畢業(yè)設(shè)計(jì)（論文）文獻(xiàn)翻譯：用BP神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)的BP神經(jīng)網(wǎng)絡(luò)算法研究預(yù)測(cè)電滲析過程的分離百分比

畢業(yè)設(shè)計(jì)（論文）--文獻(xiàn)翻譯原文題目StudiesonpredictionofseparationpercentinelectrodialysisprocessviaBPneuralnetworksandimprovedBPalgorithms譯文題目用BP神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)的BP神經(jīng)網(wǎng)絡(luò)算法研究預(yù)測(cè)電滲析過程的分離百分比專業(yè)信息與計(jì)算科學(xué)姓名學(xué)號(hào)指導(dǎo)教師用BP神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)的BP神經(jīng)網(wǎng)絡(luò)算法研究預(yù)測(cè)電滲析過程的分離百分比摘要在電滲析過程中，分離百分比(SP)與一些影響因素(進(jìn)料濃度(C)、稀室的流通率(Q)、反應(yīng)溫度(T)和應(yīng)用電壓(V))有非線性關(guān)系，并且這些關(guān)系很難用一個(gè)簡(jiǎn)單的公式來表示。四個(gè)影響因素對(duì)SP產(chǎn)生了顯著影響。在這篇論文中，對(duì)四個(gè)因素進(jìn)行了電滲析實(shí)驗(yàn)研究。反向傳播(BP)神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)BP算法被用于SP的預(yù)測(cè)，并且他們的預(yù)測(cè)能力可以反映出他們?cè)诜蔷€性關(guān)系的復(fù)雜數(shù)據(jù)上的適應(yīng)能力。使用不同的神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)、神經(jīng)元傳遞函數(shù)和學(xué)習(xí)率，可以獲得最佳訓(xùn)練參數(shù)。比較BP神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)的BP神經(jīng)網(wǎng)絡(luò)算法，由于改進(jìn)BP神經(jīng)網(wǎng)絡(luò)算法適當(dāng)?shù)馗淖兞苏_學(xué)習(xí)率和權(quán)值的比率，所以它比BP神經(jīng)網(wǎng)絡(luò)算法更好。在高溫和高電壓的情況下，改進(jìn)BP神經(jīng)網(wǎng)絡(luò)算法將有更好的預(yù)測(cè)性能，這是因?yàn)楦倪M(jìn)BP神經(jīng)網(wǎng)絡(luò)算法有大數(shù)值的泛化能力。關(guān)鍵字：BP神經(jīng)網(wǎng)絡(luò)算法;改進(jìn)BP算法;電滲析法分離百分比;改進(jìn)BP算法;自適應(yīng)學(xué)習(xí)算法1.導(dǎo)言電滲析（ED）是在電勢(shì)差驅(qū)動(dòng)力的幫助下，離子從溶液的一個(gè)帶電膜分離到另一個(gè)電膜的過程。這一過程廣泛用于生產(chǎn)飲用水及從半咸水和海水中處理水、處理工業(yè)廢水、從污水和鹽生產(chǎn)恢復(fù)有用的物料。文獻(xiàn)[1-6]中對(duì)電滲析的應(yīng)用和基本原則進(jìn)行了檢驗(yàn)。因?yàn)槠浠瘜W(xué)穩(wěn)定性高、靈活性和由于其強(qiáng)大的離子特征帶來的高離子電導(dǎo)率，人們開發(fā)了許多使用離子交換膜的電滲析應(yīng)用并且商業(yè)化[7-10]。兩種不同類型的離子交換膜用于常規(guī)電滲析：陽離子交換(CEM)和陰離子交膜換(AEM)，分別滲透陽離子和陰離子[11]。然而，在性能經(jīng)營(yíng)過程中，電流密度應(yīng)保持小于極限電流密度，因?yàn)樗碾x解引起的結(jié)垢和膜破損[12]。所以測(cè)定的極限電流密度和系統(tǒng)的潛力也被執(zhí)行。極限電流密度是最大電流密度（當(dāng)前每單位面積膜），它可以使用而且不會(huì)導(dǎo)致高的電阻和較低的電流功率等負(fù)面影響。在極限電流密度下，在陽離子交換膜或陰離子交換膜表面的陽離子或陰離子的濃度，恰到好處的，在稀室內(nèi)消耗的溶液是零[12-14]。超越極限電流密度后，水分解時(shí)生成的H+和OH?運(yùn)輸一部分的電流[15]。人工神經(jīng)網(wǎng)絡(luò)(人工神經(jīng)網(wǎng)絡(luò)）利用相互聯(lián)系的數(shù)學(xué)節(jié)點(diǎn)或神經(jīng)元以形成一個(gè)網(wǎng)絡(luò)，可以模擬復(fù)雜的功能關(guān)系[16]。它的發(fā)展始于20世紀(jì)40年代以幫助認(rèn)知科學(xué)家理解中樞神經(jīng)系統(tǒng)的復(fù)雜性。它已經(jīng)穩(wěn)步發(fā)展，并適應(yīng)科學(xué)的許多領(lǐng)域?；旧?，人工神經(jīng)網(wǎng)絡(luò)是源自人類的大腦在學(xué)習(xí)的過程中的數(shù)值結(jié)構(gòu)靈感。他們構(gòu)造作為替代的數(shù)學(xué)工具用于解決不同領(lǐng)域問題的系統(tǒng)辨識(shí)、預(yù)測(cè)、模式識(shí)別、分類、過程控制及其他許多[17]。人工神經(jīng)網(wǎng)絡(luò)已廣泛的在膜過程中應(yīng)用（反滲透、納濾、超濾、微濾膜、膜過濾、氣體分離、膜生物反應(yīng)器和燃料電池)[18]。然而，在文獻(xiàn)中很少有幾條應(yīng)用人工神經(jīng)網(wǎng)絡(luò)預(yù)測(cè)電滲析過程中SP（分離百分比）的記錄。人工神經(jīng)網(wǎng)絡(luò)中受到最多關(guān)注的是反向傳播網(wǎng)絡(luò)(BPN)[19]。BPNs有分層的前饋網(wǎng)絡(luò)框架。在經(jīng)典BPNs結(jié)構(gòu)中，產(chǎn)出的每個(gè)圖層被直接送到每個(gè)神經(jīng)元的下一層。BPNs有許多層，但人們認(rèn)為至少三個(gè)圖層：一個(gè)接收和分發(fā)輸入的輸入層、捕捉輸入和輸出的非線性關(guān)系的中間層或隱藏層，和一個(gè)生產(chǎn)計(jì)算數(shù)據(jù)的輸出層。BPNs神經(jīng)元也可能包含產(chǎn)生恒定的輸出但沒有收到輸入這樣的偏差[20-21]。BP算法基于神經(jīng)網(wǎng)絡(luò)錯(cuò)誤最小化。這些錯(cuò)誤被描述為期望的產(chǎn)出與實(shí)際之間的差異[22]。當(dāng)訓(xùn)練精度滿足時(shí)即訓(xùn)練完成（圖1）。BPNs操作具有更好的推廣和容錯(cuò)功能，然而，它也有一些不足之處：(1)慢收斂性可能導(dǎo)致較長(zhǎng)的訓(xùn)練時(shí)間。(2)在訓(xùn)練過程中出現(xiàn)可能局部極值點(diǎn)。所以在這項(xiàng)研究中，改進(jìn)的BP算法被用來改進(jìn)電滲析過程中分離百分比的預(yù)測(cè)能力。在這篇論文中，自適應(yīng)學(xué)習(xí)算法和靈活的BP算法是改進(jìn)的BP算法在電滲析過程中的應(yīng)用。2.材料和方法2.1.實(shí)驗(yàn)儀器和材料電滲析過程中，在表1中顯示了實(shí)驗(yàn)儀器和材料。此外，其他實(shí)驗(yàn)材料：量筒、燒杯、去離子水等。這些實(shí)驗(yàn)的目的是研究進(jìn)料濃度、溫度、電壓和流通率對(duì)電滲析電池性能的影響。2.2.