基于BP神經(jīng)網(wǎng)絡(luò)的不同時(shí)間尺度泵站前池水位預(yù)測(cè)模型

薛萍，張召，雷曉輝，盧龍彬，顏培儒，李月強(qiáng)

(1.濟(jì)南大學(xué)水利與環(huán)境學(xué)院，濟(jì)南 250022；2.中國(guó)水利水電科學(xué)研究院水資源所，北京 100038；3.天津大學(xué)建筑工程學(xué)院，天津 300072；4.河海大學(xué)水利水電學(xué)院，南京 210098)

明渠調(diào)水工程在進(jìn)行長(zhǎng)距離輸水調(diào)度時(shí)，一般通過(guò)在渠道中設(shè)置泵站、節(jié)制閘、倒虹吸等水工建筑物解除地形條件對(duì)輸水限制的影響，同時(shí)在建筑物前設(shè)置水位計(jì)、流量計(jì)等監(jiān)測(cè)設(shè)備獲取水情信息監(jiān)控通水安全。相比于實(shí)時(shí)水位監(jiān)測(cè)，高精度的水位預(yù)測(cè)更能在水量調(diào)度過(guò)程中為調(diào)度人員提供科學(xué)指導(dǎo)，尤其是泵站前池水位預(yù)測(cè)，對(duì)泵站調(diào)控、水量調(diào)度、渠道安全均具有重要意義。受氣候、溫度、人類活動(dòng)等多種因素影響，監(jiān)測(cè)設(shè)備采集到的水情序列往往呈現(xiàn)出非線性和不確定性的特點(diǎn)，常規(guī)方法很難對(duì)其進(jìn)行規(guī)律分析和趨勢(shì)預(yù)測(cè)。學(xué)者[1-3]曾通過(guò)建立水力學(xué)模型模擬渠道水流的變化過(guò)程，但建模要求完整且準(zhǔn)確的地形資料、工程參數(shù)和實(shí)測(cè)數(shù)據(jù)，糙率率定過(guò)程也較為反復(fù)和繁瑣[4]，因此存在較大的局限性。隨著人工智能技術(shù)和機(jī)器學(xué)習(xí)方法的不斷進(jìn)步，采用數(shù)據(jù)驅(qū)動(dòng)的方法進(jìn)行預(yù)測(cè)可避免水力學(xué)建模的多方面要求和諸多限制，直接探索數(shù)據(jù)間的內(nèi)在規(guī)律[5]。

到目前為止，大部分學(xué)者[6-9]通過(guò)構(gòu)建神經(jīng)網(wǎng)絡(luò)模型進(jìn)行水位預(yù)測(cè),如采用優(yōu)化后的RBF神經(jīng)網(wǎng)絡(luò)、LSTM神經(jīng)網(wǎng)絡(luò)模型、小波神經(jīng)網(wǎng)絡(luò)等應(yīng)用于地下水位預(yù)測(cè)，預(yù)測(cè)精度高且預(yù)測(cè)效果處于較優(yōu)水平；雖可建立向量機(jī)RVM預(yù)測(cè)模型[10]、Mike模型[11]、相似模型[12]、統(tǒng)計(jì)模型[13]、貝葉斯模型[14]等進(jìn)行水位預(yù)測(cè)，但使用時(shí)受限于一定的條件，故應(yīng)用于調(diào)水工程中水位預(yù)測(cè)時(shí)不太廣泛；因神經(jīng)網(wǎng)絡(luò)已廣泛應(yīng)用于水位預(yù)測(cè)，發(fā)展逐漸趨于成熟，也有眾多學(xué)者[15-26]通過(guò)將神經(jīng)網(wǎng)絡(luò)模型、算法組合或者改進(jìn)算法的方式進(jìn)行水位預(yù)測(cè)，如吳美玲[27]等將KNN、GA、BP相結(jié)合，對(duì)秦淮河的洪水位進(jìn)行預(yù)測(cè)，相比于未組合的神經(jīng)網(wǎng)絡(luò)模型預(yù)測(cè)精度提高但略為復(fù)雜,但未組合的神經(jīng)網(wǎng)絡(luò)模型較為簡(jiǎn)單實(shí)用，如高學(xué)平等[28]利用BP神經(jīng)網(wǎng)絡(luò)對(duì)泵站站前水位進(jìn)行預(yù)測(cè)，發(fā)現(xiàn)BP神經(jīng)網(wǎng)絡(luò)在解決非線性問(wèn)題上有很大優(yōu)勢(shì)，在智能預(yù)測(cè)方面存在巨大潛力。同時(shí)，常用的評(píng)價(jià)指標(biāo)有ERMS(均方根誤差)、R2(決定系數(shù))[29]等。

