張長勝,韓 濤*,錢 斌,胡 蓉,田海湧,毛 輝,王 卓

改進(jìn)BFO優(yōu)化BPNN的自來水混凝加藥預(yù)測

張長勝1,韓 濤1*,錢 斌1,胡 蓉1,田海湧2,毛 輝3,王 卓1

(1.昆明理工大學(xué)信息工程與自動(dòng)化學(xué)院,云南 昆明 650500；2.云南樹業(yè)科技有限公司,云南 昆明 650032；3.中國市政工程華北設(shè)計(jì)研究總院有限公司昆明分公司,云南 昆明 650051)

本文給出一種量子粒子群 (QPSO)算法、改進(jìn)菌群覓食(IBFO)算法優(yōu)化反向傳播神經(jīng)網(wǎng)絡(luò)(BPNN)的混凝投藥預(yù)測模型,利用量子粒子群的個(gè)體極值與群體極值更新細(xì)菌覓食算法趨化過程中細(xì)菌位置;通過細(xì)菌協(xié)同改進(jìn)趨化算子提高優(yōu)化精度,結(jié)合差分算法改進(jìn)繁殖算子解決部分維度退化問題,加入輪盤賭方法作為選擇機(jī)制改進(jìn)遷移算子來克服優(yōu)化過程中優(yōu)秀解消失的缺陷;進(jìn)而優(yōu)化BP神經(jīng)網(wǎng)絡(luò)的權(quán)值、閾值以此預(yù)測混凝劑投藥量.對云南某自來水廠的數(shù)據(jù)進(jìn)行離線訓(xùn)練和模型測試,結(jié)果表明,所提算法預(yù)測結(jié)果的均方誤差(MSE)達(dá)0.0116mg/L,平均絕對誤差百分比(MAPE)達(dá)1.36%,在預(yù)測精度和穩(wěn)定性上優(yōu)于BFO-BPNN、PSO-BPNN等模型.

混凝加藥；預(yù)測模型；BPNN；BFO；QPSO

自來水廠水處理流程包括凝聚、混凝、沉淀、消毒及過濾5個(gè)階段,混凝效果直接影響后續(xù)處理設(shè)備生產(chǎn)負(fù)擔(dān)及成本,精準(zhǔn)投藥對其具有決定性作用.故混凝投藥量閉環(huán)控制是自來水廠生產(chǎn)工藝的核心,也是水處理專家和研究學(xué)者急需解決的問題.自來水廠水處理混凝投藥過程存在非線性、多干擾等問題,并且我國地域遼闊、氣候復(fù)雜多樣、局部地區(qū)存在旱雨季,提高生產(chǎn)過程中抗干擾能力、保證出廠水質(zhì),對其穩(wěn)定生產(chǎn)意義深遠(yuǎn).

近年,將自抗擾控制器與Smith預(yù)估器相結(jié)合的智能算法[1]、數(shù)據(jù)驅(qū)動(dòng)控制[2]等彌補(bǔ)了加藥輸出信息滯后的缺點(diǎn),但抗突變干擾能力較弱鑒于此,有學(xué)者提出通過對源水典型水質(zhì)參數(shù)的檢測,利用神經(jīng)網(wǎng)絡(luò)[3-4]的容錯(cuò)性、自學(xué)習(xí)性和自適應(yīng)能力,建立混凝投藥系統(tǒng)投藥量預(yù)測模型.于是Chan等[5]研究基于均值聚類和自適應(yīng)神經(jīng)模糊推理的混合算法,利用來自Bansong WTP的數(shù)據(jù)來預(yù)測沉降水的濁度和最佳混凝劑用量,對雨季的混凝預(yù)測作出了補(bǔ)充.徐少川等[6]引入CMAC改進(jìn)自學(xué)習(xí)算法構(gòu)建混凝投藥控制器,在穩(wěn)定保證出廠水質(zhì)的同時(shí),降低凈水生產(chǎn)成本.饒小康[7]采用Elman神經(jīng)網(wǎng)絡(luò)算法對獲取的歷史數(shù)據(jù)預(yù)處理后進(jìn)行訓(xùn)練和自適應(yīng)學(xué)習(xí),構(gòu)建了用于混凝投藥的凈水控制器.與神經(jīng)模糊控制、CMAC神經(jīng)網(wǎng)絡(luò)、Elman神經(jīng)網(wǎng)絡(luò)相比[5-8],BP神經(jīng)網(wǎng)絡(luò)在非線性映射、自學(xué)習(xí)和自適應(yīng)、容錯(cuò)等方面具有獨(dú)特的優(yōu)勢.

