駱正山，歐陽長風(fēng)，王小完，張新生

鹽穴儲氣庫注采管柱內(nèi)腐蝕速率預(yù)測模型研究

駱正山，歐陽長風(fēng)，王小完，張新生

（西安建筑科技大學(xué) 管理學(xué)院，西安 710055）

鹽穴儲氣庫；注采管柱；腐蝕速率預(yù)測；主成分分析法（KPCA）；改進(jìn)灰狼優(yōu)化（IGWO）；極限學(xué)習(xí)機(jī)（ELM）

近年來，我國天然氣供需量穩(wěn)步增長，高質(zhì)量發(fā)展戰(zhàn)略能源儲備設(shè)施地下儲氣庫具有重大意義[1]。鹽穴儲氣庫具有孔隙率低、滲透率小、塑性形變能力強(qiáng)等優(yōu)勢[2-3]。注采管柱是鹽穴儲氣庫的重要組成，長期處于地下復(fù)雜環(huán)境使其易受多種腐蝕因素的影響并造成運(yùn)維災(zāi)害[4-5]。因此，探究鹽穴儲氣庫注采管柱的腐蝕機(jī)理與規(guī)律，建立高精度的腐蝕預(yù)測模型意義重大。

目前，國內(nèi)外學(xué)者已對管線腐蝕現(xiàn)象展開了大量研究。張新生等[6]研究了海洋立管的腐蝕發(fā)展規(guī)律，建立了初始條件滑動(dòng)的非等間距管道腐蝕預(yù)測灰色模型SUGM（1,1,）。Chen等[7]利用主成分分析法提取海底管道內(nèi)腐蝕的關(guān)鍵腐蝕因素，消除冗余信息并確定管道失效原因。王曉敏等[8]基于時(shí)變可靠性方法提出了一種多失效模式腐蝕影響下的地下管道失效概率預(yù)測方法。謝飛等[9]從化學(xué)反應(yīng)、電化學(xué)反應(yīng)和傳質(zhì)過程3個(gè)方面探究了天然氣管道CO2腐蝕機(jī)理，提出了基于腐蝕機(jī)理的腐蝕速率預(yù)測模型。但以上傳統(tǒng)研究方法針對管線腐蝕預(yù)測問題仍存在不足：SUGM（1,1,）初始條件的確定方式復(fù)雜，大幅更新腐蝕數(shù)據(jù)對預(yù)測結(jié)果的準(zhǔn)確性存在較大影響；主成分分析法僅適用于處理線性映射問題，對非線性數(shù)據(jù)的特征提取效果較差；基于時(shí)變可靠性的失效概率方法難以準(zhǔn)確定義失效事件的關(guān)聯(lián)性，預(yù)測前提存在主觀因素；機(jī)理模型研究僅考慮在理想溶液環(huán)境內(nèi)的單一電化學(xué)腐蝕作用，未能考慮到非理想環(huán)境中管道的復(fù)雜流動(dòng)等問題。隨著智能信息處理技術(shù)的高速發(fā)展，大量智能優(yōu)化算法得以應(yīng)用于管道的腐蝕預(yù)測研究。凌曉等[10]通過優(yōu)化反向傳播神經(jīng)網(wǎng)絡(luò)（BPNN）參數(shù)，對輸油管道的內(nèi)腐蝕速率進(jìn)行了預(yù)測分析。駱正山等[11]建立基于動(dòng)態(tài)貝葉斯網(wǎng)絡(luò)（DBN）的疲勞壽命模型，預(yù)測了海底腐蝕管道的失效概率。Peng等[12]通過優(yōu)化支持向量回歸（SVR）模型參數(shù)，對多相流管道的腐蝕速率進(jìn)行了預(yù)測分析。曲志豪等[13]利用網(wǎng)格搜索算法優(yōu)化了隨機(jī)森林回歸模型，建立了GA–RFC模型并對油氣管道腐蝕速率進(jìn)行了預(yù)測。但上述智能算法仍存在不足：BPNN存在結(jié)構(gòu)復(fù)雜、訓(xùn)練速度慢、易陷入局部極小值等缺點(diǎn)；DBN的先驗(yàn)概率假設(shè)具有較強(qiáng)的主觀性，對于屬性非完全獨(dú)立的大規(guī)模樣本適用性不佳；SVR中參數(shù)的確定存在強(qiáng)隨機(jī)性，使得模型預(yù)測結(jié)果的波動(dòng)性較大；RFC模型中含有噪聲樣本時(shí)容易發(fā)生過擬合現(xiàn)象。