綜上可知，構(gòu)建神經(jīng)網(wǎng)絡(luò)進(jìn)行水位預(yù)測(cè)是一種切實(shí)可行的研究方法。人工神經(jīng)網(wǎng)絡(luò)等智能算法在水文預(yù)測(cè)應(yīng)用中具有一定的適用性條件，如：ANN有強(qiáng)大非線性能力，但結(jié)構(gòu)簡(jiǎn)單不能保存前時(shí)信息而無(wú)法學(xué)習(xí)時(shí)間序列數(shù)據(jù)；RNN能保持先前時(shí)刻的水位預(yù)測(cè)，可有效處理序列數(shù)據(jù)，但梯度傳遞中存在缺陷；LSTM具有長(zhǎng)短期記憶功能，在一定程度上解決梯度消失和梯度爆炸，但長(zhǎng)序列依舊存在問(wèn)題且不能并行；受信息單向流動(dòng)特點(diǎn)的限制，經(jīng)典BP神經(jīng)網(wǎng)絡(luò)考慮有限數(shù)量的歷史信息，僅適用于短時(shí)預(yù)測(cè)，但結(jié)構(gòu)穩(wěn)定，具有多功能性和簡(jiǎn)便性的特征，可靈活處理非線性問(wèn)題并達(dá)到較高的預(yù)測(cè)精度，具有極強(qiáng)的非線性映射能力；而水文預(yù)測(cè)中的水情序列因受人為因素影響較大，呈現(xiàn)出較大的非線性特點(diǎn)，故BP神經(jīng)網(wǎng)絡(luò)適用于水文預(yù)測(cè)。BP神經(jīng)網(wǎng)絡(luò)自1986年被Rumelhart等[30]提出后，已被廣泛應(yīng)用于水文預(yù)測(cè)領(lǐng)域的研究。本文通過(guò)建立BP神經(jīng)網(wǎng)絡(luò)，利用歷史數(shù)據(jù)預(yù)測(cè)泵站前池未來(lái)時(shí)刻的水位，分析時(shí)間序列比例及影響因子對(duì)水位預(yù)測(cè)的影響，預(yù)測(cè)結(jié)果既可為泵站前池水位預(yù)測(cè)提供一種預(yù)測(cè)方式，也給泵站前池水位變化趨勢(shì)提供參考數(shù)據(jù)。

1 研究方法

選取泵站前池水位為研究對(duì)象，利用相關(guān)性分析確定影響因子，并將其作為輸入進(jìn)行BP神經(jīng)網(wǎng)絡(luò)模型構(gòu)建，預(yù)測(cè)結(jié)果用各指標(biāo)參數(shù)情況評(píng)判優(yōu)劣。

1.1 影響因子識(shí)別

受各種水力因素(斷面面積、水力比降、糙率等)影響，渠道內(nèi)斷面流量和水位之間存在對(duì)應(yīng)關(guān)系。泵站前池水位作為監(jiān)測(cè)斷面之一，與相鄰斷面的水位、泵站的流量、上游流量、流量差等均可能存在水力聯(lián)系。將這些相關(guān)的水位、流量等作為變量，對(duì)各變量與預(yù)測(cè)因子進(jìn)行相關(guān)性分析，識(shí)別出具有一定關(guān)聯(lián)度的影響因子。

采取的影響因子識(shí)別方法有皮爾遜(Pearson)相關(guān)系數(shù)法、肯德?tīng)?Kendall)相關(guān)性系數(shù)法、斯皮爾曼(Spearman)等級(jí)相關(guān)系數(shù)法及灰關(guān)聯(lián)分析。皮爾遜相關(guān)系數(shù)法用于度量2個(gè)變量之間的相關(guān)程度，2個(gè)變量之間的皮爾遜相關(guān)系數(shù)定義為2個(gè)變量之間的協(xié)方差和標(biāo)準(zhǔn)差的商；肯德?tīng)栂嚓P(guān)性系數(shù)法是表示多列等級(jí)變量相關(guān)程度的一種方法，若n個(gè)同類的統(tǒng)計(jì)對(duì)象按特定屬性排序，其他屬性通常是亂序的，同序?qū)彤愋驅(qū)χ钆c總對(duì)數(shù)[n(n-1)/2]的比值定義為肯德?tīng)栂禂?shù)；斯皮爾曼等級(jí)相關(guān)系數(shù)法是根據(jù)等級(jí)資料研究2個(gè)變量間相關(guān)關(guān)系的方法，依據(jù)2列成對(duì)等級(jí)的各對(duì)等級(jí)數(shù)之差來(lái)進(jìn)行計(jì)算，利用單調(diào)方程評(píng)價(jià)2個(gè)統(tǒng)計(jì)變量的相關(guān)性。上述3種方法的相關(guān)性指標(biāo)或相關(guān)系數(shù)為-1～1：絕對(duì)值越接近1，相關(guān)性越高；絕對(duì)值等于0時(shí)，不具備相關(guān)性?；谊P(guān)聯(lián)分析是一種分析系統(tǒng)中各因子關(guān)聯(lián)程度的量化方法，根據(jù)不同變量序列間發(fā)展趨勢(shì)的相似或相異程度，衡量因素間關(guān)聯(lián)程度?；疑P(guān)聯(lián)度小于0.6時(shí)，不具有相關(guān)性；灰色關(guān)聯(lián)度越趨近1，相關(guān)性程度越高。

