Case base adaptation using solution-space metrics

In this paper we propose a generalisation of the k-nearest neighbour (k-NN) retrieval method based on an error function using distance metrics in the solution and problem space. It is an interpolative method which is proposed to be effective for sparse case bases. The method applies equally to nominal, continuous and mixed domains, and does not depend upon an embedding n-dimensional space. In continuous Euclidean problem domains, the method is shown to be a generalisation of the Shepard's Interpolation method. We term the retrieval algorithm the Generalised Shepard Nearest Neighbour (GSNN) method. A novel aspect of GSNN is that it provides a general method for interpolation over nominal solution domains. The performance of the retrieval method is examined with reference to the Iris classification problem,and to a simulated sparse nominal value test problem. The introducion of a solution-space metric is shown to out-perform conventional nearest neighbours methods on sparse case bases.

Case base reduction using solution-space metrics

In this paper we propose a case base reduction technique which uses a metric defined on the solution space. The technique utilises the Generalised Shepard Nearest Neighbour (GSNN) algorithm to estimate nominal or real valued solutions in case bases with solution space metrics. An overview of GSNN and a generalised reduction technique, which subsumes some existing decremental methods, such as the Shrink algorithm, are presented. The reduction technique is given for case bases in terms of a measure of the importance of each case to the predictive power of the case base. A trial test is performed on two case bases of different kinds, with several metrics proposed in the solution space. The tests show that GSNN can out-perform standard nearest neighbour methods on this set. Further test results show that a caseremoval order proposed based on a GSNN error function can produce a sparse case base with good predictive power.

A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.