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The submitted manurcript has been authoredby a contractor of the U. S. Governmentunder contract No. W-31-104ENG-38.Accordingly the U. S. Government retains anonexclusive. royalty-free license to publishor reproduce the published form of thiscontribution. or allow others to do SO forU. S. Government purposes.

APPLICATION OF NEURAL NETWORKSTO SEISMIC ACTIVE CONTROL

Yu TangReactor Engineering DivisionArgonne National LaboratoryArgonne Illinois

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ABSTRACTn exploratory study on seismic active control using anartificial neural network ANN) is presented in which a single-degree-of-freedom (SDF) structural system is controlled by atrained ne ural network. A feed-forward neural network and thebackpropa gation training method a re used in the study. Inbackpropa gation training, the le arning rate is determined byensuring the decrease of the erro r function at each training cycle.The training patterns for the Bu ra l net are generated randomly.

Then, the trained NN is used to compute the control forceaccording to the control algorithm. The control strategyproposed herein is to apply the control force at every time stepto destroy the build-up of the system response. The groundmotions considered in the simulations re the N21E and N69Wcomponents of the Lake Hughes No. 12 ecord that occurred inthe San Fernando Valley in California on February 9, 1971.Significant reduction of the structural response by one order ofmagnitude is observed. Also, it is shown that the proposedcontrol strategy has the ability to reduce the peak that occursduring the first few cycles of the tim e history. These promisingresults assert the potential of a pplying ANNs o active structuralcontrol under seismic loads.

INTRODUCTIONActive Structural Control is to equip the structure with anactive control device to counteract or minimize the motionexperienced by the structke so that the d ynam ic response of thestructure is reduced. This idea w as first proposed by Yao in1972 (Yao, 1972). Since then , this area of research has receivedconsiderable attention. Rece ntly, considering the importance ofthis area, the U.S. Panel on Structural Control Research was

formed in 1991 (Soong, Masri, and Housner, 1991) and thInternational Association for Structural Control was formed 1994 (Housner, Soong, and Masri, 1994). So, the actistructural control is right now a booming research area. Mancontrol laws, linear and nonlinear, have been proposed anstudied, and two types of mech anical co ntrol systems, the activbracing ABS) and variable stiffness method VSM), ave beelaboratory tested. Despite all the se develop ments, there are stproblems that must be addressed before it is implemented to restructures. For example, the structural mo del ing mo rs and timdelay. The majority of the control algorithms proposed abased on he optima l control the ory w hich usually assumes ththe system under control can be precisely mathematicalmodeled. This is almost an unattainable condition for civstructures. Also, t is assumed that all operations in the contrcan be performed instantaneously. In reality,- ime needs to bconsumed in the data process, in the computation, and in thactivation of the co ntrol device.Because an ANN is not sensitive to the noise present in thinput data, it can handle the mode ling e rror more gracefully, analso because an ANN involves only the matrix multiplicationand additions, it can cut dow n the process time. Or, if thsoftware simulation is not fast enough, an NN may bfabricated in a very large-scale integration VLSI) for real timresponse. Once the network has been trained, a chip c a n bconstructed. The chip is the n placed into electronics by whica real-time operation can be ac hieved. Therefore, an NN sgood candidate for the imp lementa tion of the active control. Thpotential of applying ANNs with the backpropagation Btraining algorithm to active control has been explored by Wenet al. (1992), and the result is promising. However, in thepaper, the time delay problem was not addressed. In this stud

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DISCLAIMERPortions of this docum ent may be illegiblein electronic image products. lmages areproduced from the best available originaldocument.

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the simple control strategy proposed in Tang (1995) is employedherein. This strategy is heuristic in nature and is a non-optimaltype of con trol rule. In othe r words , there is no objectivefunction to be optimized. The basic idea behind this controlstrategy is the same as that of the pulse control proposed byUdwadia and Tabaie (1981), i.e., to destroy the gradu al rhythm icbuild-up of the structural response; however, details of thealgorithm and implem entation are quite different from those ofUdwadia and Tabaie (1981). It can be implemented for aclosed-loop control or an open-closed loop control. In thispaper, it is assumed that a closed-loop control is implemented.The effectiveness of the control strategy used herein isdemonstrated by numerical examples in which a SDF systemunder seismic excitations is studied. The dynam ic responses ofthe SD F system with and without control are compared, and alsothe controlled system response s obtained by the control strategyused herein are compared with those o btained by co ntrol strategyproposed in Wen, et al. (1992). The results show that thecontrol strategy used herein is superior to that of Wen, et al., andit is able to produce a significant peak reduction for the peakoccurring during the first few cycles of the time history, anability the linear control laws lack (Gattlli, Lin, and Soong,1994). The ground motions considered in the examples are theN21E and N69W com ponents of the Lake Hughes No. 1 2 ecordthat occurred in the San Fernando Valley in California onFebruary 9, 1971. The d uration of the record is 36.76 seconds,and the ma gnitudes for the two comp onents considered are 0.902g for N21E and 0.711 g for N69W. However, the magnitudesof the accelerations are scaled down to 0.0775g in the numericalexamples.

