Inuence of Control Strategy in Risk Mitigation of Building Damage Due to Earthquake

7 Building structures are prone to damage due to natural disasters, and this challenges structural engineers to design 8 safer and more robust building structures. This study is conducted to prevent these consequences by implementing 9 a control strategy that can enhance a building's stability and reduce the risk of damage. Therefore, to realize the 10 structural integrity of a building, a hybrid control device is equipped with control strategies to enhance robustness. 11 The control strategy proposed in this study is adaptive nonsingular terminal sliding mode control (ANTSMC). 12 ANTSMC is an integrated controller of radial basis function neural network (RBFNN) and nonsingular terminal 13 sliding mode control (NTSMC), which has a fast dynamic response, finite-time convergence, and the ability to 14 enhance the control performance against a considerable uncertainty. The proposed controller is designed based on 15 the sliding surface and the control law. The building with a two-degree-of-freedom (DOF) system is designed in 16 Matlab/Simulink and validated with the experimental work connected to the LMSTest.Lab software. The 17 performance of this controller is compared with those of the terminal sliding mode control (TSMC) and NTSMC in 18 terms of the displacement response, sliding surface, and the probability of damage. The result showed that the 19 proposed controller, ANTSMC can suppress vibrations up to 46%, and its percentage probability of complete 20 damage is 15% from the uncontrolled structure. Thus, these findings are imperative towards increasing the safety 21 level in building structures and occupants, and reducing damage costs in the event of a disaster. 22 23


