Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

The influence of tool geometry on the performance of drilling tools

The main objective of the work presented in this thesis is to investigate the two sides of the flute, the face and the heel of a twist drill. The flute face was designed to yield straight diametral lips which could be extended to eliminate the chisel edge, and consequently a single cutting edge will be obtained. Since drill rigidity and space for chip conveyance have to be a compromise a theoretical expression is deduced which enables optimum chip disposal capacity to be described in terms of drill parameters. This expression is used to describe the flute heel side. Another main objective is to study the effect on drill performance of changing the conventional drill flute. Drills were manufactured according to the new flute design. Tests were run in order to compare the performance of a conventional flute drill and non conventional design put forward. The results showed that 50% reduction in thrust force and approximately 18% reduction in torque were attained for the new design. The flank wear was measured at the outer corner and found to be less for the new design drill than for the conventional one in the majority of cases. Hole quality, roundness, size and roughness were also considered as a further aspect of drill performance. Improvement in hole quality is shown to arise under certain cutting conditions. Accordingly it might be possible to use a hole which is produced in one pass of the new drill which previously would have required a drilled and reamed hole. A subsidiary objective is to design the form milling cutter that should be employed for milling the foregoing special flute from drill blank allowing for the interference effect. A mathematical analysis in conjunction with computing technique and computers is used. To control the grinding parameter, a prototype drill grinder was designed and built upon the framework of an existing cincinnati cutter grinder. The design and build of the new grinder is based on a computer aided drill point geometry analysis. In addition to the conical grinding concept, the new grinder is also used to produce spherical point utilizing a computer aided drill point geometry analysis.