智能地探測(cè)故障的電力變壓器 中英翻譯

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1、廣東工業(yè)大學(xué) 華立學(xué)院 本科畢業(yè)設(shè)計(jì)〔論文〕 外文參考文獻(xiàn)譯文及原文 系 部 機(jī)械電氣學(xué)部 專 業(yè) 電氣工程及其自動(dòng)化 年 級(jí) 2006級(jí) 班級(jí)名稱 06本電氣工程及其自動(dòng)化〔1〕班 學(xué) 號(hào) 1060946 學(xué)生姓名 何東太

2、 指導(dǎo)教師 張亞婉 2021 年6月 一種新型能智能地探測(cè)故障的電力變壓器 摘 要 本文提出了一種智能神經(jīng)網(wǎng)絡(luò)〔INNS〕的變壓器故障診斷方法。INNS自動(dòng)協(xié)調(diào)網(wǎng)絡(luò)的參數(shù)，把權(quán)值和神經(jīng)網(wǎng)絡(luò)的斜線段聯(lián)系起來，以到達(dá)基于遺傳算法那么的最好模型。INNS可以識(shí)別溶解在變壓器油中的氣體和相應(yīng)的故障類型之間的復(fù)雜聯(lián)系，利用全球?qū)z傳算法那么的研究和神經(jīng)網(wǎng)絡(luò)的高度非線性映射。INNS的提議已經(jīng)在臺(tái)灣電力公司接受測(cè)試，診斷記錄并和人工神經(jīng)網(wǎng)絡(luò)〔ANNS〕進(jìn)行比擬。測(cè)試結(jié)果肯定了I

3、NNS，它有很高的診斷精確性和比ANNS需更少的學(xué)習(xí)時(shí)間。 1． 介紹 分析溶解氣體〔DGA〕的方法已經(jīng)被廣泛應(yīng)用于因變壓器油的絕緣惡化而產(chǎn)生溶解氣體的有效解釋。對(duì)變壓器油所溶解的H2 ,CH4,C2H6,C2H4,C2H2,CO,CO2氣體濃度進(jìn)行分析。DGA技術(shù)可根據(jù)溶解氣體的濃度，產(chǎn)生速度，特殊氣體的比率和所探測(cè)到總的可燃?xì)怏w來決定變壓器的運(yùn)行條件。實(shí)際上的診斷還必須考慮令變壓器產(chǎn)生溶解氣體的其他可能，例如，廠商，變壓器大小，油的體積，產(chǎn)生氣體的速度，安裝歷史和環(huán)境因素。因此有歷史性的診斷記錄對(duì)于未來同樣時(shí)間的診斷是很重要的。 盡管能有效地被廣泛使用，IEC/IEEE DGA的編碼

4、是根據(jù)經(jīng)驗(yàn)所得的結(jié)果。此外，結(jié)合所有的故障類型的可能編碼，DGA的方法并不能提供一個(gè)完整的對(duì)象和正確的根據(jù)。因此，并不能肯定診斷的結(jié)果正確性，而診斷專家必須最后決定可能的故障。 模糊專家系統(tǒng)已經(jīng)被用于變壓器起初故障的診斷。診斷結(jié)果是允許的，但是，模糊專家系統(tǒng)并不能從之前的診斷結(jié)果中學(xué)習(xí)，因?yàn)殡`屬函數(shù)和診斷規(guī)那么是由實(shí)際經(jīng)驗(yàn)或誤差試驗(yàn)所決定的。圍繞著模糊專家系統(tǒng)的缺點(diǎn)，為了能在變壓器故障診斷中直接從訓(xùn)練數(shù)據(jù)中獲得資料，開展了能夠自學(xué)的模糊診斷系統(tǒng)。 人工神經(jīng)網(wǎng)絡(luò)〔ANNS〕被方案用來應(yīng)付變壓器故障診斷，由于它們的精確性和在數(shù)字模型問題上的效率以及在實(shí)際運(yùn)用中的內(nèi)部故障誤差。ANNS能通過從新

