基于數(shù)據(jù)的流程工業(yè)生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法綜述

陳龍 劉全利 王霖青 趙珺 王偉

流程工業(yè)是通過(guò)分離、混合、成型或物理、化學(xué)變化使生產(chǎn)原材料增值的行業(yè),其生產(chǎn)過(guò)程一般是連續(xù)或成批進(jìn)行,主要包括化工、冶金、石油、橡膠、輕工、制藥等[1].現(xiàn)如今我國(guó)流程工業(yè)發(fā)展迅速,主要產(chǎn)品產(chǎn)量居世界前列.以粗鋼生產(chǎn)為例,2015年全球粗鋼產(chǎn)量達(dá)到16.21億噸,其中中國(guó)粗鋼產(chǎn)量達(dá)到8.038億噸,占全球粗鋼總產(chǎn)量的49.6%[2].然而目前我國(guó)流程工業(yè)普遍面臨著過(guò)程結(jié)構(gòu)復(fù)雜,工序設(shè)備多,能耗高等突出問(wèn)題.因此,提高我國(guó)流程工業(yè)自動(dòng)化水平以達(dá)到降低能耗和提高效率的目標(biāo)迫在眉睫.

流程工業(yè)普遍包含諸多重要的生產(chǎn)過(guò)程指標(biāo)或變量,現(xiàn)場(chǎng)操作人員往往會(huì)根據(jù)經(jīng)驗(yàn)對(duì)某些特別關(guān)注的關(guān)鍵指標(biāo)進(jìn)行監(jiān)測(cè),從而調(diào)控整個(gè)生產(chǎn)過(guò)程,最終達(dá)到穩(wěn)定生產(chǎn)的目標(biāo),如高爐煉鐵過(guò)程中鐵水溫度,硅含量[3]以及多種質(zhì)量指標(biāo)[4]等.生產(chǎn)過(guò)程指標(biāo)一般分為兩類,一類是生產(chǎn)過(guò)程運(yùn)行參數(shù),如溫度、壓力等;另一類是定義的生產(chǎn)過(guò)程指標(biāo),如選礦過(guò)程中的精尾礦品位等,而此類指標(biāo)往往與其他過(guò)程變量之間存在著復(fù)雜的非線性關(guān)系.考慮到工業(yè)生產(chǎn)過(guò)程通常具有非線性和大滯后等特征,對(duì)這些指標(biāo)的測(cè)量往往耗時(shí)長(zhǎng),難以檢測(cè),或根本無(wú)法檢測(cè),因此針對(duì)其建立有效的數(shù)學(xué)模型進(jìn)行實(shí)時(shí)預(yù)測(cè)(估計(jì))就顯得尤為重要[5].另一方面,從實(shí)時(shí)生產(chǎn)調(diào)度角度來(lái)講,操作人員希望預(yù)先了解某些關(guān)鍵指標(biāo)的未來(lái)變化趨勢(shì),這也使得指標(biāo)趨勢(shì)預(yù)測(cè)成為目前流程工業(yè)生產(chǎn)過(guò)程監(jiān)控的重要任務(wù)[6?7].傳統(tǒng)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)采用基于機(jī)理建模的方法,此類方法在工藝機(jī)理分析的基礎(chǔ)上,依據(jù)物料平衡、熱量平衡和動(dòng)力學(xué)建立數(shù)學(xué)模型[8].然而機(jī)理建模很大程度上依賴于對(duì)過(guò)程機(jī)理的認(rèn)知,由于工業(yè)生產(chǎn)常具有非平衡、非穩(wěn)定和強(qiáng)非線性等特點(diǎn),此類機(jī)理模型成本高、難度大,其準(zhǔn)確性和可靠性難以保證,往往存在模型精度低和容易失配等問(wèn)題[8].

隨著計(jì)算機(jī)和網(wǎng)絡(luò)技術(shù)的發(fā)展,流程工業(yè)企業(yè)基于監(jiān)控與數(shù)據(jù)采集系統(tǒng)(Supervisory control and data acquisition,SCADA)獲取了大量涉及生產(chǎn)過(guò)程特點(diǎn)、設(shè)備、質(zhì)量和能源的歷史數(shù)據(jù).目前基于數(shù)據(jù)的方法成為較盛行的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法,此類方法通過(guò)建立輸入–輸出數(shù)據(jù)變量間的關(guān)系模型完成預(yù)測(cè)任務(wù),而無(wú)需對(duì)生產(chǎn)過(guò)程的反應(yīng)或動(dòng)力學(xué)等機(jī)理信息進(jìn)行研究.通常基于數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)過(guò)程包含三個(gè)方面,即 1)特征(變量)選擇;2)預(yù)測(cè)模型建立;3)模型參數(shù)優(yōu)化.特征(變量)選擇過(guò)程指從大量的候選輸入特征中挑選出與預(yù)測(cè)指標(biāo)最相關(guān)的特征作為預(yù)測(cè)模型的輸入變量.通常數(shù)據(jù)特征選擇包括經(jīng)驗(yàn)知識(shí)手動(dòng)選擇和基于數(shù)據(jù)分析的選擇方法.基于經(jīng)驗(yàn)知識(shí)的方法雖然方便快捷,但時(shí)常會(huì)因經(jīng)驗(yàn)不足出現(xiàn)錯(cuò)選漏選或特征冗余的情況.基于數(shù)據(jù)的預(yù)測(cè)建模可采用機(jī)器學(xué)習(xí)方法(如人工神經(jīng)網(wǎng)絡(luò)[9]、支持向量機(jī)[10]等)來(lái)完成,與機(jī)理模型不同的是此類方法只關(guān)注模型的輸入和輸出.模型的輸入是選擇的相關(guān)特征變量,模型輸出即是待預(yù)測(cè)的關(guān)鍵指標(biāo).預(yù)測(cè)模型參數(shù)選取對(duì)模型精度影響較大,模型參數(shù)優(yōu)化過(guò)程通常以減小預(yù)測(cè)誤差為目標(biāo),使模型獲得較好的預(yù)測(cè)精度.最常見(jiàn)的模型參數(shù)優(yōu)化方法有基于梯度的方法,如梯度下降法[11]、共軛梯度法[11]等;智能優(yōu)化方法如遺傳算法[12]、模擬退火算法[13]等.圖1給出了基于數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法的基本流程.