27
Alleviating the structural building response in the event of an earthquake becomes an increasingly challenging task. 28 The forces of nature threaten human existence, cause financial losses and environmental destruction. Large 29 magnitude earthquakes damage properties and structures, and cause casualties. The earthquake magnitude of greater 30 than 5.0 Mw may cause slight damage to the structures and buildings. The earthquake magnitude of greater than 6.0 31 Mw causes a lot of damage in a populated area. Moreover, major earthquakes that wreak severe damage occur at 7.0 32 Mw or higher. The higher moment magnitude with 8.0 Mw above will cause totally destroy to the community near 33 the seismic location (Abu-Faraj et al. 2008; Grünthal and Musson 2020). A tool known as HAZUS is used to estimate 34 the existing building stock potential of losses caused by earthquake ground motion. HAZUS estimates the economic, 35 physical, and social impacts of a disaster by using the geographic information system through an agency called the 36 Federal Emergency Management Agency (FEMA). The estimation of the losses estimation is crucial for 37 preparedness plans and rehabilitation strategies of building stocks from earthquake disasters (Duan and Pappin 38 2008). Besides, the HAZUS damage functions is used to simulate the vulnerability of various types of structural 39 buildings and it provides the information on deriving the building fragility curves for various types of structures 40 consist of the probability of slight, moderate, extensive, and complete structural damage states (Vazurkar and 41 Chaudhari 2016; Peyghaleh et al. 2018). 42 Robinson et al. (2018) shows empirically derived structural fragility curves of different building types. 43 According to the fragility curves, at 0.4 g, the building made from stone and mud has 98% probability of collapsing. 44 The earthquake effect causes many fatalities based on the 2015 Gorkha earthquake with the recorded magnitude of 45 7.3 Mw to 8.8 Mw. The curves show that at the magnitude of 8.6 Mw, the number of fatalities was up to 100,000, 46 and at the magnitude of 7.3 Mw, the earthquake caused more than 50,000 fatalities. 47 Giordano et al. (2021) examined the fragility of the structural building made of masonry, RC frame, steel 48 frame and timber frame. This vulnerability assessment study can be adopted to assess the possible loss of Nepal's 49 school infrastructure due to an earthquake. heritage buildings are affected (D'Ayala and Ansal, 2012). An earthquake warning system that delivers the ground 66 shaking alert known as earthquake early warning (EEW) can be used as a precautionary tool to provide the society 67 to take action before an incoming earthquake occurs. However, this tool has an obstacle in delivering false and 68 missed EEW alarms especially for mid and high-rise buildings due to these buildings shaking occurrence may be mention that it is difficult to predict when and where the earthquake will occur. Even if an earthquake can be 71 predicted, the society is not safe as well. 72 Therefore, innovative seismic solutions must be produced to overcome structural failures and defects. Hence, 73 structural control for buildings is needed to provide safety and more efficient designs to prevent the structures from 74 destruction. Moreover, structural vibration control has attracted more attention due to its robustness in eliminating 75 vibrations. The technique can be categories into passive, active control, semi-active and hybrid control device (Xu structure has used a variety of input excitations to observe the effectiveness of the control device in reducing the 81 structural response. It was found that the implementation of HMD produced better control performance than the 82 passive device for most cases. Then in 2017, Djedoui et al. (2017) investigated the hybrid control consisting of base 83 isolator, TMD and HMD to their structure system. Base isolators which are installed between the foundation and the 84 superstructure are some of the most widely used devices for vibration control. However, the floor acceleration and 85 the inter-story drift are increased, resulting in an adverse effect on the structure. The efficiency of the base isolator 86 depends on the type of excitation. A control signal required to suppress the building vibration is produced using a 87 control algorithm measured by the structural response. Based on the control signal, the actuator will generate the 88 secondary vibration response, decreasing the overall building vibration. Zamani et al. (2018) proposed adaptive 89 fractional order fuzzy proportional-integral-derivative control strategy at smart base-isolate structure to control 90 seismic. The fuzzy rule weight was adaptively tuned based on the values of the velocity of ground floor and the 91 acceleration of the top floor. The proposed control strategy had a better response in decreasing the maximum base 92 displacement and structure acceleration of the earthquake excitation given. 93 Chesne and Colette (2018) performed experimental validation of fail-safe HMD using a single DOF structure. 94 They introduced a compensator into the feedback loop by actively softening the actuator to increase the stability 95 margins of the control system. Then the same author proposed HMD to the structure system in 2017 by introducing 96 a new control law for hybrid vibration absorbers referred to as α-HMD. α-HMD requires smaller active forces and 97 less energy for the active element than the AMD and TMD (Chesné et al. 2019). In recent years, some researchers 98 were interested in the theory of finite time mechanisms. Therefore, TSMC with this characteristic is introduced to 99 overcome the problem caused by sliding mode control which involves in finite time state convergence. As a result, 100 TSMC attracts widespread attention and is known as a nonlinear switching manifold, whereas the state will reach 101 equilibrium in a finite time (Cao et al. 2013). The derivation of TSMC can be found in the study proposed by Liu 102 and Wang (2012). According to Cao et al. (2013), TSMC causes singularity to occur if the initial conditions are not 103 appropriately selected will cause an infinite control law. 104 Nonsingular terminal sliding mode control (NTSMC) has an advantage in giving a fast dynamic response, 105 finite-time convergence, high control precision and eliminating the paranormal phenomenon in the control input of 106 the system (Xu et al. 2015 to control robot manipulators. This controller is used to estimate all the system parameters via Gee-Lee matrix and 120 its produce operators. The application of ANTSMC in robot manipulators shows that the proposed controller 121 effectively controls the nonlinear system with robustness even under model changes and parameter uncertainties. 122 The majority of the previous studies applied this controller in the vehicle, robotic and spacecraft systems. 123 However, no empirical evidence on the influence of a control strategy in minimizing the risk of building damage has 124 been found to date. This control strategy, on the other hand, has excellent vibration control characteristics. software. Therefore, this study presented the details on experimental work that assembled and connected to LMS 135 Test.Lab sofware. The result from the experimental work has strengthened the building structure that has been built 136 in simulation. 137 138 The building structure is represented by the mass, spring and damper system that consists of two DOFs. The 142

System Design
controlling device, HMD is installed at the top floor of the building. The building structure and its free body diagram 143 for the system is shown in Figure 1 and An actuator is implemented to control HMD, and it is written as; where is the thrust constant, Ke is the induced voltage constant, R is the resistance value, Fu is the control force 170 generated by the actuator, and i is current.
The experimental work is assembled as shown in Figure 3, the assembly is consist of the shaker, amplifier, 176 mobile Signal Conditioning and Data Acquisition System (SCADAS), accelerometer and the miniature of 2-DOF 177 building structure. Electrodynamic exciter (S 50350/LS-120), known as shaker, generates vibrations that can be 178 operated either in a horizontal or vertical position. In this case, the vibration of the shaker is set up to a vertical 179 position to reproduce similar seismic movement. The power amplifier received the signal from the input and frontend 180 into the shaker. The voltage or current required by the amplifier depends on the size of the tested system and levels 181 of the target vibration. The accelerometer is used to measure the movement of basement and mass at each floor. The 182 sensitivity of the accelerometer is choosen based on the maximum vibration level. SCADAS is a modular data 183 acquisition device which consists of the frame for housing components containing all the cards, controller and power 184 supply. The power supply includes the battery for autonomous operation, where for this model the duration of battery 185 (2) (4) is around 2.5 hours. The mobile controller card is an ethernet interface linked with the Test.Lab software installed in 186 the personal computer (PC) which consists of two output sources and two encoder inputs. SCADAS is used to capture 187 dynamic signals, measure the accelerometer data and link the PC with Test.Lab software with amplifier. The LMS 188 Test.Lab software was used to control the shaker and received the data from the experimental work. This software 189 is designed as the solution for testing the equipment involved with vibration testing. It also offers quick visualization, 190 easy reporting, and powerful analysis. It produces accurate closed-loop shaker control and has high built-in safety 191 mechanism that reduces the risks of damaged items.

192
The connections between each component are illustrated in Figure 4. The input excitation for moving the 193 shaker is generated by the software and then memorized by SCADAS. The controller card will give the signal to the 194 amplifier and then the amplifier will generate the vibration to the shaker. Three accelerometers are placed in this 195 study to measure the acceleration taken from the base, first floor, and second floor of the building structure. Once 196 the accelerometer detects the movement, the signal is sent to SCADAS DAC in acceleration value and recorded by 197 the LMS Test.Lab software in the PC. The parameters for the experimental system parameter are shown in Table 1.  Before running the experiment, it is required to pre-test the closed-loop system by configuring the SelfCheck 231 setting. SelfCheck configuration is used to verify the experimental setup according to the connection, amplifier, and 232 shaker problems. If problems occur, the status in the software window will appear "warning" or "not ok". In this 233 case, the status showing 'Open Channel' appeared. This is because the connection between the accelerometer and 234 data acquisition card output is not stable. The accelerometer channel did not generate a significant result above the 235 background noise level. Other problems that occured were caused by DAC issues while running the SelfCheck 236 configuration. The DAC issue occurs because of the situation by the shaker amplifier that has not enough output to 237 run the full-scale equipment. The explanation of the overall process for the validation of the system is shown in 238 Figure 5. The terminal sliding surface is described as (7) where is a design constant that must be more remarkable 256 than 0, and the value of p and q are positive odd integers that meet the condition; > .

258
Assemble and connect all the experimental component

Nonsingular terminal sliding mode control 308 309
Terminal sliding mode control type nonsingular has an advantage in giving a fast dynamic response, finite-310 time convergence, high control precision, and can eliminate the abnormal phenomena in the control input of the 311 system.