但BP神經(jīng)網(wǎng)絡(luò)也存在過擬合[9]和泛化能力較弱[10]的問題.遺傳算法(GA)與粒子群算法(PSO)具有良好的全局搜索能力,可以快速地將解空間中的全體解搜索出.國內(nèi)學(xué)者[11]研究GA-BP網(wǎng)絡(luò)結(jié)構(gòu)的投藥量預(yù)測模型,實(shí)現(xiàn)混凝劑的實(shí)時(shí)最佳投加.魏津瑜等[12]將PSO與BP相結(jié)合,使得預(yù)測精度明顯提高.

與GA、PSO相比,菌群覓食(BFO)[13]算法收斂速度更快、且更易于跳出局部極小值.因此,本文以云南某自來水廠的混凝投藥為研究對象,將量子粒子群(QPSO)算法與改進(jìn)型菌群覓IBFO)算法相結(jié)合來優(yōu)化BP神經(jīng)網(wǎng)絡(luò)混凝投藥預(yù)測模型.通過對比不同優(yōu)化算法在標(biāo)準(zhǔn)函數(shù)下的全局最優(yōu)值,以及對比不同優(yōu)化算法下BP神經(jīng)網(wǎng)絡(luò)的損失值、預(yù)測投藥量和預(yù)測投藥量誤差,綜合評估各算法性能,旨在為水廠混凝投藥環(huán)節(jié)提供參考.

1 模型方法

1.1 量子粒子群

QPSO算法以狄拉克(DELTA)趨阱為基礎(chǔ),認(rèn)為每個(gè)粒子具有量子行為,即不能同時(shí)確定位置和速度的精確值[14-15],因此具有量子行為的粒子在移動(dòng)時(shí)并沒有確定的軌跡,可以在全部可行解空間中進(jìn)行搜素,以便得到全局最優(yōu)解,故QPSO比標(biāo)準(zhǔn)PSO算法具有更優(yōu)的全局搜索能力.其動(dòng)力學(xué)原理如圖1所示.

圖1 QPSO算法示意

粒子更新迭代方程為[16]:

式中:是粒子群種群數(shù)量;best是個(gè)體極值best的平均值;best是粒子群群體極值;generation為當(dāng)前進(jìn)化代數(shù);max generation為設(shè)定的最大進(jìn)化代數(shù);為[0,1]之間的隨機(jī)數(shù);為收縮擴(kuò)張系數(shù).

1.2 菌群覓食算法

1.2.1 傳統(tǒng)細(xì)菌覓食優(yōu)化算法BFO算法基于大腸桿菌的搜索和最佳覓食決策能力,細(xì)菌坐標(biāo)代表了優(yōu)化問題的單個(gè)解決方案,根據(jù)覓食群體的動(dòng)態(tài),這些試驗(yàn)解決方案集合趨向于最優(yōu)解決方案細(xì)菌種群.

初始細(xì)菌位置,每一個(gè)細(xì)菌代表待求解函數(shù)的一個(gè)解,即:

適應(yīng)度函數(shù)選擇如公式(6):

如圖2所示,細(xì)菌覓食系統(tǒng)3種主要機(jī)制為趨化、繁殖和遷移.趨化模擬了大腸桿菌細(xì)胞通過鞭毛泳動(dòng)和翻轉(zhuǎn)的過程,在細(xì)菌生命周期內(nèi),可以沿著相同的方向游泳一段時(shí)間,當(dāng)朝著喜歡的營養(yǎng)梯度地方移動(dòng)并且避免進(jìn)入有害的環(huán)境時(shí),就需要進(jìn)行順、逆時(shí)針翻轉(zhuǎn)改變方向,它根據(jù)環(huán)境變化交替這兩種模式.繁殖是在一定數(shù)量的完全游泳后,最不健康的細(xì)菌最終死亡,而每一個(gè)更健康的細(xì)菌(產(chǎn)生更高健康值的細(xì)菌)無性分裂成兩種放置在同一位置的細(xì)菌,以保持種群大小不變.遷移是為了逃避局部最優(yōu)而進(jìn)行的消除分散事件,即一些細(xì)菌小概率地被隨機(jī)清算,新的替換細(xì)菌被初始化在搜索空間的隨機(jī)位置.細(xì)菌間吸引和排斥的蜂擁模式有負(fù)面影響,排斥作用在趨化階段降低了優(yōu)化的精度,且趨化階段還存在著部分維度的退化問題以及尋優(yōu)過程中優(yōu)秀解消失問題[17-18].

