張建偉，楊 燦，黃錦林，曹克磊，葉合欣，李紫瑜

基于傳遞熵的泵站管道振動(dòng)傳遞路徑特性分析

張建偉1，楊 燦1，黃錦林2，曹克磊1，葉合欣3，李紫瑜1

（1. 華北水利水電大學(xué)水利學(xué)院，鄭州 450046；2. 廣東省水利水電科學(xué)研究院，廣州 510635；3. 廣東省水利水電技術(shù)中心，廣州 510635）

泵站管道因結(jié)構(gòu)復(fù)雜，產(chǎn)生多種振源，且振動(dòng)的傳遞路徑難以確定，對(duì)輸水管道的安全運(yùn)行具有較大威脅。針對(duì)此問(wèn)題，以某泵站管道為研究對(duì)象，結(jié)合原型觀測(cè)數(shù)據(jù)與傳遞熵方法識(shí)別主振源的振動(dòng)傳遞路徑；并以信息傳遞率為定量標(biāo)準(zhǔn)，驗(yàn)證管道振動(dòng)傳遞路徑的有效性。結(jié)果表明：穩(wěn)定運(yùn)行及開(kāi)機(jī)時(shí)，葉頻引起的振動(dòng)為主振源，并由彎管或三通管處向其他部位傳遞，其信息傳遞率均值分別為27.2%與42%；關(guān)機(jī)時(shí)，水流脈動(dòng)及管-水耦合引起的振動(dòng)為主振源，且振動(dòng)主要在閥門與彎管或三通管之間呈周期性傳遞，信息傳遞率均值為51.4%；穩(wěn)定運(yùn)行時(shí)信息傳遞率較低，表明在鎮(zhèn)墩控制下，管道穩(wěn)定運(yùn)行時(shí)傳遞能量較少，但開(kāi)關(guān)機(jī)時(shí)，管道閥門、彎管及三通管處仍有較大振動(dòng)能量傳遞。本研究方法受管道結(jié)構(gòu)影響較小，能準(zhǔn)確識(shí)別管道主振源，且從能量角度識(shí)別振動(dòng)傳遞路徑，相較于傳統(tǒng)方法更加高效、直觀。研究結(jié)果有助于準(zhǔn)確識(shí)別泵站管道主振源的振動(dòng)傳遞路徑，展現(xiàn)管道各工況下的危險(xiǎn)部位，并提出減振措施，為泵站管道運(yùn)行管理提供理論依據(jù)。

