General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

A probabilistic model for trust and reputation

This paper concerns the problem of agent trust in an electronic market place. We maintain that agent trust involves making decisions under uncertainty and therefore the phenomenon should be modelled probabilistically. We therefore propose a probabilistic framework that models agent interactions as a Hidden Markov Model (HMM). The observations of the HMM are the interaction outcomes and the hidden state is the underlying probability of a good outcome. The task of deciding whether to interact with another agent reduces to probabilistic inference of the current state of that agent given all previous interaction outcomes. The model is extended to include a probabilistic reputation system which involves agents gathering opinions about other agents and fusing them with their own beliefs. Our system is fully probabilistic and hence delivers the following improvements with respect to previous work: (a) the model assumptions are faithfully translated into algorithms; our system is optimal under those assumptions, (b) It can account for agents whose behaviour is not static with time (c) it can estimate the rate with which an agent's behaviour changes. The system is shown to significantly outperform previous state-of-the-art methods in several numerical experiments. Copyright © 2010, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.

Design of a genetic algorithm for bi-objective flow shop scheduling problems with re-entrant jobs

This paper presents a simulated genetic algorithm (GA) model of scheduling the flow shop problem with re-entrant jobs. The objective of this research is to minimize the weighted tardiness and makespan. The proposed model considers that the jobs with non-identical due dates are processed on the machines in the same order. Furthermore, the re-entrant jobs are stochastic as only some jobs are required to reenter to the flow shop. The tardiness weight is adjusted once the jobs reenter to the shop. The performance of the proposed GA model is verified by a number of numerical experiments where the data come from the case company. The results show the proposed method has a higher order satisfaction rate than the current industrial practices.

Experiments to assess the transport of fibrous insulation debris

Loss of coolant accidents (LOCA) in the primary cooling circuit of a nuclear reactor may result in damage to insulation materials that are located near to the leak. The insulation materials released may compromise the operation of the emergency core cooling system (ECCS). Insulation material in the form of mineral wool fibre agglomerates (MWFA) maybe transported to the containment sump strainers mounted at the inlet of the emergency cooling pumps, where the insulation fibres may block or penetrate the strainers. In addition to the impact of MWFA on the pressure drop across the strainers, corrosion products formed over time may also accumulate in the fibre cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. Thus, knowledge of transport characteristics of the damaged insulation materials in various scenarios is required to help plan for the long-term operability of nuclear reactors, which undergo LOCA. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz1 is investigating the phenomena that maybe observed in the containment vessel during a LOCA. The study entails the generation of fibre agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effect that corrosion of the containment internals by the coolant has on the strainer pressure drop. The focus of this presentation is on the experiments performed that characterize the horizontal transport of MWFA, whereas the corresponding CFD simulations are described in an accompanying contribution (see abstract of Cartland Glover et al.). The experiments were performed a racetrack type channel that provided a near uniform horizontal flow. The channel is 0.1 wide by 1.2 m high with a straight length of 5 m and two bends of 0.5 m. The measurement techniques include particle imaging (both wide-angle and macro lens), concurrent particle image velocimetry, ultravelocimetry, laser detection sensors to sense the presence of absence of MWFA and pertinent measurements of the MWFA concentration and quiescent settling characteristics. The transport of the MWFA was observed at velocities of 0.1 and 0.25 m s-1 to verify numerical model behaviour in and just beyond expected velocities in the containment sump of a nuclear reactor.