5、獲的樣本增加訓(xùn)練而取得新的經(jīng)驗(yàn)。ANNS的訓(xùn)練通過一個(gè)誤差反向傳播的運(yùn)算法那么，能有很好的診斷能力。然而，某些問題，例如局部收斂和網(wǎng)絡(luò)結(jié)構(gòu)的決定以及控制參數(shù)〔學(xué)習(xí)速率和動(dòng)量常數(shù)〕，在ANNS變成一個(gè)可用工具時(shí)必須要解決。 因?yàn)榈湫偷乃褜た臻g時(shí)常持有局部極小性，梯度下降取決于誤差反向傳播技術(shù)，可能會(huì)淤塞這些潛在當(dāng)時(shí)最適合的解決方法，減少了ANNS的性能。遺傳算法那么是一個(gè)平行結(jié)構(gòu)和一個(gè)隨機(jī)程序最正確化運(yùn)算法那么，這些可以同時(shí)決定所聯(lián)系的權(quán)值和神經(jīng)網(wǎng)絡(luò)系統(tǒng)的偏移量，從而防止梯度下降的限制。 2． 神經(jīng)網(wǎng)絡(luò) 電力變壓器故障診斷的神經(jīng)網(wǎng)絡(luò)是由三層前向傳播結(jié)構(gòu)組成的，它們?yōu)檩斎雽?，隱含層，和輸出層

6、，如圖1所示。每一層的節(jié)點(diǎn)從前一層接收輸入信號(hào)和輸出給后面的層。輸入層的節(jié)點(diǎn)接收一批從外系統(tǒng)產(chǎn)生的信號(hào)和由權(quán)值鏈路直接遞送輸入數(shù)據(jù)到隱含層的輸入點(diǎn)。接下來計(jì)算，寫在下方的n,h,和k分別表示輸入層，隱含層，輸出層的節(jié)點(diǎn)。剩余的輸入網(wǎng)被定義為收入信號(hào)的權(quán)值的總數(shù)減去一個(gè)基值。隱含層的輸入節(jié)點(diǎn)h，neth，表達(dá)如下： 其中yn是輸入層的節(jié)點(diǎn)n的輸出；whn表示從輸入層的節(jié)點(diǎn)n到隱含層的節(jié)點(diǎn)h所連接的權(quán)值，是隱含層的節(jié)點(diǎn)h的基值。 節(jié)點(diǎn)h，yn的輸出，在隱含層是fh( neth)。S 傳遞函數(shù), 時(shí)常在非線性映射中用,被選作激活功能, 隱含層的輸出通過其它所整定的

7、連接權(quán)值而遞送到輸出層的節(jié)點(diǎn)。輸出層的輸出節(jié)點(diǎn)k也可以由以下方程表達(dá)： 其中是輸出層節(jié)點(diǎn)k的基值。這個(gè)參數(shù)〔連接權(quán)值和偏移量〕在神經(jīng)網(wǎng)絡(luò)能產(chǎn)生所期望的輸出前，必須要經(jīng)過學(xué)習(xí)過程。所歸納數(shù)據(jù)規(guī)那么是用來通過將節(jié)點(diǎn)誤差函數(shù)減到最小來調(diào)整權(quán)值： 其中dk表示節(jié)點(diǎn)k所期望的輸出，yk是輸出層的節(jié)點(diǎn)k計(jì)算輸出。 為了通過一個(gè)梯度下降技術(shù)將 E 減到最少，重量 wkh 被反復(fù)的更新： 其中i表示重復(fù)出現(xiàn)的數(shù)字；是學(xué)習(xí)速率，是動(dòng)量常數(shù)。 類似地，對(duì)于隱含層的節(jié)點(diǎn)h，權(quán)值可以由以下變換. 這些偏移量可以被看作是這些權(quán)值和其它因素以同樣方式反復(fù)改變

8、的，如上從〔6〕到〔11〕所描述的權(quán)值。 在輸出層的節(jié)點(diǎn)k的輸出yk暗含著網(wǎng)絡(luò)中可調(diào)的叁數(shù)， 在每個(gè)節(jié)點(diǎn)所連接的權(quán)值和偏移量。本文中，神經(jīng)網(wǎng)絡(luò)中所連接的權(quán)值和偏移量是由全球最正確的遺傳算法所決定的，以防止局部收斂叁數(shù)在ANNS中以梯度降落方式訓(xùn)練的影響。 3．遺傳算法法那么 所提出的遺傳算法法那么是用來調(diào)整網(wǎng)絡(luò)的參數(shù)，連接權(quán)值和神經(jīng)網(wǎng)絡(luò)的偏移量，如下所述。 3．1 不適當(dāng)?shù)墓δ? 讓 作為一個(gè)描繪個(gè)別的實(shí)驗(yàn)矢量， 這里的群數(shù)將會(huì)開展，其中I是群數(shù)的大小。 的元素是連接權(quán)值和神經(jīng)網(wǎng)絡(luò)的偏移量。一個(gè)不適當(dāng)功能是對(duì)每個(gè)個(gè)體進(jìn)行分配；然后，個(gè)體進(jìn)展依照不適當(dāng)功能值。