Adaptive nonsingular terminal sliding mode control 352 353
RBFNN provide a global approximation of training data gives advantages of a simple structure and excellent learning 354 ability. This method has the capability to approximate the uncertainties of unknown bound with universal error. 355 Therefore, this technique is used in this study to estimate the value of the upper bound of an uncertain parameter, lg. 356 The equation for lg is written in (31), and the output hidden layer, ∅ ( ) is written in (32). Where, is threshold 357 hidden layer, the central position for neuron, and is neuron width. The structure of RBFNN is shown in Figure  358 6, which consists of three layers. The number of input and output neuron in RBFNN are determine by the problem 359 data. The first layer of RBFNN is the input layer determined by equating the number of input variables in the process 360 data which are displacement and velocity data. 361 Five neurons in the hidden layer are the connective weight between hidden and output neurons, wT 362 (w1,w2,w3,w4,w5) is determined using rule-of-thumb method. It is crucial to find the correct number of neurons in the 363 hidden layer because too few neurons will result in underfitting. Underfitting occurs when a number of neurons in 364 the hidden layer are difficult to detect the signals in a complicated data set. Meanwhile, too many neurons in the 365 hidden layer can cause overfitting and this problem may occur when neural networks have so much information 366 processing capacity. Therefore, the calculation on this hidden layer neuron, Nh is calculated in Equation (36). Where, 367 NT is the number of samples in training data set, ∝ is arbitrary scaling factor , Ni is number of input neuron and No is 368 number of output neuron. The steps on designing ANTSMC in this study are as follow; 375 1) Simplify the system into ̇1and ̇2 376 2) Design sliding variables 377 3) Design NTSMC with an unknown parameter for ANTSMC, RBFNN The measurement for the sliding variable is obtained by using the mathematical model described by equations (7)  402 and (21). The values of p and q must be positive odd numbers. After applying all the assumption values, the best 403 performance response is obtained when the values are set to 5 and 3. After applying the control law in (40) into the building structure (1), suppose that the sliding variable in (37) and 414 (38) will converge to zero in finite time, and the proposed controller can guarantee robustness and stability of the 415 system. The controller design for the building structure is derived as; 416 417 Proof 1. 422 The proof for Theorem 1 is obtained through stability analysis of this controller.  According to equation (54), the Lyapunov controller stability of ANTSMC for the building structure can be 464 evaluated. In this study the value of η is 0.01, and the sliding surface is taken with the value of |2×10 5 | resulted -465 0.02×10 5 . Therefore, the value obtained is below than 0, thus, proving that the stability of the controller, NTSMC 466 manifold converges to zero in finite time. On the other hand, if (38) is reached, the output tracking error of the 467 building structure will converge to zero in finite time and prove the robustness and the stability of the system. This 468 completes the proof for Theorem 1.

470
This study uses two inputs, one output, and five hidden neurons. The block diagram consists of an adaptive 471 NTSM with the building structure is shown in Figure 7, where xf is the desired value for the system output, e is error, 472 s is sliding mode, u is the control input, and the output feedback is displacement and velocity of the building structure. The results of the experimental work and simulation are compiled in Figure 9. As can be seen from these 501 figures The building structure is equipped with HMD together with the implementation of the control strategy. The actual 516 parameter for the building structure is used to evaluate the effectiveness of the controller in real life as shown in 517 The results obtained for the building structure with both excitations are shown in Figure 10 for the second and 524 first floors, respectively. The result shows that the implementation of control strategies has successfully suppressed 525 the earthquake-induced vibrations. The maximum vibration occurred at 2.17 s causing the reduction percentage 526 measured at the second floor with respect to the uncontrolled system generated by each controller to be 46% for 527 ANTSMC, 36% for NTSMC, and 10% for TSMC. The reduction percentage generated by the first floor is 40% for 528 ANTSMC, 38% for NTSMC, and 7.5% for TSMC. This shows that the ANTSMC has the highest reduction 529 percentage compared to the other controllers. 530 The second excitation taken from Southern Sumatra with the duration of acceleration is longer compared to the 531 El Centro earthquake which is 320.725 s. The results obtained are shown in Figure 11 for both floors of the building. 532 The maximum vibration recorded for the second and first floors are 1.3 × 10 -3 m and 0.78 × 10 -3 m, respectively. 533 Based on these maximum displacement values, the percentage of vibration reduction from the uncontrolled structure 534 for each control strategy is 42% by NTSMC, 38% by NTSMC, and 19% by TSMC. After the implementation of 535 control strategies, it was shown that ANTSMC has the superior performance in suppressing the building vibration. The sliding surface measured by the El Centro excitation for each controller is shown in Figure 12. The sliding 552 surface design should reflect the required specification when the sliding mode is established. The figures show that 553 the state trajectories are moving towards the sliding surface that was set to 0 to maintain the position of the system 554 during an earthquake. This has fulfilled the system with a required response to obtain a stable condition. The same 555 time was setting for each controller and resulting the state trajectory generated by the ANTSMC has a faster response 556 to reach the desired sliding surface compared to NTSMC and TSMC. 557 558

