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.

Freeway traffic estimation in Beijing based on particle filter

Short-term traffic flow data is characterized by rapid and dramatic fluctuations. It reflects the nature of the frequent congestion in the lane, which shows a strong nonlinear feature. Traffic state estimation based on the data gained by electronic sensors is critical for much intelligent traffic management and the traffic control. In this paper, a solution to freeway traffic estimation in Beijing is proposed using a particle filter, based on macroscopic traffic flow model, which estimates both traffic density and speed.Particle filter is a nonlinear prediction method, which has obvious advantages for traffic flows prediction. However, with the increase of sampling period, the volatility of the traffic state curve will be much dramatic. Therefore, the prediction accuracy will be affected and difficulty of forecasting is raised. In this paper, particle filter model is applied to estimate the short-term traffic flow. Numerical study is conducted based on the Beijing freeway data with the sampling period of 2 min. The relatively high accuracy of the results indicates the superiority of the proposed model.

Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils

The unsaturated soil mechanics is receiving increasing attention from researchers and as well as from practicing engineers. However, the requirement of sophisticated devices to measure unsaturated soil properties and time consumption have made the geotechnical engineers keep away from implication of the unsaturated soil mechanics for solving practical geotechnical problems. The application of the conventional laboratory devices with some modifications to measure unsaturated soil properties can promote the application of unsaturated soil mechanics into engineering practice. Therefore, in the present study, a conventional direct shear device was modified to measure unsaturated shear strength parameters at low suction. Specially, for the analysis of rain-induced slope failures, it is important to measure unsaturated shear strength parameters at low suction where slopes become unstable. The modified device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying path and wetting path of soil-water characteristic curves (SWCCs) of soils. The results revealed that the internal friction angle of soil was not significantly affected by the suction and as well as the drying-wetting SWCCs of soils. The apparent cohesion of soil increased with a decreasing rate as the suction increased. Further, the apparent cohesion obtained from soil in wetting was greater than that obtained from soil in drying. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as the suction increased. In addition, it was observed that soil became more dilative with the increase of suction. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behaviour than that of in drying at the same net normal stress and the suction.

The crash involvement of older drivers is associated with their hazard perception latencies

Hazard perception in driving is the one of the few driving-specific skills associated with crash involvement. However, this relationship has only been examined in studies where the majority of individuals were younger than 65. We present the first data revealing an association between hazard perception and self-reported crash involvement in drivers aged 65 and over. In a sample of 271 drivers, we found that individuals whose mean response time to traffic hazards was slower than 6.68 seconds (the ROC-curve derived pass mark for the test) were 2.32 times (95% CI 1.46, 3.22) more likely to have been involved in a self-reported crash within the previous five years than those with faster response times. This likelihood ratio became 2.37 (95% CI 1.49, 3.28) when driving exposure was controlled for. As a comparison, individuals who failed a test of useful field of view were 2.70 (95% CI 1.44, 4.44) times more likely to crash than those who passed. The hazard perception test and the useful field of view measure accounted for separate variance in crash involvement. These findings indicate that hazard perception testing and training could be potentially useful for road safety interventions for this age group.

Corneal confocal microscopy : a novel noninvasive test to diagnose and stratify the severity of human diabetic neuropathy