泵；振動(dòng)；傳遞路徑；傳遞熵；信息傳遞率；振源分析

0 引 言

近年來(lái)，隨著水利事業(yè)迅速發(fā)展，大流量、高揚(yáng)程梯級(jí)輸水泵站的修建日益增多，能夠滿足跨流域供水的需求，降低水資源匱乏地區(qū)用水壓力。壓力管道是跨流域調(diào)水工程中不可或缺的重要組成部分，其運(yùn)行狀態(tài)關(guān)系到農(nóng)業(yè)生產(chǎn)灌溉等用水問(wèn)題，管道的安全穩(wěn)定運(yùn)行極為重要[1-4]。由于水力學(xué)的復(fù)雜特性與管道結(jié)構(gòu)的自身特點(diǎn)，泵站管道在各工況下產(chǎn)生的振動(dòng)十分強(qiáng)烈；但管道振動(dòng)來(lái)源復(fù)雜，振動(dòng)傳遞路徑難以分析；管道的安全運(yùn)行存在隱患，管道結(jié)構(gòu)損傷逐漸積累，耐久性不斷下降，進(jìn)而引發(fā)安全事故[5-6]。因此，解決管道振源分析及傳遞路徑識(shí)別問(wèn)題，對(duì)農(nóng)業(yè)、石油、化工等領(lǐng)域獲得持久經(jīng)濟(jì)效益，極為重要。管道振動(dòng)系統(tǒng)包括振源、振動(dòng)傳遞路徑和受振體。其中管道主振源的能量通常在全部振動(dòng)能量中占有較大比例，是管道振動(dòng)傳遞路徑研究的關(guān)鍵[7-8]。但壓力管道結(jié)構(gòu)復(fù)雜，產(chǎn)生的振源多樣且難以區(qū)分，振動(dòng)傳遞路徑更加復(fù)雜，管道主振源的振動(dòng)傳遞路徑識(shí)別存在較大困難[9]，對(duì)管道的安全運(yùn)行極為不利。針對(duì)此問(wèn)題，王海軍等[10]基于結(jié)構(gòu)聲強(qiáng)理論測(cè)得水電站廠房振動(dòng)傳遞路徑；歐陽(yáng)金惠等[11]利用脈動(dòng)壓力測(cè)試得出抽水蓄能電站廠房振動(dòng)原因；伍鶴皋等[12]通過(guò)解析計(jì)算和數(shù)值模擬相結(jié)合的方法得到水電站廠房振動(dòng)傳遞路徑；職保平等[13]基于振動(dòng)基本理論、矩陣微分理論等方法分析軸流式水輪機(jī)振動(dòng)傳遞路徑。盡管上述研究在振動(dòng)傳遞路徑上取得一定成果，但大多是對(duì)水電站廠房振動(dòng)傳遞路徑識(shí)別；泵站管道結(jié)構(gòu)與水電站廠房這類大體積混凝土結(jié)構(gòu)不同，水電站廠房振動(dòng)一般由尾水傳遞至支墩；而泵站管道較長(zhǎng)且彎管、叉管較多，振動(dòng)來(lái)源復(fù)雜，振動(dòng)傳遞識(shí)別困難，并且將傳遞熵用于泵站管道結(jié)構(gòu)振動(dòng)傳遞路徑的研究成果幾乎空白。

本文以某灌區(qū)提水泵站管道為研究對(duì)象，依據(jù)原型觀測(cè)數(shù)據(jù)，利用傳遞熵與信息傳遞率識(shí)別泵站管道結(jié)構(gòu)振源及振動(dòng)傳遞路徑。首先通過(guò)原型試驗(yàn)觀測(cè)數(shù)據(jù)，繪制頻譜圖并計(jì)算能量占比，獲得泵站管道不同工況下的振源組成，并確定主振源；然后使用傳遞熵方法識(shí)別該泵站管道不同工況下主振源傳遞路徑，確定振動(dòng)傳遞方向；最后在傳遞熵基礎(chǔ)上利用信息傳遞率定量描述泵站管道主振源的傳遞規(guī)律，并提出優(yōu)化管道運(yùn)行方法及減振措施。

1 泵站管道振源識(shí)別設(shè)備及方法

1.1 泵站管道振動(dòng)測(cè)試設(shè)備及參數(shù)

由于該灌區(qū)提水泵站管道的鋪設(shè)方式具有代表性，并且便于檢測(cè)，能夠得到精確的原始數(shù)據(jù)。以7泵站管道作為試驗(yàn)對(duì)象，管道平面布置如圖1所示。管道共連接3臺(tái)機(jī)組，額定轉(zhuǎn)速均為600 r/min；在泵站管道關(guān)鍵位置布置10個(gè)測(cè)點(diǎn)，每個(gè)測(cè)點(diǎn)均放置3個(gè)拾振器（、、方向），分別位于支管、主管及兩者交匯處，如圖1a所示。由工程經(jīng)驗(yàn)可知，管道開(kāi)關(guān)機(jī)時(shí)管道振動(dòng)劇烈，且為與穩(wěn)定運(yùn)行工況對(duì)比，在原型試驗(yàn)測(cè)試4種工況，工況、采樣時(shí)間及頻率見(jiàn)表1。

