CHAPTER3FORECAST

The boltzmann machine without learning and the

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Unformatted text preview: he constraints and the quantity to be maximised or minimised. • Human memory operates in an associative manner. If it hears only a portion of a known song, it can then produce the rest of the song. A recurrent net operates in the same manner. If an input vector has, for example, half of the data and is presented to the net, the net is sometimes capable of producing the correct output vector. • The bidirectional associative memory (BAM) is hetero-associative; that is, it accepts an input vector on one set of neurons and produces a related, but different, output vector on another set. The BAM produces correct 62 outputs despite corrupted inputs. Also, adaptive versions can be abstract, extracting the ideal from a set of noisy examples. • The adaptive resonance theory (ART) has the ability to learn new patterns while preventing the modification of patterns that were learned previously. The mathematics behind ART are complicated and many people have found the theory difficult to understand. In practice, only one or two hidden layers are used in feed-forward multilayer perceptron nets. The net can be trained by starting with both hidden layers. If one of the layers is removed, for example to look at the viability of reducing the sensitivity of the net, the process is called layer pruning. The number of neurons to be used in hidden layers is not known in advance. One possible approach is to construct a neural net with an excessive number of neurons in each hidden layer. When, during the training process, two neurons in the same hidden layer convey the same information, one of the two neurons must be removed. Neurons in the hidden layer(s) whose outputs are approximately constant for all training examples must also be removed. This process of removing neurons is called neuron pruning. • Generalisation is the ability of the net to be insensitive to variations in the input data during training and to recognise the pattern in the data despite noise and distortion. • O ver-training is almost the opposite of generalisation. If the net is overtrained, then small variations in the input data can result in the net’s output varying significantly from the actual value. For the substation load forecasts, most of the models were over-trained and again no further attempts were made to continue with neural networks. [42] 63 3.7 CONCLUSION The electrical load model defines the relationship between the key load points of the transmission load forecast. The different forecasts successfully integrate the different factors and now the results can be checked for consensus (balance by the balancing algorithm), (See Chapter 4). 3.8 REFERENCE 1) H.L. Willis , Spatial Electric Load Forecasting, Marcel Dekker, New York, 1996. 2) C.W. Gellings , Demand Forecasting In The Electric Utility Industry, PennWell Publishing Company, Oklahoma, 1996. 3) J.T. Joubert, Forecasting Electricity Demand In The Republic Of South Africa, The Graduate School of Business University of Cape Town, March 1971. 4) Makridakis, Wheelwright and Mc Gee , Forecasting Methods and Applications, John Wiley & Sons, New York, 1983. 5) “Growth Curve Modeling”, http://www.bioss.sari.ac.uk/smart/unix/mgrow , 2002. 6) A. Tamimi and Z. Kodah , “Energy Consumption in Jordan”, Energy Vol. 17, No. 11, pp. 1013 – 1017, 1992. 7) P. Harel and J. Baguant, “A Growth Prediction For Electrical Energy Consumption in Mauritius”, Energy Vol. 16, No. 4, pp. 707 – 711, 1991. 8) M.A. Kaboudan , “An Econometric Model For Zimbabwe’s Future Electricity Consumption”, Energy Vol. 2, pp. 75 – 85, 1988. 9) J.A. Nelder, “The Fitting of a Generalization of the Logistic Curve”, Biometrics, pp. 89 – 616, March 1961. 10)C.R. Rao, “The Theory of Least Squares When The Parameters Are Stochastic and Its Application to The Analysis of Growth Curves”, Biometrika, (1965), 52, 3 and 4, pp. 447 - 458. 11)R.F. Potthoff and S.N. Roy, “A Generalized Multivariate Analysis of Variance Useful Especially for Growth Curve Problems”, Biometrika, (1964), 51, 3 and 4, pp. 313 - 326. 64 12)J Petree , “Chaos Theory ”, http://www.wfu.edu/~petrejh4/. 13)“Chaos Theory ”, http://www.webslave.dircon.co.uk/alife/choas.html. 14)J. Kemp , “New Methods and Understanding in Economic Dynamics? An Introductory Guide to Chaos and Economics”, Economics Issues, Vol. 2 Part 1, March 1997, pp.1 - 26. 15)R.M. May, “Simple mathematical models with very complicated dynamics” Nature, Vol. 261, June 10 1976, pp. 459 - 467. 16)P. Mirowski, “From Mandelbrot to Chaos in Economic Theory”, University of Notre Dame, pp. 289 - 307. 17)Glover & Sarma , Power System Analysis & Design , PWS Publishing Company, Boston, 1994. 18)R. Zivanovic, “Load Regression-Based Short Term Load Forecasting”, Journal of Intelligent and Robotic Systems 31 2001, pp. 115 – 127. 19)J. E. Beasley, “OR-Notes on Forecasting”, http://graph.m s.ic.ac.uk/jeb/or/forecast.html. 20)R. Bleloch , “Load Demand Foreca...
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