1.2 BP神經(jīng)網(wǎng)絡(luò)

BP神經(jīng)網(wǎng)絡(luò)是一個(gè)利用誤差反向傳播算法進(jìn)行訓(xùn)練的多層前饋神經(jīng)網(wǎng)絡(luò)，一般包括輸入層、隱含層、輸出層3部分。輸入層具有信息接入即信號(hào)接收功能，信號(hào)接收完成后將信息傳遞到隱含層，輸入層神經(jīng)元的個(gè)數(shù)為輸入影響因子的數(shù)量n；隱含層負(fù)責(zé)信息處理、信息變換，隱含層神經(jīng)元的個(gè)數(shù)為m，小于N-1(N是訓(xùn)練樣本數(shù))，在MATLAB中經(jīng)測(cè)試取值；經(jīng)隱含層后信息傳遞到輸出層，輸出層將結(jié)果對(duì)外輸出，1個(gè)3層的典型網(wǎng)絡(luò)結(jié)構(gòu)見(jiàn)圖1。

圖1 BP神經(jīng)網(wǎng)絡(luò)模型結(jié)構(gòu)

神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)參數(shù)設(shè)置有：最大訓(xùn)練次數(shù)=100，訓(xùn)練要求精度=1×10-8，學(xué)習(xí)率=0.01。參數(shù)設(shè)置完成后，網(wǎng)絡(luò)利用誤差的反向傳播自動(dòng)調(diào)整權(quán)重和閾值，驅(qū)使BP神經(jīng)網(wǎng)絡(luò)中表達(dá)函數(shù)能夠得到最優(yōu)解，最后輸出預(yù)測(cè)結(jié)果及評(píng)判結(jié)果的各項(xiàng)指標(biāo)值。

1.3 預(yù)測(cè)結(jié)果評(píng)判標(biāo)準(zhǔn)

以R2(決定系數(shù))、ERMS(均方根誤差)、EMA(平均絕對(duì)誤差)為評(píng)判標(biāo)準(zhǔn)對(duì)預(yù)測(cè)結(jié)果的優(yōu)劣進(jìn)行評(píng)判，R2越趨近1，ERMS和EMA越趨近0，說(shuō)明預(yù)測(cè)精度越高。

2 研究區(qū)概況

膠東調(diào)水工程是山東省水利建設(shè)的重要組成部分，包括引黃調(diào)水工程和引黃濟(jì)青工程2條輸水線路。引黃濟(jì)青工程于1986年4月15日開(kāi)工興建，1989年11月25日正式通水；引黃調(diào)水工程于2003年12月19日開(kāi)工，2013年7月全線貫通，2013年12月主體工程建成通水。其中，引黃調(diào)水工程包括明渠段和管道段兩部分，明渠段以宋莊分水閘為起點(diǎn)，以黃水河泵站為終點(diǎn)，途經(jīng)灰埠、東宋、辛莊3座泵站及若干倒虹吸、渡槽等輸水建筑物，全長(zhǎng)約160 km。本文所選研究區(qū)為引黃調(diào)水工程明渠段，具體研究區(qū)域?yàn)闁|宋泵站前后，其上游控制節(jié)點(diǎn)為灰埠泵站，下游控制節(jié)點(diǎn)為埠上節(jié)制閘，該渠段及沿線建筑物分布情況見(jiàn)圖2。

圖2 研究渠段及沿線建筑物分布

3 結(jié)果與討論

3.1 影響因子識(shí)別結(jié)果

研究東宋泵站未來(lái)時(shí)刻的前池水位時(shí)，考慮到水位流量間關(guān)系及人為因素影響，除選取相鄰斷面水位作為影響因子外，還選取東宋泵站流量、灰埠泵站流量、灰埠-東宋2級(jí)泵站流量差為影響因子進(jìn)行預(yù)測(cè)，且影響因子均為當(dāng)前時(shí)刻的影響因子。表1為不同方法下的各因子與前池水位間的相關(guān)性分析結(jié)果。

表1 影響因子相關(guān)性分析結(jié)果

由表1可知，影響因子相關(guān)性排序從高到低依次為東宋泵站站前水位、2級(jí)泵站流量差、海鄭河倒虹下游水位、海鄭河倒虹上游水位、泵站流量、東宋泵站流量及上游泵站流量。前4項(xiàng)影響因子的各系數(shù)均為0.8～0.9，識(shí)別為相關(guān)性較高的影響因子，建模時(shí)優(yōu)先考慮；后3項(xiàng)影響因子的指標(biāo)中僅灰色關(guān)聯(lián)度表明其相關(guān)性程度較高，故識(shí)別為相關(guān)性較低的影響因子，建模時(shí)可考慮在內(nèi)，但不重點(diǎn)考慮。

3.2 水位預(yù)測(cè)結(jié)果分析

利用BP神經(jīng)網(wǎng)絡(luò)模型進(jìn)行泵站前池水位預(yù)測(cè)，預(yù)測(cè)結(jié)果從時(shí)間序列、影響因子2個(gè)方面進(jìn)行分析。

