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1 Research Article APPLICATION OF ARTIFICIAL NEURAL NETWORK FOR INTERFERENCE STUDIES OF LOW-RISE BUILDINGS 1 Narayan K*, 2 Gairola A Address for Correspondence 1 Associate Professor, Department of Civil Engineering Institute of Engineering & Technology Lucknow, India 2 Professor, Department of Civil Engineering I.I.T. Roorkee, India ABSTRACT Artificial neural network (ANN) representations are capable of developing functional relationship from discrete values of input-output quantities obtained from computational approaches or experimental results. Data obtained from wind tunnel tests for interference effects expressed by Interference Factor (IF) on gable roof building (25 roof slope) has been used for training the network. Training of the neural network is carried out by inputting the data sets, which consist of some selected locations of the interfering building and the corresponding values of IF for the worst design pressure coefficients (Cpq). These were determined independently for each zone of the roof. The trained network is then expected to predict the IF for Cpq for locations of interfering building not covered in the training data set. Correlation plots and contours show that most of the ANN predicted values are very close to the corresponding experimental values. 50% reduction in the experimental work can be achieved for the case studied by using the neural network modeling for interference studies in low buildings, without sacrificing any accuracy. KEYWORDS: Artificial neural network; gable roof building; interference effects; design pressure coefficients. INTRODUCTION The prediction of wind-induced pressure coefficients on the wide variety of building geometries is of considerable practical importance. Extensive amount of wind tunnel testing is required to determine the wind loads on low buildings, there being a large number of parameters with a wide range of values affecting it. Time consuming and costly wind tunnel tests can only cover a limited number of basic configurations. Artificial Neural Network (ANN) is inspired from the biological sciences by attempting to emulate the behaviour and complex functioning of the human brain in recognizing patterns. They are composed of several layers of many interconnected neurons operating in parallel. Since ANN have many inputs and outputs (responses) and allow nonlinearity in the transfer functions of the neurons, they can be used to solve multivariate and nonlinear modeling problems. Use of ANN has been reported in a number of civil engineering applications. Vanluchene and Sun (1) demonstrated the application of ANN in structural engineering applications. Authors presented the application of Back-propagation to concrete beam design and rectangular plate analysis problems. Khanduri et al (2) presented the abilities of neural network for solving wind interference problems among tall buildings. They concluded that the ability of neural network to be trained to generalize, when presented with limited data examples, makes it an attractive application for knowledge acquisition on wind interference effects where there is no acceptable theory or empirical generalization available at present. Similarly, successful application of ANN is also reported by Deshpande and Mukerjee (3) on initial design process and on structural design expert system. Girma (4) applied cascade correlation learning algorithm for determination of wind pressure distribution in buildings and found that the error was less than 15% in the predicted values. Kwatra (5) predicted interference effect on gable roof building successfully using Back-propagation training algorithm of neural network and showed that the predicted values lie within 5% variation of the corresponding experimental values. Chen et al (6) presented an artificial neural network approach for the prediction of mean and root-mean-square pressure coefficients on the gable roofs of low buildings. The performance of the ANN is demonstrated by the prediction of the pressure coefficients for roof tap locations in a corner bay. Authors concluded that the approach could be used to expand aerodynamic databases to a larger variety of geometries and increase its practical feasibility. Artificial Neural Network models have the ability to learn and generalize the problems even when input data contains error or is incomplete. Neural networks exhibit several characteristics that make them suitable to study interference effects in wind engineering. Training teaches a network to capture significant features or relationships in the data. Thus a trained network is capable of exhibiting such relationships in new related data. The ability of neural networks to perform a computation when trained with examples makes them applicable in situations where a model is needed, yet no currently acceptable theory exists for describing the input/output pattern. Neural networks are composed of several layers of simple elements operating in parallel. Each layer has a weighted input vector and an output vector. Layers whose outputs become the final network output are called output layers; all other layers are called hidden layers. The first set of neurons referred to as input layer perform no computations and serve only as distribution points. The network function is

