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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 823653, 11 pages
Research Article

Analysis of Stiffened Penstock External Pressure Stability Based on Immune Algorithm and Neural Network

1North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Received 5 November 2013; Accepted 4 January 2014; Published 19 February 2014

Academic Editor: Her-Terng Yau

Copyright © 2014 Wensheng Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The critical external pressure stability calculation of stiffened penstock in the hydroelectric power station is very important work for penstock design. At present, different assumptions and boundary simplification are adopted by different calculation methods which sometimes cause huge differences too. In this paper, we present an immune based artificial neural network model via the model and stability theory of elastic ring, we study effects of some factors (such as pipe diameter, pipe wall thickness, sectional size of stiffening ring, and spacing between stiffening rings) on penstock critical external pressure during huge thin-wall procedure of penstock. The results reveal that the variation of diameter and wall thickness can lead to sharp variation of penstock external pressure bearing capacity and then give the change interval of it. This paper presents an optimizing design method to optimize sectional size and spacing of stiffening rings and to determine penstock bearing capacity coordinate with the bearing capacity of stiffening rings and penstock external pressure stability coordinate with its strength safety. As a practical example, the simulation results illustrate that the method presented in this paper is available and can efficiently overcome inherent defects of BP neural network.