1.2 泵站管道振源測(cè)試及分析方法

通過(guò)拾振器在泵站管道上采集數(shù)據(jù)，對(duì)所有測(cè)點(diǎn)振動(dòng)信號(hào)進(jìn)行頻譜圖分析，獲得各測(cè)點(diǎn)振動(dòng)主頻。由于泵站管道結(jié)構(gòu)、邊界條件，機(jī)械條件，水力條件復(fù)雜多樣，泵站管道產(chǎn)生振動(dòng)的原因難以確定。根據(jù)以往研究可知，振動(dòng)主要從3個(gè)方面進(jìn)行分析：水力方面、機(jī)械方面和電磁方面[14-18]。由于泵站管道不同結(jié)構(gòu)產(chǎn)生的振動(dòng)特性各不相同，在計(jì)算管道內(nèi)各振源及其所占比例時(shí)可采用式（1）。

式中為不同振源的能量，J；為總能量，J；x為不同振源能量所占比例。

表1 管道原型試驗(yàn)測(cè)試工況

1.3 泵站管道振動(dòng)傳遞路徑識(shí)別方法

1.3.1 傳遞熵方法

泵站管道內(nèi)部結(jié)構(gòu)復(fù)雜、邊界條件、水體與管道的耦合作用，使其振動(dòng)傳遞路徑識(shí)別產(chǎn)生困難。而傳遞熵作為度量不同時(shí)間序列之間的耦合關(guān)系以及信息傳遞關(guān)系的熵函數(shù)，是一個(gè)動(dòng)態(tài)過(guò)程關(guān)于另一個(gè)動(dòng)態(tài)過(guò)程所產(chǎn)生的傳遞信息。傳遞熵的計(jì)算，不需要考慮物體的結(jié)構(gòu)，而是從振動(dòng)過(guò)程中不同位置振動(dòng)信息傳遞熵值的大小，判斷信息之間相關(guān)程度，來(lái)揭示振動(dòng)傳遞的方向。傳遞熵計(jì)算方式簡(jiǎn)單、識(shí)別敏感性與可靠度較高、適用于線性與非線性數(shù)據(jù)，對(duì)解決管道振動(dòng)傳遞路徑識(shí)別問(wèn)題具有較大優(yōu)勢(shì)。

按照Schreiber定義的傳遞熵[19]，如果在與這兩個(gè)穩(wěn)定的傳遞過(guò)程中，對(duì)的作用影響概率為，這個(gè)過(guò)程表示為式（2）。為了減少計(jì)算傳遞熵時(shí)繁瑣的高維概率密度函數(shù)，在不影響利用傳遞熵判斷傳遞的方向和關(guān)聯(lián)程度的前提下，Nichols等[20]和Overbey等{21]假設(shè)過(guò)程和過(guò)程均為一階馬爾可夫過(guò)程，即==1。式（2）可以化簡(jiǎn)為式（3）。

其中：

1.3.2 信息傳遞率方法

為了更全面地描述管道振動(dòng)的傳遞路徑，利用信息傳遞率[21]（Information Translate Rate，ITR），ITR來(lái)計(jì)算管道振動(dòng)能量傳遞效率。信息傳遞率通過(guò)兩點(diǎn)傳遞熵值計(jì)算，對(duì)振動(dòng)信號(hào)之間的傳遞效率進(jìn)行定量描述，可以更進(jìn)一步描繪管道振動(dòng)傳遞路徑。對(duì)于管道振動(dòng)傳遞過(guò)程和，信息傳遞率計(jì)算過(guò)程為式（7），其中(y→x)與(x→y)與式（2）相同，表示與兩點(diǎn)間的傳遞熵：

