Automatic generation of smart earthquake-resistant building system: Hybrid system of base-isolation and building-connection

A base-isolated building may sometimes exhibit an undesirable large response to a long-duration, long-period earthquake ground motion and a connected building system without base-isolation may show a large response to a near-fault (rather high-frequency) earthquake ground motion. To overcome both deficiencies, a new hybrid control system of base-isolation and building-connection is proposed and investigated. In this new hybrid building system, a base-isolated building is connected to a stiffer free wall with oil dampers. It has been demonstrated in a preliminary research that the proposed hybrid system is effective both for near-fault (rather high-frequency) and long-duration, long-period earthquake ground motions and has sufficient redundancy and robustness for a broad range of earthquake ground motions.An automatic generation algorithm of this kind of smart structures of base-isolation and building-connection hybrid systems is presented in this paper. It is shown that, while the proposed algorithm does not work well in a building without the connecting-damper system, it works well in the proposed smart hybrid system with the connecting damper system.


Introduction
In the seismic resistant design of building structures, the concept of resilience is becoming more and more important and it is highly desired to design building structures safely for a broader class of possible earthquake ground motions (Takewaki 2006(Takewaki , 2013Takewaki et al., 2012). This is based on the common understanding that earthquake ground motions are highly uncertain both in its occurrence and property. It appears therefore difficult to predict the forthcoming events precisely in time, space and character (Takewaki 2006(Takewaki , 2013Takewaki et al., , 2012Takewaki et al., , 2013. It is also recognized that the properties of building structural elements (especially the properties of base-isolation systems and passive control systems, etc.) are not deterministic (Ben-Haim, 2001) and their variation brings various difficulties in the seismic resistant design of building structures in terms of robustness and redundancy ([ 4 _ T D $ D I F F ] AIJ, 2011). In fact, it is code-specified in Japan to take into account the variability of mechanical properties of isolators and dampers in the design of base-isolated buildings and passively controlled buildings. In this design process, the worst combination of mechanical properties of isolators and dampers is investigated (Ben-Haim 2001; Elishakoff and Ohsaki, 2010;Takewaki et al., 2012) and all the design conditions are checked for this worst case.
While base-isolated buildings are understood to be effective for high-frequency (impulsive) ground motions [ 5 _ T D $ D I F F ] and base-isolation systems were used for rather rigid super structures in an early stage (Jangid and Datta, 1994;Hall et al., 1995;Heaton et al., 1995;Jangid, 1995;Jangid and Banerji, 1998;Kelly, 1999;Naeim and Kelly, 1999;Jangid and Kelly, 2001;Morales, 2003;Takewaki, 2005;Li and Wu, 2006;[ 6 _ T D $ D I F F ] 2008; Hino et al., 2008;Takewaki and Fujita, 2009), they are not necessarily resistant for long-period [ 7 _ T D $ D I F F ] ground motions with the characteristic period of 5-8s (Ariga et al., 2006;Irikura et al., 2004;Kamae et al., 2004). Actually it is reported that a resonance of the base-isolated buildings with the long-period ground motions was observed during the 2011 Tohoku (Japan) earthquake. Nevertheless, the base-isolation system is used recently even for a rather tall building especially in Japan and the long-period ground motions with the characteristic period of 5-8s are of great interest in the structural design of base-isolated buildings and super high-rise buildings. On the other hand, it is also well understood that, while building structures including passive energy dissipating systems are effective for long-duration, long-period ground motions (Takewaki 2007(Takewaki , 2015Patel and Jangid, 2011;Takewaki et al., , 2012, they are not necessarily effective for near-fault (rather high-frequency) ground motions (Xu et al., 2007;Takewaki and Tsujimoto, 2011). This is because the passive damper systems cannot respond effectively to impulsive loadings. Smart resolution of these two issues may be one of the most controversial issues in the field of seismic resistant and control design (Koo et al., 2009;Petti et al., 2010;Karabork, 2011).

Article No~e00069
In this paper, a new hybrid passive control system is investigated in which a base-isolated building is connected to another non-base-isolated building (free wall) with oil dampers. A similar type of buildings without base-isolation is being designed and constructed by Obayashi Corporation in Japan as an apartment house with a car parking tower (Nishimura et al., 2008) and buildings incorporating such hybrid system [ 8 _ T D $ D I F F ] are under construction in Tokyo by Obayashi Corporation and Shimizu Corporation. It may also be interesting to note that, if the free wall becomes stiffer, the connecting damper system yields a building with dampers attached directly to the ground (Trombetti and Silvestri, 2004). A preliminary investigation was conducted by Murase et al. (2013). However it seems that more detailed and deeper investigations are required. An automatic generation algorithm of this kind of smart structures of base-isolation and building-connection hybrid systems is presented in this paper.

