An efficient null space inexact Newton method for hydraulic simulation of water distribution networks

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015 (https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015. Includes extended exposition, additional case studies and new simulations and analysi

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Graph-theoretic Surrogate Measures for Analysing the Resilience of Water Distribution Networks

AbstractHydraulic resilience can be formulated as a measure of the ability of a water distribution network to maintain a minimum level of service under operational and failure conditions. This paper explores a hybrid approach to bridge the gap between graph-theoretic and hydraulic measures of resilience. We extend the concept of geodesic distance of a pipeline by taking into account energy losses associated with flow. New random-walk algorithms evaluate hydraulically feasible routes and identify nodes with different levels of hydraulic resilience. The nodes with the lowest scores are further analysed by considering the availability and capacity of their supply routes

Identification of the Methanogenesis Inhibition Mechanism Using Comparative Analysis of Mathematical Models

The application of cationic polymers to enhance membrane fluxes in anaerobic membrane bioreactors has been proposed by several authors. However, literature shows contradictory results on the influence of those chemicals on the biological activity. In this research, we studied the effect of a cationic polymer on the production of methane from acetate by acetoclastic methanogens. We assessed the effect of polymer concentration on the accumulated methane production (AMP) and the specific methanogenic activity (SMA) in batch tests. Batch tests results showed lower SMA values at higher concentrations of polymer and no effect on the final AMP. Different inhibition models were calibrated and compared to find the best fit and to hypothesize the prevailing inhibition mechanisms. The assessed inhibition models were: competitive (M1a), non-competitive (M2a), un-competitive (M3a), biocide-linear (M4a), and biocide-exponential (M5a). The parameters in the model related to the polymer characteristics were adjusted to fit the experimental data. M2a and M3a were the only models that fitted both experimental SMA and AMP. Although M1a and M4a adequately fitted the experimental SMA, M1a simulations slightly deviated from the experimental AMP, and M4a considerably underpredicted the AMP at concentrations of polymer above 0.23 gCOD L−1. M5a did not adequately fit either experimental SMA and AMP results. We compared models a (M1a to M5a), which consider the inhibition by the concentration of polymer in the bulk liquid, with models b (M1b to M5b) considering the inhibition being caused by the total concentration of polymer in the reactor. Results showed that the difference between a and b models' simulations were negligible for all kinetic models considered (M1, M2, M3, M4, and M5). Therefore, the models that better predicted the experimental data were the non-competitive (M2a and M2b) and un-competitive (M3a and M3b) inhibition models, which are biostatic inhibition models. Consequently, the decreased methanogenic activity caused by polymer additions is presumably a reversible proces

Nonlinear model predictive control of salinity and water level in polder networks: Case study of Lissertocht catchment

A significant increase in surface water salinization in low-lying deltas is expected globally due to saline groundwater exfiltration driven by rising sea levels and decreasing freshwater availability. Sustaining fresh water-dependent agriculture in such areas will entail an increased demand for fresh water flushing. Unfortunately, the flushing of surface water is not operationally optimised and results in excessive use of scarce freshwater. To meet the increased demand for flushing, while minimizing the need for diverted freshwater, new operational designs are required. This paper presents a novel network model based approach that uses De Saint Venant (SV) and Advection Dispersion (AD) equations to optimize multiple objectives on water level and salinity control using a Nonlinear Model Predictive Control (NMPC). The resulting NMPC problem is solved with a receding horizon implementation, where the nonlinear program (NLP) at each iteration is solved using state-of-the-art large scale interior point solver (IPOPT). We evaluate the performance of the proposed approach and compare it to the traditional fixed flushing for a representative Dutch polder. Firstly, the approach is shown to be capable of controlling the water level and salinity level in the polder. Secondly, the results highlight that the network of canals, which were originally made for drainage, could not be made sufficiently fresh with current intake capacity. A simple design approach was used to identify appropriate new capacities for two of the gates that allow optimal flushing to guarantee the required water level and salinity constraints

The stellar-to-halo mass relation of GAMA galaxies from 100 deg2of KiDS weak lensing data

We study the stellar-to-halo mass relation of central galaxies in the range 9.7 5 × 1010h-2M&sun;, the stellar mass increases with halo mass as ˜ {}M_h^{0.25}. The ratio of dark matter to stellar mass has a minimum at a halo mass of 8 × 1011h-1M&sun; with a value of M_h/M_*=56_{-10}^{+16} [h]. We also use the GAMA group catalogue to select centrals and satellites in groups with five or more members, which trace regions in space where the local matter density is higher than average, and determine for the first time the stellar-to-halo mass relation in these denser environments. We find no significant differences compared to the relation from the full sample, which suggests that the stellar-to-halo mass relation does not vary strongly with local density. Furthermore, we find that the stellar-to-halo mass relation of central galaxies can also be obtained by modelling the lensing signal and stellar mass function of satellite galaxies only, which shows that the assumptions to model the satellite contribution in the halo model do not significantly bias the stellar-to-halo mass relation. Finally, we show that the combination of weak lensing with the stellar mass function can be used to test the purity of group catalogues

Prevention of dementia using mobile phone applications (PRODEMOS): protocol for an international randomised controlled trial.

IntroductionProfiles of high risk for future dementia are well understood and are likely to concern mostly those in low-income and middle-income countries and people at greater disadvantage in high-income countries. Approximately 30%-40% of dementia cases have been estimated to be attributed to modifiable risk factors, including hypertension, smoking and sedentary lifestyle. Tailored interventions targeting these risk factors can potentially prevent or delay the onset of dementia. Mobile health (mHealth) improves accessibility of such prevention strategies in hard-to-reach populations while at the same time tailoring such approaches. In the current study, we will investigate the effectiveness and implementation of a coach-supported mHealth intervention, targeting dementia risk factors, to reduce dementia risk.Methods and analysisThe prevention of dementia using mobile phone applications (PRODEMOS) randomised controlled trial will follow an effectiveness-implementation hybrid design, taking place in the UK and China. People are eligible if they are 55-75 years old, of low socioeconomic status (UK) or from the general population (China); have ≥2 dementia risk factors; and own a smartphone. 2400 participants will be randomised to either a coach-supported, interactive mHealth platform, facilitating self-management of dementia risk factors, or a static control platform. The intervention and follow-up period will be 18 months. The primary effectiveness outcome is change in the previously validated Cardiovascular Risk Factors, Ageing and Incidence of Dementia dementia risk score. The main secondary outcomes include improvement of individual risk factors and cost-effectiveness. Implementation outcomes include acceptability, adoption, feasibility and sustainability of the intervention.Ethics and disseminationThe PRODEMOS trial is sponsored in the UK by the University of Cambridge and is granted ethical approval by the London-Brighton and Sussex Research Ethics Committee (reference: 20/LO/01440). In China, the trial is approved by the medical ethics committees of Capital Medical University, Beijing Tiantan Hospital, Beijing Geriatric Hospital, Chinese People's Liberation Army General Hospital, Taishan Medical University and Xuanwu Hospital. Results will be published in a peer-reviewed journal.Trial registration numberISRCTN15986016