Determining the material properties for heavily over-consolidated bagasse through parameter estimation

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process. For example, there are opportunities to decrease bagasse moisture from a milling unit. Also, the behaviour of bagasse in chutes is poorly understood. Previous investigations have shown that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software. The objective has been to be able to simulate simple mechanical loading conditions measured in the laboratory, which, when combined together, have a high probability of reproducing the complicated stress conditions in a milling unit. This paper reports on the successful simulation of part of the fifth and final (and most challenging) loading condition, the shearing of heavily over-consolidated bagasse, and determining material property values through the use of powerful and free parameter estimation software.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

Faster parameter estimation using risk-sensitive filters

In this paper, we propose a risk-sensitive approach to parameter estimation for hidden Markov models (HMMs). The parameter estimation approach considered exploits estimation of various functions of the state, based on model estimates. We propose certain practical suboptimal risk-sensitive filters to estimate the various functions of the state during transients, rather than optimal risk-neutral filters as in earlier studies. The estimates are asymptotically optimal, if asymptotically risk neutral, and can give significantly improved transient performance, which is a very desirable objective for certain engineering applications. To demonstrate the improvement in estimation simulation studies are presented that compare parameter estimation based on risk-sensitive filters with estimation based on risk-neutral filters.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Short-data recursive HMM parameter estimation for rapid vision-based aircraft heading estimation

Rapid recursive estimation of hidden Markov Model (HMM) parameters is important in applications that place an emphasis on the early availability of reasonable estimates (e.g. for change detection) rather than the provision of longer-term asymptotic properties (such as convergence, convergence rate, and consistency). In the context of vision- based aircraft (image-plane) heading estimation, this paper suggests and evaluates the short-data estimation properties of 3 recursive HMM parameter estimation techniques (a recursive maximum likelihood estimator, an online EM HMM estimator, and a relative entropy based estimator). On both simulated and real data, our studies illustrate the feasibility of rapid recursive heading estimation, but also demonstrate the need for careful step-size design of HMM recursive estimation techniques when these techniques are intended for use in applications where short-data behaviour is paramount.

Comparison of the gate drive parameter space for driving power MOSFETs using conventional and cascode configurations

Conventional voltage driven gate drive circuits utilise a resistor to control the switching speed of power MOS-FETs. The gate resistance is adjusted to provide controlled rate of change of load current and voltage. The cascode gate drive configuration has been proposed as an alternative to the conventional resistor-fed gate drive circuit. While cascode drive is broadly understood in the literature the switching characteristics of this topology are not well documented. This paper explores, through both simulation and experimentation, the gate drive parameter space of the cascode gate drive configuration and provides a comparison to the switching characteristics of conventional gate drive.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Some comparison on whole-proteome phylogeny of large dsDNA viruses based on dynamical language approach and feature frequency profiles method

There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. Among them, CVTree method, feature frequency profiles method and dynamical language approach were used to investigate the whole-proteome phylogeny of large dsDNA viruses. Using the data set of large dsDNA viruses from Gao and Qi (BMC Evol. Biol. 2007), the phylogenetic results based on the CVTree method and the dynamical language approach were compared in Yu et al. (BMC Evol. Biol. 2010). In this paper, we first apply dynamical language approach to the data set of large dsDNA viruses from Wu et al. (Proc. Natl. Acad. Sci. USA 2009) and compare our phylogenetic results with those based on the feature frequency profiles method. Then we construct the whole-proteome phylogeny of the larger dataset combining the above two data sets. According to the report of The International Committee on the Taxonomy of Viruses (ICTV), the trees from our analyses are in good agreement to the latest classification of large dsDNA viruses.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Prediction of GMA welding characteristic parameter by artificial neural network system

Nowadays, demand for automated Gas metal arc welding (GMAW) is growing and consequently need for intelligent systems is increased to ensure the accuracy of the procedure. To date, welding pool geometry has been the most used factor in quality assessment of intelligent welding systems. But, it has recently been found that Mahalanobis Distance (MD) not only can be used for this purpose but also is more efficient. In the present paper, Artificial Neural Networks (ANN) has been used for prediction of MD parameter. However, advantages and disadvantages of other methods have been discussed. The Levenberg–Marquardt algorithm was found to be the most effective algorithm for GMAW process. It is known that the number of neurons plays an important role in optimal network design. In this work, using trial and error method, it has been found that 30 is the optimal number of neurons. The model has been investigated with different number of layers in Multilayer Perceptron (MLP) architecture and has been shown that for the aim of this work the optimal result is obtained when using MLP with one layer. Robustness of the system has been evaluated by adding noise into the input data and studying the effect of the noise in prediction capability of the network. The experiments for this study were conducted in an automated GMAW setup that was integrated with data acquisition system and prepared in a laboratory for welding of steel plate with 12 mm in thickness. The accuracy of the network was evaluated by Root Mean Squared (RMS) error between the measured and the estimated values. The low error value (about 0.008) reflects the good accuracy of the model. Also the comparison of the predicted results by ANN and the test data set showed very good agreement that reveals the predictive power of the model. Therefore, the ANN model offered in here for GMA welding process can be used effectively for prediction goals.

Towards strongly consistent online HMM parameter estimation using one-step Kerridge inaccuracy

In this paper, we propose a novel online hidden Markov model (HMM) parameter estimator based on the new information-theoretic concept of one-step Kerridge inaccuracy (OKI). Under several regulatory conditions, we establish a convergence result (and some limited strong consistency results) for our proposed online OKI-based parameter estimator. In simulation studies, we illustrate the global convergence behaviour of our proposed estimator and provide a counter-example illustrating the local convergence of other popular HMM parameter estimators.

Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of Bayesian design for model discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.