式中ITR為信號(hào)到的傳遞率；|(y→x)(x→y)|為到的振動(dòng)信息凈傳遞量。

2 泵站管道振源分析及振動(dòng)傳遞路徑識(shí)別結(jié)果

2.1 振源分析

泵站管道在開(kāi)關(guān)機(jī)時(shí)振動(dòng)較為劇烈，可以檢測(cè)到具有代表性的振動(dòng)頻率，本文以開(kāi)關(guān)機(jī)工況時(shí)靠近泵站機(jī)組的兩測(cè)點(diǎn)為例，方便檢測(cè)更全面的頻率。圖2為工況2和工況4下兩拾振器信號(hào)頻譜圖。由圖2a知，3機(jī)組開(kāi)機(jī)時(shí)，7#拾振器幅值最大為59.38 Hz，是引起管道振動(dòng)的主頻，69.25、29.69 Hz等為次頻；同理可知，1、2機(jī)組關(guān)機(jī)瞬間，其主頻為39.63、69.38 Hz。

統(tǒng)計(jì)泵站管道4種工況下各測(cè)點(diǎn)振動(dòng)主頻出現(xiàn)次數(shù)并列表，表2為4種工況下主頻出現(xiàn)次數(shù)統(tǒng)計(jì)。由表2可知，測(cè)點(diǎn)頻率在0～2、9.9、19.8、29.7、39.6、49.5、59.4及60 Hz以上均有分布。

由式（1）結(jié)合振動(dòng)信號(hào)頻譜圖與表2，參考已有研究[22]計(jì)算得出泵站管道振源?？偨Y(jié)如下：1）低頻成分。泵站管道穩(wěn)定運(yùn)行時(shí)，低流速的水流沖擊管道引起的低頻脈動(dòng), 頻率在10 Hz以下；2）葉頻、轉(zhuǎn)頻。泵機(jī)運(yùn)行時(shí)，高速水流與機(jī)組葉片摩擦，使管道產(chǎn)生中高頻振動(dòng)，由泵機(jī)參數(shù)計(jì)算，該泵站機(jī)組葉頻為60 Hz左右，屬于中高頻率，存在管道各種工況下所有位置，多為振動(dòng)主頻，且比較突出；3）管-水耦合產(chǎn)生的高頻。泵站開(kāi)關(guān)機(jī)瞬間，由于水錘作用，管道內(nèi)產(chǎn)生高速水流沖擊管道產(chǎn)生高頻振動(dòng)。

表2 各工況主要頻率出現(xiàn)次數(shù)統(tǒng)計(jì)表

在研究該灌區(qū)提水泵站管道的振源對(duì)管道的影響時(shí)，參考Zhang等[23-24]對(duì)管道振動(dòng)的研究，結(jié)合上述振源實(shí)測(cè)分析與振源組成計(jì)算，得出7 泵站管道不同工況下影響管道振動(dòng)的主振源：1）機(jī)組穩(wěn)定運(yùn)行時(shí)，葉頻、轉(zhuǎn)頻倍頻產(chǎn)生的振動(dòng)能量占比最大，是管道振動(dòng)的主振源。2）機(jī)組開(kāi)機(jī)時(shí)，葉頻仍是主振源。3）機(jī)組關(guān)機(jī)時(shí)，低頻水流與管-水耦合引起的高頻振動(dòng)占比最大，為管道主振源。

2.2 管道振源傳遞路徑識(shí)別

2.2.1 傳遞熵識(shí)別管道振動(dòng)傳遞路徑

在泵站管道中，彎管及三通管、閥門等應(yīng)力集中部位與水流作用產(chǎn)生強(qiáng)烈激振力，引起彎管及三通管處產(chǎn)生汽蝕和空蝕，加大管道表面摩擦力，進(jìn)而增強(qiáng)彎管及三通管處振動(dòng)；并且在機(jī)組開(kāi)關(guān)機(jī)時(shí)，流體流速變化較大，管道內(nèi)形成水錘，產(chǎn)生壓力波與反射波，在閥門與其余部位產(chǎn)生具有一定周期的振動(dòng)，沿著管道傳遞。

