Sum-of-Squares approach to feedback control of laminar wake flows

A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable approach to the solution of such optimisation problems, based on Sum-of-Squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at Re=100, via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is derived using Proper Orthogonal Decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, energy efficiency, and physical control mechanisms identified are analysed. Key elements, implications and future work are discussed

Survey on the use of computational optimisation in UK engineering companies

The aim of this work is to capture current practices in the use of computational optimisation in UK engineering companies and identify the current challenges and future needs of the companies. To achieve this aim, a survey was conducted from June 2013 to August 2013 with 17 experts and practitioners from power, aerospace and automotive Original Equipment Manufacturers (OEMs), steel manufacturing sector, small- and medium-sized design, manufacturing and consultancy companies, and optimisation software vendors. By focusing on practitioners in industry, this work complements current surveys in optimisation that have mainly focused on published literature. This survey was carried out using a questionnaire administered through face-to-face interviews lasting around 2 h with each participant. The questionnaire covered 5 main topics: (i) state of optimisation in industry, (ii) optimisation problems, (iii) modelling techniques, (iv) optimisation techniques, and (v) challenges faced and future research areas. This survey identified the following challenges that the participant companies are facing in solving optimisation problems: large number of objectives and variables, availability of computing resources, data management and data mining for optimisation workflow, over-constrained problems, too many algorithms with limited help in selection, and cultural issues including training and mindset. The key areas for future research suggested by the participant companies are as follows: handling large number of variables, objectives and constraints particularly when solution robustness is important, reducing the number of iterations and evaluations, helping the users in algorithm selection and business case for optimisation, sharing data between different disciplines for multi-disciplinary optimisation, and supporting the users in model development and post-processing through design space visualisation and data mining

Uncertainty modelling in power system state estimation

A method for uncertainty analysis in power system state estimation is proposed. The two-step method uses static weighted least-squares analysis to compute 'point' state estimates. Linear programming is then employed to obtain the upper and lower bounds of the uncertainty interval. It is shown that the method can provide useful additional information for both metered and nonmetered elements of the system. The effects of network parameter errors are also studied. For illustrative purposed, the proposed method is tested using the six-bus and IEEE 30-bus standard systems. Results show that the proposed method is an accurate and reliable tool for estimating the uncertainty bounds in power system state estimation

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

MOOCs Meet Measurement Theory: A Topic-Modelling Approach

This paper adapts topic models to the psychometric testing of MOOC students based on their online forum postings. Measurement theory from education and psychology provides statistical models for quantifying a person's attainment of intangible attributes such as attitudes, abilities or intelligence. Such models infer latent skill levels by relating them to individuals' observed responses on a series of items such as quiz questions. The set of items can be used to measure a latent skill if individuals' responses on them conform to a Guttman scale. Such well-scaled items differentiate between individuals and inferred levels span the entire range from most basic to the advanced. In practice, education researchers manually devise items (quiz questions) while optimising well-scaled conformance. Due to the costly nature and expert requirements of this process, psychometric testing has found limited use in everyday teaching. We aim to develop usable measurement models for highly-instrumented MOOC delivery platforms, by using participation in automatically-extracted online forum topics as items. The challenge is to formalise the Guttman scale educational constraint and incorporate it into topic models. To favour topics that automatically conform to a Guttman scale, we introduce a novel regularisation into non-negative matrix factorisation-based topic modelling. We demonstrate the suitability of our approach with both quantitative experiments on three Coursera MOOCs, and with a qualitative survey of topic interpretability on two MOOCs by domain expert interviews.Comment: 12 pages, 9 figures; accepted into AAAI'201

Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)

SP models combine the paradigm of dynamic linear programming with modelling of random parameters, providing optimal decisions which hedge against future uncertainties. Advances in hardware as well as software techniques and solution methods have made SP a viable optimisation tool. We identify a growing need for modelling systems which support the creation and investigation of SP problems. Our SPInE system integrates a number of components which include a flexible modelling tool (based on stochastic extensions of the algebraic modelling languages AMPL and MPL), stochastic solvers, as well as special purpose scenario generators and database tools. We introduce an asset/liability management model and illustrate how SPInE can be used to create and process this model as a multistage SP application

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe