Stochastic Optimal Control of Structures by Yongbo Peng & Jie Li

Author:Yongbo Peng & Jie Li
Language: eng
Format: epub
ISBN: 9789811367649
Publisher: Springer Singapore

Parameters

Initial value

100

100

10−12

Optimal value

102.8

163.7

10−12

Objective function

1.122 × 10−5 (Pf,d = 0.0023, Pf,v = 0.0035, Pf,u = 0.0022)

Fig. 4.6Convergence process of objective function against iteration number

Time histories of the mean and standard deviation of the 1st interstory drift and of the 8th interstory drift with and without controls are shown in Fig. 4.7, respectively. It is seen that the interstory drift decreases significantly and arises to an equally proportional reduction along story level , where the interstory drift is nearly four times smaller than that of uncontrolled structure. Meanwhile, the interval of time histories with significant variation is reduced more seriously than other intervals. Time histories of the mean and standard deviation of the first story acceleration and of the eighth story acceleration with and without controls are shown in Fig. 4.8. It is seen that the first story acceleration with smaller peak is nearly not changed; while the eighth story acceleration with larger peak is reduced significantly, which attains a more smooth story acceleration along structural height. With consideration of interstory drift, the control effectiveness relies on the applied probabilistic criterion that the story exhibiting a larger response attains a better improvement, resulting in the desired structural performance. In comparison with Figs. 3.​19 and 3.​20, the mean-square responses of the controlled structure are almost identical both using the exceedance probability criterion in optimization criterion group on energy trade-off and the criterion on system second-order statistics evaluation.

Fig. 4.7Time histories of mean and standard deviation of interstory drifts with and without controls

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