圖2 細(xì)菌覓食算法示意

細(xì)菌翻轉(zhuǎn)行為的隨機(jī)性導(dǎo)致尋優(yōu)速度過慢,且不能分享其它細(xì)菌在運(yùn)動(dòng)過程中的知識與經(jīng)驗(yàn)特點(diǎn)[19],故引入細(xì)菌向個(gè)體與種群學(xué)習(xí)的思想,使得其能夠記憶群體的適應(yīng)度最優(yōu)值與最優(yōu)位置.在翻轉(zhuǎn)過程適應(yīng)度變差時(shí),則向群體最優(yōu)學(xué)習(xí),并克服隨機(jī)轉(zhuǎn)向變差的不足,從而進(jìn)行位置更新.改進(jìn)算法流程如圖3所示:

(2)繁殖算子改進(jìn)經(jīng)過N次趨化后,對第個(gè)細(xì)菌的健康值可累加為:

針對趨化過程中不是所有的維度都在進(jìn)化、而部分維度退化現(xiàn)象,導(dǎo)致細(xì)菌可能出現(xiàn)局部最優(yōu)狀況的問題,在繁殖環(huán)節(jié)引入差分算法,通過變異、交叉、選擇3個(gè)算子來尋優(yōu).

圖3 細(xì)菌協(xié)同

變異算子通過考慮種群內(nèi)個(gè)體信息、縮放因子來拓展搜索空間,定義為:

交叉算子定義為:

選擇操作為貪婪策略,即只有當(dāng)產(chǎn)生的子代個(gè)體優(yōu)于父代個(gè)體時(shí)才被保留,否則父代個(gè)體會(huì)被保留至下一代.

(3)遷移算子改進(jìn)根據(jù)健康狀況及遷移概率Ped的設(shè)定值,將細(xì)菌消除并遷移到優(yōu)化域中的隨機(jī)位置,可避免細(xì)菌陷入局部最佳狀態(tài).但固定的Ped值會(huì)導(dǎo)致尋優(yōu)過程中優(yōu)秀解消失,影響算法的全局尋優(yōu)能力,故結(jié)合輪盤賭方法優(yōu)化遷移概率的選擇機(jī)制:

1.2.3 基于QPSO優(yōu)化的細(xì)菌覓食算法 BFO算法具有較強(qiáng)全局優(yōu)化能力,但可能會(huì)過早收斂導(dǎo)致全局解延遲[20-23].QPSO算法尋優(yōu)速度較快,但可能出現(xiàn)局部最優(yōu)解.為了克服二者缺點(diǎn),利用QPSO算法優(yōu)化BFO中的細(xì)菌初始位置,可進(jìn)一步提高前者性能.QPSO-IBFO算法偽代碼如下:

表1 QPSO-IBFO算法偽代碼

2 仿真及結(jié)果分析

2.1 QPSO-IBFO與各優(yōu)化算法性能比較

為了準(zhǔn)確測試算法性能,使用相同的隨機(jī)種子初始化方法,令BFO、PSO-BFO、QPSO-BFO算法中吸引劑數(shù)量、吸引劑釋放速度、排斥劑數(shù)量、排斥劑釋放速度及適應(yīng)度增量因子為:d_attract = v_attract=d_repellant =v_repellant= 0.05,Jf = 0.5,其余參數(shù)設(shè)置如表2:

表2 優(yōu)化算法參數(shù)

表3 標(biāo)準(zhǔn)測試函數(shù)

表4 不同優(yōu)化算法迭代30次對應(yīng)的f1- f7全局最優(yōu)值

用表3中7個(gè)標(biāo)準(zhǔn)測試函數(shù)[24]來評估QPSO- IBFO算法的優(yōu)化性能.

QPSO-IBFO與PSO、GA、BFO、QPSO、PSO-BFO等6種算法在測試函數(shù)下評價(jià)指標(biāo)如表4所示:

顯然,QPSO-IBFO優(yōu)化算法的尋優(yōu)性能優(yōu)于其它常規(guī)算法.

2.2 QPSO-IBFO-BPNN與各預(yù)測模型性能比較

以云南施甸某自來水廠為例,源水為水庫中上層低濁度水,每小時(shí)以勻速投5%濃度聚合氯化鋁(PAC)[25]溶液作為混凝劑.把原水濁度(NTU)、pH值、溫度(℃)、原水流量(m3/h)、出水濁度(NTU)作為影響因子,通過圖4所示基于QPSO-IBFO算法優(yōu)化BP神經(jīng)網(wǎng)絡(luò)的投藥控制器來預(yù)測混凝劑劑量(mg/L).根據(jù)水廠SCADA系統(tǒng)采集的1020組數(shù)據(jù)(750組為訓(xùn)練集,250組為測試集,20組為驗(yàn)證集),對投藥預(yù)測模型進(jìn)行訓(xùn)練、測試及驗(yàn)證.

圖4 群智能算法優(yōu)化BP神經(jīng)網(wǎng)絡(luò)的投藥預(yù)測

2.2.1 菌群覓食算法優(yōu)化的BPNN性能比較 BP神經(jīng)網(wǎng)絡(luò)的參數(shù)設(shè)置如表5所示.