電滲析池和電滲析膜有機(jī)玻璃(PMMA)做成的板和框架的電滲析池被用來進(jìn)行電滲析實(shí)驗(yàn)（圖2）。電滲析池由三部分組成，一對(duì)CEM（陽離子交換膜）和AEM（陰離子交換膜）和一對(duì)電極。電滲析池的長(zhǎng)度、寬度和高度分別為0.191m、0.021m和0.181m。陽離子交換膜和陰離子交換膜有效區(qū)域都是0.11×0.09m2。這兩個(gè)電極由純鉑金制成，每個(gè)電極的表面積是0.115×0.09m2。稀釋容量和濃縮容量分別是0.12×0.1×0.003m3和0.12×0.1×0.006m3。NaCl(氯化鈉)溶液被輸入到電滲析池的三個(gè)單元格中。陽離子交換膜(CEM)和陰離子交換膜(AEM)分別有陽離子滲透性和陰離子滲透性。兩層膜被并排沉浸在溶液中，并有電流通過溶液。正離子遷移到陰極，陰離子遷移到陽極。注入的溶液被劃分成兩個(gè)流。一個(gè)是稀釋水，另一個(gè)是濃縮水。在一定的流速下，可以操作電滲析池去除電離子。離子在電滲析池中被電解，陰極和陽極發(fā)生的反應(yīng)如下所示：陽極反應(yīng)：2Cl??2e→Cl2↑H2O?2e→1/2O2↑+2H+陰極反應(yīng)：2H2O+2e→H2↑+2OH?。在陽極反應(yīng)中，生成了Cl2和O2。此外，在陰極反應(yīng)中生成了H2。這些氣體可能增加電滲析池的電阻，因此兩個(gè)小洞被用來釋放電滲析池板上的氣體。集中的氣流被處理掉，以防止這些氣體積聚。電解膜的物理和化學(xué)特性列表(表2)。2.3.電滲析設(shè)備安裝程序電滲析設(shè)備安裝包括注入溶液的一個(gè)水槽(TK-01)、直流電源供應(yīng)器和控制注入溶液的流動(dòng)速率的兩個(gè)閥門(GB-01,GB-02)（圖3）。電滲析設(shè)備的總高度是0.5m。兩個(gè)集中的濃縮流和稀釋流沒有循環(huán)利用，并為預(yù)測(cè)和分析電導(dǎo)率收集稀釋流。2.4.實(shí)驗(yàn)原理電滲析過程是膜分離技術(shù)之一。根據(jù)直接電場(chǎng)電滲析技術(shù)利用選擇性的離子交換膜將電解質(zhì)從溶液中分開的能力，以實(shí)現(xiàn)稀釋、濃縮或純化溶液的目的（圖4）。2.5.極限電流密度的測(cè)定極限電流密度(LCD)在電滲析過程中是一個(gè)重要參數(shù),用于確定電阻和目前的利用率。通常情況下,極限電流密度取決于膜、溶液屬性、電滲析棧結(jié)構(gòu)以及各種操作參數(shù)，如稀釋流的速度[23]。極限電流的測(cè)量方法是伏安法、pH值法等等。本文用伏安方法來確定極限電流密度,具體步驟如下。在恒定溫度、濃度和流量的情況下，調(diào)整電壓表按鈕并記錄每一組的電壓和電流。當(dāng)電壓很低時(shí)，電流與電壓有線性關(guān)系。隨著電壓的增加,電流發(fā)生微妙的變化。極限電流是轉(zhuǎn)折點(diǎn),我們就得到了極限電流密度。例如，T=35°C，C=0.5g/L，Q=0.5mL/s，隨著電壓逐漸增加，電流與電壓有線性關(guān)系。當(dāng)電流達(dá)到0.51A時(shí)，電壓對(duì)電流有輕微影響，所以極限電流即拐點(diǎn)是0.51A(圖5)。膜的有效面積是兩個(gè)0.11×0.09m2，所以極限電流密度是51.515A/m2.在實(shí)驗(yàn)中，工作電流不能超過極限電流。否則電滲析過程中將發(fā)生極化，分離百分比的預(yù)測(cè)也就毫無意義。使用伏安法，在所有的實(shí)驗(yàn)條件下獲得的極限電流密度（表3）。為了防止發(fā)生電滲析池極化，所有電流被控制限制電流下。在電滲析實(shí)驗(yàn)中，極限電流最大值是0.80A，離子交換膜的有效面積0.11×0.09m2，所以極限電流密度的最大值是80.808A/m2.2.6.實(shí)驗(yàn)數(shù)據(jù) 實(shí)驗(yàn)在極限電流密度下開展(表4)。對(duì)四個(gè)因素進(jìn)行研究:進(jìn)料濃度(0.5g/L,1g/L和1.5g/L),稀釋艙的流量(0.05毫升/秒,0.25毫升/秒,0.5毫升/秒,0.75毫升/秒和1毫升/s),反應(yīng)溫度(20°C,25°C,30°C,35°C,40°C和45°C),外加電壓(2V,5V和8V)。3.基于BP神經(jīng)網(wǎng)絡(luò)算法和改進(jìn)的BP算法3.1.BP神經(jīng)網(wǎng)絡(luò)典型BP神經(jīng)網(wǎng)絡(luò)是一個(gè)全神經(jīng)網(wǎng)絡(luò)包括一個(gè)輸入層、隱藏層和輸出層[24,25],訓(xùn)練過程的目標(biāo)是調(diào)整權(quán)值。網(wǎng)絡(luò)訓(xùn)練是一個(gè)無約束非線性最小化問題[26]。研究人員聲稱,一個(gè)隱層的網(wǎng)絡(luò)所需的任何精度逼近任意連續(xù)函數(shù)[27-29]。BP神經(jīng)網(wǎng)絡(luò)由向前反饋和誤差反向傳播兩部分組成。向前傳播,輸入從輸入層開始傳播，被一些隱藏層處理后到達(dá)輸出層，輸出層的輸出預(yù)測(cè)值與實(shí)際輸出比較,它們之間的區(qū)別是聚合生成的誤差。在誤差反向傳播中,當(dāng)誤差超出誤差范圍,誤差被調(diào)整回傳播權(quán)值。學(xué)習(xí)過程一直持續(xù)到誤差聚合目標(biāo)值(圖6)。3.2.BP神經(jīng)網(wǎng)絡(luò)的構(gòu)建有關(guān)于BP神經(jīng)網(wǎng)絡(luò)的一些預(yù)防措施：(1)預(yù)處理樣品。通常樣品沒有直接使用網(wǎng)絡(luò)訓(xùn)練,而是從原始數(shù)據(jù)預(yù)處理。實(shí)驗(yàn)數(shù)據(jù)包含一些不確定因素訓(xùn)練。預(yù)處理方法是提高訓(xùn)練和測(cè)試數(shù)據(jù)可靠性的必要準(zhǔn)備。(2)優(yōu)化初始權(quán)值。網(wǎng)絡(luò)的初始權(quán)值影響最終的訓(xùn)練結(jié)果,影響網(wǎng)絡(luò)是否能達(dá)到可接受的精度。(3)選擇隱藏的圖層數(shù)和神經(jīng)元的隱藏圖層。隱藏圖層和神經(jīng)元的隱藏圖層的選擇，是直接影響復(fù)雜問題的映射能力的最關(guān)鍵的一步?，F(xiàn)在可靠的算法從隱藏層和大量的神經(jīng)元開始,訓(xùn)練和測(cè)試,然后增加它們的數(shù)量。比較不同訓(xùn)練和測(cè)試樣本的結(jié)果,選擇更合適的隱藏層個(gè)數(shù)及其神經(jīng)元。在這項(xiàng)研究中,具有不同神經(jīng)元隱層的三層神經(jīng)網(wǎng)絡(luò)用于這次電滲析實(shí)驗(yàn)。(4)選擇訓(xùn)練樣本。網(wǎng)絡(luò)所需的樣本取決于復(fù)雜程度的映射關(guān)系。一般情況下，映射關(guān)系越復(fù)雜，需要越多訓(xùn)練樣本。從所有數(shù)據(jù)中選擇樣本時(shí)，BPNs需要遵守以下原則：足夠數(shù)量的、典型的和均勻的。3.3.改進(jìn)的BP算法BPNs基于堅(jiān)實(shí)的理論和嚴(yán)格的推導(dǎo)，然而BPNs包括慢收斂、偶爾出現(xiàn)的局部極值點(diǎn)，所以訓(xùn)練過程中有許多不足之處。在實(shí)際應(yīng)用中，BP算法很難是見效，因此人們提出了一些改進(jìn)的BP算法，以提高預(yù)測(cè)能力。有幾種方法改進(jìn)的BP算法，如附加動(dòng)量方法，自適應(yīng)學(xué)習(xí)率方法，靈活的BP算法，等等。在此論文中，自適應(yīng)學(xué)習(xí)率方法和靈活的BP算法被用來預(yù)測(cè)在電滲析過程中的分離百分比并用于與BPNs比較預(yù)測(cè)能力。3.3.1.自適應(yīng)學(xué)習(xí)算法BP算法的訓(xùn)練過程受不當(dāng)學(xué)習(xí)速率的影響有慢收斂的缺點(diǎn)。