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ANN based methodology for active control of buildings for seismic excitation for different seismic zones of India
4th International Conference on Advances in Control and Optimization of Dynamical Systems Optimization Dynamical Systems 4th Conference on in 4th International International Conference on Advances Advances in Control Control and and February 1-5, of 2016. NIT Tiruchirappalli, India 4th International Conference on Advances in Control February 1-5, of 2016. NIT Tiruchirappalli, India Available onlineand at www.sciencedirect.com Optimization of Dynamical Systems Optimization Dynamical Systems Optimization of Dynamical Systems February February 1-5, 1-5, 2016. 2016. NIT NIT Tiruchirappalli, Tiruchirappalli, India India February 1-5, 2016. NIT Tiruchirappalli, India
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49-1 (2016) 095–099 ANNIFAC-PapersOnLine based methodology for active control ANN based methodology for active control of buildings for seismicfor excitation for ANN based methodology active control of buildings for seismicfor excitation for ANN based methodology active control different seismic zones of Indiafor of buildings for seismic excitation different seismic zones of Indiafor of buildings for seismic excitation different seismic zones of India A. Goel * P. Kamatchi** P. Jayabalan *** different seismic zones of India A. Goel * P. Kamatchi** P. Jayabalan ***
A. Goel ** P. Kamatchi** P. Jayabalan *** A. P. P. *** A. Goel Goel *Department P. Kamatchi** Kamatchi** P. Jayabalan Jayabalan ***IIT, Madras * Project Associate, Engineering, of Ocean * Project Associate, Department of Ocean Engineering, IIT, Madras (e-mail: [email protected]) ** Project Associate, Department of Ocean Engineering, IIT, Madras (e-mail: [email protected]) Project Associate, Department of Ocean Engineering, IIT, Madras Principal Scientist, Risk and of Reliability, CSIR-SERC, Chennai * ** Project Associate, Department Ocean Engineering, IIT, Madras (e-mail: [email protected]) ** Principal Scientist, Risk and Reliability, CSIR-SERC, Chennai (e-mail: [email protected]) (email:[email protected]) [email protected]) (e-mail: ** Principal Scientist, Risk and Reliability, CSIR-SERC, Chennai (email: ** Principal Scientist, Risk and CSIR-SERC, Chennai *** [email protected]) CivilReliability, Engineering, NIT, Tiruchirappalli **Professor, Principal Department Scientist, Risk and Reliability, CSIR-SERC, Chennai (email: [email protected]) *** Professor, Department of Civil Engineering, NIT, Tiruchirappalli (email: [email protected]) (e-mail: [email protected]) (email: [email protected]) *** Professor, Department of Civil Engineering, NIT, Tiruchirappalli (e-mail: [email protected]) *** of Engineering, *** Professor, Professor, Department Department of Civil Civil Engineering, NIT, NIT, Tiruchirappalli Tiruchirappalli (e-mail: [email protected]) (e-mail: [email protected]) (e-mail: [email protected]) Abstract: In the last two decades, many studies are reported in literature for determining the control force Abstract: In the last two decades, studies are reported in literature determining the control force for the active control systems for many damage mitigation of buildings due tofor earthquake. However, no study Abstract: In the last two decades, many studies are reported in literature for determining the control force for the active control systems for damage mitigation of buildings due to earthquake. However, no study Abstract: In the last two decades, many studies are reported in literature for determining the control force has the been reported prediction of control force the due seismic zones in India. thenopresent Abstract: In the lastfor two decades, many studies areconsidering reported in literature for determining theIncontrol force for active control for damage of buildings to earthquake. However, study has been reported for systems prediction of controlmitigation force considering the seismic seismic zones IV in India. In the present for the active control systems for damage mitigation of buildings due to earthquake. However, no study study, spectrum compatible time histories are generated for the zones and V as per Indian for the active control systems for damage mitigation of buildings due to earthquake. However, nopresent study has been reported for prediction of control force considering the seismic zones in India. In the study, spectrum compatible timedesign histories are generated for the seismic zones IV and as the per Indian has been reported for of control force considering the seismic zones in In present standard IS 1893(Part 1):2002 spectrum. Time history carried outVwith spectrum has been reported for prediction prediction of control force considering theanalysis seismicare zones in India. India. In the present study, spectrum compatible time histories are generated for the seismic zones IV and V as per Indian standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum study, spectrum compatible time histories are generated for the seismic zones IV and V as per Indian compatible time histories fortime shearhistories type buildings modelled multi-degree of freedom system (MDOF) study, spectrum compatible are generated forasthe seismic are zones IV and Vwith as per Indian standard IS 1893(Part 1):2002 design spectrum. Time history analysis out spectrum compatible time histories for shear type buildings modelled as multi-degree ofcarried freedom system (MDOF) standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum with a computer program developed in MATLAB by modal superposition using Newmark-beta method. standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum compatible time histories for shear type buildings modelled as multi-degree of freedom system (MDOF) with a computer program developed in MATLAB by modalin superposition Newmark-beta method. compatible time type buildings modelled as multi-degree of system (MDOF) Control forces obtainedfor byshear adopting algorithm literature andusing input and output patterns are compatible timearehistories histories for shear type buildings proposed modelled as multi-degree of freedom freedom system (MDOF) with a computer program developed in MATLAB by modal superposition using Newmark-beta method. Control forces are obtained by adopting algorithm proposed in literature and input and output patterns are with a computer program developed in MATLAB by modal superposition using Newmark-beta method. generated for development of Artificial Neural Network (ANN) models using in Stuttgart Neural Network with a computer program developed in MATLAB by modal superposition Newmark-beta method. Control forces are obtained by algorithm proposed in literature and input and output patterns are generated for development of adopting Artificial Neural Network (ANN) models in Stuttgart Neural Network Control forces are by adopting proposed in literature and input and output patterns are Simulator (SNNS). In the present studyalgorithm the methodology with five building by Control forces are obtained obtained by adopting algorithm proposedis indemonstrated literature andin input and storey output patterns are generated for development of Artificial Neural Network (ANN) models Stuttgart Neural Network Simulator (SNNS). In the present study the methodology is demonstrated with five storey building by generated for development of Artificial Neural Network (ANN) models in Stuttgart Neural Network developing 24 ANN models consisting of two ANN architectures viz., NET1 and NET2 for each seismic generated for development of Artificial Neural Network is (ANN) models in Stuttgartstorey Neural Network Simulator (SNNS). In the present study methodology demonstrated with building by developing 24 soil ANN models consisting ofthe twoof ANN architectures viz., NET1 and five NET2 forthe each seismic Simulator (SNNS). In the present study methodology demonstrated five storey building by zone and three types. the validation results fromis models it iswith observed that maximum Simulator (SNNS). In theFrom present studyofthe the methodology isANN demonstrated with five storey building by developing 24 ANN models consisting two ANN architectures viz., NET1 and NET2 for each seismic zone and three soil types. From the validation of results from ANN models it is observed that the maximum developing 24 ANN models consisting of two ANN architectures viz., NET1 and NET2 for each seismic difference in24percentage response reduction ofANN peak architectures displacementviz., is less thanand 10% whenforit each is compared developing ANN models consisting of two NET1 NET2 seismic zone and three soil types. From the reduction validation of results from ANN models is observed that difference in percentage response of peak displacement is less it than 10% when itthe is maximum compared zone and three soil types. From validation of results from it is that maximum with the value of percentage response reduction. zone andtarget three soil types. From the the reduction validation of peak resultsdisplacement from ANN ANN models models itthan is observed observed thatitthe the maximum difference in percentage response of is less 10% when is compared with the target value of percentage response reduction. difference in percentage response reduction of peak displacement is less than 10% when it is compared difference in percentage response reduction of peak displacement is less than 10% whenBuilding. it is compared Keywords: ANN, Active Control, Seismic Zones, Stochastic GM generation, Earthquake, with the target value of percentage response reduction. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. with the value of response reduction. Keywords: ANN, Active Control, Seismic Stochastic GM generation, Earthquake, Building. with the target target value of percentage percentage responseZones, reduction. Keywords: GM Keywords: ANN, ANN, Active Active Control, Control, Seismic Seismic Zones, Zones, Stochastic Stochastic GM generation, generation, Earthquake, Earthquake, Building. Building. Keywords: ANN, Active Control, Seismic Zones, Stochastic GM generation, Earthquake, Building. 1. INTRODUCTION velocity of current time step as inputs for neural network 1. INTRODUCTION velocity of and current stephave as inputs for neural network model. Rao Dattatime (2006) developed a procedure for velocity of current time step as inputs for neural network INTRODUCTION Various semi-active 1. and active control strategies are adopted model. Rao and Datta (2006) have developed a procedure for 1. INTRODUCTION velocity of current time step as inputs for neural network active control of structures using two setsfor of neural networks 1. INTRODUCTION velocity of current time step as inputs neural network Various semi-active and active control strategies are adopted Rao and Datta (2006) have developed aa procedure for for vibration control of civil engineering structures model. active control of structures using two sets of neural networks model. Rao and Datta (2006) have developed procedure for general stochastic simulations of earthquake based for on Various semi-active and active control strategies are adopted model. Rao and Datta (2006) havetwo developed a procedure for for vibration control of efforts civil engineering structures Various semi-active and active control strategies are adopted active control of structures using sets of neural networks (Chu et al. (2005)). Recently, are made to develop the general stochastic simulations ofsets earthquake based on Various semi-active and active control strategies arestructures adopted for active control of structures using two of neural networks Kanai Tajmi power spectral density function. From the limited for vibration control of civil engineering active control of structures using two sets of neural networks (Chu et al. (2005)). Recently, efforts are made to develop the for vibration control of civil engineering structures for general stochastic simulations of earthquake based on structural control concept into workable technology and fullKanai Tajmi power spectral density function. From the limited for vibration control of aefforts civil engineering structures for general stochastic simulations of earthquake based on (Chu et al. (2005)). Recently, are made to develop the literature review made, simulations it is observedofthat, no study based has been for general stochastic earthquake on structural control concept into aefforts workable technology and full(Chu al. (2005)). Recently, are made to develop the Kanai Tajmi power spectral density function. From the limited scale et implementation in several structures. Many semi-active (Chu et al. (2005)). Recently, efforts are made to develop the literature review made, it is observed that, no study has been Kanai Tajmi power spectral density function. From the limited structural control concept into a workable technology and fullreported for prediction of control force considering the seismic Kanai Tajmi power spectral density function. From the limited scale implementation in several structures. Many semi-active structural control concept into a workable technology and fullliteraturefor review made,ofit itcontrol is observed observed that, no study study has been and activecontrol controlconcept systems implemented in buildings in reported structural intoare a workable technology and fullprediction force that, considering thehas seismic literature made, is no been scale implementation in several structures. Many semi-active andreview soil types of India. literature review made, itcontrol is observed no study been and active control systems are implemented buildings in zones scale implementation in several structures. semi-active reported for prediction of force that, considering thehas seismic Japan (Nishitani (1998)). Research studiesMany areinbeing carried scale implementation in several structures. Many semi-active zones and soil types of India. reported for prediction of control force considering the seismic and active control systems are implemented in buildings in reported for prediction of control force considering the seismic Japan (Nishitani (1998)). Research studies are being carried and active control systems are implemented in buildings in zones and soil types of India. out on various active controlare algorithms viz., optimal control, and active control systems implemented inbeing buildings in zones soil India. Japan (1998)). Research studies carried In the and present study,of and soil types types ofcontrol India. algorithm proposed by Rao and out on (Nishitani variousmodal active control algorithms viz.,are optimal control, Japan (Nishitani (1998)). studies are being carried independent spaceResearch control, neural network based zones Japan (Nishitani (1998)). Research studies are being carried In the present study, control algorithm proposed by Rao and out on various active control algorithms viz., optimal control, Datta (2006) is adopted and two sets of neural networks NET1, independent modal space control, neural network based out on various active control algorithms viz., optimal control, pole assignment technique and bounded state control, control In the present study, control algorithm proposed by Rao and out on various active control algorithms viz., optimal control, Datta (2006) is adopted and two sets of neural networks NET1, In the present study, control algorithm proposed by Rao and independent modal space control, neural network based NET2 are developed for seismic zones IV and V and soil control, pole assignment technique and bounded state (2011), control In the(2006) present study, control algorithm proposed by three Rao and independent modal space control, neural network based as seen in state of the art reports (Fisco and Adeli Datta is adopted and two sets of neural networks NET1, independent modal space control, neural network based NET2 are developed for seismic zones IV and V and three soil Datta (2006) is adopted and two sets of neural networks NET1, control, pole assignment technique and bounded state (2011), control Datta types (2006) of India with spectrum compatible time histories as seen in state of the art reports (Fisco and Adeli is adopted and two sets of neural networks NET1, control, pole assignment technique and bounded state control are developed for seismic zones IV and V and three soil Datta (2003), Housner etart al.reports (1997)). Numerous applications control, pole assignment technique and bounded state control NET2 types of India with spectrum compatible time histories NET2 are developed for seismic zones IV and V and three soil as seen in state of the (Fisco and Adeli (2011), developed using forSHAKE2000 (2000), NET2 are developed seismic zones IV(Ordonez and Vtime and three soil Datta (2003), Housner etartal.reports (1997)). Numerous applications as seen in state of the (Fisco and Adeli (2011), types of India with spectrum compatible histories of Artificial Neural Network (ANN) for structural Control are as seen in state of the art reports (Fisco and Adeli (2011), developed using SHAKE2000 (Ordonez (2000), types of India with spectrum compatible time histories Datta (2003), Housner et al. (1997)). Numerous applications Jennings etIndia al. (1968)). Studies compatible reported in this paper are types of with spectrum time histories of Artificial Neural Network (ANN) for structural Control are Datta (2003), Housner et al. (1997)). Numerous applications reported in literature (Bani-Hani and Ghaboussi (1998), developed using SHAKE2000 (Ordonez (2000), Datta (2003), Housner et al. (ANN) (1997)).for Numerous applications Jennings et al. (1968)). Studies in this paper are developed using (Ordonez (2000), of Artificial Neural Network structural Control are carried out using theSHAKE2000 computerreported program developed in reported in literature (Bani-Hani and Ghaboussi (1998), developed using SHAKE2000 (Ordonez (2000), of Artificial Neural Network (ANN) for structural Control are Ghaboussi and Joghataie (1995),forLiut et al. (1999), Jennings et al. (1968)). Studies reported in this paper are of Artificial Neural Network (ANN) structural Control are carried out using the computer program developed in Jennings et al. (1968)). Studies reported in this paper are reported in literature (Bani-Hani and Ghaboussi (1998), MATLAB which uses generalized mode shape forpaper response Ghaboussi and Joghataie (1995), Liut et al. (1999), Jennings et al. (1968)). Studies reported in this are reported in literature (Bani-Hani and Ghaboussi (1998), Tang (1996), Rao and Datta, 2006). and Ghaboussi (1998), MATLAB carried out outwhich usinguses thegeneralized computer mode program developed in reported in literature (Bani-Hani shape for response carried using the computer program developed in Ghaboussi Joghataie (1995), Liut et al. (1999), evaluation and Penzien (1993)). Tang (1996),and Rao and Datta, 2006). carried out(Clough usinguses thegeneralized computer program developed in Ghaboussi and Joghataie (1995), Liut et al. (1999), MATLAB which mode shape for response Ghaboussi and Joghataie (1995), Liut et al. (1999), evaluation (Clough and Penzien (1993)). MATLAB which uses generalized mode shape for response Tang (1996), Rao and Datta, 2006). MATLAB which uses generalized mode shape for response Tang (1996), Rao and Datta, 2006). evaluation (Clough and Penzien (1993)). Bani-Hani andRao Ghaboussi (1998) used a neural network-based evaluation (Clough and Penzien (1993)). Tang (1996), and Datta, 2006). 