2 determined largely by the connections between neurons or processors. Each neuron accepts a set of inputs from other neurons and computes an output which is propagated to connected neurons. Networks are trained with available test examples to recognize input patterns and produce appropriate output responses. Each connection is associated with a measure of the strength of the connection, called its weight, which is used to modify the signals. For a given neural architecture, it is the weight of the connections between the neurons which determines the output. Changing the strength or weight of connections with experience (new examples) is akin to learning, the memory of a network being embedded in the strength (weight) of the connections. An elementary back propagation neuron with n inputs and weighted connections is shown in Fig. 1. The activity pattern in a hidden layer follows an encoding of the significant features of the input. The collective activity of all the hidden units (neurons or nodes) determines the behavior of a network. Hidden units work as internal representations for the inputs, and outputs are generated from these internal representations rather than by the original example pattern. Thus, an appropriate output pattern can be generated from any input-output pattern by employing an adequate number of hidden units. There are currently no universal rules for selecting the number of hidden nodes and layers. These vary from problem to problem and are generally fixed after several trials with the network. A network may not get trained to the acceptable level of error with too few hidden nodes, whereas with too many hidden nodes, the network may work a bit better but not generalize well. It then becomes merely a look-up table and tends to increase training time and the size of weight matrices in the solution. Generally one hidden layer is enough for most problems, but for very complex, fuzzy and highly non-linear problems, more than one hidden layers might be required to capture the significant features in the data. The changing of interconnection patterns and the setting of weights that determine the strength of a connection is done by training the network to exhibit the correct behaviour. One of the most common training algorithms is known as the Generalized Delta Rule or back propagation Neural Network (BPNN) (Rumelhart et al, 1986). The present study uses Back Propagation algorithm for modeling wind interference problems. DEVELOPMENT AND VALIDATION OF ANN ALGORITHM Back-propagation learning algorithm is assumed to be composed of only three layers: input-hiddenoutput. The application of the Back propagation for training a network involves two phases. In the first (feed forward) phase, each input is weighted with an appropriate weight w (initialized to small random numbers, usually between -0.3 and +0.3) and the products are summed up at each neuron (node) of the network. This summation S of the weighted inputs at each neuron of the network is then modified by an activation or transfer function F, thereby generating an output signal O. A continuous, non-linear logistic or sigmoid (meaning S-shaped) transfer function is commonly used, mainly because it meets the differentiability requirement of the Back propagation algorithm. The sigmoid transfer function forces the output to lie between 0 and 1 as the neuron s net input (S) goes from negative to positive infinity. The summation is continued up to the output layer of the network, the outputs of each layer serving as inputs to subsequent layers. The transfer function (see Fig 1) is given by: F(S) = 1 (1+ e S ) (1) Fig. 1 Basic Neuron Model and the Feed Forward Phase

3 Fig. 2 Overall BPNN Architecture and the Back Propagation Phase In the second (Back propagation) phase, the error between output of the network and the training set is propagated backward through the network where it is used to adjust the weight according to the Back propagation algorithm. The algorithm makes a small adjustment to the strength of each connection in such a manner that each alternative reduces the total network error in the direction of the steepest descent of the error. This is called the gradient descent method. Derivatives of the error are calculated for the network s output layer and then back-propagated through the network until all the weights are adjusted and the sum squared error of the network is within acceptable limits. The back-propagation process is briefly described below and illustrated in Fig. 2. At the output layer, the error ( δ ) between the actual network output (say O r at the r th neuron) and the desired or training example output (say T r at the r th neuron) is calculated by multiplying the difference between T r and O r by the derivative of the transfer function F(S r )/ S r = O r (1-O r ). Thus, δ = (T r O r ){ O r (1- O r )} (2) r This error is back-propagated from the output layer, where it is used to adjust the weights of connections between the hidden layer and the output layer, according to the back-propagation algorithm as follows: r W qr = ηδ O q (3) r W qr (m+1) = W qr (m ) + W qr (4) where η is the training rate coefficient; δ is the error for neuron r in the output layer; O q is the value of the output for neuron q (hidden layer); W qr (m ) is the value of weight of connection from neuron q in the hidden layer to neuron r in the output layer at iteration m, before adjustment and W qr (m+1) is the value of weight at iteration m+1, after adjustment. The training rate coefficient (η) serves to adjust the size of the average weight change, and is typically set between 0.01 and 1.0. The larger this coefficient, the larger the changes in the weights and more rapid will be the learning. However, in some cases, larger training rates often lead to oscillation of weight changes and the model does not converge to a solution. Errors at the output layer are backpropagated to the hidden layers preceding the output layer and weight adjustments for the connections from the hidden layer to the input layer are made as follows: n δ = { q i= 1 δ W }{ O q (1- O q )} (5) i qi W pq = ηδ O p (6) q W pq (m+1) = W pq (m) + W pq (7) r

