Optimal catalyst thickness in titanium dioxide fixed film reactors: Mathematical modelling and experimental validation

The use of immobilised TiO2 for the purification of polluted water streams introduces the necessity to evaluate the effect of mechanisms such as the transport of pollutants from the bulk of the liquid to the catalyst surface and the transport phenomena inside the porous film. Experimental results of the effects of film thickness on the observed reaction rate for both liquid-side and support-side illumination are here compared with the predictions of a one-dimensional mathematical model of the porous photocatalytic slab. Good agreement was observed between the experimentally obtained photodegradation of phenol and its by-products, and the corresponding model predictions. The results have confirmed that an optimal catalyst thickness exists and, for the films employed here, is 5 μm. Furthermore, the modelling results have highlighted the fact that porosity, together with the intrinsic reaction kinetics are the parameters controlling the photocatalytic activity of the film. The former by influencing transport phenomena and light absorption characteristics, the latter by naturally dictating the rate of reaction.

Optimal sizing of combined PV-energy storage for a grid-connected residential building

In this paper, load profile and operational goal are used to find optimal sizing of combined PV-energy storage for a future grid-connected residential building. As part of this approach, five operational goals are introduced and the annual cost for each operation goal has been assessed. Finally, the optimal sizing for combined PV-energy storage has been determined, using direct search method. In addition, sensitivity of the annual cost to different parameters has been analyzed.

An algebraic approach for determination of DG parameters to support voltage profiles in radial distribution networks

Rapidly increasing electricity demands and capacity shortage of transmission and distribution facilities are the main driving forces for the growth of Distributed Generation (DG) integration in power grids. One of the reasons for choosing a DG is its ability to support voltage in a distribution system. Selection of effective DG characteristics and DG parameters is a significant concern of distribution system planners to obtain maximum potential benefits from the DG unit. This paper addresses the issue of improving the network voltage profile in distribution systems by installing a DG of the most suitable size, at a suitable location. An analytical approach is developed based on algebraic equations for uniformly distributed loads to determine the optimal operation, size and location of the DG in order to achieve required levels of network voltage. The developed method is simple to use for conceptual design and analysis of distribution system expansion with a DG and suitable for a quick estimation of DG parameters (such as optimal operating angle, size and location of a DG system) in a radial network. A practical network is used to verify the proposed technique and test results are presented.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Reduced complexity on-line estimation of hidden Markov model parameters

In this paper we propose and study low complexity algorithms for on-line estimation of hidden Markov model (HMM) parameters. The estimates approach the true model parameters as the measurement noise approaches zero, but otherwise give improved estimates, albeit with bias. On a nite data set in the high noise case, the bias may not be signi cantly more severe than for a higher complexity asymptotically optimal scheme. Our algorithms require O(N3) calculations per time instant, where N is the number of states. Previous algorithms based on earlier hidden Markov model signal processing methods, including the expectation-maximumisation (EM) algorithm require O(N4) calculations per time instant.

Optimal HMM filtering and decision feedback equalisation for differential encoded transmission systems

In this paper conditional hidden Markov model (HMM) filters and conditional Kalman filters (KF) are coupled together to improve demodulation of differential encoded signals in noisy fading channels. We present an indicator matrix representation for differential encoded signals and the optimal HMM filter for demodulation. The filter requires O(N3) calculations per time iteration, where N is the number of message symbols. Decision feedback equalisation is investigated via coupling the optimal HMM filter for estimating the message, conditioned on estimates of the channel parameters, and a KF for estimating the channel states, conditioned on soft information message estimates. The particular differential encoding scheme examined in this paper is differential phase shift keying. However, the techniques developed can be extended to other forms of differential modulation. The channel model we use allows for multiplicative channel distortions and additive white Gaussian noise. Simulation studies are also presented.