綜上，本文在核主成分分析中引入小波核函數(shù)，對鹽穴儲氣庫注采管柱內(nèi)的腐蝕因素進(jìn)行特征提取，利用改進(jìn)灰狼優(yōu)化算法優(yōu)化極限學(xué)習(xí)機(jī)的輸入權(quán)值矩陣和隱含層閾值，建立小波KPCA–IGWO–ELM的鹽穴儲氣庫注采管柱內(nèi)腐蝕速率預(yù)測模型。在MATLAB中對比分析多種預(yù)測模型的仿真結(jié)果，驗(yàn)證所建模型的適用性與準(zhǔn)確性，為鹽穴儲氣庫注采系統(tǒng)安全運(yùn)行提供可靠支撐。

1 KPCA

2 IGWO–ELM模型

2.1 ELM

求解線性方程組式（7）得到最小二乘解：

2.2 IGWO

改進(jìn)灰狼優(yōu)化[23]（IGWO）是Mirjalili等人于2020年提出的一種新型群體智能優(yōu)化算法，算法在灰狼優(yōu)化[24]（GWO）的基礎(chǔ)上引入了基于維度學(xué)習(xí)狩獵（DLH）的改進(jìn)搜索策略，有效解決了GWO種群多樣性差、后期收斂速度慢、易陷入局部最優(yōu)等缺點(diǎn)。

重復(fù)以上過程，當(dāng)?shù)螖?shù)等于最大迭代次數(shù)時(shí)循環(huán)結(jié)束，輸出最優(yōu)適應(yīng)度值作為獵物最終位置，IGWO獲全局最優(yōu)解。

2.3 IGWO–ELM預(yù)測模型構(gòu)建

2.4 預(yù)測模型評價(jià)指標(biāo)

本文選用均方根誤差（RMSE）、平均絕對百分比誤差（MAPE）和決定系數(shù)（2）3個(gè)指標(biāo)[25]對IGWO–ELM模型預(yù)測結(jié)果進(jìn)行評價(jià)，計(jì)算公式見式（22）—（24）。

圖1 IGWO–ELM模型腐蝕預(yù)測流程

3 實(shí)例應(yīng)用

3.1 指標(biāo)構(gòu)建與數(shù)據(jù)采集

以某鹽穴儲氣庫注采管柱的實(shí)測試驗(yàn)為例，選取10種常見腐蝕因素構(gòu)建鹽穴儲氣庫注采管柱的內(nèi)腐蝕指標(biāo)體系，如圖2所示。結(jié)合項(xiàng)目運(yùn)行資料，設(shè)定預(yù)測模型工況條件適用范圍如表1所示，取250組實(shí)測數(shù)據(jù)用作預(yù)測模型樣本，部分?jǐn)?shù)據(jù)見表2。

圖2 鹽穴儲氣庫注采管柱的內(nèi)腐蝕指標(biāo)體系

3.2 特征提取

將采集的250組數(shù)據(jù)做歸一化處理，后用小波KPCA對腐蝕指標(biāo)進(jìn)行特征提取，得出綜合腐蝕因素特征值與貢獻(xiàn)率，如表3所示。

