In this paper, a new algorithm is introduced for reliability analysis of structures using response surface method based on a group method of data handling-type neural networks with general structure (GS-GMDH-type NN). A multilayer network of quadratic neurons, GMDH, offers an effective solution to modeling nonlinear systems without an explicit limit state function. In the proposed method, the response surface function is determined using GMDH-type neural networks. This is then connected to a reliability method, such as first-order or second-order reliability methods (FORM or SORM) or Monte Carlo simulation method to predict the failure probability (Pf). In the proposed method, the use of the GMDH-type neural network with general structure, where all neurons from previous layers are used to produce neurons in the new layer, can improve the limit state function. In addition, the structure of the neural network and its weight are simultaneously optimized by genetic algorithm and singular value decomposition. As a result, the obtained model has no significant error, despite its simplicity. Moreover, the obtained limit state function is explicit and allows direct use of FORM and SORM methods. To determine the accuracy and efficiency of the proposed method, four numerical examples are solved and their results are compared to other conventional methods. The results show that the proposed method is simply applicable to analyzing the reliability of large complex and sophisticated structures without an explicit limit state function. The proposed approach is a high accurate method that can significantly reduce computing time compared with direct Monte Carlo method.
Muzzammil M, Alam J, Danish M (2015) The GMDH model for prediction of scour at bridge pier in cohesive bed. In: Hydro 2015 international, 20th international conference on hydraulics, water resources and river engineering, IIT Roorkee, IndiaGoogle Scholar
Nariman-zadeh N, Darvizeh A, Darvizeh M, Gharababaei H (2002) Modelling of explosive cutting process of plates using GMDH-type neural network and singular value decomposition. J Mater Process Tech 128(1–3):80–87CrossRefzbMATHGoogle Scholar
Beheshti Nezhad H, Nariman-Zadeh N, Ranjbar MM (2008) Prediction of concrete diffusion factor under aggressive environment with GMDH-type neural networks. In: Proceedings of the 8th international conference on creep, shrinkage and durability mechanics of concrete and concrete structures, pp 1131–1137. ISBN 978-0-415-48508-1Google Scholar
Nariman-Zadeh N, Darvizeh A, Ahmad-Zadeh GR (2003) Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modelling and prediction of the explosive cutting process. Proc Inst Mech Eng B J Eng 217:779–790CrossRefzbMATHGoogle Scholar