3.2.1時(shí)間序列

將不同時(shí)間尺度的數(shù)據(jù)按照一定的比例進(jìn)行訓(xùn)練和驗(yàn)證，對(duì)比訓(xùn)練時(shí)長(zhǎng)和預(yù)測(cè)精度。結(jié)果表明，訓(xùn)練期和預(yù)見(jiàn)期的最優(yōu)比例為7∶3，減小該比例會(huì)使預(yù)測(cè)精度降低，增大該比例預(yù)測(cè)精度與之相差無(wú)幾，且數(shù)據(jù)需求量大幅提升。

采用3 600個(gè)數(shù)據(jù)預(yù)測(cè)未來(lái)2 h的水位變化，7∶3比例下的R2、ERMS、EMA分別維持在0.95、0.04、0.03左右。增大該比例時(shí)各指標(biāo)預(yù)測(cè)效果略有提高，但相差不大，高于5∶1時(shí)其預(yù)測(cè)精度基本不提高。具體對(duì)比見(jiàn)圖3和圖4。

圖3 未來(lái)2 h水位預(yù)測(cè)結(jié)果(7∶3)

圖4 未來(lái)2 h水位預(yù)測(cè)結(jié)果(5∶1)

以7∶3的比例分別對(duì)3組3個(gè)月的數(shù)據(jù)進(jìn)行訓(xùn)練和驗(yàn)證，R2維持在0.93～0.98，ERMS維持在0.02～0.05、EMA維持在0.02～0.04，預(yù)測(cè)結(jié)果見(jiàn)圖5。

圖5 未來(lái)2 h水位預(yù)測(cè)結(jié)果(7∶3)

以7∶3的比例對(duì)1個(gè)月的數(shù)據(jù)進(jìn)行驗(yàn)證，驗(yàn)證結(jié)果表明該比例對(duì)1個(gè)月的數(shù)據(jù)量依舊適用，具體見(jiàn)圖6。

圖6 未來(lái)2 h水位預(yù)測(cè)結(jié)果(7∶3)

由上述可知，最優(yōu)比例適用于不同時(shí)間尺度的數(shù)據(jù)，且最優(yōu)比例的確定既可節(jié)省神經(jīng)網(wǎng)絡(luò)學(xué)習(xí)的時(shí)間，又能提高預(yù)測(cè)精度，在模型中具有較大影響力。

3.2.2影響因子

影響因子數(shù)量。當(dāng)影響因子與預(yù)測(cè)因子之間都具有較高相關(guān)性時(shí)，影響因子數(shù)量越多，預(yù)測(cè)結(jié)果越精確。但影響因子的數(shù)量會(huì)增加訓(xùn)練期的數(shù)據(jù)需求量，為減少數(shù)據(jù)需求量且保證預(yù)測(cè)精度，利用不同數(shù)量的影響因子進(jìn)行訓(xùn)練和驗(yàn)證，驗(yàn)證結(jié)果表明：短期(1～3個(gè)月)內(nèi)至少選擇3～5個(gè)影響因子進(jìn)行訓(xùn)練，3個(gè)月至1 a的數(shù)據(jù)量則至少需要5～7個(gè)相關(guān)性最大的影響因子。

影響因子種類。研究表明，選取相關(guān)性最高的影響因子構(gòu)建模型，預(yù)測(cè)精度更高。由影響因子相關(guān)性分析結(jié)果可知，相關(guān)性最高的3個(gè)影響因子為泵站當(dāng)前時(shí)刻的水位、上游相鄰節(jié)點(diǎn)的水位、流量差。采用3個(gè)影響因子對(duì)1個(gè)月的數(shù)據(jù)進(jìn)行訓(xùn)練和預(yù)測(cè)，上述3個(gè)影響因子的預(yù)測(cè)效果最佳，具體見(jiàn)圖7。

圖7 3個(gè)因子水位預(yù)測(cè)結(jié)果(7∶3)

影響因子的時(shí)間間隔。數(shù)據(jù)間隔均為2 h時(shí)，對(duì)東宋泵站未來(lái)時(shí)刻的水位進(jìn)行預(yù)測(cè)：未來(lái)2 h的水位預(yù)測(cè)結(jié)果較穩(wěn)定，R2結(jié)果均在0.9以上，ERMS和EMA也較??；未來(lái)4 h的水位預(yù)測(cè)結(jié)果一般，R2為0.8～0.9，ERMS和EMA比2 h預(yù)測(cè)略大；未來(lái)6 h的水位預(yù)測(cè)結(jié)果較差，R2不穩(wěn)定且變化區(qū)間較大，結(jié)果較好時(shí)也僅為0.7左右，ERMS和EMA則預(yù)測(cè)結(jié)果偏大，分別在0.11和0.09左右。即訓(xùn)練期內(nèi)數(shù)據(jù)不發(fā)生改變時(shí)，預(yù)測(cè)時(shí)間越長(zhǎng)，預(yù)測(cè)精度越低。對(duì)3個(gè)月的數(shù)據(jù)進(jìn)行篩選，使2 h間隔轉(zhuǎn)為4 h間隔，并預(yù)測(cè)東宋泵站未來(lái)4 h的水位，預(yù)測(cè)結(jié)果見(jiàn)圖8。