BP算法中的權(quán)值調(diào)整取決于學(xué)習(xí)速率和斜率。在BP算法中，學(xué)習(xí)速率是恒定的。事實(shí)上，當(dāng)學(xué)習(xí)速率較低、訓(xùn)練時(shí)間變長(zhǎng)，收斂變得較慢。當(dāng)學(xué)習(xí)率太高，出現(xiàn)了振蕩和分歧，這會(huì)造成系統(tǒng)不穩(wěn)定。自適應(yīng)學(xué)習(xí)率如圖7中所示。自適應(yīng)學(xué)習(xí)速率的基本原理：當(dāng)學(xué)習(xí)速率(η)增加，將造成學(xué)習(xí)時(shí)間縮短；學(xué)習(xí)速率越高，越難收斂。在這種情況，學(xué)習(xí)速率應(yīng)該會(huì)減少直到訓(xùn)練過程的收斂。可以通過改變誤差和斜率，也可以根據(jù)誤差函數(shù)通過改變學(xué)習(xí)速率梯度調(diào)整學(xué)習(xí)速率。此外，通過探性地進(jìn)行調(diào)整試可能改變總誤差，規(guī)則如下所示：(1)如果的總誤差(E)減少，學(xué)習(xí)速率需要增加。(2)如果的總誤差(E)增加，學(xué)習(xí)速率需要減少。當(dāng)新誤差與原來誤差的比值超過某一個(gè)值時(shí)（例如1.04），學(xué)習(xí)速率迅速下降。3.3.2.靈活的BP算法一般來說，用sigmoid函數(shù)來將數(shù)據(jù)從輸入層傳遞到隱藏層。此外，sigmoid函數(shù)保持無限輸入和有限界內(nèi)輸出。當(dāng)輸入大變量時(shí)，sigmoid函數(shù)的斜率將接近0。即使梯度發(fā)生了微妙的變化,這可能引起權(quán)值發(fā)生巨大的變化,所以權(quán)值逐漸傾斜最佳值,甚至使網(wǎng)絡(luò)權(quán)值在修改過程中停止。當(dāng)訓(xùn)練過程振動(dòng)時(shí)，數(shù)量可變的權(quán)值將會(huì)減少。在幾個(gè)迭代中權(quán)值變化方向保持不變時(shí)，可變數(shù)量的權(quán)值將會(huì)增加。因此，靈活的BP算法在收斂速度上有超越其他改進(jìn)BP算法的優(yōu)勢(shì)。4.結(jié)果和討論BP神經(jīng)網(wǎng)絡(luò)和改進(jìn)的BP算法的設(shè)計(jì)中，需要確定四個(gè)重要方面：1）神經(jīng)元傳遞函數(shù)的選擇2）隱藏圖層節(jié)點(diǎn)的選擇3）學(xué)習(xí)率增加比率的選擇4）BP神經(jīng)網(wǎng)絡(luò)和改進(jìn)的BP算法的泛化測(cè)試4.1神經(jīng)元傳遞函數(shù)的選擇 傳遞函數(shù)用于彼此相鄰的兩層中的神經(jīng)元之間的傳遞。而且這些傳遞函數(shù)必須是可誘導(dǎo)的。BP神經(jīng)網(wǎng)絡(luò)有一個(gè)或多個(gè)隱藏層,隱藏層神經(jīng)元使用Sigmoid傳遞函數(shù)。輸出層神經(jīng)元使用純線性傳遞函數(shù)且輸出可以是任意值。如果輸出層神經(jīng)元的傳遞函數(shù)是Sigmoid傳遞函數(shù),則整個(gè)網(wǎng)絡(luò)輸出會(huì)被限制在(?1,1)內(nèi)。 Sigmoid傳遞函數(shù)包括log-sigmoid和tan-sigmoid兩個(gè)函數(shù)。對(duì)于這兩個(gè)函數(shù)，輸入分別映射到(0,1)和(?1,+1)。log-sigmoid函數(shù)是一個(gè)單向傳遞函數(shù)。Tansigmoid函數(shù)是一個(gè)雙向傳遞函數(shù)，并被稱為雙曲正切函數(shù)(圖8)。 在實(shí)際應(yīng)用中，根據(jù)輸入輸出的關(guān)系使用某一個(gè)傳遞函數(shù)。如果輸入不含負(fù)值，所以采納log-sigmoid函數(shù)。如果包括負(fù)值，則采納tan-sigmoid函數(shù)。在本文中，隱藏層神經(jīng)元使用Sigmoid傳遞函數(shù)，輸出層神經(jīng)元用純線性傳遞函數(shù)。4.2隱藏圖層節(jié)點(diǎn)的選擇 許多學(xué)者曾從事研究隱藏層的最佳節(jié)點(diǎn)?？聽柲缏宸蚨ɡ碜C明，只要一個(gè)隱層的節(jié)點(diǎn)足夠多，神經(jīng)網(wǎng)絡(luò)的隱藏層可以以任意精度逼近非線性函數(shù)。然而，對(duì)于一個(gè)從輸入到輸出有限的映射，無限多的隱藏層節(jié)點(diǎn)是沒有必要的。以及如何選擇隱藏層節(jié)點(diǎn)仍是一個(gè)尚未解決的問題。隱藏層節(jié)點(diǎn)是通過經(jīng)驗(yàn)和實(shí)驗(yàn)設(shè)計(jì)確定的。一般地，基于對(duì)輸入和輸出關(guān)系準(zhǔn)確的反映，選擇一個(gè)隱藏層的小節(jié)點(diǎn)，以保持網(wǎng)絡(luò)的結(jié)構(gòu)簡(jiǎn)單。但規(guī)模越小的節(jié)點(diǎn)，神經(jīng)網(wǎng)絡(luò)的泛化能力越糟糕。在相反，如果隱藏層的節(jié)點(diǎn)越大，訓(xùn)練過程中的復(fù)雜度也會(huì)隨之升高，那么這種情況將導(dǎo)致過度擬合現(xiàn)象。在設(shè)計(jì)過程中，許多因素必須結(jié)合起來。在具體設(shè)計(jì)中，首先選擇一個(gè)隱藏層。如果增加隱含層節(jié)點(diǎn)無法獲得更好的網(wǎng)絡(luò)，層號(hào)和隱藏層節(jié)點(diǎn)仍需要添加。 在本文中,四個(gè)影響因素(電壓、濃度、溫度、流量)是一個(gè)輸入層節(jié)點(diǎn),并且分離百分比是一個(gè)輸出層節(jié)點(diǎn)。所以一個(gè)隱藏層的節(jié)點(diǎn)數(shù)應(yīng)在4和12之間。網(wǎng)絡(luò)的結(jié)構(gòu)是4:4:1,4:10:1,4:12:1。通過MATLAB軟件訓(xùn)練,性能圖表如圖9所示。 在圖9(A)中,總訓(xùn)練時(shí)間是74,最佳驗(yàn)證性能高于10?3，訓(xùn)練數(shù)據(jù)的MSE(均方差)低于10?3并且MSE的測(cè)試樣品和有效數(shù)據(jù)約0.005。在圖9(B)中,總訓(xùn)練時(shí)間是33，最佳驗(yàn)證性能高于10?3，訓(xùn)練數(shù)據(jù)的MSE低于10?3并且MSE的測(cè)試樣品和有效數(shù)據(jù)可能略高于10?3。在圖9(C)中,總訓(xùn)練時(shí)間是101,最佳驗(yàn)證性能高于10?3,訓(xùn)練數(shù)據(jù)的MSE、測(cè)試樣品和有效數(shù)據(jù)均高于10?3。這三個(gè)圖的結(jié)果表明,4:10:1是最好的網(wǎng)絡(luò)結(jié)構(gòu),因?yàn)樗凶畹偷腗SE值、最短的訓(xùn)練時(shí)間。5.結(jié)論BP神經(jīng)網(wǎng)絡(luò)和改進(jìn)的BP算法作為預(yù)測(cè)氯化鈉溶液電滲析實(shí)驗(yàn)分離百分比兩種方法,改進(jìn)的BP算法比BP神經(jīng)網(wǎng)絡(luò)優(yōu)越。改進(jìn)的BP算法彌補(bǔ)了BP神經(jīng)網(wǎng)絡(luò)不合適的學(xué)習(xí)速率和權(quán)重訓(xùn)練過程中的缺陷,并且改進(jìn)的BP算法使用增加學(xué)習(xí)速率和權(quán)值的方法。靈活的BP算法是一種改進(jìn)的BP算法的方法,其預(yù)測(cè)顯然比BP神經(jīng)網(wǎng)絡(luò)更好。