圖1 基于數(shù)據(jù)生產(chǎn)關(guān)鍵指標(biāo)預(yù)測(cè)的基本流程圖Fig.1 A flow chart of data-based prediction on performance indicators in process industry

本文針對(duì)目前基于數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)在上述三個(gè)方面進(jìn)行綜述,并結(jié)合當(dāng)前最新的機(jī)器學(xué)習(xí)技術(shù)、自動(dòng)化發(fā)展趨勢(shì)以及工業(yè)過(guò)程的需求,探討基于工業(yè)數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法的可能發(fā)展方向.

1 生產(chǎn)過(guò)程指標(biāo)的特征(變量)選擇

被預(yù)測(cè)的指標(biāo)值往往與生產(chǎn)過(guò)程中的多個(gè)過(guò)程變量相關(guān),進(jìn)行生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)首先需將與被預(yù)測(cè)指標(biāo)最相關(guān)的特征變量從眾多候選變量中挑選出來(lái).以熱軋生產(chǎn)過(guò)程為例,針對(duì)板帶厚度的預(yù)測(cè)問(wèn)題,經(jīng)過(guò)特征選擇最終得到影響板帶厚度的輸入因素多達(dá)20個(gè)[14].基于數(shù)據(jù)的特征選擇根據(jù)是否獨(dú)立于后續(xù)的建模算法,可分為過(guò)濾式(Filter)和封裝式(Wrapper)兩種[15].過(guò)濾式特征選擇的基本思路是采用一種評(píng)價(jià)準(zhǔn)則來(lái)增強(qiáng)特征與輸出的相關(guān)性,削減各個(gè)特征之間的相關(guān)性從而選擇最相關(guān)特征,再將被選擇的最相關(guān)特征參與建模.而封裝式方法則將特征選擇步驟與建模過(guò)程融合,其缺點(diǎn)在于與過(guò)濾式方法相比較為耗時(shí).目前,應(yīng)用在工業(yè)生產(chǎn)過(guò)程中最常見(jiàn)的特征選擇方法有過(guò)濾式方法,如基于相關(guān)性分析的方法[16?19]等;封裝式方法,如變量修剪方法[20]、基于遺傳算法的方法[21]等.

基于相關(guān)性分析的方法如灰色關(guān)聯(lián)分析法[22],其基本思路是通過(guò)線性插值將時(shí)間離散觀測(cè)值轉(zhuǎn)化為分段連續(xù)的折線,進(jìn)而根據(jù)折線的幾何特征構(gòu)造測(cè)度關(guān)聯(lián)程度模型來(lái)評(píng)價(jià)各狀態(tài)變量之間的關(guān)聯(lián)程度.如文獻(xiàn)[23]針對(duì)燒結(jié)過(guò)程中燒結(jié)質(zhì)量的預(yù)測(cè)問(wèn)題,將8個(gè)過(guò)程變量分別與燒結(jié)質(zhì)量進(jìn)行灰色關(guān)聯(lián)分析,并最終挑選了4個(gè)與燒結(jié)質(zhì)量最相關(guān)的因素來(lái)作為預(yù)測(cè)模型的輸入.文獻(xiàn)[24]針對(duì)鋼鐵工業(yè)轉(zhuǎn)爐煤氣系統(tǒng)中煤氣柜位預(yù)測(cè)問(wèn)題提出了一種一致T型灰色關(guān)聯(lián)分析算法來(lái)確定轉(zhuǎn)爐煤氣柜位的主要影響因素.文獻(xiàn)[25]針對(duì)煉焦生產(chǎn)過(guò)程綜合生產(chǎn)指標(biāo)(焦炭質(zhì)量、產(chǎn)量和焦?fàn)t能耗)預(yù)測(cè),采用主元分析和灰色關(guān)聯(lián)分析確定了神經(jīng)網(wǎng)絡(luò)預(yù)測(cè)模型的輸入輸出因素.針對(duì)硫酸鋅溶液凈化過(guò)程中鈷離子濃度預(yù)測(cè)[26]和高爐爐溫預(yù)測(cè)[27]問(wèn)題,灰色關(guān)聯(lián)方法表現(xiàn)出較好的精度優(yōu)勢(shì).此外,基于F評(píng)分的方法也是一類基于相關(guān)性分析的特征選擇方法[19],該方法通過(guò)定義一種F評(píng)分來(lái)表示每個(gè)輸入特征與輸出之間的相關(guān)程度,F值越大說(shuō)明該特征與輸出的相關(guān)性越大.如文獻(xiàn)[28]針對(duì)高爐爐溫變化趨勢(shì)預(yù)測(cè)問(wèn)題,提出了一種依次驗(yàn)證和F評(píng)分方法相結(jié)合的特征選擇方法,從所有的高爐煉鐵過(guò)程變量中找出與爐溫變化趨勢(shì)最相關(guān)的8個(gè)輸入特征.目前大部分基于相關(guān)性分析的特征選擇方法僅僅分析了候選特征與被預(yù)測(cè)指標(biāo)之間的關(guān)聯(lián)性,而未考慮各輸入特征之間可能存在的聯(lián)系,從而導(dǎo)致選出的特征中存在冗余,也會(huì)在一定程度上影響預(yù)測(cè)模型的建模效率.

