Global Local Approximations Research Articles

An improved ANN-based global-local approximation for small medical data analysis

INTRODUCTION: The task of approximation of complex nonlinear dependencies, especially in the case of short datasets, is important in various applied fields of medicine. Global approximation methods describe the generalized behavior of the model, while local methods explain the behavior of the model at specific data points. Global-local approximation combines both approaches, which makes such methods a powerful tool for processing short sets of medical data that can have both broad trends and local variations.OBJECTIVES: This paper aims to improve the method of sequential obtaining global and local components of the response surface to increase the accuracy of prediction in the case of short sets of medical data.METHODS: In this paper, the authors developed a new method that combined two ANNs: a non-iterative SGTM neural-like structure for obtaining the global component and GRNN as a powerful tool of local approximation in the case of short datasets.RESULTS: The authors have improved the method of global-local approximation due to the use of a General Regression Neural Network instead of RBF ANN for obtaining the local component, which ensured an increase in the accuracy of the body fat prediction task. The authors optimized the operation of the method and investigated the efficiency of the sequential obtaining global and local components of the response surface in comparison with the efficiency using a number of existing methods.CONCLUSION: The conducted experimental studies for solving the body fat prediction task showed the high efficiency of using the improved method in comparison with a number of existing methods, including ensemble methods.

A hybrid Fox and Kirsch’s reduced basis method for structural static reanalysis

Fox and Kirsch's static reanalysis methods are reviewed firstly, and then a new hybrid Fox and Kirsch's reduced basis method is presented for structural static reanalysis in this paper. Reduced basis vectors are derived from Neumann series expansion about multiple initial structures, which is a universal format of reduced basis. The hybrid method combines the merits of Fox's polynomial fitting reanalysis and Kirsch's combined approximations reanalysis and has the advantage of global-local approximation. Error evaluation of the approximations is given and the number of algebraic operations is also discussed. The reanalysis accuracy and efficiency are tested by four numerical examples. For the large modification, the hybrid method generally has higher accuracy than Kirsch's method at the same computational cost. Moreover, the hybrid method does accelerate the process of structural optimization using genetic algorithm and slightly affect the accuracy of the optimal solutions.

CFD-based aerodynamic approximation concepts optimization of a two-dimensional scramjet vehicle

A direct numerical optimization methodology combining nonlinear programming and approximation concepts is studied in the context of CFD-based engine/airframe integration. It aims at reducing the number of full CFD analyses required in the course of an optimization, by replacing the original optimization problem by a set of approximate problems, thus reducing computational cost considerably. The performance of global local approximations (GLA) is tested and compared to that of a more common first-order Taylor series approximation. These approximations are obtained with alternative simplified aerodynamic analysis techniques corrected by CFD computations. A two-dimensiona l NASP-like configuration serves as a test case. In this article the basic procedure is reviewed and results based on optimization studies of the nozzle and forebody are presented. Problems associated with the application of GLA to CFD-based optimization are discussed and some solutions and insights are provided. Nomenclature flcurvc = curvature

Combining global and local approximations

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Algorithm for modification of parameters in vibrating systems

Concluding Remarks A global-local approximation based on a linear approximation to a scaling factor has been presented. The approximation permits us to use a global approximation based on a simple model of our problem to extend the range of usefulness of derivative-based approximations to a more refined model. The method was demonstrated for a simple beam example with a crude and more refined finite element model.