OBJECTIVE: The accurate quantification of human diabetic neuropathy is important to define at-risk patients, anticipate deterioration, and assess new therapies. ---------- RESEARCH DESIGN AND METHODS: A total of 101 diabetic patients and 17 age-matched control subjects underwent neurological evaluation, neurophysiology tests, quantitative sensory testing, and evaluation of corneal sensation and corneal nerve morphology using corneal confocal microscopy (CCM). ---------- RESULTS: Corneal sensation decreased significantly (P = 0.0001) with increasing neuropathic severity and correlated with the neuropathy disability score (NDS) (r = 0.441, P < 0.0001). Corneal nerve fiber density (NFD) (P < 0.0001), nerve fiber length (NFL), (P < 0.0001), and nerve branch density (NBD) (P < 0.0001) decreased significantly with increasing neuropathic severity and correlated with NDS (NFD r = −0.475, P < 0.0001; NBD r = −0.511, P < 0.0001; and NFL r = −0.581, P < 0.0001). NBD and NFL demonstrated a significant and progressive reduction with worsening heat pain thresholds (P = 0.01). Receiver operating characteristic curve analysis for the diagnosis of neuropathy (NDS >3) defined an NFD of <27.8/mm2 with a sensitivity of 0.82 (95% CI 0.68–0.92) and specificity of 0.52 (0.40–0.64) and for detecting patients at risk of foot ulceration (NDS >6) defined a NFD cutoff of <20.8/mm2 with a sensitivity of 0.71 (0.42–0.92) and specificity of 0.64 (0.54–0.74). ---------- CONCLUSIONS: CCM is a noninvasive clinical technique that may be used to detect early nerve damage and stratify diabetic patients with increasing neuropathic severity. Established diabetic neuropathy leads to pain and foot ulceration. Detecting neuropathy early may allow intervention with treatments to slow or reverse this condition (1). Recent studies suggested that small unmyelinated C-fibers are damaged early in diabetic neuropathy (2–4) but can only be detected using invasive procedures such as sural nerve biopsy (4,5) or skin-punch biopsy (6–8). Our studies have shown that corneal confocal microscopy (CCM) can identify early small nerve fiber damage and accurately quantify the severity of diabetic neuropathy (9–11). We have also shown that CCM relates to intraepidermal nerve fiber loss (12) and a reduction in corneal sensitivity (13) and detects early nerve fiber regeneration after pancreas transplantation (14). Recently we have also shown that CCM detects nerve fiber damage in patients with Fabry disease (15) and idiopathic small fiber neuropathy (16) when results of electrophysiology tests and quantitative sensory testing (QST) are normal. In this study we assessed corneal sensitivity and corneal nerve morphology using CCM in diabetic patients stratified for the severity of diabetic neuropathy using neurological evaluation, electrophysiology tests, and QST. This enabled us to compare CCM and corneal esthesiometry with established tests of diabetic neuropathy and define their sensitivity and specificity to detect diabetic patients with early neuropathy and those at risk of foot ulceration.

Corneal sensitivity as an ophthalmic marker of diabetic neuropathy

Purpose. The objective of this study was to explore the discriminative capacity of non-contact corneal esthesiometry (NCCE) when compared with the neuropathy disability score (NDS) score—a validated, standard method of diagnosing clinically significant diabetic neuropathy. Methods. Eighty-one participants with type 2 diabetes, no history of ocular disease, trauma, or surgery and no history of systemic disease that may affect the cornea were enrolled. Participants were ineligible if there was history of neuropathy due to non-diabetic cause or current diabetic foot ulcer or infection. Corneal sensitivity threshold was measured on the eye of dominant hand side at a distance of 10 mm from the center of the cornea using a stimulus duration of 0.9 s. The NDS was measured producing a score ranging from 0 to 10. To determine the optimal cutoff point of corneal sensitivity that identified the presence of neuropathy (diagnosed by NDS), the Youden index and “closest-to-(0,1)” criteria were used. Results. The receiver-operator characteristic curve for NCCE for the presence of neuropathy (NDS ≥3) had an area under the curve of 0.73 (p = 0.001) and, for the presence of moderate neuropathy (NDS ≥6), area of 0.71 (p = 0.003). By using the Youden index, for an NDS ≥3, the sensitivity of NCCE was 70% and specificity was 75%, and a corneal sensitivity threshold of 0.66 mbar or higher indicated the presence of neuropathy. When NDS ≥6 (indicating risk of foot ulceration) was applied, the sensitivity was 52% with a specificity of 85%. Conclusions. NCCE is a sensitive test for the diagnosis of minimal and more advanced diabetic neuropathy and may serve as a useful surrogate marker for diabetic and perhaps other neuropathies.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.

A geometric approach to trajectory design for an autonomous underwater vehicle : surveying the bulbous bow of a ship

In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship for implications of harbor and port security. In recent years, engineers and researchers have been collaborating on automating ship hull inspections by employing autonomous vehicles. Despite the progresses made, human intervention is still necessary at this stage. To increase the functionality of these autonomous systems, we focus on developing model-based control strategies for the survey missions around challenging regions, such as the bulbous bow region of a ship. Recent advances in differential geometry have given rise to the field of geometric control theory. This has proven to be an effective framework for control strategy design for mechanical systems, and has recently been extended to applications for underwater vehicles. Advantages of geometric control theory include the exploitation of symmetries and nonlinearities inherent to the system. Here, we examine the posed inspection problem from a path planning viewpoint, applying recently developed techniques from the field of differential geometric control theory to design the control strategies that steer the vehicle along the prescribed path. Three potential scenarios for surveying a ship?s bulbous bow region are motivated for path planning applications. For each scenario, we compute the control strategy and implement it onto a test-bed vehicle. Experimental results are analyzed and compared with theoretical predictions.

A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Decoupled trajectory planning for a submerged rigid body subject to dissipative and potential forces

This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Controlling a submerged rigid body : a geometric analysis

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.