2. CONTROL and PenzienALGORITHM (1993)). Bani-Hani trained and Ghaboussi usedfor a neural controller using the(1998) emulator linearnetwork-based control of the evaluation (Clough 2. CONTROL ALGORITHM Bani-Hani and Ghaboussi (1998) used aa neural network-based controller trained using the emulator for linear control of the Bani-Hani and Ghaboussi (1998) used neural network-based structure. In Ghaboussi ANN model proposed by Bani-Hani and In the present study, 2. CONTROL ALGORITHM the control algorithm proposed by Rao Bani-Hani trained and (1998) usedfor a neural network-based 2. ALGORITHM controller using the emulator linear control of the structure. In ANN model proposed by Bani-Hani and 2.isCONTROL CONTROL ALGORITHM controller trained using the emulator for linear control of the In the present study, the control algorithm proposed Rao Ghaboussi (1998) structural displacement and acceleration and Datta (2006) adopted for determination of controlbyforce. controller trained usingmodel the emulator for by linear control of and the In the present study, the control structure. In ANN proposed Bani-Hani algorithm proposed by Rao Ghaboussi (1998) structural displacement and acceleration structure. In ANN model proposed by Bani-Hani and and Datta (2006) is adopted for determination of control force. In the present study, the control algorithm proposed by Rao responses of previous two time steps and actuator electric should be noted that, response of a building is directly structure. In ANNstructural model proposed by and Bani-Hani and It In the present study, thethe control algorithm proposed byforce. Rao and Datta (2006) is adopted for determination of control Ghaboussi (1998) displacement acceleration responses of previous two time steps and actuator electric Ghaboussi (1998) structural displacement and acceleration It should be noted that, the response of a building is directly and Datta (2006) is adopted for determination of control force. signals of previous three time displacement steps are usedand as inputs to the dependent upon the magnitude and epicentre of the Ghaboussi (1998) structural acceleration and Datta be (2006) is that, adopted for determination ofdistance control force. It should noted the response of a building is directly responses of previous two time steps and actuator electric signals of previous threetwo time steps are used as inputselectric to and the dependent responses of previous time steps and actuator upon the magnitude and epicentre distance of the It should be noted that, the response of aa will building is directly neural network model. Tang (1996) used displacement earthquake. The force that a building experience is responses of previous two time steps and actuator electric It should be noted that, the response of building is directly signals of previous three time steps are used as inputs to the dependent magnitude and epicentre distance of the neural model. Tang (1996) used displacement and signals of three time steps are used as inputs to the earthquake.upon Thethe force thatof athe building will experience is dependent upon the magnitude and epicentre distance of the velocitynetwork ofprevious preceding time step, and the displacement and dependent upon the mass building and acceleration signals of previous three time steps are used as inputs to the upon the magnitude and epicentre distance of the neural network model. Tang (1996) and earthquake. The force that aathe building will experience is velocity of preceding time step, andused the displacement neural network model. Tang (1996) used displacement and dependent upon the mass of building and acceleration earthquake. The force that building will experience is neural network model. time Tangstep, (1996) used displacement and earthquake.upon The the force thatof athe building will experience is velocity of preceding and the displacement and dependent mass building and acceleration velocity of preceding time step, and the displacement and dependent upon the mass of the building and acceleration Copyright © 2016 IFAC time step, and the displacement and 95 dependent upon the mass of the building and acceleration velocity of preceding Copyright © 2016, 2016 IFAC 95 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright ©under 2016 responsibility IFAC 95 Peer review© of International Federation of Automatic Copyright 2016 IFAC 95 Control. Copyright © 2016 IFAC 95 10.1016/j.ifacol.2016.03.035
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z1 (1 p)z1 u1 (t ) 1 xg (1 p)[ z1 21 z1 12 z1 ] z2 2 xg (1 p)[2 2 z 2 22 z 2 ] u 2 (t ) z3 3 xg (1 p)[2 3 z 3 32 z 3 ] u 3 (t )
experienced at it. The earthquake design philosophy of a building is based upon the peak ground acceleration which is classified as per different seismic zones in Indian code (IS 1893(Part 1): 2002) taking into account the maximum considered earthquake for that region. Therefore, a control technique, based upon the seismic zone and utilising force matching principle, can reduce the damage of buildings taken for consideration. The control algorithm proposed by Rao and Datta (2006) based on force matching technique utilizing modal contribution of prominent modes, is suitable for extending into seismic zones. In the present study one horizontal dynamic degrees of freedom is only considered representing shear type buildings with symmetrically constructed story units. Further one horizontal component of the earthquake is only considered. However the methodology proposed can be extended to asymmetric buildings and other components of earthquake as well.
u 2 (t )
k k2 u1 (t ); u 3 (t ) 3 u1 (t ) k1 k1 kj
(7) (8)
3. MATHEMATICAL MODEL OF STRUCTURE In order to demonstrate the application of control algorithm a five-story shear type building with identically constructed story units is considered for training and testing of the ANN as shown in the Fig. 1. The lumped mass concentrated on each story is taken as 150 x 103 kg. The elastic stiffness and the structural damping ratio are taken as 200x10 6 N/m and 0.02 respectively. For calculating dynamic response of the MDOF structure, the step-by-step integration procedure of differential equations as proposed by Newmark is adopted (Chopra (2012), Clough and Penzien (1993)) in the computer program. A target percentage reduction of 50% is considered in the present study.
(1) (2) (3)
Tj R Tj M j
(6)
where, 𝑥𝑥̈ 𝑖𝑖 (𝑖𝑖 = 1,2,3,4,5) is the acceleration response of the structure at the 𝑖𝑖 𝑡𝑡ℎ story of the building; 𝜙𝜙𝑖𝑖 𝑗𝑗 (𝑗𝑗 = 1,2,3) is the mode shape coefficients for 𝑖𝑖 𝑡𝑡ℎ story; and 𝑗𝑗𝑡𝑡ℎ mode; 𝑧𝑧̈𝑗𝑗 (𝑗𝑗 = 1,2,3) modal acceleration contributions to the control force; 𝑢𝑢𝑗𝑗 (𝑡𝑡)(𝑗𝑗 = 1,2,3) are the modal contribution towards a single control force; 𝑢𝑢(𝑡𝑡) is the control force; 𝑅𝑅 is the location vector; 𝑝𝑝 is the target percentage reduction; 𝑧𝑧̅1̈ is the uncontrolled modal acceleration; 𝜌𝜌2 & 𝜌𝜌3 are the modal participation factors for 2nd and 3rd mode; 𝜂𝜂 is the damping ratio; 𝜔𝜔2 & 𝜔𝜔3 are the natural frequencies of the building in 2nd and 3rd mode; 𝑧𝑧̅2̇ & 𝑧𝑧̅3̇ are the uncontrolled velocity in 2nd and 3rd mode and 𝑧𝑧̅2 & 𝑧𝑧̅3 are the uncontrolled displacement in 2nd and 3rd mode respectively.
For the development of generalized control scheme for MDOF structure, response feedbacks are utilized along with target percentage reduction and position of control force to get modal contributions for controlled response (equations (1-8); Rao and Datta (2006)). The control technique utilises the principle of modal superposition of structural acceleration of the structure. The structural acceleration of the structure can be determined from superposition of its modal acceleration components (equation 1). Moreover, as controlled modal accelerations are related to control force (equation 2, 5, 7 and 8); it is used for training of neural nets. The control force is applied at top and is determined from modal contributions from first three modes, which in turn are determined from uncontrolled modal accelerations based upon a target percentage reduction. It is assumed that the major contribution to control force is from first mode shape of the building having a target percentage reduction (equation 5). Therefore, the modal contribution of first mode for control force is determined from equation-6. The contributions to control force from the second and third mode are obtained from equation 7 and 8. Here, it should be noted that, modal theory is a mathematical supposition and none of its components like contributions from different modes to control force (u1(t), u2(t) and u3(t)) can be directly measured through sensors. Therefore, a neural network model is developed based upon the realizable quantities whose values are found for various spectrum compatible time histories to develop a neural network architecture for prediction of the building’s behaviour pattern. This theory is the basis for training of the neural network architecture having the controlled structural acceleration response as its input and the control force as its output, for a given set of spectrum compatible time histories.
xi i1 z1 i2 z2 i3 z3 u 2,3 (t ) k 2,3u(t )
(5)
(4) Fig. 1. Model of a five storey frame 96
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For generation of dataset for training of neural networks, the five storey frame is analyzed using spectrum compatible ground motion accelerations obtained consistent with response spectrum of three soil types viz., rock, medium soil, soft soil and seismic zones IV and V as per Indian standard (IS 1893(Part 1): 2002) using SHAKE2000 computer program. For each response spectra eleven acceleration time histories are generated with 3002 sampling points at an interval of 0.01s out of which results for 10 simulations of earthquake are used for training and result for one simulation is used for testing of the neural networks developed.
