PINNÍPEDOS

Since the settings of the GA parameters can significantly affect the convergence of the global optimum and the computational time consumed for the convergence, several principles for balancing the parameters of the GA solver are identified based on the practical optimization test and the general knowledge of GA.

As is mentioned in Chapter 4, the capability of GA for fully exploring the search space depends on maintaining an appropriate diversity of the individuals in the population during the evolution. Generally, this can be achieved by increasing the size of the initial population and adjusting the evolutionary operators which could produce new individuals or new genes (e.g. crossover and mutation). In the practical optimization with MATLAB, the excessive increase of the population size can sharply increase the total calculations of the functions in the GA solver that undesirably enlarges the computational time. Therefore, considering the computational efficiency, it is recommended to ensure the population diversity by adjusting the parameters of the evolutionary operators rather than solely using a huge population size.

94

In accordance to the recommendation of the MATLAB official guiding documentations (MATLAB 2014), the mutation option needs to be set with the default mutation function ‘@mutationadaptfeasible’ to satisfy the bounds and the constraints while dealing with a constrained optimization problem. With this mutation function, the intensity of the mutation is not allowed to assign and hence the users are not allowed to adjust the diversity of the population by modifying the probability of mutation. However, the default crossover function ‘@crossoverintermediate’, which is set for the crossover option when there are linear constraints, enable the users to specify the weights for creating children individuals by a single parameter ‘ratio’. By enlarging the value of this parameter, the children individual created by the parents can randomly include new characteristics and hence enhances the population diversity.

In addition to ensure the diversity of the population during the evolution to explore potential search space, the superior characteristics of some elite individuals should be properly retained otherwise the superior characteristics will be occasionally lost during the selection process. In this case, the elite number is set by the parameter ‘EliteCount’ as shown in Table 5.3 and Table 5.4. Base on the practical test, the ‘EliteCount’ is suitable to be set at the value from 3 to 5, while considering its negative effect to maintain the population diversity.

5.5 Conclusions

This chapter presents a baseline study on the optimal distribution of viscous dampers in elastic frames with the help of genetic algorithms interfaced with nonlinear response analysis. For an elastic frame designed with regular distribution of storey stiffness, the GA-NRH method is slightly superior to

95

other damping distribution strategies including the Takewaki Method, the SSSA Method, the uniform damping method and the stiffness damping distribution method. For an elastic frame designed with irregular distribution of storey stiffness, for example the frame with weak storeys, the GA is relatively effective and efficient to detect the weak points of the structure and to improve the structural seismic response by strategically allocating supplemental damping. In contrast with the GA-NRH method, the traditional damping distribution methods could not intelligently consider the weakness of the elastic frame and the seismic response is not optimally improved.

It can be concluded that the genetic algorithm is a powerful tool to conduct the global optimization for the damper distribution problem under random earthquakes. The ability of GA for exploring the search space is identified to be stronger than other approaches. Given that GA is efficient to mitigate the seismic response of elastic frames with irregular stiffness distribution, the frames designed in practice are generally in accordance to regular distribution of lateral stiffness. In addition, the realistic buildings undergo inelastic behaviors under seismic excitations, while the elastic building could not accurately represent the nonlinear behaviors in the realistic buildings.

The following chapter will focus on investigating the damper optimization techniques with GA for moment resisting frames which is subjected to performance-based design. The nonlinear behaviors of the beams and columns of the frames will be explicitly considered, while the effectiveness of GA for optimum distribution of viscous fluid damper under strong earthquakes associated with collapse will be further explored.

96

Charter 6

Height-wise Damper Placement Optimization with Genetic

Algorithms in Steel Moment Resisting Frames

6.0 Introduction

The aim of this chapter is to explore the effectiveness and the feasibility of the GA and NRH analysis in optimizing dampers distribution in the code- compliant inelastic steel buildings under strong earthquakes. As discussed in Chapter 3, a few of previous studies initially show that the damper optimization throughout the floors does not play a significant role with respect to the structural performance parameters under the DBE. Hence, the steel buildings investigated in this study are optimized for a seismic environment under various intensity levels, especially under higher intensity levels. In addition, since the damper optimization under strong earthquakes triggering building collapses has never been evaluated in previous studies, Incremental Dynamic Analyses (IDA) are introduced to this study to assess the collapse performance of the retrofitted building. Furthermore, both far- fault and near-fault earthquakes are considered in this work and steel MRF buildings of different stories are involved to explore the influence of higher modes.

In this chapter, two steel MRF buildings designed in accordance to the Eurocode are described. The design criteria and the modeling assumptions for these prototype MRFs are specifically presented. Based on the existing method of evaluating the total supplemental viscous damping, both of the MRFs are designed with supplemental fluid viscous dampers, of which the damping coefficients are distributed according to stiffness proportional damping distribution throughout the height of the building. In order to

97

perform collapse simulations for comparing collapse performance between the optimized frames and the original designed frames, a set of far-fault ground motions and a set of near-fault ground motions are considered for the seismic environments respectively.