基于上述對(duì)泵站管道振源研究，結(jié)合CEEMDAN和SVD方法[25]進(jìn)行主振源特征信息提取，得到泵站管道 4種工況下的主振源及其對(duì)應(yīng)頻率；并利用傳遞熵方法對(duì)各工況下相鄰測(cè)點(diǎn)間主振源振動(dòng)傳遞路徑進(jìn)行識(shí)別。泵站管道在三通管與彎管間的振動(dòng)較為明顯，為研究泵站管道振動(dòng)傳遞路徑規(guī)律，以工況2下16測(cè)點(diǎn)至13與19測(cè)點(diǎn)間的傳遞熵為例分析開(kāi)機(jī)時(shí)三通管傳遞至直管與彎管的傳遞路徑，以工況4下10測(cè)點(diǎn)至7測(cè)點(diǎn)、9測(cè)點(diǎn)至3測(cè)點(diǎn)分析關(guān)機(jī)時(shí)三通管傳遞至直管與彎管的傳遞路徑。7泵站管道在工況2與工況4下，上述兩測(cè)點(diǎn)之間的傳遞熵值隨時(shí)間的變化曲線分別見(jiàn)圖3、圖4。

由圖3可知：(16→19)的傳遞熵值明顯大于(19→16)；(16→13)的傳遞熵值明顯大于(13→16)。表明在2號(hào)泵機(jī)開(kāi)機(jī)期間，由葉頻引起的振動(dòng)通過(guò)彎管或三通管傳向其余支路的信息量明顯較多，可以判斷泵站管道在開(kāi)機(jī)狀況下葉頻振動(dòng)由彎管或三通管傳至其他部位；同理，由圖 4 傳遞熵值關(guān)系可以得出：當(dāng)1號(hào)、2號(hào)泵機(jī)關(guān)機(jī)時(shí)，水流脈動(dòng)和管-水耦合振動(dòng)，在關(guān)機(jī)瞬間閘門附近由于水錘使振動(dòng)增強(qiáng)，稍高于彎管處；并在短時(shí)間內(nèi)在閘門附近與彎管或三通管之間進(jìn)行周期性傳遞。通過(guò)對(duì)泵站管道各個(gè)工況相鄰測(cè)點(diǎn)的傳遞熵值進(jìn)行計(jì)算分析，得出與上述結(jié)果一致結(jié)論，限于篇幅不再贅述。

2.2.2 信息傳遞率識(shí)別管道振動(dòng)傳遞路徑

在傳遞熵基礎(chǔ)上使用信息傳遞率對(duì)7泵站管道相鄰測(cè)點(diǎn)之間主振源的能量傳遞進(jìn)行定量分析。以工況2與工況4測(cè)點(diǎn)的信息傳遞率為例，所選測(cè)點(diǎn)原則與計(jì)算傳遞熵時(shí)原因一致，不再贅述。表3為兩工況不同測(cè)點(diǎn)之間主振源的信息傳遞率。

表3 工況2與工況4相鄰測(cè)點(diǎn)之間的信息傳遞率

由表3可知：工況2泵站管道信號(hào)在3組測(cè)點(diǎn)之間的傳遞率分別為37.3%、44.8%與28.6%，表明彎管處很大一部分能量傳至管道其余部位；工況4泵站管道信號(hào)在3組測(cè)點(diǎn)之間的傳遞率分別為59.6%、27.0%與45.6%。表明關(guān)機(jī)時(shí)，短暫時(shí)間內(nèi)振動(dòng)由閥門傳至彎管部位，能量較高的部位在閥門附近，振動(dòng)在閥門彎管及三通管之間傳遞。