9、個(gè)體擁有越低的不適當(dāng)功能值就有越高的生存概率。 本文中，最小平方的錯(cuò)誤功能Ek是用來描繪INNS聯(lián)合. 的不適當(dāng)值的，它由以下定義： 其中是指INNS計(jì)算出的，〔4〕使用作的采樣矢量；p表示采樣矢量的總數(shù)；是輸出節(jié)點(diǎn)指出的相應(yīng)實(shí)際故障。 3.2 開頭 最初的實(shí)驗(yàn)矢量是從每個(gè)維數(shù)的合理范圍內(nèi)任意產(chǎn)生的，通過整定一個(gè)元素，就像：，這里，，其中表示統(tǒng)一分配任意變量的結(jié)果，范圍超過所給的最低值和上限值，聯(lián)系神經(jīng)網(wǎng)絡(luò)的權(quán)值和偏移量和。 3.3 新生的產(chǎn)物 通過無意地增加一個(gè)高斯隨機(jī)變異和在母實(shí)驗(yàn)溶液中增加一個(gè)標(biāo)準(zhǔn)的成比例的不適合值，每個(gè)母產(chǎn)生一個(gè)矢量，，例如： 其中表示

10、無意地增加一個(gè)任意變化的高斯值和偏離標(biāo)準(zhǔn)，通過以下方程式得出： 其中表示從〔12〕得出的不適合功能，與實(shí)驗(yàn)矢量相聯(lián)合，s是一個(gè)衡量因素而F是一個(gè)偏移量。產(chǎn)物的產(chǎn)生是基于最小的相關(guān)值。如果是與低值〔高值〕有關(guān)，實(shí)驗(yàn)溶液的產(chǎn)物的產(chǎn)生就接近〔遠(yuǎn)離〕現(xiàn)在的溶液。 3.4 競(jìng)爭(zhēng)和選擇 對(duì)于為了生存的競(jìng)爭(zhēng)在遺傳算法法那么是隨機(jī)程序。個(gè)別的2I，母液和新的產(chǎn)物，和為了從它們的不適合值中獲得，而與從其它單個(gè)里任意選擇的個(gè)體來競(jìng)爭(zhēng)。從每個(gè)個(gè)體中獲得的標(biāo)準(zhǔn)，由以下描繪： ＝0， 等 其中表示在的個(gè)體中的起點(diǎn)線，表示任意選擇的競(jìng)爭(zhēng)者的數(shù)字，指示個(gè)體中的不適合值，和是對(duì)手的不適

11、合值。另外，表示最大的完整事物少于或等于y，和是[0,1]之間的任意相同的實(shí)際數(shù)字。 在所有個(gè)體有了競(jìng)爭(zhēng)的經(jīng)驗(yàn)后，個(gè)體2I歸類于在它們相應(yīng)的值的下降命令。這時(shí)，第一個(gè)I個(gè)體和它們相應(yīng)的不適合值被選為下一代的新的母體。 3.5 停止規(guī)那么 當(dāng)滿足最大一代的停止規(guī)那么或者在〔12〕的E值的最小標(biāo)準(zhǔn)，進(jìn)化過程會(huì)停止而對(duì)于最小不適合值的解決方法被當(dāng)作最好的故障診斷INNS。另外，新生的產(chǎn)物重復(fù)以上的選擇步驟。 4. 數(shù)字測(cè)試 INNS作為臺(tái)灣電力公司的162.69kv變壓器目前所收集的630氣體的工具。故障類型通過不同的DGA方法，成組討論和對(duì)可疑的變壓器的內(nèi)部檢測(cè)，由臺(tái)灣電力變壓器