變量修剪算法是一種封裝式特征選擇方法,其思路是基于前饋神經(jīng)網(wǎng)絡(luò)回歸模型從復(fù)雜的初始模型出發(fā),以最小化預(yù)測(cè)誤差為目標(biāo),通過(guò)逐個(gè)將相應(yīng)輸入權(quán)值設(shè)置為零來(lái)剔除不相關(guān)變量[20].該算法在修剪輸入變量的同時(shí)優(yōu)化模型的網(wǎng)絡(luò)結(jié)構(gòu)(隱含節(jié)點(diǎn)數(shù)目).如針對(duì)高爐鐵水硅含量預(yù)測(cè)問(wèn)題,文獻(xiàn)[29?30]分別采用前饋神經(jīng)網(wǎng)絡(luò)模型作為基礎(chǔ)預(yù)測(cè)模型,并采用變量修剪算法來(lái)去除不相關(guān)變量,最終找到了影響鐵水硅含量的主要輸入因素.此外,基于遺傳算法的封裝式方法是將候選特征隨機(jī)構(gòu)造預(yù)測(cè)模型組成種群并進(jìn)行遺傳操作來(lái)選擇最優(yōu)的輸入特征.如文獻(xiàn)[31]提出了一種基于遺傳算法優(yōu)化的神經(jīng)網(wǎng)絡(luò)非線性建模算法,建模過(guò)程中采用遺傳算法同時(shí)最小化預(yù)測(cè)誤差和模型復(fù)雜度兩個(gè)目標(biāo),從而得到最優(yōu)輸入特征組合和網(wǎng)絡(luò)結(jié)構(gòu),并將其應(yīng)用到高爐煉鐵過(guò)程中的鐵水硅含量預(yù)測(cè)問(wèn)題.文獻(xiàn)[21]針對(duì)石油化學(xué)制品工業(yè)中的質(zhì)量指標(biāo)預(yù)測(cè)問(wèn)題,將候選輸入變量隨機(jī)構(gòu)造的一系列預(yù)測(cè)模型組成一個(gè)種群,以最小化預(yù)測(cè)誤差為目標(biāo),通過(guò)類似遺傳算法的策略來(lái)找到最優(yōu)的候選變量組合.封裝式特征選擇方法由于以最小化預(yù)測(cè)誤差為目標(biāo)進(jìn)行特征選擇,其預(yù)測(cè)精度可能優(yōu)于基于相關(guān)性分析的方法,但是由于其在建模過(guò)程中融入了特征選擇步驟,算法的時(shí)間成本也相對(duì)較高.以上針對(duì)特定工業(yè)應(yīng)用的無(wú)論是基于相關(guān)性分析的方法還是封裝式特征選擇方法大都是以離線的方式完成,這對(duì)于具有時(shí)變特性的工業(yè)生產(chǎn)過(guò)程并不總是適合.因此針對(duì)實(shí)際工業(yè)問(wèn)題開(kāi)展實(shí)時(shí)在線式的特征選擇對(duì)基于數(shù)據(jù)的特征選擇方法尚具有一定的挑戰(zhàn).

2 生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)建模

針對(duì)工業(yè)生產(chǎn)過(guò)程建模問(wèn)題,傳統(tǒng)基于物理、化學(xué)機(jī)理建立精確數(shù)學(xué)模型的方法已越來(lái)越困難.而相當(dāng)數(shù)量的工業(yè)企業(yè)每天都在產(chǎn)生并存儲(chǔ)著大量隱含工藝變動(dòng)和設(shè)備運(yùn)行等信息的生產(chǎn)、設(shè)備和過(guò)程數(shù)據(jù),如何有效利用大量的離線、在線數(shù)據(jù)和知識(shí),在難于建立系統(tǒng)機(jī)理模型的情況下,實(shí)現(xiàn)對(duì)生產(chǎn)過(guò)程和設(shè)備的優(yōu)化控制和評(píng)價(jià),已成為迫切需要解決的問(wèn)題.數(shù)據(jù)驅(qū)動(dòng)的方法是解決機(jī)理不明確或含不確定性機(jī)理模型對(duì)象建模問(wèn)題的有效方法[32],此類方法利用離線、在線數(shù)據(jù)來(lái)描述對(duì)象的運(yùn)行規(guī)律和相關(guān)模式,并結(jié)合反映系統(tǒng)參數(shù)、結(jié)構(gòu)等數(shù)據(jù),來(lái)實(shí)現(xiàn)復(fù)雜系統(tǒng)的建模[33].近年來(lái),針對(duì)工業(yè)系統(tǒng)的指標(biāo)預(yù)測(cè)問(wèn)題,已有不少數(shù)據(jù)驅(qū)動(dòng)方法(如迭代學(xué)習(xí)[34]、無(wú)模型自適應(yīng)方法[35]和自適應(yīng)動(dòng)態(tài)規(guī)劃[36]等)被提出.基于數(shù)據(jù)的預(yù)測(cè)建模方法中,根據(jù)是否嵌入了機(jī)理模型,可將建模方法分為基于數(shù)據(jù)的方法和數(shù)據(jù)–機(jī)理相結(jié)合的方法.

2.1 基于數(shù)據(jù)的預(yù)測(cè)建模

機(jī)器學(xué)習(xí)技術(shù)的發(fā)展為基于數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)奠定了建模基礎(chǔ).如針對(duì)煉鐵過(guò)程鐵水硅含量預(yù)測(cè)、產(chǎn)品質(zhì)量指標(biāo)預(yù)測(cè)、選礦生產(chǎn)指標(biāo)預(yù)測(cè)等問(wèn)題[37?39].較為常用的方法如人工神經(jīng)網(wǎng)絡(luò)[40]、支持向量機(jī)[41]、高斯過(guò)程回歸方法[42]以及偏最小二乘回歸方法[43]等.文獻(xiàn)[44]針對(duì)鐵水硅含量預(yù)測(cè),通過(guò)聯(lián)合人工神經(jīng)網(wǎng)絡(luò)和定性分析的方法建立預(yù)測(cè)模型.文獻(xiàn)[45?46]采用人工神經(jīng)網(wǎng)絡(luò)分別對(duì)鋼板軋制過(guò)程中的軋制力和串聯(lián)軋制機(jī)組的震顫進(jìn)行了預(yù)測(cè).文獻(xiàn)[47]針對(duì)高爐煉鐵過(guò)程中的硅含量變化趨勢(shì)預(yù)測(cè),提出了二編碼支持向量機(jī)模型.基于偏最小二乘回歸方法和核偏最小二乘法的預(yù)測(cè)模型也應(yīng)用于化工生產(chǎn)過(guò)程的產(chǎn)品質(zhì)量[48]和銅轉(zhuǎn)爐吹煉過(guò)程的關(guān)鍵操作參數(shù)預(yù)測(cè)[49].基于混沌的多步迭代預(yù)測(cè)和基于AdaBoost的預(yù)測(cè)模型也分別應(yīng)用于鐵水硅含量預(yù)測(cè)[50]和選礦生產(chǎn)指標(biāo)預(yù)測(cè)[51]中.此外,基于數(shù)據(jù)的預(yù)測(cè)模型不僅被應(yīng)用在生產(chǎn)監(jiān)控與調(diào)度需求中,也被應(yīng)用在預(yù)測(cè)優(yōu)化控制中[52?53],而采用基于數(shù)據(jù)的機(jī)器學(xué)習(xí)方法(如人工神經(jīng)網(wǎng)絡(luò)、支持向量機(jī)等)來(lái)進(jìn)行預(yù)測(cè)建模是當(dāng)前較為流行的方法[54?58].其基本思路是將當(dāng)前時(shí)刻的系統(tǒng)輸入值和真實(shí)輸出值作為基于數(shù)據(jù)預(yù)測(cè)模型的輸入來(lái)預(yù)測(cè)系統(tǒng)的輸出,并將此預(yù)測(cè)輸出值反饋到系統(tǒng)輸入端以進(jìn)行滾動(dòng)優(yōu)化.此類方法充分利用了機(jī)器學(xué)習(xí)技術(shù)較強(qiáng)的非線性擬合能力,而無(wú)需關(guān)注系統(tǒng)內(nèi)在機(jī)理,具有較強(qiáng)的可應(yīng)用性;但卻需要大量的歷史數(shù)據(jù)來(lái)作為預(yù)測(cè)模型的建模基礎(chǔ).

