Acta Technica Corviniensis

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ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGacknowledgment, control and identification ofthe non-linear processes, etc. These propertiesare obtained through learning, such as in thecase of the physiological systems. Specifictraining algorithms could be used in order todetermine the values of those weights/ercentages who represent the solution to theproblems we solve by using the neuronalnetworks. The training algorithms could bedivided in two separate categories: supervisedinstruction methods and non-supervisedinstruction methods. In the case of thosemethods belonging to the first category, theinstruction is called supervised because weknow both the input and the output sizes. Thesystem is shaped up with the help of a neuronalnetwork and the weight amongst the layers haverandom values. By comparing the input sizesthat we already know and those of the output ofthe network (after we have used the input dataset), we get an error signal. This signal helps usestablish and adjust the weights amongst thelayers of the network, in order to diminish aperformance criterion [8].Figure 1 Classic perceptron modelfor neuronal networksFigure 2 Supervised instruction mechanismThe non-supervised learning methods do notuses already-known input sizes during thetraining stage of the neuronal network, by usingonly the input sizes for adjusting the weights.Thus, we can establish some input categorieswho correspond to some inputs from the dataset, or „winner take all” outputs – in this case,the output neuron who has the highest activitywins and turns active, meanwhile the others donot work. This method is called self-organisationand we could use it successfully in matters ofshape acknowledgement.a) b) c)Figure 3„Feed forward” neuronal networks topologiesa), b) and „feedback” neuronal networks topology c)According to this topology, the artificialneuronal networks could be classified in twocategories - „feedback” and „feed forward”. Inthe case of a „feed forward” network theneuronal output is sent to other neurons who donot receive any information from the inputneurons from the surface layers - Figure 3 a) andb).NEURONAL NETWORKS USED FOR SIGNALPREDICTIONThe design of the linear prediction neuron isdescribed in Figure 4. The network is made of alinear active neuron and the input receives thelast five values of the useful signal x(t) - thissignal must be predicted [4], [7].We write the matrix P,[ x( t) x( t −1) x( t − 2) x( t − 3) x( − 4)]p = t ,and the five delay values of the x(t) signal, whoare going to be represented at the input of theneuronal network. The matrix and the values aregoing to represent the data we need for thesupervised training, by using the Widrow-Hoffalgorithm. This algorithm decreases the sum ofthe square errors between the output and therequired value, and establishes the weight vectorwho is able to solve the problem..Figure 4 Linear prediction neuron542008/ACTA TECHNICA CORVINIENSIS/Tome I
ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGFigure 5 The proposed sinusoidal signal(blue) and the network predicted signal (red)We consider a sinusoid signalx() t = 0 .5 + sin( 2⋅π⋅t)- in Figure no. 5 it iscoloured in blue. The learning ratio of thetraining algorithm is η = 0. 1 , considering that itis constant during the training process. Thenetwork turns active and the training algorithmis used for a period of 200 steps. We could seethat after about 100 repetitions the network isable to predict the signal we propose – Figureno. 5, where the red signal represents the outputof the neuronal network during the trainingprocess. Figure no. 6 describes the predictionerror - the difference between the real and thepredicted signal. This signal tends to reach 0after a certain time.Figure no. 7 describes the values of the simpleperception weights during the training process.The identification time of the process lastsaccording to the value we choose for thelearning ratio. If we want a faster identificationthen, the value must be increased, but the valueswe have estimated during the first stages reachimportant values. We could also use anothertraining method that should vary the learningratio throughout the process, for improving themethods.Figure 6 Prediction error between the realand predicted signalFigure 7 The evolution of the weights during thetraining processCONCLUSIONAll the neuronal networks could be made ofsimple processing elements, such as perceptionsor neurons, so they should make up some singlelayernetworks, or made of several elements andthey should make up some multi-layer networks.The „information” within all these networks isdistributed within the connection weightsamongst the different layers that make thenetwork. Studies have proven that theprediction of the neuronal networks signals isextremely effective.This paper work has described the linear neuronused for predictions, the training process, andthe results we had obtained. The network ismade of one neuron, according to the linearactive process, which has the last five inputvalues we have to predict.REFERENCES[1] DUMITRESCU, D., COSTIN, H. „Reţele neuronaleteorie şi aplicaţii” Editura Teora, 1996.[2] LJUNG, L. “System Identification” Theory for theUser Prentice Hall, Inc., Englewood Cliffs, NewJersey 07632.[3] LJUNG, L., SODERSTROM T. “Theory andPractice of Recursive Identification”, MIT Press,1983.[4] MOKTANI, M, MARIE, M. ”Engineering Applicationof Matlab 5.3”, Springer, 2000.[5] NARENDRA, K. S., PARTHASARATY, K.“Identification and Control of DynamicalSystems Using Neural Networks”, IEEETransactions on Neural Networks, vol. 1 nr. 11990, pag. 4-27.[6] TIRIAN G.O. „High speed neuronal estimator forthe command of the induction machine”2008/ACTA TECHNICA CORVINIENSIS/Tome I 55
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