圖8 未來(lái)4 h水位變化結(jié)果(7∶3)

對(duì)10個(gè)月的數(shù)據(jù)進(jìn)行4 h間隔的篩選并預(yù)測(cè)未來(lái)4 h水位，預(yù)測(cè)結(jié)果見(jiàn)圖9。

圖9 未來(lái)4 h水位變化結(jié)果(7∶3)

研究結(jié)果表明，與采用2 h間隔的數(shù)據(jù)直接預(yù)測(cè)相比，采用4 h間隔的數(shù)據(jù)預(yù)測(cè)泵站未來(lái)4 h的水位，其預(yù)測(cè)精度更高，R2變化基本維持在0.82～0.93，ERMS和EMA分別維持在0.05～0.06、0.04～0.05。

對(duì)1 a的數(shù)據(jù)進(jìn)行篩選，使2 h間隔轉(zhuǎn)為6 h間隔，并預(yù)測(cè)東宋泵站未來(lái)6 h的水位。預(yù)測(cè)結(jié)果表明，篩選后進(jìn)行預(yù)測(cè)比用2 h的數(shù)據(jù)直接預(yù)測(cè)其預(yù)測(cè)效果更差。經(jīng)分析，上述現(xiàn)象是由6 h的時(shí)間間隔太長(zhǎng)不能完全反映各因子變化規(guī)律導(dǎo)致，所以篩選后進(jìn)行預(yù)測(cè)的結(jié)果比直接采用2 h間隔的數(shù)據(jù)進(jìn)行預(yù)測(cè)結(jié)果更差。

4 結(jié) 論

時(shí)間序列比例對(duì)水位預(yù)測(cè)結(jié)果的影響：訓(xùn)練期和預(yù)測(cè)期的最佳比例為7∶3，提高比例其預(yù)測(cè)精度無(wú)明顯變化，降低比例則預(yù)測(cè)效果變差。

影響因子對(duì)預(yù)測(cè)結(jié)果的影響：數(shù)據(jù)量與影響因子數(shù)量呈對(duì)應(yīng)關(guān)系，3個(gè)月的數(shù)據(jù)量需3～5個(gè)影響因子進(jìn)行訓(xùn)練，3個(gè)月至1 a的數(shù)據(jù)量則需5～7個(gè)影響因子確保相同預(yù)測(cè)效果。

數(shù)據(jù)的時(shí)間間隔對(duì)預(yù)測(cè)結(jié)果的影響：一般情況下，數(shù)據(jù)間隔不變，預(yù)測(cè)精度隨預(yù)測(cè)時(shí)間的增加而逐漸降低；但當(dāng)數(shù)據(jù)能夠反映各因子變化規(guī)律時(shí)，數(shù)據(jù)間隔和預(yù)測(cè)時(shí)間相同，預(yù)測(cè)效果更佳。

Prediction model for forebay water level of pumping stations with different time scales based on BP neural networks

XUE Ping1,ZHANG Zhao2,LEI Xiaohui2,LU Longbin1,YAN Peiru3,LI Yueqiang4

(1.School of Water Conservancy and Environment,University of Jinan,Jinan 250022,China;2.Institute of Water Resources,China Institute of Water Resources and Hydropower Research,Beijing 100038,China;3.School of Civil Engineering,Tianjin University,Tianjin 300072,China;4.College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210098,China)

Abstract:Considering the difficulty in water level prediction under building control,a water level prediction model for the forebay of a pumping station was built on the basis of back-propagation(BP)neural networks,and the influence of time series and impact factors on the accuracy of water level prediction was analyzed under different time scales.The constructed model was applied to the Dongsong Pumping Station of the Jiaodong Water Transfer Project.The research results revealed that:when the total amount of data was fixed,and the ratio of the training period to the prediction period was 7∶3,the prediction result was good;a larger amount of data was accompanied by a greater number of positively correlated impact factors required for certain prediction accuracy;in a short period of time,when the prediction time interval was the same as the time interval of the data itself,the prediction effect was better.The constructed model can meet the demand for dynamic prediction of the water level in the forebay of the open channel water transfer project and can achieve the 2 h accurate prediction of the forebay water level of the pumping station and the 4 h general accurate prediction.Additionally,it can be popularized and applied in other similar open channel water transfer projects.