根據(jù)生產(chǎn)過(guò)程中不同的預(yù)測(cè)需求或不同的生產(chǎn)狀況,基于數(shù)據(jù)的預(yù)測(cè)建模通常有以下幾種分類方法.根據(jù)預(yù)測(cè)時(shí)長(zhǎng)需求,可分為長(zhǎng)期預(yù)測(cè)模型和短期預(yù)測(cè)模型;根據(jù)預(yù)測(cè)輸出指標(biāo)的數(shù)量,可分為多輸出預(yù)測(cè)和單輸出預(yù)測(cè);根據(jù)模型中是否考慮時(shí)滯因素,可以分為時(shí)滯因素模型和非時(shí)滯模型;根據(jù)是否有在線更新模型參數(shù),可分為離線模型和在線模型;根據(jù)是否使用單一的機(jī)器學(xué)習(xí)預(yù)測(cè)模型,可以分為多模型集成和單一模型等.下面將重點(diǎn)綜述幾類預(yù)測(cè)建模問(wèn)題,包括長(zhǎng)期預(yù)測(cè)模型、多輸出模型、時(shí)滯因素模型、在線預(yù)測(cè)模型、集成預(yù)測(cè)模型和時(shí)間序列預(yù)測(cè)模型.

1)長(zhǎng)期預(yù)測(cè)模型

流程工業(yè)生產(chǎn)中為了達(dá)到生產(chǎn)資源的合理配置,通常需要一個(gè)相對(duì)長(zhǎng)期生產(chǎn)規(guī)劃(如天、月等),因此對(duì)生產(chǎn)過(guò)程指標(biāo)的長(zhǎng)期預(yù)測(cè)就顯得尤為重要.短期預(yù)測(cè)一般采用單步迭代的方法,然而此方法應(yīng)用在長(zhǎng)期預(yù)測(cè)問(wèn)題時(shí)預(yù)測(cè)誤差會(huì)隨著迭代步數(shù)的增加而積累,導(dǎo)致最終的誤差很大[59?61].如文獻(xiàn)[61]針對(duì)轉(zhuǎn)爐煤氣流量的長(zhǎng)期預(yù)測(cè),提出了一種基于鋼鐵生產(chǎn)狀態(tài)估計(jì)的轉(zhuǎn)爐煤氣流量長(zhǎng)期預(yù)測(cè)方法,通過(guò)特征提取和特征融合得到全局性特征,利用全局性特征來(lái)實(shí)現(xiàn)轉(zhuǎn)爐煤氣流量的長(zhǎng)期預(yù)測(cè).文獻(xiàn)[62]提出粒度時(shí)間序列的概念,并采用模糊聚類方法構(gòu)造時(shí)間粒度以進(jìn)行長(zhǎng)期趨勢(shì)預(yù)測(cè).針對(duì)鋼鐵能源系統(tǒng)的副產(chǎn)煤氣流量長(zhǎng)期預(yù)測(cè)問(wèn)題,文獻(xiàn)[63]提出了一種基于粒度計(jì)算的長(zhǎng)期預(yù)測(cè)方法,通過(guò)對(duì)工業(yè)原始數(shù)據(jù)根據(jù)過(guò)程操作工藝進(jìn)行時(shí)間上的粒度劃分,采用動(dòng)態(tài)時(shí)間彎曲技術(shù)和模糊聚類產(chǎn)生類別實(shí)現(xiàn)長(zhǎng)期預(yù)測(cè).而文獻(xiàn)[64]針對(duì)鋼鐵工業(yè)中氧氮能源系統(tǒng)的調(diào)度問(wèn)題,采取了預(yù)測(cè)–調(diào)度兩階段的調(diào)度方法,其中長(zhǎng)期預(yù)測(cè)部分同樣采用了基于時(shí)間粒度劃分的方法.

基于時(shí)間粒度劃分的方法雖然可以有效地避免單步迭代預(yù)測(cè)帶來(lái)的誤差積累問(wèn)題,但是以上文獻(xiàn)中的時(shí)間粒度劃分都是采用人工劃分的方式,極度依賴于人工經(jīng)驗(yàn),粒度劃分的效果很難科學(xué)評(píng)判,而且難以推廣到其他工業(yè)應(yīng)用,有一定的局限性.因此更智能的自動(dòng)劃分方法以及更合理的粒度劃分評(píng)判方法是目前研究的重點(diǎn)[63].

2)多輸出預(yù)測(cè)模型

工業(yè)生產(chǎn)過(guò)程往往需要同時(shí)關(guān)注多個(gè)關(guān)鍵預(yù)測(cè)指標(biāo),分別對(duì)各個(gè)指標(biāo)建立預(yù)測(cè)模型的方法會(huì)丟失被預(yù)測(cè)指標(biāo)之間的內(nèi)在關(guān)聯(lián)耦合信息,從而導(dǎo)致預(yù)測(cè)精度不高.如鋼鐵工業(yè)轉(zhuǎn)爐煉鋼生產(chǎn)中,文獻(xiàn)[24,65]針對(duì)兩個(gè)轉(zhuǎn)爐煤氣柜柜位預(yù)測(cè),考慮兩個(gè)煤氣柜之間的相互關(guān)聯(lián)影響,建立了多輸出最小二乘支持向量機(jī)預(yù)測(cè)模型.文獻(xiàn)[66]針對(duì)轉(zhuǎn)爐煤氣柜柜位的長(zhǎng)期預(yù)測(cè)問(wèn)題,提出采用基于粒度計(jì)算的協(xié)作式模糊聚類方法建立了兩柜位長(zhǎng)期預(yù)測(cè)模型.文獻(xiàn)[67]針對(duì)高爐煉鐵過(guò)程中的四個(gè)關(guān)鍵質(zhì)量指標(biāo)(鐵水溫度、硅含量、硫含量和磷含量)的預(yù)測(cè)問(wèn)題,建立了基于建模精度綜合評(píng)價(jià)與遺傳參數(shù)優(yōu)化的鐵水質(zhì)量多輸出支持向量回歸動(dòng)態(tài)預(yù)測(cè)模型.文獻(xiàn)[68]采用多輸出最小二乘支持向量機(jī)同時(shí)預(yù)測(cè)氧化鋁蒸發(fā)過(guò)程的全堿濃度、氧鋁濃度和苛堿濃度.在以上的工業(yè)預(yù)測(cè)應(yīng)用中多輸出預(yù)測(cè)模型都提高了模型預(yù)測(cè)精度.

