Many-objective control optimization of high-rise building structures using replicator dynamics and neural dynamics model

Abstract

Recently the authors presented a single-agent Centralized Replicator Controller (CRC) and a decentralized Multi-Agent Replicator Controller (MARC) for vibration control of high-rise building structures. It was shown that the use of agents and a decentralized approach enhances the vibration control system. Two key parameters in the proposed control methodologies using replicator dynamics are the total population (total available resources or the sum of actuators forces) and the growth rate. In the previous research, a sensitivity analysis was performed to determine the appropriate values for the population size and growth rate. In this paper, the aforementioned control methodologies are integrated with a multi-objective optimization algorithm in order to find Pareto optimal values for growth rates with the goal of achieving maximum structural performance with minimum energy consumption. A modified neural dynamic model of Adeli and Park is used in this research to solve the many-objective optimization problem where the Normal Boundary Intersection method is employed to find Pareto optimality. Sample results are presented using a 20-story steel benchmark structure subjected to historical and artificial accelerograms.

Appendix

The performance criteria used in this research to compare control algorithms is the following:

$$ {J}_1=\frac{\underset{t,i}{\max}\left|{u}_i(t)\right|}{u^{max}} $$

(51)

J ₁ represent the maximum displacement corresponding to the horizontal displacement u _i (t), u ^max is the maximum uncontrolled displacement.

$$ {J}_2=\frac{\underset{t,i}{\max}\frac{\left|{d}_i(t)\right|}{h_i}}{d_{max}} $$

(52)

J ₂ denotes the maximum inter-story displacement or drift, h _i is the height of each floor stories (h ₁ = 5.49m; h _i = 3.96m for i=1,...,20) and d ^max is the maximum uncontrolled drift.

$$ {J}_3=\frac{\underset{t,i}{\max}\left|{\ddot{u}}_i(t)\right|}{{\ddot{u}}^{max}} $$

(53)

J ₃ denotes the maximum relative floor acceleration and ${\ddot{u}}^{max}$ is the maximum uncontrolled absolute floor acceleration

$$ {J}_4=\left(\frac{\underset{t}{\max }{\sum}_{i=1}^N{m}_i{\ddot{u}}_{ai}(t)}{V_b^{max}}\right) $$

(54)

J ₄ denotes the maximum base shear, ${V}_b^{max}$ is the maximum base shear for the uncontrolled case and m _i is the seismic mass of floor i.

The following are the root-mean-squared (RMS) measurements criteria:

$$ {J}_5=\frac{\underset{t,i}{\max}\left\Vert {u}_i(t)\right\Vert }{{\widehat{u}}^{max}}\kern0.5em i=1,\dots k $$

(55)

where J ₅ is the normalized maximum RMS displacement of the controlled structure, $\left\Vert {u}_j(t)\right\Vert =\sqrt{\int_0^{t_{\mathrm{end}}}\left[{u}_j^2(t)\right]\mathrm{dt}}$ divided by the maximum uncontrolled RMS displacement, ${\widehat{u}}^{max}$.

$$ {J}_6=\frac{\max_{t,i}\frac{\left\Vert {d}_i(t)\right\Vert }{h_i}}{{\widehat{d}}^{max}}\kern0.5em \mathrm{i}=1,\dots, \mathrm{k} $$

(56)

J ₆ is the normalized maximum RMS inter-story displacement or drift, and ${\widehat{d}}^{max}=\mathit{\max}\left\Vert {d}_i(t)\right\Vert$ is the maximum uncontrolled RMS drift.

$$ {J}_7=\frac{\underset{t,j}{\max}\left\Vert {\ddot{u}}_i(t)\right\Vert }{{\widehat{\ddot{u}}}^{max}}\kern0.5em i=1,\dots k $$

(57)

where J ₇ is the normalized maximum RMS absolute floor acceleration of the controlled structure, $\left\Vert {\ddot{u}}_j(t)\right\Vert =\sqrt{\int_0^{t_{\mathrm{end}}}\left[{\ddot{u}}_i^2(t)\right]\mathrm{dt}}$ divided by the maximum uncontrolled RMS absolute floor acceleration, ${\widehat{\ddot{u}}}^{max}$. J ₈ is the number of control devices and J ₉ is the number of sensors.