12、診斷系統(tǒng)確認(rèn)。 INNS由電腦Pentium III-600 的Turbo C 語言程序來運(yùn)行。有兩種情況，情況Ⅰ和情況Ⅱ，是設(shè)計(jì)用來評(píng)估所提供診斷程序的診斷精度。情況Ⅰ是用來選擇三種廣泛使用氣體的比率[4]-[6], 和，作為輸入變量。情況Ⅱ用作五種氣體的濃度，和，作為分別故障類型的輸入變量。 表1的目錄是INNS-Ⅰ和INNS-Ⅱ的參數(shù)。ANNS-Ⅰ與ANNS-Ⅱ是分別和INNS-Ⅰ與INNS-Ⅱ的參數(shù)一樣的，除了當(dāng)用作為梯度搜尋方式。為了這個(gè)開展的系統(tǒng)要估計(jì)兩種性能：對(duì)訓(xùn)練數(shù)據(jù)的學(xué)習(xí)能力和對(duì)測(cè)試數(shù)據(jù)泛化能力。 4.1 學(xué)習(xí)能力測(cè)試 測(cè)試的結(jié)果顯示出在兩種情況下INNS都

13、比ANNS更加精確。另外，INNS比ANNS的方法需要更少的建造時(shí)間，擁有遺傳算法的全球搜索能力。值得注意的是，在情況Ⅱ的ANNS(44 sec) 增加的建造時(shí)間，大幅度地增加，如輸入變量增加，但是用INNS的方法增加得較慢〔17 sec〕。在接近INNS－Ⅰ〔INNS-Ⅱ的22代〕的19代的最適合的方法，聯(lián)系權(quán)值和神經(jīng)網(wǎng)絡(luò)的偏移量，從每個(gè)遺傳算法的個(gè)體獲得，通常接近最好的一個(gè)。 表1 神經(jīng)網(wǎng)絡(luò)參數(shù)的設(shè)定 參數(shù) INNs－Ⅰ INNs－Ⅱ 神經(jīng)網(wǎng)絡(luò) 輸入層節(jié)點(diǎn) 3 5 隱含層節(jié)點(diǎn) 8 12 輸出層節(jié)點(diǎn) 5 5 學(xué)習(xí)速率 0．25 動(dòng)量常數(shù) 0

14、．8 迭代編號(hào) 4000 權(quán)值范圍 [-1,1] 偏壓范圍 [-1,1] 進(jìn)化算法 群體大小 50 衡量因素 0.01 偏移量 0 競(jìng)爭(zhēng)數(shù) 50 最大代數(shù) 50 4．2 泛化能力測(cè)試 十個(gè)折層的十字架確認(rèn)測(cè)試[17]被用來作為評(píng)估在新的情況下開展的INNS的能力。數(shù)據(jù)分成10種設(shè)定，大約給每個(gè)整定為相反的數(shù)據(jù)。從十分之九的整定中取得的數(shù)據(jù)被作為訓(xùn)練整定，剩余的整定作為測(cè)試整定，這些數(shù)據(jù)被用作訓(xùn)練數(shù)據(jù)去估計(jì)其診斷的準(zhǔn)確性。每十個(gè)整定被交替的當(dāng)作測(cè)試整定。INNS更能展示診斷的準(zhǔn)確性，在情況Ⅰ是91.90％，在情況Ⅱ是95.08％，

15、對(duì)于測(cè)試的組合( 從不送到訓(xùn)練整定) 作為訓(xùn)練數(shù)據(jù)，在情況Ⅰ是90.47％，在情況Ⅱ是93.33%。這些發(fā)現(xiàn)確定了在學(xué)習(xí)的一些新的情形時(shí)，INNS的泛化能力比ANNS更好。 5. 結(jié)論 本文呈現(xiàn)了對(duì)于電力變壓器的故障探測(cè)的DGA方法的智能神經(jīng)網(wǎng)絡(luò)。根據(jù)歷史的診斷記錄，自動(dòng)地生成使用遺傳算法構(gòu)造的INNS。遺傳算法那么決定聯(lián)系權(quán)重和神經(jīng)網(wǎng)絡(luò)的偏移量以到達(dá)一個(gè)對(duì)DGA的精確診斷模型。另外，由於他們的精度和高效建模的情況，INNS更能正確地抓取溶解的瓦斯的非線性關(guān)系和所對(duì)應(yīng)的故障。那接近實(shí)際情況的估計(jì)，在臺(tái)灣電力公司的練習(xí)DGA數(shù)據(jù)中作為測(cè)試且與ANNS作比擬。測(cè)試結(jié)果顯示INNS能