ARTIFICIAL NEURAL NETWORKSAn artificial neural network is an information-processingsystem based on observed behavior of biological nervoussystems. A neural net consists of a large number of simpleprocess elem ents (PES). Each PE is connected to ano ther PE bymeans of direct communication links, each with an associatedweight. It is these w eights that represent the information storedin the system and hold the key to the functioning of an ANN.Among many different types of A N N s the feedforwardmultilayer perceptron with the backpropagation algorithm, theso-called backpropagation (BP) net, is the most widely usedsupervised learning algorithm in neural network applications.The structureof a typical PE in a BP net is shown in Fig. 1 nwhich (xl, x2,...,xd is the input vector, b is the bias, (wl,wu...,wn) is the associated weight vector, I is the intermediatescalar, f o is the so-called activation functio n, and y is the outputfrom the PE. Specifically, I is computed by the equation

Y f o (2)In this study, the activation function used is given by

21 + e - 'f(x) = 1 (3)

The architecture of an example of a BP net consisting of aninput layer, a hidden layer and an output layer, is shown in Fig.2. In the training process, an error function is used to assess theperformance of the net. This error function is defined by

4)in which P is the number of patterns in the training set, and tpjand opj(w) are the target and actual output of the jth outputneuron for the pth pattern, respectively. o is denoted as afunction of w to indicate the dependency of tf e network outputson the weight vector w. The weight vector is updated by

where a = the learning rate which is a constant in the range of(0 1) in a standard BP algorithm, and V q w ) is the gradientvector. Note that in Eq. 2) the w eights are updated after all ofthe patterns in the training set have been passed through the net.A comm on variation is to update the we ights after each trainingpattern is presented. In this study an adaptive BP algorithm isused, Le., th e learning rate is chang ing durin g training. Thealgorithm is based on the gradient phase of the SGRA algorithmproposed by Miele, et al. (1970). The advantage of thisalgorithm is that the dec rease of error function at each epoch isguaranteed; otherwise, the program stops. The capability of BPnets for approximating a continuous mapping is proved by theKolmogorov mapping neural network existence theorem(Funahashi, 1989, and Hecht-Nielsen, 1987). Also, Cybenko(1989) has proved that a co ntinuous function may be arbitrarilywell approximated by feedforward neural networks with anonlinear continuous activation function. For more details aboutthe BP net the reader is referred to Freem an and Skapura (1991)and Hecht-Nielsen (1990).The B P net used in this study has five PES for the input layer,eight PES each for the two hidden layers, and one PE for theoutput layer, This BP net need s to be trained before it can beused in the application. The prepara tion details for the trainingpatterns can be found in Tang (unpublished report 1995).

ni = l

I = wixi + band y is obtained from the equation

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SYSTEM CONSIDERED x j = x(t) .Descriptionof System ConsideredA linear single-degree-of-freedom SDF) system isused hereinto demo nstrate the application of an ANN to seismic activecontrol. The system is shown in Fig. 1. It is the same onedemonstrated experimentally for the active structural control inthe paper by Chung. et al. (1988). The structural properties ofthe SDF system are listed below:Mass,m: 16.69 lb-se&in.Structure Stiffness, k 7934 lb/in.Natural Frequency, &: 3.47 HzDamping Factor, 5: 5%

For more details on he experimental setup, the reader is referredto the paper by Chung, e t al. (1988). Note that the linear controltheory w as use d in that study.

CONTROL STRATEGYequation of motion is given byFor a linear SDF system subjected to base excitation, the

X(t) + 4Zf&X(t) + 4Z*f;x(t) = -%,(t) (6)in which a dot indicate s the deriva tive with respect to time, &and t; are the natural frequency and dam ping ratio of the system,respectively, and x, t) is the effective base excitation consistingof two parts. One part is the c ontrol force, denoted by Fc(t), andthe other is the ground ac ce ka tio n, denoted by x,(t), i.e.,

F,(t)%,(t) = %,(t) + mwhere m = the mass of the SDF system.If the Duhamel integral is used to solve Eq. 3) and thepiecewise-linear nterpolation for the loading is assumed, it c nbe shown, e.g., Craig, Jr. (1981), that the sy stem response at t=ti,x(tJ and x(ti), may be determined from the information of x(ti-At), x(t-Ar), %,(ti-At), and ,(ti> where At is the data samplingrate. In this study it is assumed that the sensors provide theinformation about x(t) an d x (t) a t a rate of 0.01 second (assumea closed-lo op control). The se measured data are fed into atrained ANN to estim ate the control force needed. The inputvector for the ANN includes five elements: the displacement,velocity and load at the preceding time step, and thedisplacement, velocity and load at the current time step. Theyare denoted by xl, x2, x3, x4 and x5, respectively, i.e.,

XI = x(t-At)XZ = d ( t d t )

xq = X(t)

The output from an NN is a single PE that contains information of the load, %,(t).