A three dimensional numerical investigation of hillslope flow processes

Physically based distributed models of catchment hydrology are likely to be made available as engineering tools in the near future. Although these models are based on theoretically acceptable equations of continuity, there are still limitations in the present modelling strategy. Of interest to this thesis are the current modelling assumptions made concerning the effects of soil spatial variability, including formations producing distinct zones of preferential flow. The thesis contains a review of current physically based modelling strategies and a field based assessment of soil spatial variability. In order to investigate the effects of soil nonuniformity a fully three dimensional model of variability saturated flow in porous media is developed. The model is based on a Galerkin finite element approximation to Richards equation. Accessibility to a vector processor permits numerical solutions on grids containing several thousand node points. The model is applied to a single hillslope segment under various degrees of soil spatial variability. Such variability is introduced by generating random fields of saturated hydraulic conductivity using the turning bands method. Similar experiments are performed under conditions of preferred soil moisture movement. The results show that the influence of soil variability on subsurface flow may be less significant than suggested in the literature, due to the integrating effects of three dimensional flow. Under conditions of widespread infiltration excess runoff, the results indicate a greater significance of soil nonuniformity. The recognition of zones of preferential flow is also shown to be an important factor in accurate rainfall-runoff modelling. Using the results of various fields of soil variability, experiments are carried out to assess the validity of the commonly used concept of `effective parameters'. The results of these experiments suggest that such a concept may be valid in modelling subsurface flow. However, the effective parameter is observed to be event dependent when the dominating mechanism is infiltration excess runoff.

Numerical modelling of agglomerate degradation

In the processing industries particulate materials are often in the form of powders which themselves are agglomerations of much smaller sized particles. During powder processing operations agglomerate degradation occurs primarily as a result of collisions between agglomerates and between agglomerates and the process equipment. Due to the small size of the agglomerates and the very short duration of the collisions it is currently not possible to obtain sufficiently detailed quantitative information from real experiments to provide a sound theoretically based strategy for designing particles to prevent or guarantee breakage. However, with the aid of computer simulated experiments, the micro-examination of these short duration dynamic events is made possible. This thesis presents the results of computer simulated experiments on a 2D monodisperse agglomerate in which the algorithms used to model the particle-particle interactions have been derived from contact mechanics theories and, necessarily, incorporate contact adhesion. A detailed description of the theoretical background is included in the thesis. The results of the agglomerate impact simulations show three types of behaviour depending on whether the initial impact velocity is high, moderate or low. It is demonstrated that high velocity impacts produce extensive plastic deformation which leads to subsequent shattering of the agglomerate. At moderate impact velocities semi-brittle fracture is observed and there is a threshold velocity below which the agglomerate bounces off the wall with little or no visible damage. The micromechanical processes controlling these different types of behaviour are discussed and illustrated by computer graphics. Further work is reported to demonstrate the effect of impact velocity and bond strength on the damage produced. Empirical relationships between impact velocity, bond strength and damage are presented and their relevance to attrition and comminution is discussed. The particle size distribution curves resulting from the agglomerate impacts are also provided. Computer simulated diametrical compression tests on the same agglomerate have also been carried out. Simulations were performed for different platen velocities and different bond strengths. The results show that high platen velocities produce extensive plastic deformation and crushing. Low platen velocities produce semi-brittle failure in which cracks propagate from the platens inwards towards the centre of the agglomerate. The results are compared with the results of the agglomerate impact tests in terms of work input, applied velocity and damage produced.

Verification and validation of numerical models of the transport of insulation debris

Damage to insulation materials located near to a primary circuit coolant leak may compromise the operation of the emergency core cooling system (ECCS). Insulation material in the form of mineral wool fiber agglomerates (MWFA) maybe transported to the containment sump strainers, where they may block or penetrate the strainers. Though the impact of MWFA on the pressure drop across the strainers is minimal, corrosion products formed over time may also accumulate in the fiber cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz is investigating the phenomena that maybe observed in the containment vessel during a primary circuit coolant leak. The study entails the generation of fiber agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effect that corrosion and erosion of the containment internals by the coolant has on the strainer pressure drop. The focus of this paper is on the verification and validation of numerical models that can predict the transport of MWFA. A number of pseudo-continuous dispersed phases of spherical wetted agglomerates represent the MWFA. The size, density, the relative viscosity of the fluid-fiber agglomerate mixture and the turbulent dispersion all affect how the fiber agglomerates are transported. In the cases described here, the size is kept constant while the density is modified. This definition affects both the terminal velocity and volume fraction of the dispersed phases. Note that the relative viscosity is only significant at high concentrations. Three single effect experiments were used to provide validation data on the transport of the fiber agglomerates under conditions of sedimentation in quiescent fluid, sedimentation in a horizontal flow and suspension in a horizontal flow. The experiments were performed in a rectangular column for the quiescent fluid and a racetrack type channel that provided a near uniform horizontal flow. The numerical models of sedimentation in the column and the racetrack channel found that the sedimentation characteristics are consistent with the experiments. For channel suspension, the heavier fibers tend to accumulate at the channel base even at high velocities, while lighter phases are more likely to be transported around the channel.