16、提高診斷的準(zhǔn)確性和比ANNS有更高的學(xué)習(xí)速度。 6. 參考文獻(xiàn) [1] P. S. Pugh and H. H. Wagner, "Detection of incipient faults in transformer by gas analysis," AIEE Transactions, vol. 80, pp. 189-195, 1961. [2] J. J. Kelly, "Transformer fault diagnosis by dissolved-gas analysis," IEEE Trans. Industry Applications, vol. 16, n

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18、99, 1978. [5] R. R. Rogers, "IEEE and IEC codes to interpret incipient faults in transformers using gas in oil analysis," IEEE Trans. Electrical Insulation, vol. 13, no. 5, pp. [6] IEEE Guide for the Interpretation of Gases Generated in Oil-immersed Transformers, ANSI/IEEE Std C57.104-1991, 1992.

19、 [7] M. Duval, "Dissolved gas analysis: It can save your transformer," IEEE Electrical Insulation Magazine, vol. 5, no. 6, pp. 22-27, 1989. [8] C. E. Lin, J. M. Ling, and C. L. Huang, "An expert system for transformer fault diagnosis and maintenance using dissolved gas analysis," IEEE Trans. Power

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23、Griffin, "A combined ANN and expert system tool for transformer fault diagnosis," IEEE Trans. Power Delivery, vol. 13, no. 4, pp. 1224-1229, 1998. [14] J. A. Freeman and D. M. Skapura, Neural Networks: Algorithms, Applications, and Programming Techniques, Addison-Wesley, 1991. [15] D. B. Fogel, "A

24、n introduction to simulated evolutionary optimization," IEEE Trans. Neural Networks, vol. 5, no. 1, pp. 3-14, 1994. [16] D. B. Fogel, System Identification Through Simulated Evolution: A Machine Learning Approach to Modeling, Needham, MA: Ginn Press, 1991. [17] S. M. Weiss and C. A. Kulikowski, Co

25、mputer Systems that Learns, San Mateo, CA: Morgan Kaufman, 1991. A New Intelligent Approach to Fault Detection of Electr ic Power Transformers ABSTRACT This paper proposes intelligent neural networks (INNs) for fault detection of electric power transformers. The INNs automatically tun

26、e the network parameters, connectionweights and bias terms of the neural networks, to achieve the best model based on the proposed evolutionary algorithm. The INNs can identify complicated relationships among dissolved gas contents in transformer oil and corresponding fault types,using the global se

27、arch capabilities of the evolutionary algorithm and the highly non-linear mapping nature of the neural networks. The proposed INNs have been tested on the Taipower Company diagnostic records and compared with the artificial neural networks (ANNs). The test results confirm that the proposed INNs have

28、 remarkable diagnosis accuracy and require less learning time than the ANNs. 1. INTRODUCTION Dissolved gas analysis (DGA) methods [1]-[7] have been broadly used by utilities to interpret dissolved gases due to theinsulation deterioration of transformer oil. Chromatographic analysis of the insul

29、ation oil contains concentrations (ppm by volume) of dissolved hydrogen (H2), methane (CH4), ethane (C2H6), ethylene (C2H4), acetylene (C2H2), carbon monoxide (CO), and carbon dioxide (CO2). DGA techniques can determine the conditions of the transformers according to the concentrations of the dissol

30、ved gases, their generation rates, ratios of specific gases, and the total combustible gas detected by sampling and testing of the transformer insulation oil. Actual diagnosis must also consider other information relating to the conditions of dissolved gas in the transformer such as the manufacturer

31、, transformer size, volume of oil, gassing rates, loading history, and environmental factors. Therefore, historic diagnosis records are important in further similar case diagnosis. Although widely used by utilities, the IEC/IEEE DGA coding [4]-[6] is only the result of empirical evidence. Moreover,

32、 the DGA methods cannot provide a acompletely objective and accurate basis [6] for all faults since the number of possible code combinations exceeds that of fault types. Therefore, no decision may follow from the diagnosis, and diagnostic experts must determine the final possible faults. Fuzzy exp

33、ert system [8] has been proposed to diagnose incipient faults of transformers. The diagnosis results were promising; however, the fuzzy expert system could not learn from previous diagnosis results because the membership functions and the diagnostic rules were determined by practical experience or

