Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Design of a nonlinear excitation controller using inverse filtering for transient stability enhancement

This paper proposes a nonlinear excitation controller to improve transient stability, oscillation damping and voltage regulation of the power system. The energy function of the predicted system states is used to obtain the desired flux for the next time step, which in turn is used to obtain a supplementary control input using an inverse filtering method. The inverse filtering technique enables the system to provide an additional input for the excitation system, which forces the system to track the desired flux. Synchronous generator flux saturation model is used in this paper. A single machine infinite bus (SMIB) test system is used to demonstrate the efficacy of the proposed control method using time-domain simulations. The robustness of the controller is assessed under different operating conditions.

Development and application of Palygorskite porous ceramsite in a biological aerated filter (BAF)

Novel filter Palygorskite porous ceramsite (PC) was prepared using Palygorskite clay, poreforming material sawdust, and sodium silicate with a mass ratio of 10:2:1 after sintering at 700°C for 180 min. PC was characterized with X-ray diffraction, X-ray fluorescence, scanning electron microscopy, elemental, and porosimetry. PC had a total porosity of 67% and specific surface area of 61 m2/g. In order to assess the usefulness of PC as a medium for biological aerated filters (BAF), PC and (commercially available ceramsite) CAC were used to treat wastewater city in two laboratory-scale upflow BAFs. The results showed that the reactor containing PC was more efficient than the reactor containing CAC in terms of total organic carbon (TOC), ammonia nitrogen (NH3-N), and the removal of total nitrogen (TN) and phosphorus (P). This system was found to be more efficient at water temperatures ranging from 20 to 26°C, an air–water (A/W) ratio of 3:1, dissolved oxygen concentration >4.00 mg/L, and hydraulic retention time (HRT) ranging from 0.5 to 7 h. The interconnected porous structure produced for PC was suitable for microbial growth, and primarily protozoan and metazoan organisms were found in the biofilm. Microorganism growth also showed that, under the same submerged culture conditions, the biological mass in PC was significantly higher than in CAC (34.1 and 2.2 mg TN/g, respectively). In this way, PC media can be considered suitable for the use as a medium in novel biological aerated filters for the simultaneous removal of nitrogen and phosphorus.

Wide area control of SVCs for first swing stabilisation and damping in longitudinal systems

A non-linear Kalman filter based control strategy for SVCs located in major load groups is presented. This focusses on the limitation and damping of inter-area modes. It does this through treating local modes as noise and uses a tunable nonlinear control algorithm to improve both first swing stability and system damping. Simulation on a four machine system shows that the Kalman filer can successfully lock on to a desired inter-area mode and obtain a 31% improvement in critical clearing time as well as improved damping.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Improved Kalman filter initialisation using neurofuzzy estimation

It is traditional to initialise Kalman filters and extended Kalman filters with estimates of the states calculated directly from the observed (raw) noisy inputs, but unfortunately their performance is extremely sensitive to state initialisation accuracy: good initial state estimates ensure fast convergence whereas poor estimates may give rise to slow convergence or even filter divergence. Divergence is generally due to excessive observation noise and leads to error magnitudes that quickly become unbounded (R.J. Fitzgerald, 1971). When a filter diverges, it must be re initialised but because the observations are extremely poor, re initialised states will have poor estimates. The paper proposes that if neurofuzzy estimators produce more accurate state estimates than those calculated from the observed noisy inputs (using the known state model), then neurofuzzy estimates can be used to initialise the states of Kalman and extended Kalman filters. Filters whose states have been initialised with neurofuzzy estimates should give improved performance by way of faster convergence when the filter is initialised, and when a filter is re started after divergence

Strength properties of composite clay balls containing additives from industry wastes as new filter media in water treatment

Pebble matrix filtration (PMF) is a water treatment technology that can remove suspended solids in highly turbid surface water during heavy storms. PMF typically uses sand and natural pebbles as filter media. Hand-made clay pebbles (balls) can be used as alternatives to natural pebbles in PMF treatment plants, where natural pebbles are not readily available. Since the high turbidity is a seasonal problem that occurs during heavy rains, the use of newly developed composite clay balls instead of pure clay balls have the advantage of removing other pollutants such as natural organic matter (NOM) during other times. Only the strength properties of composite clay balls are described here as the pollutant removal is beyond the scope of this paper. These new composite clay balls must be able to withstand dead and live loads under dry and saturated conditions in a filter assembly. Absence of a standard ball preparation process and expected strength properties of composite clay balls were the main reasons behind the present study. Five different raw materials from industry wastes: Red Mud (RM), Water Treatment Alum Sludge (S), Shredded Paper (SP), Saw Dust (SD), and Sugar Mulch (SM) were added to common clay brick mix (BM) in different proportions. In an effort to minimize costs, in this study clay balls were fired to 1100 0C at a local brick factory together with their bricks. A comprehensive experimental program was performed to evaluate crushing strength of composite hand-made clay balls, using uniaxial compression test to establish the best material combination on the basis of strength properties for designing sustainable filter media for water treatment plants. Performance at both construction and operating stages were considered by analyzing both strength properties under fully dry conditions and strength degradation after saturation in a water bath. The BM-75% as the main component produced optimum combination in terms of workability and strength. With the material combination of BM-75% and additives-25%, the use of Red Mud and water treatment sludge as additives produced the highest and lowest strength of composite clay balls, with a failure load of 5.4 kN and 1.4 kN respectively. However, this lower value of 1.4 kN is much higher than the effective load on each clay ball of 0.04 kN in a typical filter assembly (safety factor of 35), therefore, can still be used as a suitable filter material for enhanced pollutant removal.

Wide-area damping control for inter-area oscillations using inverse filtering technique

In this study, a non-linear excitation controller using inverse filtering is proposed to damp inter-area oscillations. The proposed controller is based on determining generator flux value for the next sampling time which is obtained by maximising reduction rate of kinetic energy of the system after the fault. The desired flux for the next time interval is obtained using wide-area measurements and the equivalent area rotor angles and velocities are predicted using a non-linear Kalman filter. A supplementary control input for the excitation system, using inverse filtering approach, to track the desired flux is implemented. The inverse filtering approach ensures that the non-linearity introduced because of saturation is well compensated. The efficacy of the proposed controller with and without communication time delay is evaluated on different IEEE benchmark systems including Kundur's two area, Western System Coordinating Council three-area and 16-machine, 68-bus test systems.