97
All the subnets in NET1 have 6 neurons in the input layer and one neuron in the output layer and NET2 has 4 neurons in the input layer and one neuron in the output layer. Number of neurons in the hidden layer for the network models are given in Table 1. Typical network architecture for the NET1 (subnets) and NET2 are shown in Fig. 3. In the present study a total of 24 neural network models are developed as given in Fig. 4 for the different seismic zones and soil types considered. In the present study, Stuttgart Neural Network Simulator SNNS (Zell et al. (1989)) has been used for development of neural network models. The inputs to the neural network are combined linearly and feeding the neural nets will raw values will not work very well. Therefore, normalization of the input dataset in the interval of [0, 1] is preferred. In this study, we have normalized the input dataset, according to Maximumminimum normalization principle utilizing input variables. A Multilayer fully connected feed-forward neural net architecture with logistic activation function, Backprop Momentum learning function and Topological_order update function, are used for training. The learning rate and update parameter for different network models are given in Table 2.
4. NEURAL NETWORK MODELS As it is described earlier, the inputs for NET1 are acceleration feedback measurement time histories at each story, input acceleration and the output is the modal contribution acceleration time history for the first three modes for calculation of control force. From the studies made with modal superposition of five and three modes, it is seen that inclusion of three modes results in better accuracy in the prediction of control force time history. Further, mass participation of 98.4% is achieved while considering the modal superposition of first three modes. Hence three subnets NET11, NET12, NET13 are developed to predict the modal contribution of first three modes. For the second network NET2, modal acceleration time history contributions from first three modes, and the input excitation (spectrum compatible acceleration time history) are the inputs and the control force time history is the output. A systematic model of the methodology is presented in Fig. 2.
Table 1. Number of neurons in the hidden layer for ANN models Number of nodes in Hidden Layers (1 and 2) Soil Seismic Type NET11 NET12 NET13 NET2 Zone 1 2 1 2 1 2 1 2 Soft 6 6 6 6 6 6 9 Zone 5 Medium 6 6 6 6 6 6 4 4 Rock 6 6 6 6 6 6 9 Soft 9 - 9 9 9 Zone 4 Medium 6 6 6 6 6 6 4 4 Rock 6 6 6 6 6 6 9 Table 2. Learning parameters for ANN models
Seismic Zone
Zone 5
Zone 4
Fig. 2. Methodology for active control of buildings for seismic excitation 97
Soil Type
Neural Network Configuration for Subnets (NET11, NET12, NET13) and NET2 Learning rate
Update Parameter
NET11 NET12 NET13
NET2
NET11 NET12 NET13
NET2
Soft
0.01
0.0001
0
0.001
Medium
0.01
0.01
0
0
Rock
0.01
0.0001
0
0.001
Soft
0.0001
0.0001
0.001
0.001
Medium
0.01
0.01
0
0
Rock
0.01
0.0001
0
0.001
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5. TESTING OF NEURAL NETWORK For testing the neural network, the building frame is analyzed for one simulation of spectrum compatible accelerogram which has not been used in training. Maximum percentage errors of results from ANN models with respect to algorithm based detailed analysis for the test pattern are given in Table 3. The percentage reduction in the peak response displacement obtained from ANN model for a typical input is given Table 4. It is observed that maximum difference in peak displacement of the controlled and uncontrolled building is less than 10% when it is compared with the target response reduction percentage. Table 3. Maximum percentage error of results from ANN models with respect to algorithm based detailed analysis Maximum error Seismic Soil Zone Type NET11 NET12 NET13 NET2 Zone 5
Soft
30.816
Medium 13.959 Zone 4
8.803
7.479
31.779
9.1
8.251
33.05
Rock
31.13
13.86
13.59
17
Soft
12.424 15.095
11.51
3.71
Medium 10.533 12.418 10.185 Rock
4.171
7.708
5.802
19.999 18.85
Table 4. Percentage reduction in the story displacement Story Level Percentage Reduction
Fig. 3. Architecture of ANN models (a) NET11, NET12, NET13 and (b) NET2
1st story
43
2nd story
45
3rd story
49
4th story
53
5th story
56 6. CONCLUSIONS
In this paper, an ANN based methodology for active control of buildings for earthquake excitation is demonstrated for different seismic zones and soil types of India. Input and output patterns are generated from time history analysis results with spectrum compatible time histories for shear type buildings using a computer program developed in MATLAB by modal superposition using Newmark-beta method. Inputs for NET1 are acceleration feedback measurement time histories at each floor, input acceleration and the output is acceleration contribution time history from each mode for calculation of control force. The inputs for NET2 are the modal acceleration time history contributions from first three modes and the spectrum compatible acceleration time history and the output from NET2 is the control force time history. Twentyfour ANN models are developed and tested. Methodology demonstrated can be extended for any building and any location wherever the relevant information is available.
Fig. 4. A schematic view of the ANN models developed for seismic zone IV &V in the present study 98
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ACKNOWLEDGEMENTS
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Tang, Yu. (1996). Active control of SDF systems using artificial Neural networks. Computer & structures, 60(5), 695-703. Zell, A., et al. (1989) SNNS user manual, version 4.1. Univ. of Stuttgart, Institute for parallel and Distributed High Performance Systems; Univ. of Tubingen.
The authors acknowledge The Director and Advisor [Management], CSIR-Structural Engineering Research Centre, Chennai, for granting permission to carry out the studies reported in this paper at CSIR-SERC. The support extended by Dr. K. Balaji Rao, Chief Scientist and Head Risk and Reliability of Structures, Dr. N. Gopalakrishnan, Chief Scientist and Head, ASTAR lab and Dr. M. B. Anoop, Pr. Scientist, Risk and Reliability of Structures is highly acknowledged. REFERENCES Bani-Hani, K. and Ghaboussi, J. (1998). Nonlinear structural control using neural networks. ASCE Journal of Engineering Mechanics, 124 (3), 319–327. Chopra, A.K. (2012). Dynamics of Structures: Theory and Applications to Earthquake Engineering 4th edition, Prentice Hall, Englewood Cliffs, New Jersey. Chu, S.Y., Soong, T.T. and Reinhorn, A.M. (2005). Active, Hybrid, and Semi-Active Structural Control: A Design and Implementation Handbook, Wiley, New York. Clough R.W. and Penzien J. (1993). Dynamics of Structures, New York, McGraw Hill. Datta, T. K. (2003). State of the art review on active control of structures. ISET Journal of Earthquake Technology, 40 (1), 1-17. Fisco, N. R. and Adeli, H. (2011). Smart structures: part II— hybrid control systems and control strategies. Scientia Iranica, 18(3), 285-295. Ghaboussi, J. and Joghataie, A. (1995). Active Control of Structures Using Neural Networks. J. Eng. Mech., 121(4), 555-567. Housner, G. W., Bergman, L_A, Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri, S. F., Skelton, R. E., Soong, T. T., Spencer, B. F., and Yao, J. (1997). Structural control: past, present, and future. Journal of engineering mechanics, 123(9), 897-971. IS 1893: (Part 1): (2002). Criteria for earthquake resistant design of structures - Part1: General provisions and buildings. Bureau of Indian Standards, New Delhi. Jennings, P.C., Housner, G.W., and Tsai, N.C. (1968). “Simulated earthquake motions.” CaltechEERL. Karnin, E. D. (1990). A simple procedure for pruning Backpropogation trained neural networks. IEEE Trans. on Neural Networks, 1(2), 239-242. Liut, D. A., Matheu, E. E., and Singh, M. P. (1999). NeuralNetwork control of building structures by a forcematching training scheme. Earthquake Eng. Struct. Dy., 28(12), 1601-1620. Nishitani, Akira. (1998). Application of Active Structural Control in Japan. Progress in Structural Engineering and Materials, 1, 301- 307. Ordonez, G.A. (2000). SHAKE 2000: A computer program for the I-D analysis of geotechnical earthquake engineering problems. Rao, M.M. and Datta, T.K. (2006). Modal Seismic Control of Building Frames by Artificial Neural Network. J. Comp. Civil Eng., 20(1), 69-73.
