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1590 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 B. The Design of Membership Degree BP Neural Network The paper adopted a three layers BP network to build the membership degree BP network for water quality assessment. In the structure, the network has one input layer one output layer and one hidden layer. The output layer can expressed water quality classification by one neuron, actual testing parameters are six, so input layer has six neurons, hidden layer has three neurons [9]. In order to make the assessment more objective and certain, this paper puts the membership degree of fuzzy mathematics into BP network. The membership degree BP network model is built on combining the fuzzy system and neural network in series. In the series connection, output of neural network is input of the fuzzy system. Membership degree can be computed, then the exact and concrete water quality classification can be put out. The membership degree BP network for water quality assessment is shown as fig. 2. In the formula, abstand , for the classification of neighboring two water quality samples, the membership degree to every standard water quality classification of test sample can be computed by the formula (17). IV. THE PRINCIPLE OF BACK PROPAGATION NEURAL NETWORK MODEL A.. The Model of BP Neural Network Algorithm According to the point of mathematics, BP algorithm is a generalized function convergence numeric method, and it has training and testing processes. The whole training process includes forward and back propagation. After being built, the BP network model is tested by other samples to testify the effectiveness and validity of the model. The results show that the BP network model and its algorithm are effective. The algorithm of BP neural network is shown as in fig.3. Figure 2. The framework of BP neural network combining membership degree According to fuzzy mathematics theory, the standard water quality classification 1-5 as co domain can be defined. For n assessment parameters of some standard water quality classification, we suppose that the membership degree to itself is zero, so a fuzzy subset E can be gotten. We suppose that the membership degree to other is zero, subset F can also be gotten. In here, the membership degree to standard water quality classification for n assessment parameters of other water quality samples must belong to[0,1] , and building fuzzy subset A . Therefore, the problem of assessing water quality sample transforms into computing the membership degree to two neighboring standard water quality classification. In this paper, the membership function is built as following formula. ⎧1 x = a ⎪ ux ( ) = ⎨1 − f( x) a< xining of BP Neural Network The whole network training process includes forward propagation and error back-propagation, the training process are shown as followed. 1) Assignment the weighs w_ xh , w_ hy between nodes and need threshold u_ h, u_ y , the assigned values are Nonzero Random initial valuebetween (-1,1). 2) Inputting input vector X of one training sample and target output vector T . 3) Computing output vector Y . Computing output vector H of hidden layers: © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1591 ∑ neth = w _ xhih⋅X i −u _ hh ⎫ ⎪ i ⎬ Hh = ( neth) = 1 1+ exp( −neth) ⎪⎭ Computing output vector Y of output layers: net j = ∑ w _ hyhj ⋅Hh −u _ y ⎫ j ⎪ h ⎬ Yj = ( netj) = 1 (1 + exp( −netj)) ⎪ ⎭ 4) Computing the difference mountδ δ j (18) (19) Computing difference mount of output layers δ = Y (1 −Y )( T − Y ) (20) j j j j j δ Computing difference mount of hidden layers h : δ = H (1 −H ) ∑ w_ hy δ (21) h h h hj j j 5) Computing correction mount of weigh dw , and correction mount of threshold du . Computing weigh correction mount of output layers dw _ hy , correction mount of threshold du _ y : dw _ hyhj = δ jH h ⎫⎪ ⎬ (22) du _ y j =−ηδ j ⎪⎭ Computing weigh correction mount of hidden layers dw , correction mount of threshold du : dw _ xhih = ηδh X i ⎫ ⎬ (23) du _ H h =−ηδh ⎭ 6) Updating weigh mount w_ hy , and threshold u_ y. Updating weigh mount of output layer w_ hy and threshold u_ y: w _ hyhj = w _ hyhj + dw _ hyhj ⎫⎪ ⎬ (24) u_ yj = u_ yj + du_ yj ⎪⎭ Updating weigh mount of hidden layer w_ hy and threshold u_ y: w _ xhih = w _ xhih + dw _ xhih ⎫ ⎬ (25) u_ hh = u_ hh + du_ hh ⎭ (c) The testing of BP neural network After being building, the character of model must be tested by using the samples which are not used in building the model, so that the Correctness and Practicality of the model can be verified. The computing format of the testing process is showed as followed. 1) Adopted the stable Weight matrices after trained w_ xh, w_ hy and Threshold vector u_ h, u_ y. 2)Input vector X of testing samples. 3)Computing output vector Y . Computing the output vector of hidden layer H : ∑ neth = w _ xhih⋅X i −u _ hh⎫ i ⎪ 1 ⎬ Hh = f( neth) = ⎪ −neth 1+ exp ⎪⎭ (27) Computing the output vector of hidden layer Y : net j = ∑ w _ hyhj⋅H h −u _ y ⎫ j h ⎪ 1 ⎬ (28) Yj = f( netj) = −net ⎪ j 1+ exp ⎪⎭ V. THE EXPERIMENT AND ANALYSIS OF BP NEURAL NETWORK FOR WATER QUALITY ASSESSMENT In the learning process of network, some standard water quality classification is adopted in learning samples. With considering that the range of activation function is[0,1] , and water quality classification is from the first class to the fifth class, so the five water quality classifications are only part of the whole range, and no attaching the limited values 0 and 1. In this paper, target outputs are 0.1,0.3,0.5,0.7,0.9 , and the output represents No.1-5 water quality classifications. As the most important parameters in debugging the BP network, learning rate η = 0.68 , Impulse coefficient α = 0.5 , then the network can be trained after 1600 iterations. (a) Errors curve of learning process (b) Testing result curve of network for some samples Fig. 4 The learning process curve of the network © 2013 ACADEMY PUBLISHER
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Journal of Computers ISSN 1796-203X
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Corn Moisture Measurement using a C
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Page 168 and 169: 1540 JOURNAL OF COMPUTERS, VOL. 8,
Page 261: Call for Papers and Special Issues
Page 264: (Contents Continued from Back Cover
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