3)時(shí)滯因素模型

流程工業(yè)生產(chǎn)過(guò)程通常具有時(shí)滯性,輸入變量的變化往往需要經(jīng)過(guò)一段時(shí)間才能反映到被預(yù)測(cè)指標(biāo)上,如選礦過(guò)程、鋼鐵生產(chǎn)過(guò)程等.一方面預(yù)測(cè)建模需將輸入變量的時(shí)滯性考慮在預(yù)測(cè)建模中;另一方面被預(yù)測(cè)指標(biāo)本身通常具有連續(xù)性,其當(dāng)前時(shí)刻取值與歷史時(shí)刻值有著相互關(guān)聯(lián),考慮輸入輸出閉環(huán)聯(lián)系,通常需將被預(yù)測(cè)指標(biāo)歷史時(shí)刻的變量值作為模型的輸入特征來(lái)進(jìn)行建模.如文獻(xiàn)[69]針對(duì)高爐煤氣系統(tǒng)柜位波動(dòng)的建模問(wèn)題,將前一時(shí)刻的高爐煤氣柜柜位值添加到預(yù)測(cè)模型的輸入向量中進(jìn)行了T-S模糊預(yù)測(cè)建模.對(duì)于煉鋼轉(zhuǎn)爐煤氣柜柜位預(yù)測(cè),也需要將歷史時(shí)刻的柜位值反饋到輸入變量中以形成輸入輸出閉環(huán)聯(lián)系[24,65].文獻(xiàn)[70?71]分別針對(duì)高爐煉鐵過(guò)程多元鐵水質(zhì)量預(yù)測(cè)問(wèn)題和鐵水溫度預(yù)測(cè)問(wèn)題,考慮到煉鐵過(guò)程中的時(shí)滯性質(zhì),將相關(guān)輸入輸出變量的時(shí)序和時(shí)滯關(guān)系融合到建模過(guò)程.文獻(xiàn)[31]考慮了5小時(shí)的輸入延遲影響,針對(duì)高爐鐵水硅含量預(yù)測(cè)問(wèn)題,將輸入變量的時(shí)滯影響考慮到模型中,提高了預(yù)測(cè)精度.然而此種考慮輸入延遲的方法的關(guān)鍵在于選定輸入變量的延遲時(shí)間,這對(duì)于模型的性能有著重要影響.但目前文獻(xiàn)中通常基于人工經(jīng)驗(yàn)來(lái)手動(dòng)選取延遲時(shí)間,預(yù)測(cè)模型建模的效果往往是難以保證的.

4)在線預(yù)測(cè)模型

在線模型是將采集的新樣本不斷參與到現(xiàn)有模型的再訓(xùn)練中,此類預(yù)測(cè)模型的內(nèi)部參數(shù)會(huì)根據(jù)新樣本實(shí)時(shí)更新,模型會(huì)實(shí)時(shí)反映新的工況,從而提高預(yù)測(cè)精度.如文獻(xiàn)[72]針對(duì)選礦過(guò)程精礦品位的預(yù)測(cè)問(wèn)題,提出了一種自適應(yīng)在線支持向量機(jī)預(yù)測(cè)模型.模型依據(jù)新工況樣本對(duì)現(xiàn)有樣本集統(tǒng)計(jì)特性的影響,引入了模型參數(shù)自適應(yīng)調(diào)整機(jī)制,并采用在線迭代學(xué)習(xí)機(jī)制更新模型.文獻(xiàn)[73]針對(duì)濕法煉鋅凈化過(guò)程中雜質(zhì)離子濃度預(yù)測(cè)問(wèn)題,提出了基于在線支持向量回歸的離子濃度預(yù)測(cè)模型.另外,文獻(xiàn)[74]針對(duì)全廠級(jí)的產(chǎn)品質(zhì)量指標(biāo)預(yù)測(cè)問(wèn)題,提出了一種根據(jù)訓(xùn)練樣本的統(tǒng)計(jì)特性能在線更新參數(shù)的支持向量機(jī)預(yù)測(cè)模型.文獻(xiàn)[75]針對(duì)轉(zhuǎn)爐煤氣系統(tǒng)中煤氣柜柜位和煤氣流量的預(yù)測(cè)問(wèn)題,提出了一種基于最小二乘支持向量機(jī)預(yù)測(cè)模型.其中模型的參數(shù)優(yōu)化采用了一種并行化的粒子群和并行驗(yàn)證方法,實(shí)現(xiàn)了模型參數(shù)快速的在線更新.