Limitations of a laboratory scale model in predicting optimal pilot scale conditions for dilute acid pretreatment of sugarcane bagasse

Pilot and industrial scale dilute acid pretreatment data can be difficult to obtain due to the significant infrastructure investment required. Consequently, models of dilute acid pretreatment by necessity use laboratory scale data to determine kinetic parameters and make predictions about optimal pretreatment conditions at larger scales. In order for these recommendations to be meaningful, the ability of laboratory scale models to predict pilot and industrial scale yields must be investigated. A mathematical model of the dilute acid pretreatment of sugarcane bagasse has previously been developed by the authors. This model was able to successfully reproduce the experimental yields of xylose and short chain xylooligomers obtained at the laboratory scale. In this paper, the ability of the model to reproduce pilot scale yield and composition data is examined. It was found that in general the model over predicted the pilot scale reactor yields by a significant margin. Models that appear very promising at the laboratory scale may have limitations when predicting yields on a pilot or industrial scale. It is difficult to comment whether there are any consistent trends in optimal operating conditions between reactor scale and laboratory scale hydrolysis due to the limited reactor datasets available. Further investigation is needed to determine whether the model has some efficacy when the kinetic parameters are re-evaluated by parameter fitting to reactor scale data, however, this requires the compilation of larger datasets. Alternatively, laboratory scale mathematical models may have enhanced utility for predicting larger scale reactor performance if bulk mass transport and fluid flow considerations are incorporated into the fibre scale equations. This work reinforces the need for appropriate attention to be paid to pilot scale experimental development when moving from laboratory to pilot and industrial scales for new technologies.

An optimal design for screening trials

Yao, Begg, and Livingston (1996, Biometrics 52, 992-1001) considered the optimal group size for testing a series of potentially therapeutic agents to identify a promising one as soon as possible for given error rates. The number of patients to be tested with each agent was fixed as the group size. We consider a sequential design that allows early acceptance and rejection, and we provide an optimal strategy to minimize the sample sizes (patients) required using Markov decision processes. The minimization is under the constraints of the two types (false positive and false negative) of error probabilities, with the Lagrangian multipliers corresponding to the cost parameters for the two types of errors. Numerical studies indicate that there can be a substantial reduction in the number of patients required.

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Pen parameters for improving the performance of sheep imported from Australia to Persian Gulf feedlots

Summer in the Persian Gulf region presents physiological challenges for Australian sheep that are part of the live export supply chain coming from the Australian winter. Many feedlots throughout the Gulf have very high numbers of animals during June to August in order to cater for the increased demand for religious festivals. From an animal welfare perspective it is important to understand the necessary requirements of feed and water trough allowances, and the amount of pen space required, to cope with exposure to these types of climatic conditions. This study addresses parameters that are pertinent to the wellbeing of animals arriving in the Persian Gulf all year round. Three experiments were conducted in a feedlot in the Persian Gulf between March 2010 and February 2012, totalling 44 replicate pens each with 60 or 100 sheep. The applied treatments covered animal densities, feed-bunk lengths and water trough lengths. Weights, carcass attributes and health status were the key recorded variables. Weight change results showed superior performance for animal densities of ≥1.2 m2/head during hot conditions (24-h average temperatures greater than 33 °C, or a diurnal range of around 29–37 °C). However the space allowance for animals can be decreased, with no demonstrated detrimental effect, to 0.6 m2/head under milder conditions. A feed-bunk length of ≥5 cm/head is needed, as 2 cm/head showed significantly poorer animal performance. When feeding at 90 ad libitum 10 cm/head was optimal, however under a maintenance feeding regime (1 kg/head/day) 5 cm/head was adequate. A minimum water trough allowance of 1 cm/head is required. However, this experiment was conducted during milder conditions, and it may well be expected that larger water trough lengths would be needed in hotter conditions. Carcass weights were determined mainly by weights at feedlot entry and subsequent weight gains, while dressing percentage was not significantly affected by any of the applied treatments. There was no demonstrated effect of any of the treatments on the number of animals that died, or were classified as unwell. However, across all the treatments, these animals lost significantly more weight than the healthy animals, so the above recommendations, which are aimed at maintaining weight, should also be applicable for good animal health and welfare. Therefore, best practice guidelines for managing Australian sheep in Persian Gulf feedlots in the hottest months (June–August) which present the greatest environmental and physical challenge is to allow feed-bunk length 5 cm/head on a maintenance-feeding program and 10 cm/head for 90 ad libitum feeding, and the space allowance per animal should be ≥1.2 m2/head. Water trough allocation should be at least 1 cm/head with provision for more in the summer when water intake potentially doubles.