在不同的訓(xùn)練參數(shù)(神經(jīng)元的傳遞函數(shù),大量的隱藏層的神經(jīng)元和學(xué)習(xí)速率)這個(gè)條件下討論、研究BP神經(jīng)網(wǎng)絡(luò)和改進(jìn)的BP算法的預(yù)測(cè)能力。我們獲得了最優(yōu)訓(xùn)練參數(shù)。本文的隱藏層神經(jīng)元使用Sigmoid傳遞函數(shù)，并且輸出層神經(jīng)元使用純線性傳遞函數(shù)。4:10:1網(wǎng)絡(luò)是最好的網(wǎng)絡(luò)結(jié)構(gòu),因此最優(yōu)的隱藏層節(jié)點(diǎn)是10.1.05在學(xué)習(xí)速度訓(xùn)練數(shù)據(jù)中作為最佳的增加比率。然而,由于實(shí)驗(yàn)器材的定位和極化，導(dǎo)致最優(yōu)訓(xùn)練參數(shù)值受限。濃度、流量、溫度和電壓與分離比例呈現(xiàn)非線性關(guān)系,溫度和電壓與分離比例呈現(xiàn)正相關(guān)關(guān)系,濃度和流率與分離比例呈現(xiàn)負(fù)相關(guān)關(guān)系。對(duì)于非線性關(guān)系,改進(jìn)的BP算法能夠更好的預(yù)測(cè)。實(shí)驗(yàn)結(jié)果表明,改進(jìn)的BP算法對(duì)復(fù)雜的數(shù)據(jù)組有泛化的、高效的和自適應(yīng)的能力,使得為復(fù)雜系統(tǒng)建模成為有吸引力的選擇,比如水處理過程和膜技術(shù)。StudiesonpredictionofseparationpercentinelectrodialysisprocessviaBPneuralnetworksandimprovedBPalgorithmsabstractIntheelectrodialysisprocess,separationpercent(SP)hadnonlinearrelationshipswithanumberofinfluencingfactors(feedconcentration(C),flowrateofdilutecompartment(Q),reactiontemperature(T)andappliedvoltage(V)),andtherelationshipswerehardtoexpressbyasimpleformula.AndfourinfluencingfactorshadremarkableeffectsonSP.Inthispaper,thefourfactorswerestudiedintheelectrodialysisexperiments.Backpropagation(BP)neuralnetworksandimprovedBPalgorithmswereappliedonthepredictionofSP,andtheirpredictioncapabilitiescouldreflectgeneralizationandadaptiveabilitiesoncomplexdatawhichhadnonlinearrelationshipswitheachother.Andwithdifferentstructuresofneuralnetworks,transferfunctionsofneuronsandlearningrates,theoptimumtrainingparameterswereobtained.ComparingBPneuralnetworkswithimprovedBPalgorithms,improvedBPalgorithmswerebetterthanBPalgorithm,duetochangingwithincreasingratiosoflearningratesandweightsproperly.Andintheconditionofhightemperaturesandvoltages,theimprovedBPalgorithmswerepredictedtohavebetterperformance,thiswasbecauseimprovedBPalgorithmshadthegeneralizationabilityforhighvalues.Keywords:BPneuralnetworks;ImprovedBPalgorithms;Electrodialysis Separationpercent;FlexibleBPalgorithm;Adaptivelearningratemethod1.Introduction Electrodialysis(ED)isanelectro-membraneprocessforseparationofionsacrosschargedmembranesfromonesolutiontoanotherwiththeaidofanelectricalpotentialdifferenceusedasadrivingforce.Thisprocesshasbeenwidelyusedforproductionofdrinkingandprocessedwaterfrombrackishwaterandseawater,treatmentofindustrialeffluents,recoveryofusefulmaterialsfromeffluentsandsaltproduction.ThebasicprinciplesandapplicationsofEDwerereviewedintheliteratures[1–6].NumerousversatileindustrialapplicationsofEDusingion-exchangemembranesweredevelopedandcommercializedbecauseoftheirhighchemicalstability,flexibilityandhighionicconductivityduetotheirstrongioniccharacteristics[7–10].Twodifferenttypesofion-exchangemembranesareusedinconventionalelectrodialysis:cation-exchange(CEM)andanion-exchange(AEM)membranes,whicharepermeabletocationicandanionicspecies,respectively[11]. However,inoperatinganelectrodialyzer,thecurrentdensityshouldbemaintainedlessthanthelimitingcurrentdensitybecausewaterdissociationgivesrisetoscaleformationandmembranebreakages[12].Sothedeterminationofthelimitingcurrentdensityandpotentialforthesystemisalsoperformed.Thelimitingcurrentdensityisthemaximumcurrentdensity(currentperunitmembranearea)thatcanbeusedwithoutcausingnegativeeffectssuchashigherelectricalresistanceandlowercurrentefficiency.Atthelimitingcurrentdensity,theconcentrationofacationorananionatthesurfacesofthecationexchangeoranion-exchangemembrane,asappropriate,inthecellswiththedepletedsolutionwillbezero[12–14].Atandbeyondthelimitingcurrentdensity,H+andOH?generatedupondissociationofwatertransportapartoftheelectriccurrent[15]. Artificialneuralnetworks(ANNs)utilizeinterconnectedmathematicalnodesorneuronstoformanetworkthatcanmodelcomplexfunctionalrelationships[16].Itsdevelopmentstartedinthe1940stohelpcognitivescientiststounderstandthecomplexityofthenervoussystem.Ithasbeenevolvedsteadilyandwasadoptedinmanyareasofscience.Basically,ANNsarenumericalstructuresinspiredbythelearningprocessinthehumanbrain.Theyareconstructedandusedasalternativemathematicaltoolstosolveadiversityofproblemsinthefieldsofsystemidentification,forecasting,patternrecognition,classification,processcontrolandmanyothers[17].Artificialneuralnetworkshavebeenusedinawiderangeofmembraneprocessapplications(reverseosmosis,nanofiltration,ultrafiltration,microfiltration,membranefiltration,gasseparation,membranebioreactorandfuelcell)[18].However,thereareafewrecordsintheliteraturewhichapplyartificialneuralnetworksforthepredictionofSPintheelectrodialysisprocess. OneANNwhichhasreceivedthemostattentionisbackpropagationnetwork(BPN)[19].BPNshavehierarchicalfeedforwardnetworksframe.IntheclassicalstructureofBPNs,theoutputsofeachlayeraresentdirectlytoeachneuronofthenextlayer.Therearemanylayers,butatleastthreelayersareconsidered:aninputlayerreceivesanddistributesinputs,amiddleorhiddenlayercapturesthenonlinearrelationshipsofinputsandoutputs,andanoutputlayerproducescalculateddata.BPNsalsomaycontainabiasneuronthatproducesconstantoutputs,butreceivesnoinputs[20,21].BPalgorithmisbasedonminimizationoferrorsinneuralnetworks.Theerrorsaredescribedasdifferencebetweenthedesiredoutputsandtheactualones[22].Thetrainingiscompletedwhentheprecisionofthetrainingismet(Fig.1). BPNscanbeoperatedwithbettergeneralizationandfault-tolerantcapabilities,however,ithassomeshortcomings: (1)Slowastringencycanleadtoalongertrainingtime. (2)Localextremumpointmayemergeinthetrainingprocess. Sointhisstudy,improvedBPalgorithmswereusedtoimprovethepredictioncapabilityofseparationpercentintheelectrodialysisprocess.Inthispaper,adaptivelearningratemethodandflexibleBPalgorithmwerethemethodsofimprovedBPalgorithmstobeappliedintheelectrodialysisprocess.2.Materialsandmethods2.1.Experimentalinstrumentsandmaterials Intheelectrodialysisprocess,theexperimentalinstrumentsandmaterialswereshowninTable1. Moreover,otherexperimentalmaterialsweremeasuringcylinders,beakers,deionizedwaterandsoon.Thepurposeoftheseexperimentswastostudytheeffectsoffeedconcentration,temperature,voltageandflowrateontheelectrodialysiscellperformance.2.2.Cellandmembranes Aplateandframeofelectrodialysiscellwhichwasmadefrompolymethylmethacrylate(PMMA)wasusedtoconducttheelectrodialysisexperiments(Fig.2).TheelectrodialysiscellconsistedofthreepartsandpackedwithapairofCEM(cationexchangemembrane)andAEM(anionexchangemembrane)andapairofelectrodes.Theoveralldimensionsoflength,widthandheightoftheelectrodialysiscellwere0.191m,0.021mand0.181m,respectively.TheeffectiveareasoftheCEMandAEMwereboth0.11×0.09m2.Bothelectrodesweremadeofpureplatinum.Thesurfaceareaofeachelectrodewas0.115×0.09m2.Andthevolumesofdiluteandconcentratecompartmentswere0.12×0.1×0.003m3and0.12×0.1×0.006m3,respectively. NaCl(sodiumchloride)solutionwasenteredintothethreecompartmentsofthecell.Cation-exchange(CEM)andanion-exchange(AEM)membraneswerepermeabletocationicandanionicspecies,respectively.Thetwomembraneswereimmersedinparallel,andanelectriccurrentwaspassedthroughthesolution.Thecationsmigratedtothecathode,andtheanionsmigratedtotheanode.Thefeedsolutionwasdividedintotwostreams.Onestreamwasdilutedwater,andtheotherwasconcentratedwater.Underacertainflowrate,theelectrodialysiscellcouldoperatetoremoveelectrolyticions.Theionswereelectrolyzedintheelectrodialysiscell,sothecathodeandanodeoccurredreactionsasfollows: Anodereactions: 2Cl??2e→Cl2↑ H2O?2e→1=2O2↑ t2Ht Cathodereaction: 2H2Ot2e→H2↑t2OH?. Intheanodereaction,Cl2andO2wereproduced.Moreover,H2wasproducedinthecathodereaction.Thesegasescouldincreasetheresistanceoftheelectrodialysiscell,sotwolittleholeswereusedtoreleasegasesontheplateoftheelectrodialysiscell.Andtheconcentratedstreamsweredisposedofftopreventaccumulationofthesegases.Listthephysicalandchemicalcharacteristicsofthemembranes(Table2).2.3.Electrodialysissetup Electrodialysissetupconsistedofatankoffeedsolution(TK-01),aDCpowersupplyandtwovalves(GB-01,GB-02)forcontrollingflowratesoffeedsolution(Fig.3).Thetotalheightoftheelectrodialysisprocesswas0.5m.Nocyclicregimewasusedfortwoconcentratedstreamsandadilutedstream,andthedilutedstreamwascollectedforconductivitiestopredictandanalysis.2.4.Experimentalprinciple Theelectrodialysisprocesswasoneofmembraneseparationtechnologies.Underthedirectelectricfield,electrodialysistechnologyutilizedtheselectivityabilityofion-exchangemembranestoseparateelectrolytesfromthesolution,inordertorealizethepurposesofdilution,concentrationorpurificationofthesolution(Fig.4).2.5.Determinationofthelimitingcurrentdensities Thelimitingcurrentdensities(LCDs)intheelectrodialysisprocessareanimportantparameterwhichdeterminestheelectricalresistanceandthecurrentutilization.Usually,LCDsdependonmembraneandsolutionpropertiesaswellasontheelectrodialysisstackconstructionandvariousoperationalparameterssuchastheflowvelocityofthedilutedsolution[23].Themethodsofmeasurementsofthelimitingcurrentdensityarevoltage–currentmethod,pH–currentmethodandsoon.Inthispaper,voltage–currentmethodwasusedtodeterminetheLCDs,thespecificstepswereasfollows. Intheconditionofconstanttemperature,concentration,andflowrate,adjustthebuttonsofvoltmeter,andrecordthegroupsofvoltagesandcurrents.Whenthevoltageswerelow,thecurrentshadalinearrelationshipwiththevoltages.Andasthevoltagesincreased,thecurrentschangedslightly.Thelimitingcurrentsweredeterminedbyinflectionpoints,andthelimitingcurrentdensitieswerealsoobtained.Forexample,T=35°C,C=0.5g/L,Q=0.5mL/s,asthevoltagesincreased,thecurrentshadalinearrelationshipwiththevoltages.Thecurrentwasupto0.51A,thevoltageshadslightinfluenceonthecurrents,sothelimitingcurrent,namely,theinflectionpointwas0.51A(Fig.5).Theeffectiveareasofthemembraneswereboth0.11×0.09m2,soLCDwas51.515A/m2. Intheexperiments,theoperatingcurrentscouldnotexceedthelimitingcurrent.Otherwise,polarizationoccurredintheelectrodialysisprocessandthepredictionofseparationpercentwouldbemeaningless.Usingvoltage–currentmethod,LCDswereobtainedinalltheexperimentalconditions(Table3). Topreventtheoccurrenceofpolarizationoftheelectrodialysiscell,alloperatingcurrentswerecontrolledunderthelimitingcurrents.Andintheelectrodialysisexperiments,themaximumlimitingcurrentwas0.80A,andtheeffectiveareasofion-exchangemembraneswere0.11×0.09m2,sothemaximumlimitingcurrentdensitywas80.808A/m2.2.6.Experimentaldata Experimentswerecarriedoutunderthelimitingcurrentdensities(Table4).Fourfactorswerestudied:feedconcentration(0.5g/L,1g/Land1.5g/L),flowrateofdilutecompartment(0.05mL/s,0.25mL/s,0.5mL/s,0.75mL/sand1mL/s),reactiontemperature(20°C,25°C,30°C,35°C,40°Cand45°C),andappliedvoltage(2V,5Vand8V).3.BPneuralnetworksandimprovedBPalgorithms3.1.BPneuralnetworks