Model order reduction of fully parameterized systems by recursive least square optimization

This paper presents an approach for the model order reduction of fully parameterized linear dynamic systems. In a fully parameterized system, not only the state matrices, but also can the input/output matrices be parameterized. The algorithm presented in this paper is based on neither conventional moment-matching nor balanced-truncation ideas. Instead, it uses “optimal (block) vectors” to construct the projection matrix, such that the system errors in the whole parameter space are minimized. This minimization problem is formulated as a recursive least square (RLS) optimization and then solved at a low cost. Our algorithm is tested by a set of multi-port multi-parameter cases with both intermediate and large parameter variations. The numerical results show that high accuracy is guaranteed, and that very compact models can be obtained for multi-parameter models due to the fact that the ROM size is independent of the number of parameters in our approach

A Passivity-Preserving Frequency-Weighted Model Order Reduction Technique

© 2004-2012 IEEE. Frequency-weighted model order reduction techniques aim to yield a reduced order model whose output matches that of the original system in the emphasized frequency region. However, passivity of the original system is only known to be preserved in the single-sided weighted case. A frequency-weighted model order reduction technique is proposed, which guarantees the passive reduced models in the double-sided weighted case. A set of easily computable error bound expressions are also presented

Fast positive-real balanced truncation via quadratic alternating direction implicit iteration

Balanced truncation (BT), as applied to date in model order reduction (MOR), is known for its superior accuracy and computable error bounds. Positive-real BT (PRBT) is a particular BT procedure that preserves passivity and stability and imposes no structural constraints on the original state space. However, PRBT requires solving two algebraic Riccati equations (AREs), whose computational complexity limits its practical use in large-scale systems. This paper introduces a novel quadratic extension of the alternating direction implicit (ADI) iteration, which is called quadratic ADI (QADI), that efficiently solves an ARE. A Cholesky factor version of QADI, which is called CEQADI, exploits low-rank matrices and further accelerates PRBT. © 2007 IEEE.published_or_final_versio

A variational Monte Carlo approach for core excitations

We present a systematically-improvable approach to core excitations in variational Monte Carlo. Building on recent work in excited-state-specific Monte Carlo, we show how a straightforward protocol, starting from a quantum chemistry guess, is able to capture core state's strong orbital relaxations, maintain accuracy in the near-nuclear region during these relaxations, and explicitly balance accuracy between ground and core excited states. In water, ammonia, and methane, which serve as prototypical representatives for oxygen, nitrogen, and carbon core states, respectively, this approach delivers accuracies on par with the best available theoretical methods even when using relatively small wave function expansions.Comment: 10 pages, 4 figures, 1 tabl

Constrained pre-equalization accounting for multi-path fading emulated using large RC networks: applications to wireless and photonics communications

Multi-path propagation is modelled assuming a multi-layer RC network with randomly allocated resistors and capacitors to represent the transmission medium. Due to frequency-selective attenuation, the waveforms associated with each propagation path incur path-dependent distortion. A pre-equalization procedure that takes into account the capabilities of the transmission source as well as the transmission properties of the medium is developed. The problem is cast within a Mixed Integer Linear Programming optimization framework that uses the developed nominal RC network model, with the excitation waveform customized to optimize signal fidelity from the transmitter to the receiver. The objective is to match a Gaussian pulse input accounting for frequency regions where there would be pronounced fading. Simulations are carried out with different network realizations in order to evaluate the sensitivity of the solution with respect to changes in the transmission medium mimicking the multi-path propagation. The proposed approach is of relevance where equalization techniques are difficult to implement. Applications are discussed within the context of emergent communication modalities across the EM spectrum such as light percolation as well as emergent indoor communications assuming various modulation protocols or UWB schemes as well as within the context of space division multiplexing

Control of fluid flows and other systems governed by partial differential-algebraic equations

The motion of fluids, such as air or water, is central to many engineering systems of significant economic and environmental importance. Examples range from air/fuel mixing in combustion engines to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator technologies have raised the intriguing prospect of actively sensing and manipulating the motion of the fluid within these systems, making them ripe for feedback control, provided a suitable control model exists. Unfortunately, the models for many of these systems are described by nonlinear, partial differential-algebraic equations for which few, if any, controller synthesis techniques exist. In stark contrast, the majority of established control theory assumes plant models of finite (and typically small) state dimension, expressed as a linear system of ordinary differential equations. Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory to the class of systems described by partial differential-algebraic equations, that are either linear, or for which a linear approximation is valid. The problems of control system design for infinite-dimensional and algebraically constrained systems are treated separately in this thesis. With respect to the former, a new method is presented that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between low-order models of successively finer spatial resolution. This bound informs the design, on loworder models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual plant. An example is presented on a one-dimensional heat equation. Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic, as well as differential equations. In the case of fluid flows, algebraic constraints typically arise from incompressibility and the application of boundary conditions. A numerical algorithm is presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential and algebraic parts of the system, enabling application of standard control theory without the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the transient growth region of a flat-plate boundary layer, using only wall shear measurements. These separate strands are woven together in the penultimate chapter, where a transient energy controller is designed for a channel-flow system, using wall mounted sensors and actuators

An Improved Estimate of the Coupled Arctic Energy Budget

This study combines state-of-the-art reanalyses such as the fifth-generation European Re-Analysis (ERA5) and the Ocean Reanalysis System 5 (ORAS5) with novel observational products to present an updated estimate of the coupled atmosphere–ocean–sea ice Arctic energy budget, including flux and storage terms covering 2001–17. Observational products provide independent estimates of crucial budget terms, including oceanic heat transport from unique mooring-derived data, radiative fluxes from satellites, and sea ice volume from merged satellite data. Results show that the time averages of independent estimates of radiative, atmospheric, and oceanic energy fluxes into the Arctic Ocean domain are remarkably consistent in the sense that their sum closely matches the observed rate of regional long-term oceanic heat accumulation of ~1 W m−2. Atmospheric and oceanic heat transports are found to be stronger compared to earlier assessments (~100 and ~16 W m−2, respectively). Data inconsistencies are larger when considering the mean annual cycle of the coupled energy budget, with RMS values of the monthly budget residual between 7 and 15 W m−2, depending on the employed datasets. This nevertheless represents an average reduction of ~72% of the residual compared to earlier work and demonstrates the progress made in data quality and diagnostic techniques. Finally, the budget residual is eliminated using a variational approach to provide a best estimate of the mean annual cycle. The largest remaining sources of uncertainty are ocean heat content and latent heat associated with sea ice melt and freeze, which both suffer from the lack of observational constraints. More ocean in situ observations and reliable sea ice thickness observations and their routinely assimilation into reanalyses are needed to further reduce uncertainty.publishedVersio