Pen parameters for improving the performance of sheep imported from Australia to Persian Gulf feedlots

Summer in the Persian Gulf region presents physiological challenges for Australian sheep that are part of the live export supply chain coming from the Australian winter. Many feedlots throughout the Gulf have very high numbers of animals during June to August in order to cater for the increased demand for religious festivals. From an animal welfare perspective it is important to understand the necessary requirements of feed and water trough allowances, and the amount of pen space required, to cope with exposure to these types of climatic conditions. This study addresses parameters that are pertinent to the wellbeing of animals arriving in the Persian Gulf all year round. Three experiments were conducted in a feedlot in the Persian Gulf between March 2010 and February 2012, totalling 44 replicate pens each with 60 or 100 sheep. The applied treatments covered animal densities, feed-bunk lengths and water trough lengths. Weights, carcass attributes and health status were the key recorded variables. Weight change results showed superior performance for animal densities of ≥1.2 m2/head during hot conditions (24-h average temperatures greater than 33 °C, or a diurnal range of around 29–37 °C). However the space allowance for animals can be decreased, with no demonstrated detrimental effect, to 0.6 m2/head under milder conditions. A feed-bunk length of ≥5 cm/head is needed, as 2 cm/head showed significantly poorer animal performance. When feeding at 90% ad libitum 10 cm/head was optimal, however under a maintenance feeding regime (1 kg/head/day) 5 cm/head was adequate. A minimum water trough allowance of 1 cm/head is required. However, this experiment was conducted during milder conditions, and it may well be expected that larger water trough lengths would be needed in hotter conditions. Carcass weights were determined mainly by weights at feedlot entry and subsequent weight gains, while dressing percentage was not significantly affected by any of the applied treatments. There was no demonstrated effect of any of the treatments on the number of animals that died, or were classified as unwell. However, across all the treatments, these animals lost significantly more weight than the healthy animals, so the above recommendations, which are aimed at maintaining weight, should also be applicable for good animal health and welfare. Therefore, best practice guidelines for managing Australian sheep in Persian Gulf feedlots in the hottest months (June–August) which present the greatest environmental and physical challenge is to allow feed-bunk length 5 cm/head on a maintenance-feeding program and 10 cm/head for 90% ad libitum feeding, and the space allowance per animal should be ≥1.2 m2/head. Water trough allocation should be at least 1 cm/head with provision for more in the summer when water intake potentially doubles.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

Shape effect on optimal geometric conditions in surface aeration systems

The performance of surface aeration systems, among other key design variables, depends upon the geometric parameters of the aeration tank. Efficient performance and scale up or scale down of the experimental results of an aeration ystem requires optimal geometric conditions. Optimal conditions refer to the conditions of maximum oxygen transfer rate, which assists in scaling up or down the system for ommercial utilization. The present work investigates the effect of an aeration tank's shape (unbaffled circular, baffled circular and unbaffled square) on oxygen transfer. Present results demonstrate that there is no effect of shape on the optimal geometric conditions for rotor position and rotor dimensions. This experimentation shows that circular tanks (baffled or unbaffled) do not have optimal geometric conditions for liquid transfer, whereas the square cross-section tank shows a unique geometric shape to optimize oxygen transfer.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.