Keywords: structural reliability, life cycle cost, bi-level optimization, first and second order reliability method (FORM/SORM), Monte Carlo simulation, neural networks, finite element method.

In this paper a robust and efficient methodology is presented for solving life cycle-oriented optimization problems. The proposed methodology combines structural reliability, optimization and neural networks intelligently. Over the last decades optimization techniques and structural reliability analysis have stimulated the probabilistic optimum design of structures. Despite of the advances in this field, serious computational obstacles arise when treating practical problems. Life cycle cost-oriented optimization (LCCOO) is simply minimizing the aggregation of all cost components. Construction cost, annual maintenance and operation costs, repair costs and expected damage and failure costs (economic losses, deaths and injuries) are examples for different life cycle objectives. Here, two cost components are considered namely; initial (construction) cost and the expected failure cost. The latter cost includes the probability of failure. The available methods for estimating the probability of failure can be roughly classified into two groups, which can be labelled as gradient-based and simulation-based methods. Gradient-based methods such as first order/second order reliability techniques (FORM/SORM) are optimization-based techniques which turn the LCCOO into a bi-level optimization problem. Simulation-based techniques such as Monte Carlo simulation hinge upon the creation of a synthetic set of response samples. Such techniques are time-consuming procedures. Few methods are presented to solve such probabilistic bi-level optimization issues [1,2,3] but the problem is still under investigation.

For most realistic structures or systems, the response has to be computed through numerical procedures such as finite element analysis. This brings another complexity to the LCCOO because the performance function (limit state) is not available as an explicit, closed-form function of the input variables. A two stage procedure for obtaining the optimum design is presented. Two neural networks are trained: one for the implicit limit state and the other to find the relation between the probability of failure and the vector of the design parameters. The use of neural networks is motivated by the approximate concept inherent in reliability analysis and the time consuming resulted from using the other documented methods.

The proposed methodology utilizes neural networks intelligently to reduce the number of iterations required to build an approximation for the implicit limit state function under consideration. The paper discusses the need for having a design of experiments scheme for the vector of design parameters thorough an example. Another example tests the application of the approach on hand for the design of steel frames under static loads. The approach shows competitive results to those extracted from the one-level technique and the second order response surface. It is expected that this methodology will be adopted with respect of applications of Level IV design codes.

1

Abdelatif H., S.S., Maes, M. "A Comparison of Algorithms for Structural Life Cycle Utility Optmization", Proceedings of International Conference on Structural and Geotechnical Engnieering and Construction Technology (IC-SGECT'04), Mansoura, Egypt. (2004) 108-120.

2

Rackwitz, R. "Optimization-the Basis of Code Making and Reliability", Structural Safety. (2000) 22 27-60. doi:10.1016/S0167-4730(99)00037-5

3

Royset, J.O., Kiureghian, A.D., Polak, E. "Reliability-Based Optimal Design of Series Structural Systems", Journal of Engineering Mechanics. (2001) Vol.127, No.6, 607-614. doi:10.1061/(ASCE)0733-9399(2001)127:6(607)

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