For each time interval, say from t=$ to t=ti+At, an A N Nused twice sequentially to perform the following computatioFirst:Input to NN

~2 = *($-At)x3 = x(ti>x4 = X(tJXS = %,(ti-At)

output of ANNY = ,(ti)

Second:Input to N N

x1 = x(t9x2 = X t9x3 = 0x4 = 0x5 = (ti>

output of ANNy = Fc(ti+At)hn

to compute the control force, Fc(ti+At), needed for t=ti+Conceptually, the first com putation, Eq. 9), s to ask the ANwhat the load is that produces the system response, x(tJx tJ, and the second computation, Eq. lo), is to ask he ANwhat the necessary force is that c n produce the zdisplacement and velocity at t=g+At. Note that at t=O, ~ (x 0) = f, O) = Fc(0) = 0 and at t = 0 + At, Fc(O+At) = 0assumed, and the control algorithm is stopped wh

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x1=x2=x3=x4=xs=0are detected. If the strategy is implementedfor an open-closed loop control, the first computation is notneeded because x,(ti) is provided by the sens or, and x,(ti) canbe con structed by m aking use of Eq. 7).

control strategy. The effectiveness of the control law isdemonstrated by num erical examples. The results show that thesystem response is reduced by one order of magnitude, and thecontrol strategy used has the ability to produce a significant peakreduction for the peak occurring during the first few cycles ofthe time history.NUMERICAL EXAMPLESIn this section the dynamic responses of the SDF systemdescribed above subjected to base excitations are studied. Thetrained NN is used to compute the control force. Twoearthquake motions are used herein for the input baseexcitations. They are the N21E and N69W components of theLake Hughes No. 12 record that occurred in the San FernandoValley in C alifornia on February 9, 1971. The duration of theearthquake is 36.76 seconds. The magnitudes of the two recordswere scaled down to 0.0775 g. The plots of these two timehistories are shown in Figs. 3and 4, respectively. For discussionpurposes, the first time history is referred to as Base Motion 1,and the second time history is referred to as Base Motion 2.The flow chart for the control scheme using an NN isdepicted in Fig. 5.For Base Motion 1, the time histories of therelative displacemen t, x(t), w ith and withou t control arecompared in Fig. 6. The corresponding information for usingBase Motion 2 is presented in Fig. 7. For clarity, only the first

10 seconds of the responses are plotted. Examining Figs. 6 and7, one c n see clea rly the effectiveness of the A NN control; thestructural response is drastically reduced by one order ofmagnitude. Also,one may notice the sign ificant reduction for thefirst peak of the response, which, as mentioned above, cannot beproduced by the linear control laws. The c ontrol force in term sof the accele ration, F,(t)/m, for Base Motion 1 is shown in Fig.8; also plotted in the same figure by the do tted line is the inputbase motion for comparison. One can see that the controlacceleration is about 180 degrees out of phase with the inputbase motion.It should be mentioned that the c ontrol force for the proposedcontrol strategy may be computed by a closed form solution(Tang, unpublished report 1995). One should therefore beinterested in the co mparison s of the structural responsecontrolled by the ANN with that controlled by a theoreticalcontroller in which the control force is computed by the closedform solution. Such a comparison is presented in Fig. 9forBase Motion 1. One can see that, except for the constant driftbetween the two curves, these two curves are almost identical.Also, he theoretica l results are compared with those obtained bythe control strategy proposed in Wen, et. al. (1992) in which thecontrol force is set equal in magnitude but in the oppositedirection of the product of the mass and ground acceleration.These comparisons are presented in Figs. 10 and 11 for BaseMotions 1 and 2, respectively. One can see. that the controlstrategy used herein is supe rior to that of W en, et al.

ACKNOWLEDGEMENTThis paper was supported by the U.S. Department of Energy,Technology Support Programs under Contract W-31-109-Eng-38.

REFERENCESChung, L. L., Reinh orn, A. M., and Soon g, T. T., 1988,Experiments on Active Control of Seism ic Structures, Journal

of Engineering Mechanics ASCE Vol. 114, No. 2, pp. 241-256.Craig, Jr., R. R., 1981, Structura l Dynamics: An Introductio nto Compu ter Method, John Wiley Sons, Inc. New York, NY.Cybenko, G., 1989, Approximation by Superpositions of aSigmoidal Function, Math. Con trol Signal Systems Vol. 2, pp.