5)集成預(yù)測(cè)模型

單一的機(jī)器學(xué)習(xí)預(yù)測(cè)模型通常有性能不穩(wěn)定,對(duì)模型參數(shù)敏感,易過(guò)擬合等缺點(diǎn).而采集的工業(yè)數(shù)據(jù)通常可看作是幾種不同的生產(chǎn)狀態(tài)相疊加而產(chǎn)生的序列,因此單一預(yù)測(cè)模型并不能完全反映多狀態(tài)數(shù)據(jù)的變化特性.如文獻(xiàn)[76]針對(duì)赤鐵礦選生產(chǎn)率預(yù)測(cè)問(wèn)題,提出使用多個(gè)最小二乘支持向量機(jī)模型對(duì)聚類后的數(shù)據(jù)(每一類可以看作一個(gè)工況)進(jìn)行建模再進(jìn)行加權(quán)組合.文獻(xiàn)[77]針對(duì)濕法煉鋅凈化過(guò)程中鈷離子濃度預(yù)測(cè)問(wèn)題,基于集成建模思想將兩個(gè)單一支持向量機(jī)子模型進(jìn)行加權(quán)集成.文獻(xiàn)[78?79]分別針對(duì)非線性工業(yè)時(shí)間序列預(yù)測(cè)和高爐鐵水硅含量的預(yù)測(cè)問(wèn)題,都考慮到單個(gè)神經(jīng)網(wǎng)絡(luò)模型易過(guò)擬合的特點(diǎn),提出使用Bootstrap方法將多個(gè)網(wǎng)絡(luò)模型集成來(lái)構(gòu)造預(yù)測(cè)區(qū)間 (方差和均值),以增強(qiáng)模型的穩(wěn)定性.針對(duì)針鐵礦法沉鐵過(guò)程反應(yīng)器出口亞鐵離子和鐵離子濃度的預(yù)測(cè)問(wèn)題,文獻(xiàn)[80]提出將基于改進(jìn)差分進(jìn)化算法參數(shù)優(yōu)化的最小二乘支持向量機(jī)預(yù)測(cè)模型和過(guò)程神經(jīng)網(wǎng)絡(luò)模型集成來(lái)進(jìn)行預(yù)測(cè).集成模型提高了單一預(yù)測(cè)模型的穩(wěn)定性和預(yù)測(cè)精度,但是模型的參數(shù)眾多,通常較為復(fù)雜,同時(shí)也增加了模型訓(xùn)練時(shí)間.因此,此類模型大多不適用于在線模型.

6)時(shí)間序列預(yù)測(cè)模型

2.2 基于數(shù)據(jù)與機(jī)理的集成預(yù)測(cè)建模

基于數(shù)據(jù)的機(jī)器學(xué)習(xí)預(yù)測(cè)模型在描述輸入輸出非線性關(guān)系方面優(yōu)勢(shì)明顯,但此類方法在先驗(yàn)知識(shí)處理、模型計(jì)算復(fù)雜度等方面仍然存在局限性.為彌補(bǔ)基于數(shù)據(jù)建模方法的缺點(diǎn),基于機(jī)理模型和數(shù)據(jù)模型相結(jié)合的方法是一種有益的嘗試.一類方案是將機(jī)理模型和基于數(shù)據(jù)的誤差補(bǔ)償方法相結(jié)合來(lái)構(gòu)造預(yù)測(cè)模型[84?85].該類方法適用于反應(yīng)機(jī)理相對(duì)明確的工業(yè)過(guò)程,以基于動(dòng)力學(xué)、熱力學(xué)以及物料平衡、能量平衡的機(jī)理模型作為集成建模主體,利用生產(chǎn)數(shù)據(jù)建立誤差補(bǔ)償模型,補(bǔ)償主體模型輸出與實(shí)際輸出的差值.如文獻(xiàn)[84]針對(duì)針鐵礦法沉鐵過(guò)程出口亞鐵離子濃度預(yù)測(cè),采用并聯(lián)方式集成了沉鐵過(guò)程的機(jī)理模型和基于最小二乘支持向量機(jī)的輸出誤差補(bǔ)償模型.文獻(xiàn)[85]針對(duì)文獻(xiàn)[84]中的方法構(gòu)建了亞鐵離子濃度預(yù)測(cè)模型的在線參數(shù)更新策略.文獻(xiàn)[86]分析爐內(nèi)電熱轉(zhuǎn)換關(guān)系,利用能量守恒原理建立了產(chǎn)品單噸能耗機(jī)理模型,提出了由基于機(jī)理分析的單噸能耗主模型和基于神經(jīng)網(wǎng)絡(luò)的誤差補(bǔ)償模型組成的產(chǎn)品單噸能耗混合預(yù)報(bào)模型.文獻(xiàn)[87?88]基于機(jī)理模型和神經(jīng)網(wǎng)絡(luò)誤差補(bǔ)償模型相結(jié)合的建模形式,分別預(yù)測(cè)了濕法煉鋅過(guò)程中的鈷離子濃度和氧化鋁冶煉過(guò)程中的生料漿質(zhì)量,所提方法都提高了單獨(dú)使用機(jī)理預(yù)測(cè)模型的預(yù)測(cè)精度.另外一類是將機(jī)器學(xué)習(xí)模型融合到基于有限元分析的鋼板軋制機(jī)理模型中以降低有限元分析的時(shí)間消耗,其中機(jī)器學(xué)習(xí)模型的訓(xùn)練數(shù)據(jù)來(lái)源于有限元模擬過(guò)程.如文獻(xiàn)[89]采用有限元分析和神經(jīng)網(wǎng)絡(luò)相結(jié)合的建模方法對(duì)軋鋼過(guò)程中的閉合孔隙進(jìn)行預(yù)測(cè).文獻(xiàn)[90]結(jié)合軋制過(guò)程機(jī)理分析和基于數(shù)據(jù)的神經(jīng)網(wǎng)絡(luò)模型來(lái)預(yù)測(cè)軋鋼過(guò)程中的軋制力,以提高預(yù)測(cè)精度.此外,還有一種方案是將軋制過(guò)程的精確數(shù)學(xué)模型和數(shù)據(jù)模型相結(jié)合.如文獻(xiàn)[91?92]針對(duì)軋制力預(yù)測(cè),分別將貝葉斯推理和神經(jīng)網(wǎng)絡(luò)模型與軋制過(guò)程的精確數(shù)學(xué)模型相結(jié)合預(yù)測(cè)了軋制力.

此類方法僅適用于機(jī)理過(guò)程相對(duì)明確的生產(chǎn)過(guò)程,而現(xiàn)代生產(chǎn)過(guò)程越來(lái)越復(fù)雜,大部分生產(chǎn)過(guò)程并沒(méi)有一個(gè)清晰的機(jī)理模型.因此,此類建模方法的應(yīng)用受到了一定的限制.將復(fù)雜生產(chǎn)過(guò)程中的局部精確機(jī)理模型與數(shù)據(jù)模型相結(jié)合是未來(lái)一個(gè)研究方向.