559
(a) (b) (c) 560 Figure 12 Sliding surface for (a) ANTSMC (b) NTSMC (c) TSMC 561 562 The results are summarized in Figure 13 for both excitations measured at the first and second floor taken at the 563 maximum vibration of the building structure which occurred at 2.17 s for the El Centro and 108.6 s for the Southern 564 Sumatra excitations. According to both figures, the second floor generated a higher sway during the seismic activity 565 than the first floor. However, when control strategies were applied, the vibrations were suppressed. The building response with the control strategy at each floor with the input excitations of (a) El 571 Centro (b) Southern Sumatra 572 573 This study considers the ductile reinforced concrete building and the building collapse probability is measured 574 according to the graph damage of probability for the low-rise building under the 3-DOF system according to the 575 guildeline given by FEMA (2003) and structural performance under seismic load by Incremental Dynamic Analysis 576 (IDA) (Vamvatsikos and Cornell 2002). Based on the probability of the building collapse for both excitations, it is 577 clear that the implementation of the proposed controller which is the ANTSMC in the 2-DOF structure has reduced 578 the percentage of the building from collapse. From Figure 14 (a), the percentage of the building to have slight damage 579 is 98%, and after the implementation of the ANTSMC, the probability is reduced to 50%. Moreover, the probability 580 percentage of the building to have moderate damage is reduced tfrom 76% to 26%, extensive damage is reduced 581 from 25% to 6% and complete damage is reduced from 0.8% to 0.2%, respectively. From Figure 14 (b), the 582 probability of the building to have slight damage is 100% which is reduced to 98% after implementation of 583 ANTSMC. For moderate damage, the damage probability has reduced from 95% to 75%, extensive damage from 584 40% to 22% and complete damage is reduced from 15% to 0.8%, respectively. This controller shows a high 585 percentage reduction when applied to the system that is triggered by the El Centro earthquake rather than by the 586 Southern Sumatra earthquake since the magnitude of the El Centro earthquake is lower than the magnitude of the 587 Southern Sumatra earthquake. However, both responses show impressive results in reducing the probability of the 588 building collapse when implemented with the controller. Probability of collapse for the building structure with ANTSMC with the input excitations of (a) 608 El-Centro (b) Southern Sumatra 609 610 611

613
This study was aimed at investigating the influence of implementing the control strategy, namely ANTSMC to the 614 2-DOF structure in enhancing the building's structural and decreasing the risk of the building from damage. The  615 system was validated by the experimental work for the 2-DOF structure and acceleration responses were measured 616 by the LMS Test.Lab software. The result for the building system response was compared to the simulation result in 617 Simulink. ANTSMC was designed to enhance the performance of the building structure by suppressing the vibration 618 during an earthquake. The effectiveness of the controller was compared with TSMC and NTSMC. The stability of 619 ANTSMC was demonstrated as the building structure reached its equilibrium faster and maintained its position as 620 the desired response stated. Moreover, the proposed control strategy reduced the probability of damage to the 621 building structure. The probability percentage of the building to have slight damage with the implementation of 622 ANTSMC was reduced until 50% compared to an uncontrolled building with a probability of 98% to have a slight 623 damage. The lower percentage in having the probability of the building experiencing damage shows the significant 624 impact of the implementation of control strategy in the building structure.

626
Acknowledgement 627 628 The authors would like to acknowledge Universiti Teknologi Malaysia (research grant Professional Development 629 Research University: Q.K130000.21A2.05E38) for financially supporting this research.