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49-1 (2016) 095–099 ANNIFAC-PapersOnLine based methodology for active control ANN based methodology for active control of buildings for seismicfor excitation for ANN based methodology active control of buildings for seismicfor excitation for ANN based methodology active control different seismic zones of Indiafor of buildings for seismic excitation different seismic zones of Indiafor of buildings for seismic excitation different seismic zones of India A. Goel * P. Kamatchi** P. Jayabalan *** different seismic zones of India A. Goel * P. Kamatchi** P. Jayabalan ***
A. Goel ** P. Kamatchi** P. Jayabalan *** A. P. P. *** A. Goel Goel *Department P. Kamatchi** Kamatchi** P. Jayabalan Jayabalan ***IIT, Madras * Project Associate, Engineering, of Ocean * Project Associate, Department of Ocean Engineering, IIT, Madras (e-mail: [email protected]) ** Project Associate, Department of Ocean Engineering, IIT, Madras (e-mail: [email protected]) Project Associate, Department of Ocean Engineering, IIT, Madras Principal Scientist, Risk and of Reliability, CSIR-SERC, Chennai * ** Project Associate, Department Ocean Engineering, IIT, Madras (e-mail: [email protected]) ** Principal Scientist, Risk and Reliability, CSIR-SERC, Chennai (e-mail: [email protected]) (email:[email protected]) [email protected]) (e-mail: ** Principal Scientist, Risk and Reliability, CSIR-SERC, Chennai (email: ** Principal Scientist, Risk and CSIR-SERC, Chennai *** [email protected]) CivilReliability, Engineering, NIT, Tiruchirappalli **Professor, Principal Department Scientist, Risk and Reliability, CSIR-SERC, Chennai (email: [email protected]) *** Professor, Department of Civil Engineering, NIT, Tiruchirappalli (email: [email protected]) (e-mail: [email protected]) (email: [email protected]) *** Professor, Department of Civil Engineering, NIT, Tiruchirappalli (e-mail: [email protected]) *** of Engineering, *** Professor, Professor, Department Department of Civil Civil Engineering, NIT, NIT, Tiruchirappalli Tiruchirappalli (e-mail: [email protected]) (e-mail: [email protected]) (e-mail: [email protected]) Abstract: In the last two decades, many studies are reported in literature for determining the control force Abstract: In the last two decades, studies are reported in literature determining the control force for the active control systems for many damage mitigation of buildings due tofor earthquake. However, no study Abstract: In the last two decades, many studies are reported in literature for determining the control force for the active control systems for damage mitigation of buildings due to earthquake. However, no study Abstract: In the last two decades, many studies are reported in literature for determining the control force has the been reported prediction of control force the due seismic zones in India. thenopresent Abstract: In the lastfor two decades, many studies areconsidering reported in literature for determining theIncontrol force for active control for damage of buildings to earthquake. However, study has been reported for systems prediction of controlmitigation force considering the seismic seismic zones IV in India. In the present for the active control systems for damage mitigation of buildings due to earthquake. However, no study study, spectrum compatible time histories are generated for the zones and V as per Indian for the active control systems for damage mitigation of buildings due to earthquake. However, nopresent study has been reported for prediction of control force considering the seismic zones in India. In the study, spectrum compatible timedesign histories are generated for the seismic zones IV and as the per Indian has been reported for of control force considering the seismic zones in In present standard IS 1893(Part 1):2002 spectrum. Time history carried outVwith spectrum has been reported for prediction prediction of control force considering theanalysis seismicare zones in India. India. In the present study, spectrum compatible time histories are generated for the seismic zones IV and V as per Indian standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum study, spectrum compatible time histories are generated for the seismic zones IV and V as per Indian compatible time histories fortime shearhistories type buildings modelled multi-degree of freedom system (MDOF) study, spectrum compatible are generated forasthe seismic are zones IV and Vwith as per Indian standard IS 1893(Part 1):2002 design spectrum. Time history analysis out spectrum compatible time histories for shear type buildings modelled as multi-degree ofcarried freedom system (MDOF) standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum with a computer program developed in MATLAB by modal superposition using Newmark-beta method. standard IS 1893(Part 1):2002 design spectrum. Time history analysis are carried out with spectrum compatible time histories for shear type buildings modelled as multi-degree of freedom system (MDOF) with a computer program developed in MATLAB by modalin superposition Newmark-beta method. compatible time type buildings modelled as multi-degree of system (MDOF) Control forces obtainedfor byshear adopting algorithm literature andusing input and output patterns are compatible timearehistories histories for shear type buildings proposed modelled as multi-degree of freedom freedom system (MDOF) with a computer program developed in MATLAB by modal superposition using Newmark-beta method. Control forces are obtained by adopting algorithm proposed in literature and input and output patterns are with a computer program developed in MATLAB by modal superposition using Newmark-beta method. generated for development of Artificial Neural Network (ANN) models using in Stuttgart Neural Network with a computer program developed in MATLAB by modal superposition Newmark-beta method. Control forces are obtained by algorithm proposed in literature and input and output patterns are generated for development of adopting Artificial Neural Network (ANN) models in Stuttgart Neural Network Control forces are by adopting proposed in literature and input and output patterns are Simulator (SNNS). In the present studyalgorithm the methodology with five building by Control forces are obtained obtained by adopting algorithm proposedis indemonstrated literature andin input and storey output patterns are generated for development of Artificial Neural Network (ANN) models Stuttgart Neural Network Simulator (SNNS). In the present study the methodology is demonstrated with five storey building by generated for development of Artificial Neural Network (ANN) models in Stuttgart Neural Network developing 24 ANN models consisting of two ANN architectures viz., NET1 and NET2 for each seismic generated for development of Artificial Neural Network is (ANN) models in Stuttgartstorey Neural Network Simulator (SNNS). In the present study methodology demonstrated with building by developing 24 soil ANN models consisting ofthe twoof ANN architectures viz., NET1 and five NET2 forthe each seismic Simulator (SNNS). In the present study methodology demonstrated five storey building by zone and three types. the validation results fromis models it iswith observed that maximum Simulator (SNNS). In theFrom present studyofthe the methodology isANN demonstrated with five storey building by developing 24 ANN models consisting two ANN architectures viz., NET1 and NET2 for each seismic zone and three soil types. From the validation of results from ANN models it is observed that the maximum developing 24 ANN models consisting of two ANN architectures viz., NET1 and NET2 for each seismic difference in24percentage response reduction ofANN peak architectures displacementviz., is less thanand 10% whenforit each is compared developing ANN models consisting of two NET1 NET2 seismic zone and three soil types. From the reduction validation of results from ANN models is observed that difference in percentage response of peak displacement is less it than 10% when itthe is maximum compared zone and three soil types. From validation of results from it is that maximum with the value of percentage response reduction. zone andtarget three soil types. From the the reduction validation of peak resultsdisplacement from ANN ANN models models itthan is observed observed thatitthe the maximum difference in percentage response of is less 10% when is compared with the target value of percentage response reduction. difference in percentage response reduction of peak displacement is less than 10% when it is compared difference in percentage response reduction of peak displacement is less than 10% whenBuilding. it is compared Keywords: ANN, Active Control, Seismic Zones, Stochastic GM generation, Earthquake, with the target value of percentage response reduction. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. with the value of response reduction. Keywords: ANN, Active Control, Seismic Stochastic GM generation, Earthquake, Building. with the target target value of percentage percentage responseZones, reduction. Keywords: GM Keywords: ANN, ANN, Active Active Control, Control, Seismic Seismic Zones, Zones, Stochastic Stochastic GM generation, generation, Earthquake, Earthquake, Building. Building. Keywords: ANN, Active Control, Seismic Zones, Stochastic GM generation, Earthquake, Building. 