Keywords:forebay of pump station;water level prediction;BP neural network;time series;proportion

Received:2021-07-04Revised:2021-09-30Onlinepublishing:2021-10-11

Onlinepublishingaddress:https://kns.cnki.net/kcms/detail/13.1430.TV.20211009.1638.002.html

Fund:National Natural Science Foundation of China(51779268)

Author′sbrief:XUE Ping(1998-),female,Weifang Shandong Province,mainly engaged in research on hydrology and water resources.E-mail：2857487127@qq.com

Correspondingauthor：LEI Xiaohui(1974-),male,Weinan Shaanxi Province,Ph.D.,professor-level senior engineer,mainly engaged in research on hydrology and water resources,reservoir dispatching,and hydraulic control.E-mail:lxh@iwhr.com

DOI：10.13476/j.cnki.nsbdqk.2022.0040

For the long-distance water dispatching of an open channel water transfer project,hydraulic structures such as pumping stations,control gates,and inverted siphons are generally set up in the channel to relieve the influence of terrain conditions on water transfer restrictions.Meanwhile,monitoring equipment such as water level meters and flow meters are installed in front of buildings to obtain water information and monitor water safety.Compared with real-time water level monitoring,high-precision water level prediction can provide more scientific guidance for dispatchers in the process of water dispatching,especially the water level prediction in the forebay of pumping stations,which is of great significance to the regulation of pumping stations,water dispatching,and channel safety.Affected by various factors such as climate,temperature,and human activities,the hydrological sequence collected by monitoring equipment often presents the characteristics of nonlinearity and uncertainty,and it is difficult to analyze the laws and predict the trend by conventional methods.Scholars[1-3]have built hydraulic models to simulate the changing process of channel water flow,but the modeling requires complete and accurate topographic data,engineering parameters,and measured data;moreover,the calibration process of the roughness rate is also repetitive and cumbersome[4],and thus there are huge limitations.With the continuous progress of artificial intelligence technology and machine learning methods,the data-driven methods used for the prediction can avoid many requirements and limitations of hydraulic modeling and directly explore the inherent laws between data[5].

Up to now,most scholars[6-9]have built neural network models for water level prediction,such as the optimized RBF neural network,LSTM neural network model,and wavelet neural network applied in groundwater level prediction,with high prediction accuracy and an excellent prediction effect.Although the relevance vector machine(RVM)prediction model[10],Mike model[11],similarity model[12],statistical model[13],and Bayesian model[14]can be constructed for water level prediction,their applications are limited to a certain extant,and hence they are not widely used in water level prediction for water transfer projects.As the neural network has been commonly used in water level prediction,and its development has gradually matured,many scholars[15-26]have made water level predictions by combining neural network models and algorithms or improving algorithms.For instance,Wu et al.[27]combined KNN,GA,and BP to predict the flood level of the Qinhuai River,and compared with the neural network model without combination,the combined method has higher prediction accuracy but is slightly more complicated.In other words,the uncombined neural network models are simple and practical.For example,Gao et al.[28]used the BP neural network to predict the water level in front of the pumping station and found that the BP neural network has great advantages in solving nonlinear problems and has significant potential in intelligent prediction.In addition,the commonly used evaluation indicators include the root mean square error(ERMS)and determination coefficient(R2)[29].

In summary,it is a feasible research method to construct a neural network for water level prediction.Moreover,intelligent algorithms such as artificial neural networks have certain applicability conditions in hydrological prediction applications.For example,ANN has a strong nonlinear ability,but due to its simple structure,previous information can not be saved,and time series data can not be learned.RNN can retain the water level prediction at the previous moment and can effectively process sequence data,but there are defects in gradient transfer.LSTM has long and short-term memory functions and can solve gradient disappearance and gradient explosion to a certain extent,but there are still problems in long sequences,and it can not be parallelized.Restricted by the one-way flow of information,the classical BP neural network considers a limited amount of historical information and is only suitable for short-term prediction,but it has a stable structure and features versatility and simplicity,which can flexibly deal with nonlinear problems,achieve high prediction accuracy,and has strong nonlinear mapping ability.As the hydrological sequence in hydrological forecasting is greatly affected by human factors and presents a prominent nonlinear characteristic,and the BP neural network is suitable for hydrological forecasting.Since BP neural network was proposed by Rumelhart et al.[30]in 1986,it has been widely used in research on hydrological prediction.In this paper,a BP neural network was established.We used historical data to predict the water level in the forebay of the pumping station and analyzed the influence of the time series proportion and impact factors on the water level prediction.The research results can provide a new method for water level prediction and reference data for the changing trend of the water level in the forebay of the pumping station.

1 Research method

The water level in the forebay of the pumping station is selected as the research object.The impact factors are determined by correlation analysis and are used as the input to construct the BP neural network model,and then the prediction results are judged by the parameters of each indicator.

1.1 Impact factor identification

Under the influence of various hydraulic factors(section area,hydraulic gradient,roughness,etc.),there is a corresponding relationship between the section flow and the water level in the channel.As one of the monitoring sections,the water level in the forebay of the pumping station may have a hydraulic connection with the water level of the adjacent section,the flow of the pumping station,the upstream flow,and the flow difference.Taking these relevant water levels and flow as variables,we conduct a correlation analysis of each variable and the predictor,and the impact factors with a certain degree of correlation are identified.