結(jié)合表4泵站管道各工況對(duì)應(yīng)的管道主要位置主振源信息傳遞率均值所占比例可知：泵站機(jī)組穩(wěn)定運(yùn)行時(shí)，葉頻，轉(zhuǎn)頻引起的振動(dòng)傳遞到彎管及三通管處產(chǎn)生了更強(qiáng)的耦合振動(dòng)，信息傳遞率均值為27.2%，穩(wěn)定運(yùn)行時(shí)傳遞率相對(duì)較低，主要是鎮(zhèn)墩、支墩等裝置起到了一定的減振消能；泵站機(jī)組開(kāi)機(jī)時(shí)，葉頻振動(dòng)主要從彎管及三通管向管道其他部位傳遞，信息傳遞率均值為42.0%，表明開(kāi)機(jī)時(shí)彎管及三通管處較多能量傳遞至管道其它部位；泵站管道關(guān)機(jī)時(shí)，管道內(nèi)低頻水流脈動(dòng)及由水擊引起的高頻振動(dòng)，在閥門附近與彎管及三通管之間周期性傳遞，信息傳遞率均值為51.4%，表明閥門與彎管及三通管處較多能量傳遞至管道其它部位。結(jié)果證明，從信息傳遞率角度定量分析各工況下主振源的傳遞方向與傳遞熵值分析結(jié)果一致，表明信息傳遞率能有效識(shí)別泵站管道振動(dòng)傳遞方向。

表4 不同工況下兩測(cè)點(diǎn)之間信息傳遞率及其均值對(duì)比

通過(guò)上述分析可知，在管道不同工況下，彎管、三通管與閥門是振動(dòng)最為劇烈的部位，在危險(xiǎn)位置提出減振措施對(duì)管道安全運(yùn)行與泵站管道結(jié)構(gòu)設(shè)計(jì)尤為重要。如利用粒子阻尼為動(dòng)力裝置基座減振；利用磁流變減振技術(shù)控制管道低頻振動(dòng)。此外還可以通過(guò)增加彎管半徑、減少?gòu)濐^個(gè)數(shù)等方式來(lái)降低彎管、三通管、閥門的振動(dòng)。且由上述研究結(jié)合表4分析可得，機(jī)組開(kāi)關(guān)機(jī)時(shí)，與之相鄰機(jī)組管道中，中高頻振動(dòng)比例及振動(dòng)傳遞率明顯增加，管道開(kāi)關(guān)機(jī)會(huì)加劇多個(gè)管道之間振動(dòng)的相互作用。因此可通過(guò)避免同時(shí)開(kāi)啟多個(gè)機(jī)組等方式來(lái)優(yōu)化開(kāi)關(guān)機(jī)模式。

3 結(jié) 論

通過(guò)該泵站管道原型觀測(cè)資料結(jié)合傳遞熵與信息傳遞率方法對(duì)管道振動(dòng)的傳遞路徑特性進(jìn)行研究，可得如下結(jié)論：

1）泵站機(jī)組穩(wěn)定運(yùn)行時(shí)：管道內(nèi)葉頻、轉(zhuǎn)頻倍頻引起的振動(dòng)為主振源，振動(dòng)主要從彎管及三通管向其它部位傳遞，信息傳遞率均值為27.2%，穩(wěn)定運(yùn)行時(shí)傳遞率相對(duì)較低，主要是鎮(zhèn)墩、支墩等裝置起到了一定的減振消能。

2）泵站機(jī)組開(kāi)機(jī)時(shí)：管道內(nèi)葉頻引起的振動(dòng)為主振源，振動(dòng)主要從彎管及三通管向管道其它部位傳遞，信息傳遞率均值為42.0%，表明開(kāi)機(jī)時(shí)彎管及三通管處較多能量傳遞至管道其它部位。

3）泵站機(jī)組關(guān)機(jī)時(shí)：管道內(nèi)低頻水流脈動(dòng)及管-水耦合引起的高頻振動(dòng)為主振源，振動(dòng)主要在閥門與彎管及三通管之間進(jìn)行周期性傳遞，信息傳遞率均值為51.4%，表明閥門與彎管及三通管處較多能量傳遞至管道其它部位。

傳遞熵與信息傳遞率能準(zhǔn)確描繪管道振動(dòng)的傳遞路徑，確定管道危險(xiǎn)部位，且能為管道減振與優(yōu)化開(kāi)關(guān)機(jī)方法提出建議。

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Analysis of the pipeline transfer path characteristics of pumping stations based on transfer entropy