Numerical models used for the modelling of the transport of fibrous insulation debris

Mineral wool insulation material applied to the primary cooling circuit of a nuclear reactor maybe damaged in the course of a loss of coolant accident (LOCA). The insulation material released by the leak may compromise the operation of the emergency core cooling system (ECCS), as it maybe transported together with the coolant in the form of mineral wool fiber agglomerates (MWFA) suspensions to the containment sump strainers, which are mounted at the inlet of the ECCS to keep any debris away from the emergency cooling pumps. In the further course of the LOCA, the MWFA may block or penetrate the strainers. In addition to the impact of MWFA on the pressure drop across the strainers, corrosion products formed over time may also accumulate in the fiber cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. Therefore, it is essential to understand the transport characteristics of the insulation materials in order to determine the long-term operability of nuclear reactors, which undergo LOCA. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz1 is investigating the phenomena that maybe observed in the containment vessel during a primary circuit coolant leak. The study entails the generation of fiber agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effects that particles formed due to corrosion of metallic containment internals by the coolant medium have on the strainer pressure drop. The focus of this presentation is on the numerical models that are used to predict the transport of MWFA by CFD simulations. A number of pseudo-continuous dispersed phases of spherical wetted agglomerates can represent the MWFA. The size, density, the relative viscosity of the fluid-fiber agglomerate mixture and the turbulent dispersion all affect how the fiber agglomerates are transported. In the cases described here, the size is kept constant while the density is modified. This definition affects both the terminal velocity and volume fraction of the dispersed phases. Only one of the single effect experimental scenarios is described here that are used in validation of the numerical models. The scenario examines the suspension and horizontal transport of the fiber agglomerates in a racetrack type channel. The corresponding experiments will be described in an accompanying presentation (see abstract of Seeliger et al.).

Numerical and experimental investigations for insulation particle transport phenomena in water flow

The investigation of insulation debris generation, transport and sedimentation becomes more important with regard to reactor safety research for pressurized and boiling water reactors, when considering the long-term behaviour of emergency core coolant systems during all types of loss of coolant accidents (LOCA). The insulation debris released near the break during a LOCA incident consists of a mixture of a disparate particle population that varies with size, shape, consistency and other properties. Some fractions of the released insulation debris can be transported into the reactor sump, where it may perturb or impinge on the emergency core cooling systems. Open questions of generic interest are for example the particle load on strainers and corresponding pressure-drop, the sedimentation of the insulation debris in a water pool, its possible re-suspension and transport in the sump water flow. A joint research project on such questions is being performed in cooperation with the University of Applied Science Zittau/Görlitz and the Forschungszentrum Dresden-Rossendorf. The project deals with the experimental investigation and the development of computational fluid dynamic (CFD) models for the description of particle transport phenomena in coolant flow. While the experiments are performed at the University Zittau/Görlitz, the theoretical work is concentrated at Forschungszentrum Dresden-Rossendorf. In the present paper, the basic concepts for computational fluid dynamic (CFD) modelling are described and experimental results are presented. Further experiments are designed and feasibility studies were performed.

Verification and validation of numerical models of the transport of insulation debris

A combination of the two-fluid and drift flux models have been used to model the transport of fibrous debris. This debris is generated during loss of coolant accidents in the primary circuit of pressurized or boiling water nuclear reactors, as high pressure steam or water jets can damage adjacent insulation materials including mineral wool blankets. Fibre agglomerates released from the mineral wools may reach the containment sump strainers, where they can accumulate and compromise the long-term operation of the emergency core cooling system. Single-effect experiments of sedimentation in a quiescent rectangular column and sedimentation in a horizontal flow are used to verify and validate this particular application of the multiphase numerical models. The utilization of both modeling approaches allows a number of pseudocontinuous dispersed phases of spherical wetted agglomerates to be modeled simultaneously. Key effects on the transport of the fibre agglomerates are particle size, density and turbulent dispersion, as well as the relative viscosity of the fluid-fibre mixture.