IEEE Region 10Conference. T e m - 11th 13th November, 1992 Melbourne. Australia ADAPTIVE TRAINING OF ARTIFICIAL NEURAL NETWORK S.A. Khaparde Parnerkar N.S. Hiremath Indian Institute of Technology Bombay-400 076, India A. B.J. Sheshaprasad university College of Central Queensland Rockhampton Q 4702 Australia Abstract Adaptive training of neural network for non-stationary process is reported in the framework of multilayer perceptron model using Back Propagation (BP) algorithm. The error introduced by small changes in system parameters is reflected to adapt the changes in the converged weight matrix. The error is minimized using constrained optimization method like Gradient Projection Method (GPM). The method is applied for harmonic prediction in voltage waveform. The results for sample system are discussed. I. Introduction Multilayered preceptron model has established itself as a efEeck ive tool for large variety of applications owing to its BP error algorithm [l]. Occurrences of slowly varying non-stationary processes are common in real life. Ref. [21 reports how adaptation of neural network can incorporate such process, without training the network all over again. The overall error is minimized using Reduced Gradient Method (RGM). The objective function is augmented using linearization process. The appgication reported in Ref. [2] is for forecasting the load which exhibits adaptive nature. In this report Gradient Projection Method (GPM) is employed for error minimization. BP algorithm has been reported for harmonic The adaptive nature of the prediction is explored prediction [ 3 ] . and comparison of RGM and GPM is reported here [4,5]. 0-7803-W9-2192 $3.00 0 1992 IEEE 525 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:25 from IEEE Xplore. Restrictions apply. 11. Problem Formulation Consider a 2-layer network in N patterns using BP algorithm, where dimension of x(i) and d(i) is assumed as I and 1 respectively. Let h be the number of neurons in hidden layer. Let W be the weight matrix between the input and the hidden layer and V be the vector between the hidden layer and the output layer. For a given input, the corresponding output produced is given by constitutes the output of the hidden layer with the sigmoidal function f (x) = l/(l+e-x 1. W(N) and V(N) are the weight matrices and are obtained by minimizing the error U (3) The problem can be defined as Given W(N) and V(N), the N data s_e s and x(N+l), d(N+l mine W(N+1) and V(N+l) such that E(N+l) is minimized. , deter- W(N+l) = W(N) + O W V(N+1) = V(N) + AV Y(N+1) = f(VT(N)u + AVTu) defining , N A E =~ N Z X% j k b jk N hwjk +Z k=l bVk bVk 526 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:25 from IEEE Xplore. Restrictions apply. (7) and constraint equation c l = zT a where, Z 111. = [AWvec A?IT GPM Algorithm [SI GPM employs the projection of- vf(Zi) given by eq. (7) on the constraint eq. (8). The algorithm is: 0. 1. 2. Start with initial feasible solution 2 Set i = 1 Evaluate the projection matrix Pi pi = I - G ( G ~~ 1 - lG~ where G = gradient of the constraint given by eq. (8) 3. Find the search direction Si as Si = -Pi vF(Zi) 4. If IISilI 5. Update 6. Go to 2. fE then stop c 2 as Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:25 from IEEE Xplore. Restrictions apply. IV. Application and Results [ 6 ] The training sets are generated by adding known harmonics amplitudes to fundamental signal. 16 sample points on voltage waveform are considered in one cycle. Large number of training sets over entire operating range are considered. ( N + 1 ) th pattern is for adaptation lying outside the operating range. Various values of gain and momentum terms were attempted. Accuracy of RGM and GPM method was tested against training the network with ( N + 1 ) patterns afresh. The mean error for RGM 0.89 x 10” and for GPM, 1.9 x lo’*. The errors are within specified limits. The results showing the harmonic amplitude obtained by different methods are displayed on the graph in Figure shown below. 0.80 COMPARISON BETWEEN DIFFERENT METHODS - .e--- D 4 I I I - 0.60 - - c z C z 3 n a 0.40 I k- CL 0 W 0 ’> 2 0.20 f C D - A 2 a B PESULTS RESULTS RESULTS RESULTS WITH WITH WITH WITH TRAINING 6 PAlTERNS TRAINING 7 PATTERNS GRADIENT PROJECTION MRHOD(GPM: REDUCED GRADIENT METHOD(RGM) 1 0.00 1 0 I I I I I I I I I 1 I I 2 I I 1 I I 1 1 4 NO 1 1 I I OF PATTERNS 1 1 % I I I 6 I ----* I I r I r I 1 11 8 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:25 from IEEE Xplore. Restrictions apply. v. Conclusions As predicted in ref. [2] it is confirmed that RGM performs better than GPM. The feasibility of adapting the network for nonstationary process is established. This concept is closely related with the learning theory where the network would respond to varying environment automatically. However, it is observed that repetition of process increases the error. References 1. D. Rumelhart, G.E. Hinton and R.J. Williams, "Learning Internal Representation by Error Back Propagation," Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. I, MIT Press, 1986. 2. D.C. Park, M.A. El-Sharkawi and Robert J. Marks, "An Adaptively Trained Neural Network," IEEE Transactions on Neural Network, V o l . 2, NO. 3 , May 1991, pp 334-345. 3. R.K. Hartana and G.G. Richards, "Harmonic Source Monitoring and and Identification Using Neural Networks," IEEE Transactions on Power Systems, V o l . 5, No. 4, November, 1990. 4. S.S. 5. Richard L. Fox, "Optimization Methods for Engineering Design," Addison-Wesley Publishing Comppny, f971. 6. Abhay Parnerkar, '"Adaptive Training of Artificial Neural Network to Predict Harmonics in Power System," M.Tech Dissertation, E.E Department, IIT Bombay, Feb. 1992. Rao, "Optimisation Theory and Applications," Wiley Eastern Limited, 1984. Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:25 from IEEE Xplore. Restrictions apply.
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