1. INTRODUCTION velocity of current time step as inputs for neural network 1. INTRODUCTION velocity of and current stephave as inputs for neural network model. Rao Dattatime (2006) developed a procedure for velocity of current time step as inputs for neural network INTRODUCTION Various semi-active 1. and active control strategies are adopted model. Rao and Datta (2006) have developed a procedure for 1. INTRODUCTION velocity of current time step as inputs for neural network active control of structures using two setsfor of neural networks 1. INTRODUCTION velocity of current time step as inputs neural network Various semi-active and active control strategies are adopted Rao and Datta (2006) have developed aa procedure for for vibration control of civil engineering structures model. active control of structures using two sets of neural networks model. Rao and Datta (2006) have developed procedure for general stochastic simulations of earthquake based for on Various semi-active and active control strategies are adopted model. Rao and Datta (2006) havetwo developed a procedure for for vibration control of efforts civil engineering structures Various semi-active and active control strategies are adopted active control of structures using sets of neural networks (Chu et al. (2005)). Recently, are made to develop the general stochastic simulations ofsets earthquake based on Various semi-active and active control strategies arestructures adopted for active control of structures using two of neural networks Kanai Tajmi power spectral density function. From the limited for vibration control of civil engineering active control of structures using two sets of neural networks (Chu et al. (2005)). Recently, efforts are made to develop the for vibration control of civil engineering structures for general stochastic simulations of earthquake based on structural control concept into workable technology and fullKanai Tajmi power spectral density function. From the limited for vibration control of aefforts civil engineering structures for general stochastic simulations of earthquake based on (Chu et al. (2005)). Recently, are made to develop the literature review made, simulations it is observedofthat, no study based has been for general stochastic earthquake on structural control concept into aefforts workable technology and full(Chu al. (2005)). Recently, are made to develop the Kanai Tajmi power spectral density function. From the limited scale et implementation in several structures. Many semi-active (Chu et al. (2005)). Recently, efforts are made to develop the literature review made, it is observed that, no study has been Kanai Tajmi power spectral density function. From the limited structural control concept into a workable technology and fullreported for prediction of control force considering the seismic Kanai Tajmi power spectral density function. From the limited scale implementation in several structures. Many semi-active structural control concept into a workable technology and fullliteraturefor review made,ofit itcontrol is observed observed that, no study study has been and activecontrol controlconcept systems implemented in buildings in reported structural intoare a workable technology and fullprediction force that, considering thehas seismic literature made, is no been scale implementation in several structures. Many semi-active andreview soil types of India. literature review made, itcontrol is observed no study been and active control systems are implemented buildings in zones scale implementation in several structures. semi-active reported for prediction of force that, considering thehas seismic Japan (Nishitani (1998)). Research studiesMany areinbeing carried scale implementation in several structures. Many semi-active zones and soil types of India. reported for prediction of control force considering the seismic and active control systems are implemented in buildings in reported for prediction of control force considering the seismic Japan (Nishitani (1998)). Research studies are being carried and active control systems are implemented in buildings in zones and soil types of India. out on various active controlare algorithms viz., optimal control, and active control systems implemented inbeing buildings in zones soil India. Japan (1998)). Research studies carried In the and present study,of and soil types types ofcontrol India. algorithm proposed by Rao and out on (Nishitani variousmodal active control algorithms viz.,are optimal control, Japan (Nishitani (1998)). studies are being carried independent spaceResearch control, neural network based zones Japan (Nishitani (1998)). Research studies are being carried In the present study, control algorithm proposed by Rao and out on various active control algorithms viz., optimal control, Datta (2006) is adopted and two sets of neural networks NET1, independent modal space control, neural network based out on various active control algorithms viz., optimal control, pole assignment technique and bounded state control, control In the present study, control algorithm proposed by Rao and out on various active control algorithms viz., optimal control, Datta (2006) is adopted and two sets of neural networks NET1, In the present study, control algorithm proposed by Rao and independent modal space control, neural network based NET2 are developed for seismic zones IV and V and soil control, pole assignment technique and bounded state (2011), control In the(2006) present study, control algorithm proposed by three Rao and independent modal space control, neural network based as seen in state of the art reports (Fisco and Adeli Datta is adopted and two sets of neural networks NET1, independent modal space control, neural network based NET2 are developed for seismic zones IV and V and three soil Datta (2006) is adopted and two sets of neural networks NET1, control, pole assignment technique and bounded state (2011), control Datta types (2006) of India with spectrum compatible time histories as seen in state of the art reports (Fisco and Adeli is adopted and two sets of neural networks NET1, control, pole assignment technique and bounded state control are developed for seismic zones IV and V and three soil Datta (2003), Housner etart al.reports (1997)). Numerous applications control, pole assignment technique and bounded state control NET2 types of India with spectrum compatible time histories NET2 are developed for seismic zones IV and V and three soil as seen in state of the (Fisco and Adeli (2011), developed using forSHAKE2000 (2000), NET2 are developed seismic zones IV(Ordonez and Vtime and three soil Datta (2003), Housner etartal.reports (1997)). Numerous applications as seen in state of the (Fisco and Adeli (2011), types of India with spectrum compatible histories of Artificial Neural Network (ANN) for structural Control are as seen in state of the art reports (Fisco and Adeli (2011), developed using SHAKE2000 (Ordonez (2000), types of India with spectrum compatible time histories Datta (2003), Housner et al. (1997)). Numerous applications Jennings etIndia al. (1968)). Studies compatible reported in this paper are types of with spectrum time histories of Artificial Neural Network (ANN) for structural Control are Datta (2003), Housner et al. (1997)). Numerous applications reported in literature (Bani-Hani and Ghaboussi (1998), developed using SHAKE2000 (Ordonez (2000), Datta (2003), Housner et al. (ANN) (1997)).for Numerous applications Jennings et al. (1968)). Studies in this paper are developed using (Ordonez (2000), of Artificial Neural Network structural Control are carried out using theSHAKE2000 computerreported program developed in reported in literature (Bani-Hani and Ghaboussi (1998), developed using SHAKE2000 (Ordonez (2000), of Artificial Neural Network (ANN) for structural Control are Ghaboussi and Joghataie (1995),forLiut et al. (1999), Jennings et al. (1968)). Studies reported in this paper are of Artificial Neural Network (ANN) structural Control are carried out using the computer program developed in Jennings et al. (1968)). Studies reported in this paper are reported in literature (Bani-Hani and Ghaboussi (1998), MATLAB which uses generalized mode shape forpaper response Ghaboussi and Joghataie (1995), Liut et al. (1999), Jennings et al. (1968)). Studies reported in this are reported in literature (Bani-Hani and Ghaboussi (1998), Tang (1996), Rao and Datta, 2006). and Ghaboussi (1998), MATLAB carried out outwhich usinguses thegeneralized computer mode program developed in reported in literature (Bani-Hani shape for response carried using the computer program developed in Ghaboussi Joghataie (1995), Liut et al. (1999), evaluation and Penzien (1993)). Tang (1996),and Rao and Datta, 2006). carried out(Clough usinguses thegeneralized computer program developed in Ghaboussi and Joghataie (1995), Liut et al. (1999), MATLAB which mode shape for response Ghaboussi and Joghataie (1995), Liut et al. (1999), evaluation (Clough and Penzien (1993)). MATLAB which uses generalized mode shape for response Tang (1996), Rao and Datta, 2006). MATLAB which uses generalized mode shape for response Tang (1996), Rao and Datta, 2006). evaluation (Clough and Penzien (1993)). Bani-Hani andRao Ghaboussi (1998) used a neural network-based evaluation (Clough and Penzien (1993)). Tang (1996), and Datta, 2006). 