The impact factor identification methods adopted include Pearson′s correlation coefficient,Kendall′s correlation coefficient,Spearman′s rank correlation coefficient,and grey relational analysis(GRA).Pearson′s correlation coefficient is used to measure the degree of correlation between two variables,and Pearson′s correlation coefficient between two variables is defined as the quotient of the covariance and standard deviation between the two variables.Kendall′s correlation coefficient is a method to represent the degree of correlation of multi-column rank variables.Ifnsimilar statistical objects are sorted by a specific attribute,other attributes are usually out of order,and the ratio of the difference between same-order pairs and out-of-order pairs to the total number of pairs[n(n-1)/2]is defined as Kendall′s coefficient.Spearman′s rank correlation coefficient is a method to study the correlation between two variables according to the rank data;in other words,it is calculated according to the rank difference between each pair of two-column paired ranks,and the monotone equation is used to evaluate the correlation of the two statistical variables.The range of the correlation indicator or correlation coefficient of the above three methods is from-1 to 1:When the absolute value of the correlation coefficient is closer to 1,the correlation is higher;when it is equal to zero,there is no correlation.GRA is a quantitative method for analyzing the correlation degree of each factor in the system,which measures the degree of correlation between factors according to the degree of similarity or dissimilarity in development trends among different variable sequences.When GRA is less than 0.6,it is considered that there is no correlation,and when it is closer to 1,the correlation degree is higher.

1.2 BP neural networks

A BP neural network is a multilayer feedforward neural network trained by an error back-propagation algorithm,generally including the input layer,hidden layer,and output layer.The input layer has the function of information access,i.e.,signal reception.When the signal reception is completed,the information is transmitted to the hidden layer,and the number of neurons in the input layer is the numbernof input impact factors.The hidden layer is responsible for information processing and information transformation,and the number of neurons in the hidden layer ism,which is less thanN-1(Nis the number of training samples),whose value is tested in MATLAB.Then,the information is transmitted from the hidden layer to the output layer,and the output layer outputs the results.The typical structure of a three-layer network is shown in Fig.1.

Fig.1 BP neural network model structure

The neural network structure parameters are set as follows:maximum training times=100;required accuracy of training=1×10-8;learning rate=0.01.Upon the parameter setting,the network automatically adjusts the weights and thresholds by the back-propagation of errors,which drives the expression function in the BP neural network to obtain the optimal solution,and finally,it outputs the prediction results and the indicator values of the evaluation results.

1.3 Evaluation criteria of prediction results

R2,ERMS,and the mean absolute error(EMA)are used as the evaluation criteria to judge the strengths and weaknesses of the prediction results.WhenR2is closer to 1,andERMSandEMAare closer to zero,the prediction accuracy is higher.

2 Overview of study area

The Jiaodong Water Transfer Project is an important part of the water conservancy construction in Shandong Province,including two water transmission lines:the Yellow River Transfer Project and the Water Transfer Project from the Yellow River to Qingdao.The latter started on April 15,1986,and it was officially put into operation on November 25,1989;the Yellow River Water Transfer Project started on December 19,2003,and the whole line was completed in July 2013,with the main project put into operation in December.The Yellow River Transfer Project includes two parts:the open channel section and the pipeline section.The open channel section starts from the Songzhuang Transfer Gate and terminates at the Huangshuihe Pumping Station,passing through three pumping stations in Huibu,Dongsong,and Xinzhuang,several inverted siphons,aqueducts,and other water transfer structures,with a total length of about 160 km.The study area selected in this paper is the open channel section of the Yellow River Water Transfer Project.Specifically,the study area is around the Dongsong Pumping Station,with the upstream control node as the Huibu Pumping Station and the downstream control node as the control gate on the port.The building distribution of this section and buildings along the line are shown in Fig.2.

Fig.2 Canal section and building along the distribution

3 Results and discussion

3.1 Identification results of impact factors

The relationship between the water level and flow rate and the influence of human factors were considered when studying the water level in the forebay of the Dongsong Pumping Station in the future.In addition to the water level of the adjacent section,the flow of the Dongsong Pumping Station,the flow of the Huibu Pumping Station,and the flow difference between the two pumping stations were also selected as the impact factors for prediction.The impact factors are all the impact factors at the current time.Tab.1 shows the correlation analysis results between each factor and the water level of the forebay under different methods.

Tab.1 Correlation analysis of impact factors

It can be seen from Tab.1 that the order of the correlation of impact factors from high to low is the water level in front of the Dongsong Pumping Station,the flow difference of the two pumping stations,downstream water level of the Haizheng River inverted siphon,upstream water level of the Haizheng River inverted siphon,the flow of the pumping station,flow of the Dongsong Pumping Station,and upstream flow of the pumping station.The coefficients of the first four impact factors are all between 0.8 and 0.9,which are identified as impact factors with a high correlation and are given priority when modeling.Considering the indicators of the last three impact factors,only GRA indicates that the degree of correlation is high,and thus they are identified as impact factors with a low correlation,which can be considered in modeling but are not importantly considered.

3.2 Analysis of water level prediction results

The BP neural network model was used to predict the water level in the forebay of pumping stations,and the prediction results were analyzed from the aspects of time series and impact factors.