Model
[ 9 _ T D $ D I F F ] Base-isolated building interconnected to outer frame A base-isolated building and a building with connecting dampers are two representatives of passive controlled buildings (see Figs. 1(a), (b)). A [ 1 0 _ T D $ D I F F ] new hybrid passive control system consists of a multi-story base-isolated main building (apartment house), a free wall (car parking tower) and a group of interconnecting oil dampers as shown in Fig. 1(c). Oil dampers are usually installed as connecting dampers because of its sufficient stroke and damping performance. The general earthquake response properties of these buildings under near-fault and long-duration, long-period ground motions are explained in  ground motions. The hybrid passive control system can resist for the near-fault ground motion via the base-isolation mechanism and respond effectively to the long-duration, long-period ground motion via the building connection mechanism. Furthermore, the base-isolation mechanism is quite advantageous for the energy consumption at the connecting dampers in all stories as shown in objective function in terms of deformation reduction and acceleration reduction indices.
where a and b are the weighting coefficients.
In order to obtain a better design with a lower objective function, a sensitivitybased method is introduced. The stiffness of the free wall is fixed and only the stiffness of the main structure is treated as the design variable. The isolation-story stiffness can also be treated as a design variable by regarding this story stiffness as the isolation-story stiffness (insert of the isolation system at any floor is possible).
If the gradient-based algorithm is not used, the structural designer cannot find directly the most appropriate location to decrease the stiffness at the first stage.
Furthermore each set of stiffnesses of the main structure at each step obtained by the gradient-based algorithm provides the structural designers with useful information on structural design (the efficient location of stiffness). One of the popular sensitivity-free methods is GA (genetic algorithm). When GA is used, a complicated setting of GA parameters is necessary and this procedure may be cumbersome for most of structural designers.
The algorithm of the proposed method is very simple and can be summarized as follows.

[ 1 4 _ T D $ D I F F ] 4. Example
In order to demonstrate the validity of the proposed method, some numerical examples are shown in this section. As stated before, the stiffness of the free wall is fixed and only the stiffness of the main structure is treated as the design variable.

Earthquake ground motions
The general properties of this hybrid system under near-fault (rather high-frequency) and long-duration, long-period ground motions have been disclosed in the previous work (Murase et al., 2013). In this paper, general design ground motions compatible with a specific code-specified design response spectrum in Japan is used. These ground motions are used in Japan for the design of high-rise buildings and base-isolated buildings. Two representative phase properties are employed to represent the two types of ground motions, i.e. El Centro NS 1940 for the near-field (impulsive) ground motion and Hachinohe NS 1968 for the far-field (long-duration) ground motion. Fig. 4 shows the acceleration time history and the acceleration response spectrum with the code-specified design acceleration response spectrum in Japan.

Hybrid building system
Consider a 30-story building with the hybrid system. The parameters of the original main building and the original free wall are shown in Table 1. For simple investigation, the building is condensed into a three-mass model. The parameters of such simplified three-mass model (mass and story stiffness) are presented in Table 2. It should be noted that, although the original model has been reduced to a three-mass model and the terminology of 'story' may not be appropriate, the expression 'story' has been used here. This is because it is intended to demonstrate, if the reduction of stiffness (insertion of base-isolation story) is effective, which floor level is most effective. The insertion of baseisolation story (insertion into one story of the original MDOF model) induces  Table 1 for the original models. The connecting dampers are located uniformly at every mass level. The effect of higher modes will be discussed in Section 4.5 using the transfer functions.     The energy transfer function as a general transfer function for energy input is an effective index for demonstrating the energy absorption capacity of structural elements (Takewaki 2004(Takewaki , 2007(Takewaki , 2015. The energy transfer function can be obtained by applying the Fourier transformation and the inverse Fourier transformation to the expression of the total earthquake input energy in time domain. The integration in frequency domain of the energy transfer function multiplied by the squared Fourier amplitude of the input ground acceleration provides the total input energy. The area of the energy transfer function in frequency domain is relating directly to the input energy under the ground motion with the constant Fourier amplitude. Fig. 9 shows the energy transfer functions of the connecting dampers in the 1st, 2nd and 3rd stories for the initial model ( Fig. 9(a)) and the soft first-story model ( Fig. 9(b)). It can be observed that, while a large variability exists in the initial model, a fairly common distribution is realized in the soft first-story model. This indicates that the soft first-story model enables the uniform energy consumption at the connecting damper in every story.