2. CONTROL and PenzienALGORITHM (1993)). Bani-Hani trained and Ghaboussi usedfor a neural controller using the(1998) emulator linearnetwork-based control of the evaluation (Clough 2. CONTROL ALGORITHM Bani-Hani and Ghaboussi (1998) used aa neural network-based controller trained using the emulator for linear control of the Bani-Hani and Ghaboussi (1998) used neural network-based structure. In Ghaboussi ANN model proposed by Bani-Hani and In the present study, 2. CONTROL ALGORITHM the control algorithm proposed by Rao Bani-Hani trained and (1998) usedfor a neural network-based 2. ALGORITHM controller using the emulator linear control of the structure. In ANN model proposed by Bani-Hani and 2.isCONTROL CONTROL ALGORITHM controller trained using the emulator for linear control of the In the present study, the control algorithm proposed Rao Ghaboussi (1998) structural displacement and acceleration and Datta (2006) adopted for determination of controlbyforce. controller trained usingmodel the emulator for by linear control of and the In the present study, the control structure. In ANN proposed Bani-Hani algorithm proposed by Rao Ghaboussi (1998) structural displacement and acceleration structure. In ANN model proposed by Bani-Hani and and Datta (2006) is adopted for determination of control force. In the present study, the control algorithm proposed by Rao responses of previous two time steps and actuator electric should be noted that, response of a building is directly structure. In ANNstructural model proposed by and Bani-Hani and It In the present study, thethe control algorithm proposed byforce. Rao and Datta (2006) is adopted for determination of control Ghaboussi (1998) displacement acceleration responses of previous two time steps and actuator electric Ghaboussi (1998) structural displacement and acceleration It should be noted that, the response of a building is directly and Datta (2006) is adopted for determination of control force. signals of previous three time displacement steps are usedand as inputs to the dependent upon the magnitude and epicentre of the Ghaboussi (1998) structural acceleration and Datta be (2006) is that, adopted for determination ofdistance control force. It should noted the response of a building is directly responses of previous two time steps and actuator electric signals of previous threetwo time steps are used as inputselectric to and the dependent responses of previous time steps and actuator upon the magnitude and epicentre distance of the It should be noted that, the response of aa will building is directly neural network model. Tang (1996) used displacement earthquake. The force that a building experience is responses of previous two time steps and actuator electric It should be noted that, the response of building is directly signals of previous three time steps are used as inputs to the dependent magnitude and epicentre distance of the neural model. Tang (1996) used displacement and signals of three time steps are used as inputs to the earthquake.upon Thethe force thatof athe building will experience is dependent upon the magnitude and epicentre distance of the velocitynetwork ofprevious preceding time step, and the displacement and dependent upon the mass building and acceleration signals of previous three time steps are used as inputs to the upon the magnitude and epicentre distance of the neural network model. Tang (1996) and earthquake. The force that aathe building will experience is velocity of preceding time step, andused the displacement neural network model. Tang (1996) used displacement and dependent upon the mass of building and acceleration earthquake. The force that building will experience is neural network model. time Tangstep, (1996) used displacement and earthquake.upon The the force thatof athe building will experience is velocity of preceding and the displacement and dependent mass building and acceleration velocity of preceding time step, and the displacement and dependent upon the mass of the building and acceleration Copyright © 2016 IFAC time step, and the displacement and 95 dependent upon the mass of the building and acceleration velocity of preceding Copyright © 2016, 2016 IFAC 95 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright ©under 2016 responsibility IFAC 95 Peer review© of International Federation of Automatic Copyright 2016 IFAC 95 Control. Copyright © 2016 IFAC 95 10.1016/j.ifacol.2016.03.035
IFAC ACODS 2016 96 February 1-5, 2016. NIT Tiruchirappalli, India A. Goel et al. / IFAC-PapersOnLine 49-1 (2016) 095–099
z1 (1 p)z1 u1 (t ) 1 xg (1 p)[ z1 21 z1 12 z1 ] z2 2 xg (1 p)[2 2 z 2 22 z 2 ] u 2 (t ) z3 3 xg (1 p)[2 3 z 3 32 z 3 ] u 3 (t )
experienced at it. The earthquake design philosophy of a building is based upon the peak ground acceleration which is classified as per different seismic zones in Indian code (IS 1893(Part 1): 2002) taking into account the maximum considered earthquake for that region. Therefore, a control technique, based upon the seismic zone and utilising force matching principle, can reduce the damage of buildings taken for consideration. The control algorithm proposed by Rao and Datta (2006) based on force matching technique utilizing modal contribution of prominent modes, is suitable for extending into seismic zones. In the present study one horizontal dynamic degrees of freedom is only considered representing shear type buildings with symmetrically constructed story units. Further one horizontal component of the earthquake is only considered. However the methodology proposed can be extended to asymmetric buildings and other components of earthquake as well.
u 2 (t )
k k2 u1 (t ); u 3 (t ) 3 u1 (t ) k1 k1 kj
(7) (8)
3. MATHEMATICAL MODEL OF STRUCTURE In order to demonstrate the application of control algorithm a five-story shear type building with identically constructed story units is considered for training and testing of the ANN as shown in the Fig. 1. The lumped mass concentrated on each story is taken as 150 x 103 kg. The elastic stiffness and the structural damping ratio are taken as 200x10 6 N/m and 0.02 respectively. For calculating dynamic response of the MDOF structure, the step-by-step integration procedure of differential equations as proposed by Newmark is adopted (Chopra (2012), Clough and Penzien (1993)) in the computer program. A target percentage reduction of 50% is considered in the present study.
(1) (2) (3)
Tj R Tj M j
(6)
where, 𝑥𝑥̈ 𝑖𝑖 (𝑖𝑖 = 1,2,3,4,5) is the acceleration response of the structure at the 𝑖𝑖 𝑡𝑡ℎ story of the building; 𝜙𝜙𝑖𝑖 𝑗𝑗 (𝑗𝑗 = 1,2,3) is the mode shape coefficients for 𝑖𝑖 𝑡𝑡ℎ story; and 𝑗𝑗𝑡𝑡ℎ mode; 𝑧𝑧̈𝑗𝑗 (𝑗𝑗 = 1,2,3) modal acceleration contributions to the control force; 𝑢𝑢𝑗𝑗 (𝑡𝑡)(𝑗𝑗 = 1,2,3) are the modal contribution towards a single control force; 𝑢𝑢(𝑡𝑡) is the control force; 𝑅𝑅 is the location vector; 𝑝𝑝 is the target percentage reduction; 𝑧𝑧̅1̈ is the uncontrolled modal acceleration; 𝜌𝜌2 & 𝜌𝜌3 are the modal participation factors for 2nd and 3rd mode; 𝜂𝜂 is the damping ratio; 𝜔𝜔2 & 𝜔𝜔3 are the natural frequencies of the building in 2nd and 3rd mode; 𝑧𝑧̅2̇ & 𝑧𝑧̅3̇ are the uncontrolled velocity in 2nd and 3rd mode and 𝑧𝑧̅2 & 𝑧𝑧̅3 are the uncontrolled displacement in 2nd and 3rd mode respectively.
For the development of generalized control scheme for MDOF structure, response feedbacks are utilized along with target percentage reduction and position of control force to get modal contributions for controlled response (equations (1-8); Rao and Datta (2006)). The control technique utilises the principle of modal superposition of structural acceleration of the structure. The structural acceleration of the structure can be determined from superposition of its modal acceleration components (equation 1). Moreover, as controlled modal accelerations are related to control force (equation 2, 5, 7 and 8); it is used for training of neural nets. The control force is applied at top and is determined from modal contributions from first three modes, which in turn are determined from uncontrolled modal accelerations based upon a target percentage reduction. It is assumed that the major contribution to control force is from first mode shape of the building having a target percentage reduction (equation 5). Therefore, the modal contribution of first mode for control force is determined from equation-6. The contributions to control force from the second and third mode are obtained from equation 7 and 8. Here, it should be noted that, modal theory is a mathematical supposition and none of its components like contributions from different modes to control force (u1(t), u2(t) and u3(t)) can be directly measured through sensors. Therefore, a neural network model is developed based upon the realizable quantities whose values are found for various spectrum compatible time histories to develop a neural network architecture for prediction of the building’s behaviour pattern. This theory is the basis for training of the neural network architecture having the controlled structural acceleration response as its input and the control force as its output, for a given set of spectrum compatible time histories.
xi i1 z1 i2 z2 i3 z3 u 2,3 (t ) k 2,3u(t )
(5)
(4) Fig. 1. Model of a five storey frame 96
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For generation of dataset for training of neural networks, the five storey frame is analyzed using spectrum compatible ground motion accelerations obtained consistent with response spectrum of three soil types viz., rock, medium soil, soft soil and seismic zones IV and V as per Indian standard (IS 1893(Part 1): 2002) using SHAKE2000 computer program. For each response spectra eleven acceleration time histories are generated with 3002 sampling points at an interval of 0.01s out of which results for 10 simulations of earthquake are used for training and result for one simulation is used for testing of the neural networks developed.