KPCA規(guī)定，被選主成分的累計(jì)貢獻(xiàn)率應(yīng)不低于95%。分析表3易知，前3項(xiàng)主成分的累計(jì)貢獻(xiàn)率高達(dá)98.61%，故將前3項(xiàng)作為影響鹽穴儲氣庫注采管柱內(nèi)腐蝕的特征指標(biāo)。

表1 預(yù)測模型工況適用范圍

Tab.1 Application range of prediction model

3.3 腐蝕速率預(yù)測結(jié)果分析

將訓(xùn)練好的IGWO–ELM對其余50組腐蝕數(shù)據(jù)進(jìn)行測試。為體現(xiàn)IGWO–ELM預(yù)測模型的準(zhǔn)確性，選用ELM、PSO–ELM、SSA–ELM對相同數(shù)據(jù)進(jìn)行預(yù)測分析，模型的預(yù)測結(jié)果對比見圖4，預(yù)測相對誤差對比見圖5。表4為分別用高斯核函數(shù)和小波核函數(shù)進(jìn)行特征提取后，4個(gè)預(yù)測模型的相對誤差分析結(jié)果。

表2 鹽穴儲氣庫注采管柱的內(nèi)腐蝕數(shù)據(jù)

Tab.2 Internal corrosion data of injection and production string in salt cavern gas storage

表3 特征變量提取

Tab.3 Extraction of characteristic variables

圖3 IGWO–ELM適應(yīng)度收斂曲線

圖4 預(yù)測結(jié)果對比圖

圖5 預(yù)測相對誤差對比圖

表4 不同核函數(shù)的預(yù)測結(jié)果相對誤差分析

Tab.4 Relative error analysis of prediction results of different kernel functions

由圖4可知，相較于ELM、PSO–ELM和SSA– ELM，IGWO–ELM的預(yù)測結(jié)果更接近于實(shí)際值，擬合程度更高。分析圖5和表4可知，經(jīng)小波KPCA的模型預(yù)測性能均優(yōu)于經(jīng)高斯KPCA的模型，且經(jīng)小波KPCA的ELM、PSO–ELM、SSA–ELM、IGWO– ELM的平均相對誤差分別為9.404 8%、5.061 5%、1.573 7%、0.707 3%，相較于經(jīng)高斯KPCA的平均相對誤差分別降低了3.409 2%、2.933 5%、1.018 4%、0.577 1%，說明小波KPCA–IGWO–ELM模型的性能提升較大。為驗(yàn)證模型的預(yù)測效果，采用2.4節(jié)中的3項(xiàng)指標(biāo)分別對4種預(yù)測模型進(jìn)行評價(jià)分析，結(jié)果見表5。

由表5可知，IGWO–ELM的2高達(dá)0.992 5，其RMSE和MAPE分別比ELM降低了0.116 6、16.175 1%，比PSO–ELM降低了0.073 2、8.410 6%，比SSA–ELM降低了0.072 3、4.656 7%。在一定工況條件適用范圍內(nèi)，說明IGWO–ELM模型的性能優(yōu)良，鹽穴儲氣庫注采管柱內(nèi)腐蝕速率的預(yù)測結(jié)果更精準(zhǔn)。

表5 模型性能評價(jià)指標(biāo)對比

Tab.5 Comparison of model performance evaluation indicators

4 結(jié)論

1）利用小波KPCA提取出包含98.61%腐蝕信息的3項(xiàng)主成分，基于此的預(yù)測結(jié)果相對誤差最小。經(jīng)小波KPCA的ELM、PSO–ELM、SSA–ELM、IGWO– ELM的平均相對誤差分別為9.404 8%、5.061 5%、1.573 7%、0.707 3%，相較于經(jīng)高斯KPCA的平均相對誤差分別降低了3.409 2%、2.933 5%、1.018 4%、0.577 1%。

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Research on Prediction Model of Internal Corrosion Rate in Injection and Production String of Salt Cavern Gas Storage

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(School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China)