Zhang Jianwei1, Yang Can1, Huang Jinlin2, Cao Kelei1, Ye Hexin3, Li Ziyu1

(1.,,450046,; 2.,510635,; 3.510635,)

The transmission path of vibration difficult to determine has posed a great threat to the safe operation of water transmission pipeline, due mainly to the complex structure of pump station pipeline, where there are many vibration sources. In this study, an attempt was made to analyze the pipeline transfer path characteristics of pumping stations using transfer entropy. The pipeline of 7 pump stations in an irrigation area was also taken as the research object. Firstly, a prototype test was carried out to obtain the spectrum diagram, and energy proportion, thereby analyzing the main vibration source of pipeline vibration. Then, a transmission entropy method was used to identify the vibration transmission path of the main vibration source in the pump station pipeline under various working conditions. The effectiveness of the pipeline vibration transmission path was finally verified when taking the information transmission rate as the quantitative standard. The results show that: 1) The main vibration source was caused by the blade frequency and frequency doubling in the pipeline, mainly transmitting from the elbow and tee pipe to other parts when the pumping station unit operated stably. Furthermore, the average information transmission rate was 27.2%. More importantly, the transmission rate was relatively low during stable operation, mainly because the anchor block, buttress, and other devices played a critical role in the vibration reduction and energy dissipation. 2) The main vibration source was also caused by the blade frequency in the pipeline, mainly transmitted from the elbow and tee to other parts of the pipeline, when the pump station unit starting up. The average information transmission rate was 42%. It was found that a large part of the energy at the elbow and tee was transmitted to other parts of the pipeline during startup. 3) The main vibration source was the high-frequency vibration caused by low-frequency water flow pulsation and pipe water coupling in the pipeline when the pump station unit was shut down. The vibration was mainly transmitted periodically between the valve, elbow, and tee. The average information transmission rate was 51.4%. It can be seen that a large part of the energy from the valve, elbow, and tee was transmitted to other parts of the pipeline. Correspondingly, the information transmission rate of each working condition showed that a large part of vibration energy at the pipeline valve, elbow, and tee pipe was still transmitted to other parts. Whether the machine was switched on or off, the energy transmitted by the pipeline during the stable operation was less under the control of vibration reduction measures, such as anchor block. Therefore, the prototype observation data was selected to analyze the source of vibration through the spectrum diagram and energy proportion, where quantitatively determine the transmission relationship between vibration from the perspective of energy with the help of transmission entropy and information transmission rate, as well as the direction of vibration transmission. It was more efficient and intuitive than before, indicating great advantages in the application of vibration transmission path recognition. Consequently, this research can greatly contribute to accurately identify the vibration transmission path of the main vibration source in the pump station pipeline, thereby identifying the dangerous parts of the pipeline under different working conditions, where the vibration reduction measures can be further proposed. This finding can provide a promising theoretical basis for the operation and management of the pump station pipeline

pumps; vibration; transmission path; transfer entropy; information transmission rate; vibration source analysis

張建偉，楊燦，黃錦林，等. 基于傳遞熵的泵站管道振動(dòng)傳遞路徑特性分析[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2021，37(15)：47-52.doi：10.11975/j.issn.1002-6819.2021.15.006 http://www.tcsae.org

Zhang Jianwei, Yang Can, Huang Jinlin, et al. Analysis of the pipeline transfer path characteristics of pumping stations based on transfer entropy[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(15): 47-52. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2021.15.006 http://www.tcsae.org

2021-04-29

2021-08-05

國(guó)家自然科學(xué)基金（51679091）；廣東省水利科技創(chuàng)新項(xiàng)目（2020-18）；廣州市科技計(jì)劃（2020-ky34）

張建偉，博士，教授，研究方向?yàn)樗姽こ?。Email：zjwcivil@126.com

10.11975/j.issn.1002-6819.2021.15.006

TV93; TB53

A

1002-6819(2021)-15-0047-06