Application of sensitivity-based algorithm to non-connecting building
In order to investigate the applicability of the present sensitivity-based algorithm to non-connecting buildings, consider the same main structure as treated in (1) are specified as [ 1 9 _ T D $ D I F F ] a = 1, b = 1, the objective function for the initial model is 2.0. No clear tendency of the reduction of story stiffness is seen (like the soft first-story type observed for the hybrid system) and the top displacement increases gradually from the beginning. This result indicates that the proposed algorithm does not work well for the building without connecting mechanism and the proposed algorithm is suitable for the proposed smart hybrid system with the connecting damper system and the base-isolation system.
[ 2 2 _ T D $ D I F F ] 4.4. Energy response to simulated high-frequency ground motion Fig. 11 shows the energy consumptions at connecting dampers in the 1st, 2nd and 3rd stories for the initial model ( Fig. 11(a)) and the automatically generated soft first-story model ( Fig. 11(b)) under the ground motion of the phase of El Centro NS 1940. It can be understood that almost uniform energy consumption at connecting dampers is realized in all stories in the soft [ ( F i g . _ 7 ) T D $ F I G ] [ ( F i g . _ 9 ) T D $ F I G ] first-story model. Furthermore, Fig. 12 presents the energy time histories for the initial model ( Fig. 12(a)) and the soft first-story model ( Fig. 12(b)) under the ground motion of the phase of El Centro NS 1940. It can be found that the total input energy to the whole hybrid system, the total consumption energies at the connecting dampers, the total consumption energies at the structures and [ ( F i g . _ 1 0 ) T D $ F I G ]

Overall assessment of proposed hybrid system against single-mechanism models via transfer function
In the previous sections, the performance assessment of the proposed hybrid system has been conducted principally for the ground motions with rather high frequencies.
In order to demonstrate more general properties of the proposed hybrid system for a broader range of frequency, the transfer functions are shown in this section.
Consider a 40-story base-isolated main building, a free wall of 26 stories and a set of oil dampers as shown in Fig. 13. The oil dampers are installed at 4,8,12,16,18,20,22,24  [ ( F i g . _ 1 2 ) T D $ F I G ] [ ( F i g . _ 1 3 ) T D $ F I G ] Fig. 13. Hybrid system consisting of a 40-story base-isolated main building, a free wall of 26 stories and a set of interconnecting oil dampers (Murase et al., 2013).

Article No~e00069
The transfer characteristics of the present hybrid system to the base input are shown here. Fig. 14 shows the acceleration transfer functions at the top of the main frame for the hybrid system, the base-isolated model without interconnection and the interconnecting model without base-isolation. On the other hand, Fig. 15 presents the displacement transfer functions (deformation of base-isolation story) for the two models including the base-isolation story among three. It can be observed that the hybrid system is superior to other two singlemechanism models (base-isolated building and connected buildings without base-isolation) both in the acceleration and displacement transfer properties. Especially the hybrid system possesses an effective control performance at the fundamental natural period of the base-isolated main building. It can also be found that the lowest two eigenmodes are predominant. This fact supports the [ ( F i g . _ 1 4 ) T D $ F I G ] [ ( F i g . _ 1 5 ) T D $ F I G ] Fig. 15. Displacement transfer functions (deformation of base-isolation story) for the hybrid system and the base-isolated model without interconnection (Murase et al., 2013).

Article No~e00069
validity of the simplification of the original model into the model with three degrees of freedom in Section 4.2.

Conclusions
The following conclusions have been derived.
(1) An automatic generation algorithm of the proposed smart base-isolation and building-connection hybrid system has been proposed.
(2) It has been demonstrated that, once an objective function in terms of top displacement and top acceleration under a design ground motion is introduced and a sensitivity-based algorithm is devised, a smart hybrid system consisting of a base-isolation system and a building connection system can be generated automatically.
(3) While the proposed algorithm does not work well in a building without the connecting-damper system, it works well in the proposed smart hybrid system with the connecting damper system. The smart hybrid system has a soft first-story mechanism and the mechanism indicates that the automatic introduction of the base-isolation system is possible and desired in the main structure from the viewpoint of performance upgrade.
(4) It has been made clear from the energy analysis that the proposed smart hybrid system makes the connecting damper at every floor level effective.

Author contribution statement
Masatoshi Kasagi: Conceived and designed the experiments; Analyzed and interpreted the data; Wrote the paper.
Kohei Fujita, Masaaki Tsuji: Analyzed and interpreted the data.
Izuru Takewaki: Conceived and designed the experiments; Wrote the paper.

Funding statement
This work was supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science (No.15H04079).