3.2.1Timeseries

The data of different time scales were trained and verified according to a certain proportion,and the training duration and prediction accuracy were compared.The results indicate that the optimal ratio of the training period to the prediction period is 7∶3.Reducing the ratio will lessen the prediction accuracy,while increasing the ratio almost does not change the prediction accuracy,and the required data volume is significantly raised.

We used 3 600 data to predict the water level change in the next two hours,andR2,ERMS,andEMAat the ratio of 7∶3 were maintained at about 0.95,0.04,and 0.03,respectively.When the ratio was increased,the prediction effect of each indicator was slightly improved,but the difference was not large;when the ratio was higher than 5∶1,the prediction accuracy basically would not see a rise.The specific comparison is shown in Fig.3 and Fig.4.

Fig.3 The result of water level forecast in the next 2 h(7∶3)

Fig.4 The result of water level forecast in the next 2 h(5∶1)

Three groups of three-month data were trained and validated at a ratio of 7∶3.R2was maintained at 0.93-0.98,ERMSat 0.02-0.05,andEMAat 0.02-0.04.The prediction results are shown in Fig.5.

Fig.5 The result of water forecast change in the next 2 h(7∶3)

The data of one month was verified at a ratio of 7∶3,and the verification results indicated that the ratio could still be applied to the amount of data of one month,as shown in Fig.6.

Fig.6 The result of water level forecast in the next 2 h(7∶3)

It can be seen from the above that the optimal ratio is suitable for data of different time scales,and the determination of the optimal ratio can not only save the learning time of the neural network but also improve the prediction accuracy,which has a great influence on the model.

3.2.2Impactfactors

The number of impact factors.When there is a high correlation between impact factors and predictors,a higher number of impact factors leads to more accurate prediction results.However,the increase in the number of impact factors can elevate the data demand during the training period.Therefore,to reduce the data demand and ensure prediction accuracy,we employed different numbers of impact factors for training and verification.The verification results revealed that at least three to five impact factors should be selected for training in the short term(one to three months),and at least five to seven impact factors with the greatest correlation were required for the data volume of three months to a year.

Types of impact factors.Studies have shown that higher prediction accuracy can be achieved when the most relevant impact factors are selected for modeling.According to the correlation analysis results of the impact factors,the three impact factors with the highest correlation are the water level of the pumping station at the current moment,the water level of the upstream adjacent nodes,and the flow difference.Three impact factors were applied to train and predict data of one month,and the above three impact factors registered the best prediction effect,as shown in Fig.7.

Fig.7 3-factor water level prediction result map(7∶3)

The time interval of the impact factors.When the data interval was 2 h,the water level of the Dongsong Pumping Station in the future was predicted:The water level prediction results in the next two hours were relatively stable,withR2greater than 0.9 and smallERMSandEMA;the prediction results of water levels in the next four hours were general,withR2of 0.8-0.9 andERMSandEMAslightly larger than those predicted in two hours;the prediction results of the water level in the next six hours were poor:R2was unstable and had a large variation range,and it was only about 0.7 when the results were good,whileERMSandEMAwere overly great.In other words,when the data does not change during the training period,a longer prediction time is accompanied by lower prediction accuracy.The three-month data were screened to change the interval from 2 h to 4 h,and the water level of the Dongsong Pumping Station in the next 4 h was predicted.The prediction results are shown in Fig.8.

Fig.8 The result of water level change in the next 4 h(7∶3)

The ten-month data were screened at an interval of 4 h,and the water level in the next 4 h was predicted.The prediction results are shown in Fig.9.

Fig.9 The result of water level change in the next 4 h(7∶3)

The research results demonstrate that compared with the direct prediction using the data at an interval of 2 h,the prediction using the data at an interval of 4 h registers higher accuracy in predicting the water level of the pumping station in the next 4 h,withR2,ERMS,andEMAin the range of 0.82-0.93,0.05-0.06,and 0.04-0.05,respectively.

The one-year data were screened to convert the interval from 2 h to 6 h,and the water level of the Dongsong Pumping Station in the next 6 h was predicted.The prediction results show that the prediction effect after screening is worse than that of the direct prediction using data at an interval of 2 h.Upon analysis,the above phenomenon is caused by the overly long interval of 6 h,which can not fully reflect the changing laws of each factor.Therefore,the prediction result after screening is worse than that using the data at an interval of 2 h directly.

4 Conclusion

The influence of the time series ratio on the water level prediction results:The optimal ratio of the training period to the prediction period is 7∶3,and the increase in the ratio cannot significantly change the prediction accuracy,while the decrease in the ratio can lead to a worse prediction effect.

The effect of impact factors on the prediction results:The amount of data corresponds to the number of impact factors.The data volume of three months requires three to five impact factors for training,and the data volume of three months to a year requires five to seven impact factors to ensure the same prediction effect.

The influence of the data interval on the prediction results:In general,when the data interval remains unchanged,the prediction accuracy gradually decreases with the increase in the prediction time,but when the data can reflect the changing laws of each factor,the data interval and the prediction time are the same,and the prediction effect is better.