The injection and production string of the salt cavern gas storage has been in a complex underground environment for a long time, making it susceptible to a variety of corrosion factors. This work aims to improve the prediction accuracy of the corrosion rate in the injection and production string of the salt cavern gas storage, thereby ensuring the health and operational safety of these facilities. To accomplish the above objectives, the solution proposed is to establish an internal corrosion rate prediction model based on wavelet kernel principal component analysis (KPCA) and an extreme learning machine (ELM) after improved gray wolf optimization (IGWO).First of all, in the actual operation data of the injection and production string of the salt cavern gas storage, 10 indicators with larger corrosion factors are selected, such as: partial pressure of carbon dioxide, hydrogen sulfide partial pressure, inner wall surface temperature, etc. Subsequently, the internal corrosion index system of the injection and production string of the salt cavern gas storage was established.Secondly, the wavelet KPCA is used to extract the key features that affect the internal corrosion rate of the injection and production string, and then IGWO is used to iteratively optimize the input weight matrix and hidden layer threshold of the ELM model, and stop the loop until the termination condition is met. Furthermore, a prediction model of corrosion rate in the injection and production string of IGWO-ELM salt cavern gas storage is established. Finally, numerical simulation and simulation calculation are carried out in MATLAB software, and the prediction errors of the IGWO-ELM model are compared with the three models of ELM, PSO-ELM and SSA-ELM respectively. The research results show that the wavelet KPCA effectively extracts the three principal components that contain 98.61% of the original information in the corrosion data of the injection-production pipe string of the salt cavern gas storage.Applying the reconstructed corrosion data to the ELM, PSO-ELM, SSA-ELM, and IGWO-ELM models, their average relative errors are 9.404 8%, 5.061 5%, 1.573 7%, and 0.707 3%. The prediction results of the IGWO-ELM model are in good agreement with the actual values.The root mean square error of the constructed IGWO-ELM model is 0.008 8, the average absolute percentage error is 0.260 9%, and the coefficient of determination (2) is as high as 0.992 5. Its prediction result is better than the other three comparison models. The kernel principal component analysis with the introduction of wavelet kernel function has an excellent ability to extract corrosion characteristics of the injection and production string of the salt cavern gas storage. Within the applicable range of certain working conditions, the established IGWO-ELM model can effectively predict the internal corrosion rate of the injection and production string of the salt cavern gas storage.It not only provides a reference basis for the integrity evaluation and risk warning of the injection and production system of the salt cavern gas storage, but also provides new ideas and methods for the corrosion study of the injection and production string of the salt cavern gas storage.

salt cavern gas storage; injection and production string; corrosion rate prediction; principal component analysis (KPCA); improved gray wolf optimization (IGWO); extreme learning machine (ELM)

TG174

A

1001-3660(2022)06-0283-08

10.16490/j.cnki.issn.1001-3660.2022.06.026

2021–04–28；

2021–12–07

2021-04-28；

2021-12-07

國家自然科學(xué)基金（41877527）；陜西省社科基金（2018S34）

National Natural Science Foundation of China (41877527); Shaanxi Provincial Social Science Fund (2018S34)

駱正山（1969—），男，博士，教授，主要研究方向?yàn)橛蜌夤艿里L(fēng)險(xiǎn)評估。

LUO Zheng-shan (1969-), Male, Doctor, Professor, Research focus: oil and gas pipeline risk assessment.

駱正山, 歐陽長風(fēng), 王小完, 等.鹽穴儲氣庫注采管柱內(nèi)腐蝕速率預(yù)測模型研究[J]. 表面技術(shù), 2022, 51(6): 283-290.

LUO Zheng-shan, OUYANG Chang-feng, WANG Xiao-wan, et al. Research on Prediction Model of Internal Corrosion Rate in Injection and Production String of Salt Cavern Gas Storage[J]. Surface Technology, 2022, 51(6): 283-290.

責(zé)任編輯：萬長清