Optimum Design of Structures for Earthquake Loading by a Cellular Evolutionary Algorithm and Neural Networks

Introduction

Optimum design of structures is a process of selecting the design variables such that an objective function is minimized while all of the design constraints are satisfied. During the last decades, structural optimization problems have been solved using gradient-based algorithms. As the mathematical programming based methods need gradient calculations, the considerable part of the optimization process is devoted to the sensitivity analysis and the computational work of these methods is usually high. Optimal design of real-world structures subject to seismic loading is one of the major concerns in the field structural engineering. When structures are subjected to sever earthquakes a huge amount of inertia loads is imposed to the structures. In this case, considering linear elastic behavior and ignoring the nonlinear structural responses during the optimization process may lead to vulnerable structural systems. Therefore, seismic design codes suggest that, under severe earthquake events, the structures should be designed to deform inelastically. To achieve structural seismic design optimization it is necessary that the nonlinear structural time history analysis to be performed many times. In this case, the computational burden of the optimal seismic design process is so large that could prevent designer from comprehensively exploring the design space, and could ultimately result in unsuitable structures. Consequently, it is necessary to employ efficient computational strategies to achieve optimal seismic design of structures spending low computational costs.

In the last decades, soft computing procedures have been widely used to solve massive and complex engineering problems. Soft computing includes many components and the most attractive ones are meta-heuristic optimization algorithms and neural networks. As meta-heuristic or evolutionary optimization algorithms need not gradient calculations they are more robust than the mathematical programming based techniques and usually present better global behavior. Beside the mentioned computational advantages, the disadvantage of these methods is a slow rate of convergence towards the global optimum. A neural network is an interconnected network of simple processing elements. The processing elements interact along paths of variable connection strengths which when suitably adapted can collectively produce complex overall desired behavior. Neural networks operate as black box, model-free, and adaptive tools to capture and learn significant structures in data. Their computing abilities have been proven in the fields of prediction, pattern recognition, and optimization. They are suitable particularly for problems too complex to be modelled and solved by classical mathematics and traditional procedures.

The main objective of this chapter is to propose a computationally efficient methodology to optimum design of structures subject to earthquake loading considering inelastic structural behaviour. To achieve this task, an efficient genetic algorithm (GA) based evolutionary optimization algorithm is employed to reduce the required analyses. Also, a hybrid neural network system is employed to effectively predict the nonlinear time history responses of structures during the optimization process.