4 where δ q is the error for neuron q in the hidden layer; δ i is the error for neuron i in the output layer; W qi is the value of weight of connection from neuron q in the hidden layer to neuron i in the output layer; n" is the number of neurons in the output layer; O p is the value of output for neuron p (input layer); W pq (m) is the value of a weight from neuron p in the input layer to neuron q in the hidden layer at iteration m before adjustment and W pq (m+1) is the value of weight at iteration m+1, after adjustment. In practice a momentum term is frequently added to equation (6) as an aid to more rapid convergence in certain problem domain. The momentum takes into account the effect of past weight change. The momentum constant, β, determines the emphasis to place on this term. Momentum has the effect of smoothing the error surface in weight space by filtering out adjusted in the presence of momentum by: W pq (m+1)=ηδ O p +βw pq (m) (8) q The above steps are repeated for all training examples and the square of all the errors between the network and training examples outputs are added up. For a network trained on l examples, each having n outputs, the average mean square error E is calculated as follows: l n 1 2 E = ( T ij Oij ) (9) 2l j= 1 i= 1 where T ij is the i th output of the j th training example set; O ij is the network output at the i th output neuron of the j th training example set. The entire training process is repeated until the behaviour of the network is satisfactory, i.e., the average mean square error E is less than or equal to a user-defined threshold. After being trained on a large number of cases, a network will not only be able to map the input and output patters of the training examples, it will also perform well on many cases which were not present in the training set, i.e. it will display some abilities to generalize. A software (using C programming language) has been developed for this algorithm. The software allows selection of number of neurons in the input layer, number of hidden layers, number of neurons in each hidden layer, and number of neurons in output layer. It also allows selection of learning rate parameter and momentum factor. Software generates random numbered weights (as per specified range) depending upon the architecture of the network. ANN MODELING FOR INTERFERENCE STUDIES Extensive wind tunnel experiments remain the source of knowledge on interference effects on low buildings. This involves detailed parametric studies on scaled building models in the wind tunnel, incorporating a large number of variables. An experimental programme is quite demanding in terms of time and resources. The complex nature of the problem and large number of variables involved make it impossible to test all building interference situations. Till today no analytical approach or even mathematical model based on experimental results are available to predict quantitatively, the extent of interference. This shows that the wind tunnel testing is the only solution to study the interference effect on low buildings. To economise on the effort, there is always a need to explore the ways for predicting wind loads including interference effects from the comparatively reduced test programme. Artificial neural network (ANN) representations are capable of developing functional relationship from discrete values of input-output quantities obtained from computational approaches or experimental results. This generalization makes it possible to train a network on a representative set of input-output examples and get good results for new input without training the network on all possible input-output examples. Data obtained from wind tunnel testing for interference effects (IF) on gable roof building has been used for training the network. The interference factor (IF) for worst design pressure coefficients independent of wind direction for each zone of the roof on the building for single building interference has been taken as output parameter of the neural network. Locations of interfering building(s) have been considered as input parameter. Training of the neural network is carried out by the data sets, which consist of some selected locations of interfering building (s) and values of IF for Cpq for each zone of the roof at those locations. The trained network is then expected to predict the IF for Cpq for each zone of the roof for locations of interfering building(s) not covered in the training data set. ANN APPLICATION FOR INTERFERENCE WITH A SINGLE BUILDING Extensive wind tunnel testing has been carried out to study the effect of single building interference on the 25º roofed building with overhangs. Data obtained from this study has been used for training of the network. Training of neural network has been carried out for each zone of the roof. SELECTION OF NEURAL NETWORK ARCHITECTURE Neural network used for training for each zone of the roof consists of two hidden layers with an input layer and an output layer. Input layer has two neurons representing the input parameters, which are (x) and (y) coordinates of position of interfering building. Output layer has one neuron, which represents the Interference Factor (IF) for Cpq for the concerned zone for the corresponding position of interfering building. Each hidden layer consists of twenty six neurons.