34、trial-and-error tests. To circumvent the disadvantages of the fuzzy expert system, adaptive self-learning fuzzy diagnosis systems [9]-[10] were developed for transformer fault diagnosis to acquire knowledge directly from training data. Artificial neural networks (ANNs) [11]-[13] have been proposed

35、 to tackle the transformer fault diagnosis, due to their accuracy and efficiency in numerical modeling problems and built-in fault tolerance in practical applications. The ANNs can acquire new experiences by incremental training from newly obtained samples. The ANNs trained by an error back-propagat

36、ion algorithm have good diagnostic capabilities. However, certain problems, such as local convergence and determination of the network configuration and control parameters (learning rate and momentum constant), must be solved before ANNs become a useful tool. Because the typical search space often

37、possess local minima, the gradient descent based error back-propagation technique may stagnate at these potentially local optimal solutions, diminishing the performance of the ANNs. The proposed evolutionary algorithm [15]-[16] is a parallel structure and a stochastic optimization algorithm that can

38、 simultaneously determine connection weights and bias terms of the neural networks, while avoiding the limitation of the gradient descent technique. 2. THE NEURAL NETWORKS The neural networks proposed for fault diagnosis of power transformers are constructed as three-layer feed-forward structu

39、res with the input, hidden, and output layers, as shown in fig. 1. The nodes in each layer receive input signals from the previous layer and pass the output to the subsequent layer. The nodes of the input layer receive a set of input signals from outside system and directly deliver the input data to

40、 the input of the hidden layer by the weighted links. In the following computation, the subscripts n, h, and k denote any node in the input, hidden, and output layers, respectively. The net input net is defined as the weighted sum of the incoming signal minus abias term. The net input of node h, net

41、h, in the hidden layer is expressed as follows: where yn is the output of node n in the input layer; whn represents the connection weight from node n in the input layer to node h in the hidden layer, and qh is the bias of node h in the hidden layer. The output of node h, yh, in the hidden l

42、ayer is fh(neth). The sigmoid function, often used in nonlinear mapping, is selected as the activation function, The output of the hidden nodes is then delivered to the nodes in the output layer via another set of connection weights. The output of node k in the output layer can also be expressed

43、as: where qk is the bias of node k in the output layer. The parameters (connection weights and bias terms) must be determined by the learning process, before the neural networks can produce the desired outputs. The generalized data rule [18] is used to adjust the weights between the nodes by mini

44、mizing the following error function: where dk represents the desired output of node k, and yk is the computed output of node k in the output layer. The weight wkh is updated iteratively to minimize E for the training data by a gradient descent technique: where i represents the iteration number

45、; h is the learning rate, and a is the momentum constant. Similarly, for node h in the hidden layer, the weight whn can be changed as follows. The bias terms can be regarded as weights and iteratively altered in the same manner as the other weights described above, in (6) to (11). The output yk

46、 of node k in the output layer implicitly includes the tunable parameters of the networks, the connection weights and bias terms, in each node. In this paper, the connection weights and bias terms of the neural networks are determined by the evolutionary algorithm in a global-optimal manner to avoid

47、 local convergence of parameters in ANNs trained by the gradient descent approach. 3. THE EVOLUTIONARY ALGORITHM The proposed evolutionary algorithm [15]-[16] to adjust the network parameters, connection weights and bias terms of the neural networks, is described as follows. 3.1 Unfitness Fun

48、ction Let Ti = [t1i, ..., tdi, ..., tDi] be a trial vector that represents the i-th individual, i = 1, 2, ..., I, of the population to be evolved, where I is the population size. The elements of td, d =1, 2, ..., D, are the desired values of the connection weights and bias terms of the neural netwo

49、rks. An unfitness function is assigned to each individual Ti ; then, the individuals evolve according to the unfitness function value. The lower unfitness the individual possesses the higher probability it will survive. In this paper, the least-squared error function Ei, which is defined below, is

50、 used to represent the unfitness value of the INNs associated with the individual T i . where ykp indicates the k-th computed output of the INNs when (4) is used as the p-th sample vector; P denotes the total number of sample vectors; and dkp is the corresponding actual fault indicator (“1” repre

