeling the mixing of constituents in time throughout the network, which requires doubling the state space needed for a single gas and increases numerical ill-conditioning. The reduced model is shown to be a consistent approximation of the original system, which we use as the dynamic constraints in a model-predictive optimal control problem for minimizing the energy expended by applying time-varying compressor operating profiles to guarantee time-varying delivery profiles subject to system pressure limits. The optimal control problem is implemented after time discretization using a nonlinear program, with validation of the results done using a transient simulation. We demonstrate the methodology for a small test network, and discuss scalability and potential applications.

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arXiv2023

Linear System Analysis and Optimal Control of Natural Gas Dynamics in Pipeline Networks

We design nonlinear and adaptive linear model-predictive control (MPC) techniques to minimize operational costs of compressor-actuated dynamics in natural gas pipeline networks. We establish stability of the local linear system and derive rigorous bounds on error between the nonlinear and linear system solutions. These bounds are used to quantify conditions under which the linear MPC can substitute the nonlinear MPC without significant loss of predictive accuracy. Furthermore, we prove and numerically verify that the computational cost of the linear MPC is orders of magnitude lower than that of solving the baseline optimal control problem. Numerical simulations are performed on nontrivial networks to demonstrate that the proposed MPC can effectively adapt to varying load conditions while maintaining nearly 95% optimality.

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arXiv2020

Effective New Methods for Automated Parameter Selection in Regularized Inverse Problems

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data, {with no prior knowledge of the noise variance}. These concepts are developed for $\ell_2$ and consequently $\ell_1$ regularization models by way of their Bayesian interpretations. Based on these concepts, an iterative scheme is proposed and demonstrated to converge accurately, and analytical convergence results are provided that substantiate these empirical observations. For some of the most common inverse problems, including MRI, SAR, denoising, and deconvolution, an extremely efficient algorithm is derived, making the iterative scheme very attractive for real case use. The computational concerns associated with the general case for any inverse problem are also carefully addressed. A robust set of 1D and 2D numerical simulations confirm the effectiveness of the proposed approach.

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arXiv2019

Fourier Analysis, Computing, and Image Formation for Spotlight Synthetic Aperture Radar

This article is written to serve as an introduction and survey of imaging with synthetic aperture radar (SAR). The reader will benefit from having some familiarity with harmonic analysis, electromagnetic radiation, and inverse problems. After an overview of the SAR problem and some main concepts, the SAR imaging problem is contextualized in terms of classical harmonic analysis. Within this context, we consider partial Fourier sums of off-centered Fourier data and correspondingly the convolutional kernels resulting from conventional SAR image formation techniques. Following this, we revisit imaging of random complex signals from frequency data as in SAR, providing simpler derivations of some previous results and extending these ideas to the continuous setting. These concepts are tied in with the derived convolutional kernels, and it is deduced how good an image approximation is when it is obtained from only a small band of high frequency Fourier coefficients. Finally, regularization methods are presented to improve the quality of SAR images. Corresponding MATLAB software is made available for reproducibility of most figures and to facilitate further exploration of the methods presented here.

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arXiv2017

Multiscale Higher Order TV Operators for L1 Regularization

In the realm of signal and image denoising and reconstruction, $\ell_1$ regularization techniques have generated a great deal of attention with a multitude of variants. A key component for their success is that under certain assumptions, the solution of minimum $\ell_1$ norm is a good approximation to the solution of minimum $\ell_0$ norm. In this work, we demonstrate that this approximation can result in artifacts that are inconsistent with desired sparsity promoting $\ell_0$ properties, resulting in subpar results in {some} instances. With this as our motivation, we develop a multiscale higher order total variation (MHOTV) approach, which we show is related to the use of multiscale Daubechies wavelets. We also develop the tools necessary for MHOTV computations to be performed efficiently, via operator decomposition and alternatively converting the problem into Fourier space. The relationship of higher order regularization methods with wavelets, which we believe has generally gone unrecognized, is shown to hold in several numerical results, although notable improvements are seen with our approach over both wavelets and classical HOTV.

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