5 Fifteen positions of interfering building have been selected for training of the neural network for each zone. The values of learning rate parameter (η ) and momentum coefficient (β) have been changed during the training of network. Training of the neural network has been started with a value of 0.05 for learning rate parameter and 0.50 for momentum coefficient. After some cycles of training, when the convergence of the network becomes slow, the values of these parameters have been increased in steps of Finally, the values of η and β converged to 0.35 and 0.95 respectively. Training of the network was carried out till the average mean square error of the network reduced to The network has been tested for additional fifteen interfering positions i.e., total thirty interfering positions of input data for each zone (Fig. 3). Correlation plots and Interference Factor contours for each zone have been shown in Figs. 4 to 19. Fig. 3(a) Location of different zones on building roof Fig. 3(b) Locations of Single Similar used for A. N. N.

6 Fig 4 Correlation Plot Between Experimental and ANN Predicted Values for Zone A for Single Similar Fig 5 Interference Factor (I F) Contours for Cpq Obtained by Experimental and ANN Predicted for Zone A due to Change in Position of Single Similar

7 Fig 6 Correlation Plot Between Experimental and ANN Predicted Values for Zone B1 for Single Similar Fig 7 I.F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone B1 due to Change in Position of Single Similar

8 Fig 8 Correlation Plot Between Experimental and ANN Predicted Values for Zone C for Single Similar Fig 9 I.F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone C due to Change in Position of Single Similar

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10 Fig 10 Correlation Plot Between Experimental and ANN Predicted Values for Zone D for Single Similar Fig 11 I. F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone D due to Change in Position of Single Similar

11 Fig 12 Correlation Plot Between Experimental and ANN Predicted Values for Zone E for Single Similar Fig 13 I. F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone E due to Change in Position of Single Similar

12 Fig 14 Correlation Plot Between Experimental and ANN Predicted Values for Zone F for Single Similar Fig 15 I.F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone F due to Change in Position of Single Similar

13 Fig 16 Correlation Plot Between Experimental and ANN Predicted Values for Zone G for Single Similar Fig 17 I.F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone G due to Change in Position of Single Similar

14 Fig 18 Correlation Plot Between Experimental and ANN Predicted Values for Zone H for Single Similar Fig 19 I.F. Contours for Cpq Obtained by Experimental and ANN Predicted for Zone H due to Change in Position of Single Similar COMPARISON OF ANN PREDICTIONS WITH between ANN predicted values and experimental EXPERIMENTAL VALUES values of IF for Cpq for various zones of the roof and For each zone of the building roof, training of the their contours are plotted in Figs.4 to 19. It can be neural network has been performed separately. seen from these correlation plots that most of the Prediction of the values of IF for Cpq for each zone is predicted values are found to be very close to the then carried out through the trained network for all corresponding experimental values. Contours of the positions of the interfering building. Correlation plots values of IFs for Cpq predicted by ANN follow

15 closely the pattern as obtained experimentally for all the zones. Moreover, the contours of predicted values of Cpq show a generalized trend of variations, as ANN predictions attempt to map all the cases of input-output. CONCLUSION It can be concluded from the results of these comparisons that almost 50% reduction in the experimental work can be achieved by using the neural network modeling for interference studies in low buildings. ACKNOWLEDGEMENT The work presented in this paper is part of the Ph. D. Thesis of the first author awarded in the Department of Civil Engineering I. I. T. Roorkee, Roorkee, India. REFERENCES 1. Vanluchene, R.D., and Sun, R. (1990), Neural network in structural engineering, Microcomputers in Civil Engineering, Vol. 5, pp , Elsevier Science Publishing Co. Inc., 655 Avenue of the Americas, New York. 2. Khanduri, A.C., Bedard, C. and Stathopoulos T., (1995), Neural network modeling of windinduced interference effects, Proc. 9 th Int. Conf. on Wind Engineering, New Delhi, India, pp Deshpande, J.M., Mukherjee, A. (1995), Artificial neural network in modeling structural stability of compression members, Proc. International Conf. on Stability of Structures, ICSS Girma, T.B. (1998), Application of artificial neural network for determination of wind pressure distribution in buildings, M.E. thesis, University of Roorkee, Roorkee, India. 5. Kwatra, N. (2000), Experimental studies and ANN modeling of wind loads on low buildings, Ph. D. Thesis, Department of Civil Engineering, University of Roorkee, Roorkee. 6. Chen, Y., Kopp, G.A., Surry, D. (2003), Prediction of pressure coefficients on roofs of low buildings using artificial neural networks, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 91, pp Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986), Learning internal representations by error propagation, Parallel Distributed Processing: Explorations in the Microstructures of Cognition, Vol. 1: Foundations, MIT Press, Cambridge, MA, USA.