51、sents fault, “0” indicates nonfault) in the k-th output node. 3.2 Initialization The initial parent trial vectors Ti , i = 1, 2, ..., I, are generated randomly from a reasonable range in each dimension by setting the elements of Ti as: Tid ~ U(δ d,min, δ d,max) for d = 1, 2, ..., D, and i = 1,

52、 2, ..., I,where U(δ d,min, δ d,max) denotes the outcome of a uniformly distributed random variable ranging over the given lower- and upper-bounded valuesδ d,min and δ d,max of the connection weights and bias terms of the neural networks. 3.3 Offspr ing Creation By adding a Gaussian random variati

53、on with zero mean and a standard deviation proportional to the scaled unfitness value of the parent trial solution, each parent Ti creates an offspring vector, Ti+I , i.e., where N(0,σ2) designates a vector of Gaussian random variables with mean zero and standard deviation σi，σi is given accordin

54、g to following equation: where Ei represents the unfitness function from (12) associated with the trial vector Ti , s is a scaling factor and F indicates an offset. The offspring Ti+I is generated based on the relative Ei value to be minimized. If Ei is relatively low (high), the offspring trial

55、solution is produced near (far) the current solution Ti . 3.4 Competition and Selection Competition for survival is stochastic in the evolutionary algorithm. The 2I individuals, the parent and the created offspring, compete with the other randomly selected individuals for win from their unfitnes

56、s values. The criterion for win of each individual is represented as: where Wi means the score of the i-th individuals, Nc denotes the number of competitors that are selected randomly, fi indicates the unfitness value of i-th individual, and fk is the unfitness value of k-th rival. Furthermore, k

57、 = [2Iu2+ 1], [y] represents the greatest integer less than or equal to y, and u1, u2 ~U(0,1) are uniform random real numbers ranging over[0,1]. After all individuals have experienced competition, the 2I individuals are ranked in descending order of their corresponding Wi value. Then, the first I

58、individuals and their corresponding unfitness values are selected as new parents of the next generation. 3.5 Stopping Rule As the stopping rule of maximum generation or the minimum criterion of E value in (12) is satisfied, the evolution process stops and the solution with the lowest unfitness v

59、alue is regarded as the best INNs for fault diagnosis. Otherwise, the Offspring Creation and Selection steps detailed above are repeated. 4. NUMERICAL TESTS The INNs have been implemented on the 630 actual gas records collected from the Taipower Company’s 162 69kV transformers. The fault types w

60、ere confirmed by the Taipower transformer diagnosis experts according to diverse DGA methods, group discussion, and internal examinations of the suspected transformers. The INNs were run on a PC Pentium III-600 in Turbo C programming language. Two cases, Case I and Case II, were designed to evaluat

61、e the diagnosis accuracy of the proposed diagnosis system. Case I selected the three extensively used gas ratios [4]-[6], C2H2/C2H4, CH4/H2, and C2H4/C2H6, as the input variables. Case II exploited the concentrations of five gases, H2, CH4, C2H6, C2H4, and C2H2, as input variables to classify the po

62、ssible fault types. Table I lists the parameter settings of the INNs-I and INNs-II. The parameters of the ANNs-I and ANNs-II were the same as those of the INNs-I and INNs-II, respectively, except for the use of the gradient search approach. Two types of performance were evaluated for the developed

63、 system: learning ability for training data, and generalization ability for testing data 4.1 Learning Ability Tests The test results indicate that the proposed INNs were significantly more accurate than the ANNs, in both cases. Moreover, the INNs require far less constructing time than do

64、ANN methods, owing to the global search capability of the evolutionary algorithm. Notably, the additional constructing time of the ANNs (44 sec.) methods in Case II, greatly increase as the input variables increase, but that of the proposed INNs increases more slowly (17 sec.). After nearly 19 gener

65、ations of the INNs-I (22 generations of the INNs-II) optimization process, the connection weights and bias terms ofthe neural networks, obtained from each individual of the evolutionary algorithm, converge toward the best ones. 4.2 Generalization Ability Tests Ten-fold cross validation tests [17

66、] were conducted to evaluate the ability of the developed INNs on the new cases. The data were divided into ten sets, and approximately an equal number of data was given to each set. The data from nine of the ten sets served as the training set and that of the remaining set served as the testing set, which was presented to the diagnosis system that was trained to evaluate its diagnosis accuracy. Each of the ten sets was alternately employed as a testing set. The INNs exhibit higher diagnosis acc