Freeman, J. A, and Skapura, D. M., 1991, Neura l Networks:303-314.Algorithm, Applications and Programming Techniques,Addison-Wesley Publishing Co.,Reading, MA.Funahashi, K., 1989, On the Approximate Realization ofContinuous Mapping by Neural Networks, Neural NetworksGafflli, V., Lin , R. C., and Soong, T. T., 1994, NonlinearControl Laws for Enhancement of Structural ControlEffectiveness, Proceedings 5th U.S. National Conference onEarthquake Engineering Chicago, IL, pp. 971-975.Hecht-Nielsen, R., 1987, Kolmogorov's Mapping NeuralNetwork Existence Theorem, Proceedings 1st InternationalConference on Networks Vol. 111, pp. 11-14, IEEE Press, NewYork.Hech t-Nielsen , R., 1990, Neurocomputing, Addison-WesleyPublishing Co., eading, MA.Housner, G. W., Soong,T. T., and Masri, S. F., 1994, SecondGeneration of Active Structural Control in Civil Engineering,Final Program and Abstracts, First World Conference on

Structural Control LQS ngeles, CA.Miele, A., Pritchard, R. E., and Damoulakis, J. N., 1970,Sequential Gradient-Restoration Algorithm for O ptimal ControlProblems, Journalof Optimization Theory and Application Vol.Soong, T. T., Masri, S. F., and Housner, G. W., 1991, AnOverview of Active Structural Control Under Seismic Loads ,Earthquake Spectrum Vol. 7, No. 3, pp. 483-505.Udw adia, F. E., and Tabaie, S., 1981, Pulse Control of SingleDegree-of-Freedom System, Journa l of Engineering Mechanics

Vol. 2, NO. 3, pp. 183-192.

5, NO. 4, pp. 235-282.

ASCE Vol. 107, NO. 6, pp. 997-1009.CONCLUDING REMARKSA study of seism ic active control is presented. The controlalgorithm implemented is based on a heuristic, non-optimal

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Wen, Y. IC Ghaboussi, J. Venini. P., and Nikzad, K., 1992,Control of Structures Using Neural Networks, Proceedings

U.S.lItalylJapan WorkshoponStructural ontroland ntelligentSystems Sonento, Italy, pp. 232-251.Yao, J. T. P., 1972 Conceptof Structural Control, Journalof he Structural D i v b wn ASCE Vol. 98, No. 7, pp. 1567-1574.

A -

b (bias)

- = f ( I ).....Xn

(ActivationFunction) (Output)Inputs) (Weights)

FIG. 1. A TYPICAL PE IN BACKPROPAGATION NETS

-- n I

Hidden Layer

FIG. 2. ARCHITECTURE OF A BACKPROPAGATION NET

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3 -15 -

0

I

-15 -

Time sec.

FIG. 3. N21E COMPONENT OF LAKE HUGHES NO. 12 RECORD

301 . 8 ' . * . 1 * - .--15

0

-15

-3010 20 30

Time sec.

i

40

FIG. 4. N69W COMPONENT OF LAKE HUGHES NO. 12 RECORD

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xternal rStructure Structural

-.

Excitation Response

Control Force

ArtificialNeuraletwork ANN)

FIG. 5. FLOW CHART OF ANN CONTROL FOR THE EXAMPLE PROBLEM

: :

ANN ControlWithout Control

I I I

2 4 6 a 10Time, sec

FIG. 6. TIME HISTORY OF RELATIVE DISPLACEMENT INPUT: BASE MOTION 1

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.30

ANN Control.15 I I *.. ... .e. ..::: :: Without Control_.__..___0

-.15

I-.30

I2 4 6 a 10

Time, sec

FIG. 7. TIME HISTORY OF RELATIVE DISPLACEMENT INPUT: BASE MOTION2

FIG. 8. TIME HISTORY OF CONTROL FORCE INPUT BASE MOTION 1

-L

20

0

20

-40 1 2 3 4Time, sec. I

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.010 1 tt

-.010 '0 2 4 6 8 10Time, sec.

FIG. 9. COMPARISON OF NEURO-CONTROLLED RELATIVE DISPLACEMENTWITH THEORETICAL RESULT INPUT: BASE MOTION 1

.03 - i

-tic .01.--28naQv-_-.-.b-9 -.01;

-.03 I I I t0 2 4 6 8 10Time, sec.

FIG. 10. COMPARISON OF PERFORMANCEOF TWO CONTROL STRATEGIESINPUT BASE MOTION 1

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< * ? r4 s

0 2 4 6 8 10iTime, sec. Ii

FIG. 11. COMPARISON OF PERFORMANCE OF TWO CONTROL STRATEGIESINPUT BASE MOTION 2