【正文】 元素 代 ikW 表與輸入為 )(mkx 的連接權(quán)重從單元 i 到 層 m ， mL 是該層的輸入的數(shù)目，和上標表示矩陣或向量換位 矢量 )(miw 可被組合在一個單一的矩陣 )(mW 如下所示： ? ?? ?? ?? ? ??????????????????????????????TmLmTmTmTmmWWWWW)()()()(1)(　　　　　?。常? （ A４） 單元 i 的輸出的第 m 層上被定義為： )( iiimi bhfv ??）（ （ A5） 其中， f( ? )是一個非線性函數(shù)， ib 是 單位偏差 。在本文中， XVX ?? )0()1( 網(wǎng)絡(luò)的輸入。 因此，一個 M1 層妮輸入 FFNN 具有式（ A8）在 m = M 的評 估 ，即，存在一個輸出 矢 量 )(MV 和 各自輸入矢量 x的輸出。 參考文獻： [1] IEEE Std. ~. IEEE Guide f o r Protective Relay Applications to Power Transformers. [2] Sonnemann, W. K., Wagner, C. L., Rockefeller, G. D., Magizing Inrush Phenomena in Transformer Banks, AIEETransactions, Vol. rr, part. 111, pp 884892. Oct. 1958. [3] Blackburn, J. L. Protective Relaying. Principles and App h z t i o n s , Elect. Eng. and Electronics Series, Marcel Dekker, INC, NY, 1987. [4] Applied Protective Relaying Reference Book, Westinghouse Electric Corporation, Relay Instrument Division, 1976. [5] Hayward, C. D., “ HarmonicCurrentRestrained Relays for Transformer Differential Protection,” AIEE Transactions, Vol. 60, 1941, pp. 377382. [6] Sharp, R. L., Glassburn, W. E., “A Transformer Differential Relay with Second Harmonic Restraint,” AIEE Transactions ,Vol. 77, Dec. 1958, pp. 913918. [7] Phadke, A. and Thorp, J. Computer Relaying for Power Systems, John Wiley amp。 1979 年 從玻利瓦爾大學獲工程師學位 ， 1982 年 從委內(nèi)瑞拉中央大學 獲得 碩士學位。 1991 年 1 月取得 華盛頓州立大學電子工程和計算機科學學院的博士學位 。 他的研究包括房屋系統(tǒng)，電力系統(tǒng)，繼電保護，節(jié)能住宅和太陽能熱優(yōu)化分析 。他目前是華盛頓州立大學電子工程與計算機科學學院助理教授 ， 他 從事 神經(jīng)網(wǎng)絡(luò)和 VLSI 設(shè)計 的 研究。他是 Boris Kidric 研究所 “ 的 系統(tǒng)程序員， 1984 年至 1986 年，是貝爾格萊德的塞爾維亞科學和藝術(shù)學院 的 研究的科學家。我們有一些對本文提出的意見和問題。 3正如作者所指出的，計算要求的 FFNN 實現(xiàn) 數(shù)據(jù) 是非常大的，即使是單相變壓器。 參考 ； [A] , , , A StandAlone Digital Protective Relay for Power Transformers, IEEE Transactions on Power Delivery, Vol. 6, No. 1, January 1991, pp. 85 95. L. G. PQrez, A. J. Flechsig, J. L. Meador, 2. Obradovid (School of Electrical Engineering and Computer Science, W. S. U., Pullman, WA) 作者感謝 讀 者 對 本文興趣并提出寶貴意見。這樣做是有意向的訓練網(wǎng)絡(luò)，這是能夠區(qū)分故障電流具有很高的二次諧波分量和勵磁涌流 。 3在這一點上 ， 我們與 讀 者 意見一樣 。如圖 1 所示 ， 小缺圓代表處理單 元。 and a I output for the other cases (the authors do not insinuate the method can be used to do all the protection function, since additional research will be needed to prove it). Vectors pj were built from the cases in the following way (see Appendix 2 for the definition of these vectors). Suppose the first of the cases’ signals is characterized by the sequence: ? ?1 1 221 , iiiii k ??????? （ 1） this means, a sequence of 112 samples. The first vector p 1 elements corresponds to the first 12 samples of i, the vector p2 entries are the 12 samples from i2 to i13 and so on, until pleting the first 100 columns of example matrix P defined in eqn. (A11) and (A13). The same process was repeated for each cases’ signal until having an example matrix of 936 columns (the number of examples, ne). This matrix was built such that the first 600 examples correspond to inrush examples (desired output=O), and the other 336 examples correspond to faults (desired output=l). Since the FFNN has only one output, matrix D became a horizontal vector of 936 elements, the first 600 entries are 0’s and the other 336 are 1’s. In practice, a target tolerance of was used, meaning that the work was trained to produce a response of or greater to represent one class and or less to represent the other class. This is necessary because the nature of the nonlinear squashing function is such that it can never assume the precise values of or . . Training Process Once the training matrices P and D were defined, the backpropagation algorithm was applied to the problem. The MATLAB Neural Network Toolbox [24] was used for such a purpose. Function TRAINBP was used with sigmoid transfer functions and a learning rate variable between and . The admissible error (sum of square errors in an epoch) was , for which it was necessary to present the training matrices between 200 and 600,000 times, depending on the work size (number of units) and the learning rate employed. 4. IMPROVING THE NETWORK . Network Testing and Pruning As mentioned in section it is desired that the work be applied in a digital relay implementation. This implies a promise between speed and accuracy. As is well known, the FFNN classification time (the required time to produce an output given an input) depends on the number of units in the work, so it is very important to have the lowest number of units but without jeopardizing the quality of the classification. Figure 5 shows the architectures tested for this purpose. 。 Figure C1. Detailed scheme of the work shown in Figure 5e Manuscript received March 29, 1993 IEEE Transactions on Power Delivery, , No1, January 1994 TRAINING AN ARTIFICIAL NEURAL NETWORK TO DISCRIMINATE BETWEEN MAGNETIZING INRUSH AND INTERNAL FAULTS LUIS G. PEREZ ALFRED J. FLECHSIG JACK L. MEADOR ZORAN OBRADOVIC Member, IEEE Senior Member, IEEE Member, IEEE Member, IEEE School of Electrical Engineering and Computer Science Washington State University Abstract — A feed forward neural work (FFNN) has been trained to discriminate between power transformer magizing inrush and fault c