97
All the subnets in NET1 have 6 neurons in the input layer and one neuron in the output layer and NET2 has 4 neurons in the input layer and one neuron in the output layer. Number of neurons in the hidden layer for the network models are given in Table 1. Typical network architecture for the NET1 (subnets) and NET2 are shown in Fig. 3. In the present study a total of 24 neural network models are developed as given in Fig. 4 for the different seismic zones and soil types considered. In the present study, Stuttgart Neural Network Simulator SNNS (Zell et al. (1989)) has been used for development of neural network models. The inputs to the neural network are combined linearly and feeding the neural nets will raw values will not work very well. Therefore, normalization of the input dataset in the interval of [0, 1] is preferred. In this study, we have normalized the input dataset, according to Maximumminimum normalization principle utilizing input variables. A Multilayer fully connected feed-forward neural net architecture with logistic activation function, Backprop Momentum learning function and Topological_order update function, are used for training. The learning rate and update parameter for different network models are given in Table 2.
4. NEURAL NETWORK MODELS As it is described earlier, the inputs for NET1 are acceleration feedback measurement time histories at each story, input acceleration and the output is the modal contribution acceleration time history for the first three modes for calculation of control force. From the studies made with modal superposition of five and three modes, it is seen that inclusion of three modes results in better accuracy in the prediction of control force time history. Further, mass participation of 98.4% is achieved while considering the modal superposition of first three modes. Hence three subnets NET11, NET12, NET13 are developed to predict the modal contribution of first three modes. For the second network NET2, modal acceleration time history contributions from first three modes, and the input excitation (spectrum compatible acceleration time history) are the inputs and the control force time history is the output. A systematic model of the methodology is presented in Fig. 2.
Table 1. Number of neurons in the hidden layer for ANN models Number of nodes in Hidden Layers (1 and 2) Soil Seismic Type NET11 NET12 NET13 NET2 Zone 1 2 1 2 1 2 1 2 Soft 6 6 6 6 6 6 9 Zone 5 Medium 6 6 6 6 6 6 4 4 Rock 6 6 6 6 6 6 9 Soft 9 - 9 9 9 Zone 4 Medium 6 6 6 6 6 6 4 4 Rock 6 6 6 6 6 6 9 Table 2. Learning parameters for ANN models
Seismic Zone
Zone 5
Zone 4
Fig. 2. Methodology for active control of buildings for seismic excitation 97
Soil Type
Neural Network Configuration for Subnets (NET11, NET12, NET13) and NET2 Learning rate
Update Parameter
NET11 NET12 NET13
NET2
NET11 NET12 NET13
NET2
Soft
0.01
0.0001
0
0.001
Medium
0.01
0.01
0
0
Rock
0.01
0.0001
0
0.001
Soft
0.0001
0.0001
0.001
0.001
Medium
0.01
0.01
0
0
Rock
0.01
0.0001
0
0.001
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5. TESTING OF NEURAL NETWORK For testing the neural network, the building frame is analyzed for one simulation of spectrum compatible accelerogram which has not been used in training. Maximum percentage errors of results from ANN models with respect to algorithm based detailed analysis for the test pattern are given in Table 3. The percentage reduction in the peak response displacement obtained from ANN model for a typical input is given Table 4. It is observed that maximum difference in peak displacement of the controlled and uncontrolled building is less than 10% when it is compared with the target response reduction percentage. Table 3. Maximum percentage error of results from ANN models with respect to algorithm based detailed analysis Maximum error Seismic Soil Zone Type NET11 NET12 NET13 NET2 Zone 5
Soft
30.816
Medium 13.959 Zone 4
8.803
7.479
31.779
9.1
8.251
33.05
Rock
31.13
13.86
13.59
17
Soft
12.424 15.095
11.51
3.71
Medium 10.533 12.418 10.185 Rock
4.171
7.708
5.802
19.999 18.85
Table 4. Percentage reduction in the story displacement Story Level Percentage Reduction
Fig. 3. Architecture of ANN models (a) NET11, NET12, NET13 and (b) NET2
1st story
43
2nd story
45
3rd story
49
4th story
53
5th story
56 6. CONCLUSIONS
In this paper, an ANN based methodology for active control of buildings for earthquake excitation is demonstrated for different seismic zones and soil types of India. Input and output patterns are generated from time history analysis results with spectrum compatible time histories for shear type buildings using a computer program developed in MATLAB by modal superposition using Newmark-beta method. Inputs for NET1 are acceleration feedback measurement time histories at each floor, input acceleration and the output is acceleration contribution time history from each mode for calculation of control force. The inputs for NET2 are the modal acceleration time history contributions from first three modes and the spectrum compatible acceleration time history and the output from NET2 is the control force time history. Twentyfour ANN models are developed and tested. Methodology demonstrated can be extended for any building and any location wherever the relevant information is available.
Fig. 4. A schematic view of the ANN models developed for seismic zone IV &V in the present study 98
IFAC ACODS 2016 February 1-5, 2016. NIT Tiruchirappalli, India A. Goel et al. / IFAC-PapersOnLine 49-1 (2016) 095–099
ACKNOWLEDGEMENTS
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Tang, Yu. (1996). Active control of SDF systems using artificial Neural networks. Computer & structures, 60(5), 695-703. Zell, A., et al. (1989) SNNS user manual, version 4.1. Univ. of Stuttgart, Institute for parallel and Distributed High Performance Systems; Univ. of Tubingen.
The authors acknowledge The Director and Advisor [Management], CSIR-Structural Engineering Research Centre, Chennai, for granting permission to carry out the studies reported in this paper at CSIR-SERC. The support extended by Dr. K. Balaji Rao, Chief Scientist and Head Risk and Reliability of Structures, Dr. N. Gopalakrishnan, Chief Scientist and Head, ASTAR lab and Dr. M. B. Anoop, Pr. Scientist, Risk and Reliability of Structures is highly acknowledged. REFERENCES Bani-Hani, K. and Ghaboussi, J. (1998). Nonlinear structural control using neural networks. ASCE Journal of Engineering Mechanics, 124 (3), 319–327. Chopra, A.K. (2012). Dynamics of Structures: Theory and Applications to Earthquake Engineering 4th edition, Prentice Hall, Englewood Cliffs, New Jersey. Chu, S.Y., Soong, T.T. and Reinhorn, A.M. (2005). Active, Hybrid, and Semi-Active Structural Control: A Design and Implementation Handbook, Wiley, New York. Clough R.W. and Penzien J. (1993). Dynamics of Structures, New York, McGraw Hill. Datta, T. K. (2003). State of the art review on active control of structures. ISET Journal of Earthquake Technology, 40 (1), 1-17. Fisco, N. R. and Adeli, H. (2011). Smart structures: part II— hybrid control systems and control strategies. Scientia Iranica, 18(3), 285-295. Ghaboussi, J. and Joghataie, A. (1995). Active Control of Structures Using Neural Networks. J. Eng. Mech., 121(4), 555-567. Housner, G. W., Bergman, L_A, Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri, S. F., Skelton, R. E., Soong, T. T., Spencer, B. F., and Yao, J. (1997). Structural control: past, present, and future. Journal of engineering mechanics, 123(9), 897-971. IS 1893: (Part 1): (2002). Criteria for earthquake resistant design of structures - Part1: General provisions and buildings. Bureau of Indian Standards, New Delhi. Jennings, P.C., Housner, G.W., and Tsai, N.C. (1968). “Simulated earthquake motions.” CaltechEERL. Karnin, E. D. (1990). A simple procedure for pruning Backpropogation trained neural networks. IEEE Trans. on Neural Networks, 1(2), 239-242. Liut, D. A., Matheu, E. E., and Singh, M. P. (1999). NeuralNetwork control of building structures by a forcematching training scheme. Earthquake Eng. Struct. Dy., 28(12), 1601-1620. Nishitani, Akira. (1998). Application of Active Structural Control in Japan. Progress in Structural Engineering and Materials, 1, 301- 307. Ordonez, G.A. (2000). SHAKE 2000: A computer program for the I-D analysis of geotechnical earthquake engineering problems. Rao, M.M. and Datta, T.K. (2006). Modal Seismic Control of Building Frames by Artificial Neural Network. J. Comp. Civil Eng., 20(1), 69-73.
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