Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Digital image processing techniques for pavement macro-texture analysis

Road surface macro-texture is an indicator used to determine the skid resistance levels in pavements. Existing methods of quantifying macro-texture include the sand patch test and the laser profilometer. These methods utilise the 3D information of the pavement surface to extract the average texture depth. Recently, interest in image processing techniques as a quantifier of macro-texture has arisen, mainly using the Fast Fourier Transform (FFT). This paper reviews the FFT method, and then proposes two new methods, one using the autocorrelation function and the other using wavelets. The methods are tested on pictures obtained from a pavement surface extending more than 2km's. About 200 images were acquired from the surface at approx. 10m intervals from a height 80cm above ground. The results obtained from image analysis methods using the FFT, the autocorrelation function and wavelets are compared with sensor measured texture depth (SMTD) data obtained from the same paved surface. The results indicate that coefficients of determination (R2) exceeding 0.8 are obtained when up to 10% of outliers are removed.

Frequency decomposition techniques for increased discriminative 3D facial information capture

Eigen-based techniques and other monolithic approaches to face recognition have long been a cornerstone in the face recognition community due to the high dimensionality of face images. Eigen-face techniques provide minimal reconstruction error and limit high-frequency content while linear discriminant-based techniques (fisher-faces) allow the construction of subspaces which preserve discriminatory information. This paper presents a frequency decomposition approach for improved face recognition performance utilising three well-known techniques: Wavelets; Gabor / Log-Gabor; and the Discrete Cosine Transform. Experimentation illustrates that frequency domain partitioning prior to dimensionality reduction increases the information available for classification and greatly increases face recognition performance for both eigen-face and fisher-face approaches.

Experimental study of the concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller, which was placed in a glass-walled flume 0.4 m wide with a free surface depth of 0.15 m. The jet and scalar plume development were compared to that of a classical free round jet. Further, results pertaining to radial distribution, self similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration were presented and fitted with empirical correlations. Furthermore, propeller induced mixing and pollutant source concentration from a two-stroke engine were estimated.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Machine recognition of hand-drawn circuit diagrams

An application of image processing techniques to recognition of hand-drawn circuit diagrams is presented. The scanned image of a diagram is pre-processed to remove noise and converted to bilevel. Morphological operations are applied to obtain a clean, connected representation using thinned lines. The diagram comprises of nodes, connections and components. Nodes and components are segmented using appropriate thresholds on a spatially varying object pixel density. Connection paths are traced using a pixel-stack. Nodes are classified using syntactic analysis. Components are classified using a combination of invariant moments, scalar pixel-distribution features, and vector relationships between straight lines in polygonal representations. A node recognition accuracy of 82% and a component recognition accuracy of 86% was achieved on a database comprising 107 nodes and 449 components. This recogniser can be used for layout “beautification” or to generate input code for circuit analysis and simulation packages

Experimentally induced diesel engine injector faults and some preliminary acoustic emission signal observations

Diesel engine fuel injector faults can lead to reduced power, increased fuel consumption and greater exhaust emission levels and if left unchecked, can eventually lead to premature engine failure. This paper provides an overview of the Diesel, or compression ignition combustion process, and of the two basic fuel injector nozzle designs used in Diesel engines, namely, the pintle-type and hole-type nozzles. Also described are some common faults associated with these two types of fuel injector nozzles and the techniques previously used to experimentally simulate these faults. This paper also presents a recent experimental campaign undertaken using two different diesel engines whereby various fuel injector nozzle faults were induced into the engines. The first series of tests was undertaken using a turbo-charged 5.9 litre; Cummins Diesel engine whist the second series of tests was undertaken using a naturally aspirated 4 cylinder, 2.216 litre, Perkins Diesel engine. Data corresponding to different injector fault conditions was captured using in-cylinder pressure, and acoustic emission transducers along with both crank-angle encoder and top-dead centre reference signals. Using averaged in-cylinder pressure signals, it was possible to qualify the severity of the faults whilst averaged acoustic emission signals were in turn, used as the basis for wavelets decomposition. Initial observations from this signal decomposition are also presented and discussed.