AtypicalBPneuralnetworkwasafull-connectedneuralnetworkincludinganinputlayer,ahiddenlayerandanoutputlayer[24,25].Thegoalofthetrainingprocesswastoadjusttheweights.Thenetworkstrainingwasanunconstrainednonlinearminimizationissue[26].Someresearchersclaimedthatthenetworkswithasinglehiddenlayercouldapproximateanycontinuousfunctiontoanydesiredaccuracy[27–29].BPneuralnetworkswerecomposedoftwopartswhichwereforwardanderrorbackpropagation.Intheforwardpropagation,theinputsspreadfromtheinputlayer,afterbeingprocessedbysomehiddenlayers,thenreachingtheoutputlayer,thepredictivevaluesoftheoutputsintheoutputlayerwerecomparedwiththeactualoutputsandthedifferencesbetweenthemwereaggregatedtogeneratetheerrors.Intheerrorbackpropagation,whentheerrorswerenotintherangesoferrors,theerrorswerebackpropagatedbyadjustingtheweights.Thelearningprocesscontinueduntiltheerrorsconvergedtoatargetedvalue(Fig.6).3.2.ConstructionofBPneuralnetworks ThereweresomeprecautionsaboutBPneuralnetworks: (1)Pretreatsamples.Usuallysampleswerenotuseddirectlyfornetworktraining,butengagedinpretreatmentforrawdata.TheexperimentaldatacontainedsomeuncertainfactorsinBPNtraining.Apreprocessingmethodwassonecessaryforpreparingthetrainingandtestingdatatoenhancethereliability.(2)Optimizeinitialweights.Initialweightsofthenetworkshadimpactonfinaltrainingresults,andaffectedthenetworkswhethertoachieveanacceptableaccuracyornot.(3)Selectanumberofhiddenlayersandneuronsofhiddenlayers.Theselectionofhiddenlayersandneuronsofhiddenlayerswhichaffectedmappingcapabilitiesofcomplexissuesdirectlywerethemostcriticalstep.Nowthereliablealgorithmwastostartwithafewhiddenlayersandanumberofneurons,trainandtest,thenincreasetheirnumbers.Comparingtheresultsofdifferenttrainingandtestsamples,selectmoreappropriatenumbersofhiddenlayersandtheirneurons.Inthisstudy,three-layerneuralnetworkswhichhaddifferentneuronsofahiddenlayerwereappliedintheelectrodialysisexperiments.(4)Choosetrainingsamples.Therequiredsamplesofthenetworksdependedoncomplexdegreesofmappingrelationships.Generally,themorecomplicatedmappingrelationships,themoretrainingsamplesrequired.Whenchoosingsamplesfromalldata,BPNsneededtoobeythefollowingprinciples:sufficientnumbers,representative,andwell-distributed.3.3.ImprovedBPalgorithms BPNswerebasedonsolidtheoryandrigorousderivation,however,itwasfoundthatthereweremanyshortcomingsinthetrainingprocessofBPNs,includingslowconvergence,theemergenceoflocalextremumandsoon.Inthepracticalapplication,BPalgorithmwasdifficulttobecompetent,sosomeimprovedBPalgorithmswereraisedtoenhancepredictioncapability. ThereweresomemethodsaboutimprovedBPalgorithms,suchas,additionalmomentummethod,adaptivelearningratemethod,flexibleBPalgorithmandsoon.Inthispaper,adaptivelearningratemethodandflexibleBPalgorithmwereusedtopredictseparationpercentintheelectrodialysisprocessandcomparedpredictioncapabilitywiththatofBPNs.3.3.1.Adaptivelearningratemethod ThetrainingprocessofBPalgorithmhadashortcomingofslowconvergencewhichwasaffectedbyaninappropriatelearningrate.InBPalgorithm,theadjustmentsofweightsdependedonlearningratesandgradients.AndlearningratewasconstantinBPalgorithm.Infact,whenlearningratewaslower,trainingtimegotlongerandconvergencebecameslower.Whenlearningratewastoohigh,oscillationanddivergencehademerged,thiscausedanunstablesystem.AdaptivelearningratewasshowninFig.7. Thebasicprincipleofadaptivelearningrate:whenlearningrate(η)wasincreased,thiscausedshorteninglearningtime;thehigherthelearningrate,thehardertheconvergence,andinthiscondition,learningrateshouldbedecreaseduntiltheconvergenceofthetrainingprocess.Learningratewasadjustedbythechangingoferrorsandgradients,andalsobythegradientsofthelearningrateaccordingtoerrorfunction.Moreover,thechangingofthetotalerrormaybeproceededbyadjustingheuristically,theruleswereasfollows: (1)Ifthetotalerror(E)decreased,learningrateneededtoincrease. (2)Ifthetotalerror(E)increased,learningrateneededtodecrease.Whentheratioofanewerrortotheoriginalerrorexceededacertainvalue(e.g.1.04),learningratedecreasedrapidly.3.3.2.FlexibleBPalgorithm Generallyspeaking,Sigmoidfunctionwasusedtotransferdatafromtheinputlayertothehiddenlayer.Moreover,Sigmoidfunctionkeptinfiniteinputswithinthelimitedrealmsoftheoutputs.Wheninputvariableswerelarge,theslopeofSigmoidfunctionwouldbecloseto0.Evenifthegradientchangedslightly,thiscouldinducetheweightstomakegreatchanges,sotheweightsdeviatedgraduallyfromthemostoptimisticvalue,andevenmadetheweightsofthenetworksceaseintheamendmentprocess. Whenthetrainingprocessvibrated,variablequantitiesoftheweightswouldbedecreased.Andwhenthechangingdirectionoftheweightsiskeptconstantinseveraliterations,thevariablequantitiesoftheweightswouldbeincreased.Therefore,theconvergencespeedofflexibleBPalgorithmhadanadvantageoverotherimprovedBPalgorithms.4.Resultsanddiscussion FourimportantaspectsneededbedeterminedinthedesignofBPneuralnetworksandimprovedBPalgorithm:1)Selectionoftransferfunctionsofneurons2)Selectionofnodesofahiddenlayer3)Selectionofincreasingratiosoflearningrates4)TestingthegeneralizationofBPneuralnetworksandimprovedBPalgorithm4.1.Choiceoftransferfunctionsofneurons Thefunctionswereusedtotransferbetweenneuronsoftwolayersthatwereadjacentwitheachother.Andthesetransferfunctionsmustbederivable.BPneuralnetworkshadoneormorehiddenlayers,theneuronsofhiddenlayersusedSigmoidtransferfunctions.TheneuronsofanoutputlayerusedPurelinetransferfunctions,andtheoutputscouldbearbitraryvalues.IfthetransferfunctionsoftheneuronsoftheoutputlayerwereSigmoidtransferfunctions,theentireoutputsofthenetworkswererestrictedintherangeof[?1,1]. Sigmoidtransferfunctionsincludedlog-sigmoidandtan-sigmoidfunctions.Theinputsweremappedto(0,1)and(?1,+1),respectively.Log-sigmoidfunctionwasaunipolartransferfunction.Tan-sigmoidfunctionwasabipolartransferfunctionandwascalledahyperbolictangentfunction(Fig.8). Inthepracticalapplications,basedontherelationshipsofinputsandoutputs,acertaintransferfunctionwasused.Inputscontainednonegativevalues,solog-sigmoidfunctionhadbeenadopted.Ifnegativevalueswereincluded,tag-sigmoidfunctionhadbeenused.Inthispaper,theneuronsofthehiddenlayersusedSigmoidtransferfunctions,andtheneuronsoftheoutputlayerusedPurelinetransferfunctions.4.2.Choiceofnodesofhiddenlayers Manyscholarshadengagedinstudyingtheoptimumnodesofhiddenlayers.KolmogorovTheoremprovedthataslongasthenodesofahiddenlayerwereenough,ahiddenlayeroftheneuralnetworkscouldapproachanonlinearfunctionwitharbitraryprecision.However,forafinitemappingfrominputstooutputs,unlimitednodesofahiddenlayerwerenotneeded.Andhowtochoosethenodesofthehiddenlayerwasaproblemthathadnotbeensolvedyet.Thenodesofthehiddenlayerweredeterminedbyexperienceandexperimentdesign.Generally,basedonreflectingontherelationshipsofinputsandoutputsaccurately,thesmallnodesofahiddenlayerwerechosentokeepthestructureofthenetworkssimple.Butthesmallernodes,theworsegeneralizationcapabilityoftheneuralnetworks.Onthecontrary,ifthenodesofthehiddenlayerwerelarger,thecomplexitydegreesoftrainingprocesswereincreased,andthisconditioncausedover-fittingphenomenon.Duringthedesignprocess,manyfactorsmustbeintegrated.Inthespecificdesign,atfirst,ahiddenlayerwaschosen.Ifincreasingthenodesofthehiddenlayercouldnotacquirebetternetworks,layernumbersandnodesofhiddenlayersneededtobeadded. Inthispaper,fourinfluencingfactors(voltage,concentration,temperature,flowrate)werenodesofaninputlayer,andsep