3 預(yù)測(cè)模型的參數(shù)優(yōu)化

基于數(shù)據(jù)的預(yù)測(cè)模型通常包含重要的參數(shù),其選取對(duì)于預(yù)測(cè)模型的性能有著重要影響(如最小二乘支持向量機(jī)的核函數(shù)參數(shù)和懲罰因子、神經(jīng)網(wǎng)絡(luò)中隱含層神經(jīng)元個(gè)數(shù)以及學(xué)習(xí)率等).針對(duì)此類參數(shù)的優(yōu)化方法有基于梯度的方法和智能優(yōu)化方法等.

3.1 基于梯度的優(yōu)化方法

基于梯度的優(yōu)化方法利用目標(biāo)函數(shù)的梯度信息進(jìn)行優(yōu)化,是機(jī)器學(xué)習(xí)中使用較為廣泛的方法.該方法可以建立明確的優(yōu)化搜索方向,但對(duì)初始值較敏感,易陷入局部最優(yōu).常用的基于梯度的方法有梯度下降法、共軛梯度法等[11].在工業(yè)應(yīng)用中通常會(huì)將基于梯度的優(yōu)化方法和其他方法相結(jié)合,更好地優(yōu)化模型參數(shù),如與基于噪聲估計(jì)的方法[93?94],與基于誤差密度函數(shù)估計(jì)的方法[95],與網(wǎng)格搜索算法[96]相結(jié)合等.

預(yù)測(cè)誤差一般被認(rèn)為由工業(yè)數(shù)據(jù)噪聲和預(yù)測(cè)模型的欠精確共同導(dǎo)致,若將預(yù)測(cè)誤差的方差逼近噪聲方差,那么相當(dāng)于將模型的誤差逼近于零,這樣求得模型參數(shù)將會(huì)有最優(yōu)的預(yù)測(cè)性能.如文獻(xiàn)[93]考慮工業(yè)噪聲對(duì)參數(shù)的影響,提出采用一種基于噪聲估計(jì)和共軛梯度方法來(lái)優(yōu)化最小二乘支持向量機(jī)預(yù)測(cè)模型中的核函數(shù)參數(shù)和懲罰因子.文獻(xiàn)[94]同樣采用該方法優(yōu)化基于核回歸的區(qū)間預(yù)測(cè)模型中的懲罰因子、核函數(shù)權(quán)重以及核函數(shù)的寬度等參數(shù).通過(guò)控制誤差概率密度函數(shù)形狀進(jìn)行參數(shù)優(yōu)化是另一類有效的思路.如文獻(xiàn)[95]針對(duì)選礦過(guò)程中的混合精礦品位預(yù)測(cè)問(wèn)題,將誤差的概率密度函數(shù)表示成最小二乘支持向量機(jī)模型參數(shù)(核函數(shù)的寬度和懲罰因子)的函數(shù),通過(guò)調(diào)節(jié)此類參數(shù)來(lái)得到預(yù)期的誤差概率密度函數(shù),從而達(dá)到優(yōu)化模型參數(shù)的目的.此外,在基于交叉驗(yàn)證的網(wǎng)格搜索參數(shù)優(yōu)化方法中會(huì)存在反復(fù)求逆,同時(shí)缺乏指導(dǎo)的網(wǎng)格遍歷搜索會(huì)消耗大量時(shí)間,無(wú)法滿足現(xiàn)場(chǎng)實(shí)時(shí)性要求且優(yōu)化結(jié)果也不理想.而基于梯度的優(yōu)化方法會(huì)指導(dǎo)優(yōu)化方向,但同時(shí)有易陷入局部最優(yōu)的缺點(diǎn).因此文獻(xiàn)[96]將以上兩種方法相結(jié)合,針對(duì)焦?fàn)t煤氣柜位預(yù)測(cè),提出了一種基于網(wǎng)格搜索和梯度法相結(jié)合的參數(shù)優(yōu)化方法.該方法采用基于快速留一法導(dǎo)出網(wǎng)格梯度搜索方向來(lái)避免普通網(wǎng)格搜索方向的盲目性,從而快速獲得了較優(yōu)的模型參數(shù).再如文獻(xiàn)[97]將遺傳算法和梯度下降法相結(jié)合進(jìn)行參數(shù)優(yōu)化應(yīng)用于煤氣柜位預(yù)測(cè)問(wèn)題.

以上基于梯度的參數(shù)優(yōu)化方法與其他方法相結(jié)合能夠獲得更好的參數(shù)優(yōu)化結(jié)果,然而此類方法存在運(yùn)算時(shí)間長(zhǎng)的缺點(diǎn),大多不適用于工業(yè)生產(chǎn)的在線參數(shù)優(yōu)化,只能進(jìn)行離線應(yīng)用.

3.2 基于智能優(yōu)化的方法

智能優(yōu)化算法是一類啟發(fā)式優(yōu)化算法[98?100],此類方法都是從任一解出發(fā),按照某種機(jī)制,以一定的概率在整個(gè)求解空間中探索最優(yōu)解.智能優(yōu)化算法廣泛應(yīng)用于基于數(shù)據(jù)的預(yù)測(cè)模型參數(shù)優(yōu)化問(wèn)題[97,101?104],且多數(shù)應(yīng)用以最小化預(yù)測(cè)誤差為優(yōu)化目標(biāo).如文獻(xiàn)[101?102]分別針對(duì)高爐鐵水硅含量預(yù)測(cè)問(wèn)題,提出一種基于混沌粒子群優(yōu)化的支持向量回歸機(jī)參數(shù)優(yōu)化算法.文獻(xiàn)[103]針對(duì)銅閃速熔煉過(guò)程中冰銅溫度、冰銅品位及渣中鐵硅質(zhì)量比三個(gè)關(guān)鍵工藝指標(biāo)的預(yù)測(cè),采用了實(shí)數(shù)編碼的加速遺傳算法來(lái)優(yōu)化投影尋蹤回歸預(yù)測(cè)模型的參數(shù).針對(duì)石油工業(yè)中的二氧化碳腐蝕率的預(yù)測(cè)問(wèn)題,有學(xué)者采用了模擬退火算法來(lái)優(yōu)化最小二乘支持向量機(jī)預(yù)測(cè)模型的參數(shù)[104].文獻(xiàn)[65,75]分別采用粒子群算法和并行粒子群算法優(yōu)化了最小二乘支持向量機(jī)的參數(shù).文獻(xiàn)[82]采用模擬退火算法優(yōu)化了基于核函數(shù)動(dòng)態(tài)貝葉斯網(wǎng)的核函數(shù)參數(shù).此外,遺傳算法還被用來(lái)優(yōu)化支持向量機(jī)的參數(shù)[26,67].上述智能算法雖然在參數(shù)優(yōu)化過(guò)程中容易獲得全局最優(yōu)解,但是它們應(yīng)用在工業(yè)生產(chǎn)過(guò)程參數(shù)優(yōu)化問(wèn)題中依然存在較高的不確定性,沒(méi)有最優(yōu)搜索方向以及計(jì)算復(fù)雜度較高等缺點(diǎn).