Turbulence characteristics of a small subtropical estuary during and after some moderate rainfall

In natural estuaries, scalar diffusion and dispersion are driven by turbulence. In the present study, detailed turbulence measurements were conducted in a small subtropical estuary with semi-diurnal tides under neap tide conditions. Three acoustic Doppler velocimeters were installed mid-estuary at fixed locations close together. The units were sampled simultaneously and continuously at relatively high frequency for 50 h. The results illustrated the influence of tidal forcing in the small estuary, although low frequency longitudinal velocity oscillations were observed and believed to be induced by external resonance. The boundary shear stress data implied that the turbulent shear in the lower flow region was one order of magnitude larger than the boundary shear itself. The observation differed from turbulence data in a laboratory channel, but a key feature of natural estuary flow was the significant three dimensional effects associated with strong secondary currents including transverse shear events. The velocity covariances and triple correlations, as well as the backscatter intensity and covariances, were calculated for the entire field study. The covariances of the longitudinal velocity component showed some tidal trend, while the covariances of the transverse horizontal velocity component exhibited trends that reflected changes in secondary current patterns between ebb and flood tides. The triple correlation data tended to show some differences between ebb and flood tides. The acoustic backscatter intensity data were characterised by large fluctuations during the entire study, with dimensionless fluctuation intensity I0b =Ib between 0.46 and 0.54. An unusual feature of the field study was some moderate rainfall prior to and during the first part of the sampling period. Visual observations showed some surface scars and marked channels, while some mini transient fronts were observed.

Turbulent measurements in a small subtropical estuary with semidiurnal tides

Since predictions of scalar dispersion in small estuaries can rarely be predicted accurately, new field measurements were conducted continuously at relatively high frequency for up to 50 h (per investigation) in a small subtropical estuary with semidiurnal tides. The bulk flow parameters varied in time with periods comparable to tidal cycles and other large-scale processes. The turbulence properties depended upon the instantaneous local flow properties. They were little affected by the flow history, but their structure and temporal variability were influenced by a variety of parameters including the tidal conditions and bathymetry. A striking feature of the data sets was the large fluctuations in all turbulence characteristics during the tidal cycle, and basic differences between neap and spring tide turbulence.

An experimental study of a reactive plume in grid turbulence

Experimental results for a reactive non-buoyant plume of nitric oxide (NO) in a turbulent grid flow doped with ozone (O3) are presented. The Damkohler number (Nd) for the experiment is of order unity indicating the turbulence and chemistry have similar timescales and both affect the chemical reaction rate. Continuous measurements of two components of velocity using hot-wire anemometry and the two reactants using chemiluminescent analysers have been made. A spatial resolution for the reactants of four Kolmogorov scales has been possible because of the novel design of the experiment. Measurements at this resolution for a reactive plume are not found in the literature. The experiment has been conducted relatively close to the grid in the region where self-similarity of the plume has not yet developed. Statistics of a conserved scalar, deduced from both reactive and non-reactive scalars by conserved scalar theory, are used to establish the mixing field of the plume, which is found to be consistent with theoretical considerations and with those found by other investigators in non-reative flows. Where appropriate the reactive species means and higher moments, probability density functions, joint statistics and spectra are compared with their respective frozen, equilibrium and reaction-dominated limits deduced from conserved scalar theory. The theoretical limits bracket reactive scalar statistics where this should be so according to conserved scalar theory. Both reactants approach their equilibrium limits with greater distance downstream. In the region of measurement, the plume reactant behaves as the reactant not in excess and the ambient reactant behaves as the reactant in excess. The reactant covariance lies outside its frozen and equilibrium limits for this value of Vd. The reaction rate closure of Toor (1969) is compared with the measured reaction rate. The gradient model is used to obtain turbulent diffusivities from turbulent fluxes. Diffusivity of a non-reactive scalar is found to be close to that measured in non-reactive flows by others.