4 結(jié)論與展望

現(xiàn)有基于數(shù)據(jù)的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法盡管研究成果已較為豐碩,但是依然存在以下問(wèn)題.1)現(xiàn)有模型雖然對(duì)于工況穩(wěn)定的生產(chǎn)指標(biāo)預(yù)測(cè)有著較好的預(yù)測(cè)效果,然而多數(shù)生產(chǎn)過(guò)程是時(shí)變過(guò)程,且經(jīng)常受人為干擾.而現(xiàn)有預(yù)測(cè)模型本身大多不能自動(dòng)地識(shí)別工業(yè)過(guò)程中的時(shí)變特性,進(jìn)而導(dǎo)致基于數(shù)據(jù)的預(yù)測(cè)模型精度不高.因此,通過(guò)工業(yè)大數(shù)據(jù)分析方法有效識(shí)別這種時(shí)變特性是一個(gè)關(guān)鍵研究問(wèn)題.2)對(duì)于一個(gè)特定的預(yù)測(cè)模型,其預(yù)測(cè)結(jié)果的誤差通常是由工業(yè)噪聲以及模型本身的不準(zhǔn)確兩部分因素導(dǎo)致.鑒于工業(yè)噪聲難以避免,因此消除模型本身所帶來(lái)的誤差也是一個(gè)值得研究的問(wèn)題.

鄉(xiāng)建主體的多元化導(dǎo)致了鄉(xiāng)建類型的多元化，不同主體來(lái)自不同的社會(huì)階層，站在不同的立場(chǎng)，自然形成了多樣的理念與實(shí)踐。但多元化的主體都不可避免的要直面鄉(xiāng)村的現(xiàn)狀問(wèn)題，并且以解決問(wèn)題為目標(biāo)確定鄉(xiāng)建內(nèi)容和方式，因此以“問(wèn)題——目標(biāo)——實(shí)踐”模式為導(dǎo)向來(lái)分析鄉(xiāng)建的類型更具有通用性，論文提出鄉(xiāng)建的四大類型為：以經(jīng)濟(jì)可持續(xù)為目標(biāo)的產(chǎn)業(yè)發(fā)展、以社會(huì)可持續(xù)為目標(biāo)的社區(qū)重構(gòu)、以文化可持續(xù)為目標(biāo)的文化復(fù)興、以生態(tài)可持續(xù)為目標(biāo)的環(huán)境保護(hù)。

近年來(lái)也有一些新的機(jī)器學(xué)習(xí)方法在工業(yè)過(guò)程指標(biāo)預(yù)測(cè)方面的研究進(jìn)展值得關(guān)注.深度學(xué)習(xí)技術(shù)是機(jī)器學(xué)習(xí)領(lǐng)域新的研究方向,在語(yǔ)音識(shí)別、計(jì)算機(jī)視覺(jué)等領(lǐng)域取得了突破性的進(jìn)展應(yīng)用,盡管深度學(xué)習(xí)在時(shí)間序列預(yù)測(cè)問(wèn)題方面已有探索[105?108],但在特定工業(yè)預(yù)測(cè)應(yīng)用方面的研究還很少.通過(guò)采用深度學(xué)習(xí)自動(dòng)提取得到層次化的工業(yè)數(shù)據(jù)特征表示,再基于挖掘到的深層次生產(chǎn)特征構(gòu)造工業(yè)長(zhǎng)期預(yù)測(cè)模型是未來(lái)預(yù)測(cè)方法可能的一個(gè)研究方向.但目前還存在以下2個(gè)難點(diǎn):1)深度學(xué)習(xí)模型參數(shù)選取;2)深度學(xué)習(xí)特征評(píng)價(jià).

無(wú)模型預(yù)測(cè)逐漸成為學(xué)者研究的焦點(diǎn)[109?110],其特點(diǎn)是無(wú)需依賴具體的預(yù)測(cè)模型,而是通過(guò)統(tǒng)計(jì)觀測(cè)數(shù)據(jù)的方法來(lái)估計(jì)未來(lái)數(shù)據(jù)的變化趨勢(shì).此方法可有效消除由預(yù)測(cè)模型帶來(lái)的模型誤差,因此,將無(wú)模型預(yù)測(cè)方法應(yīng)用到工業(yè)生產(chǎn)過(guò)程實(shí)際預(yù)測(cè)問(wèn)題(如長(zhǎng)期預(yù)測(cè)等)是未來(lái)另一個(gè)值得研究的方向.

知識(shí)自動(dòng)化是近年來(lái)自動(dòng)化領(lǐng)域發(fā)展的新方向[111],基于知識(shí)的預(yù)測(cè)方法在某些領(lǐng)域也已形成具體的應(yīng)用[112?114].生產(chǎn)過(guò)程知識(shí)表示與獲取,以及基于生產(chǎn)知識(shí)的預(yù)測(cè)模型構(gòu)建等是基于知識(shí)自動(dòng)化的生產(chǎn)過(guò)程指標(biāo)預(yù)測(cè)方法的關(guān)鍵研究?jī)?nèi)容.

自適應(yīng)動(dòng)態(tài)規(guī)劃方法利用一個(gè)函數(shù)近似結(jié)構(gòu)(例如神經(jīng)網(wǎng)絡(luò)、模糊模型、多項(xiàng)式等)來(lái)估計(jì)代價(jià)函數(shù),用于按時(shí)間正向求解動(dòng)態(tài)規(guī)劃問(wèn)題[115],基于此方法的工業(yè)過(guò)程預(yù)測(cè)也形成一些具體應(yīng)用[116?117].將來(lái)基于自適應(yīng)動(dòng)態(tài)規(guī)劃預(yù)測(cè)方法的一個(gè)研究方向是深入探究將抽象為智能體的生產(chǎn)過(guò)程與外部環(huán)境信息相交互的機(jī)制融入預(yù)測(cè)建模過(guò)程以提高預(yù)測(cè)精度.

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