表5 神經(jīng)網(wǎng)絡(luò)參數(shù)設(shè)置

令BPNN的損失函數(shù)為均方根誤差:

如圖5所示,通過對BPNN分別結(jié)合原始BFO、改進(jìn)趨化算子的BFO、改進(jìn)繁殖算子的BFO、改進(jìn)遷移算子的BFO以及綜合三種改進(jìn)算子的BFO的混合算法進(jìn)行分析比較,綜合三種改進(jìn)算子的BFO優(yōu)化的BPNN(QPSO-IBFO-BPNN)對應(yīng)的損失值曲線收斂效果最好.

令預(yù)測性能評價(jià)指標(biāo)為MSE(均方誤差)、MAE(平均絕對誤差)、MAPE(平均絕對誤差百分比):

圖5 結(jié)合不同菌群覓食算法的BPNN損失值曲線

表6 結(jié)合不同菌群覓食算法的BPNN性能比較

由表6可見,改進(jìn)趨化算子的BFO、改進(jìn)繁殖算子的BFO、改進(jìn)遷移算子的BFO以及綜合3種改進(jìn)算子的BFO優(yōu)化BPNN的混合算法性能均好于QPSO-BFO-BPNN,相對后者,QPSO-IBFO- BPNN性能最優(yōu),其MSE提高了34.78%,MAPE提高了28.8%.

2.2.2不同優(yōu)化算法結(jié)合的BPNN性能比較 在各訓(xùn)練參數(shù)相同的條件下,對QPSO-IBFO-BPNN及其對比模型進(jìn)行訓(xùn)練和測試,各預(yù)測模型損失值的最佳值、最差值以及平均值如表7所示.

對應(yīng)損失值曲線如圖6所示,QPSO-IBFO- BPNN投藥預(yù)測模型相對于其它模型率先平穩(wěn)且損失值最低.

表7 結(jié)合不同優(yōu)化算法的BPNN損失值

圖6 結(jié)合不同優(yōu)化算法的BPNN的損失值曲線

表8為相同損失函數(shù)下,不同預(yù)測模型的性能指標(biāo).可以看出QPSO-IBFO-BPNN(本文算法)的性能最好,其MSE為0.0116mg/L,MAE (平均絕對誤差)為0.0746mg/L,MAPE為0.0136.

表8 結(jié)合不同優(yōu)化算法BPNN性能對比

為預(yù)測模型挑選20組驗(yàn)證數(shù)據(jù)如表9所示.

仿真實(shí)驗(yàn)得到如圖7所示的分析圖.如圖7所示,可看出QPSO-IBFO-BPNN預(yù)測值與真實(shí)數(shù)據(jù)擬合度最高,其預(yù)測誤差在[-0.1,0.1]區(qū)間波動(dòng).

表9 驗(yàn)證數(shù)據(jù)

綜上,基于混合算法預(yù)測模型的自動(dòng)投藥系統(tǒng)能夠有效降低藥耗,減輕過濾、消毒設(shè)備的運(yùn)行負(fù)擔(dān),對達(dá)到理想混凝效果、提高水質(zhì)產(chǎn)生了良好的經(jīng)濟(jì)和社會(huì)效益.

但文中實(shí)驗(yàn)僅對云南單一水廠較穩(wěn)定水質(zhì)數(shù)據(jù)進(jìn)行仿真計(jì)算,可針對不同水源性質(zhì)的多個(gè)不同處理規(guī)模的水廠、旱雨季、不同水處理工藝等情況繼續(xù)開展實(shí)驗(yàn),進(jìn)一步提高非線性加藥模型的魯棒性和實(shí)用性.

3 結(jié)論

3.1 利用QPSO確定IBFO的初始值,避免了QPSO算法局部最優(yōu)解的陷阱及IBFO算法的優(yōu)化延遲問題,提高了IBFO算法的尋優(yōu)速度,改善了其全局優(yōu)化能力.

3.2 利用IBFO優(yōu)化BPNN的權(quán)值和閾值,使得預(yù)測性能指標(biāo)MSE達(dá)0.0116mg/L,MAE達(dá)0.00746mg/L,MAPE達(dá)0.0136,提高了非線性預(yù)測模型的擬合精度.

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Prediction model for tap water coagulation dosing based on BPNNoptimizedwith improved BFO.

ZHANG Chang-sheng1, HAN Tao1*, QIAN Bin1, HU Rong1, TIAN Hai-yong2, MAO Hui3, WANG Zhuo1

(1.Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China；2.Yunnan Shuye Technology Co., Ltd, Kunming 650032, China；3.Kunming Branch of North China Municipal Engineering Design and Research Institute Co., Ltd, Kunming 650051, China)., 2021,41(10)：4616～4624

In this paper, a prediction control model was proposed, which was designed with BPNN optimized by the hybrid algorithm with quantum particle swarm optimization (QPSO) and improved bacterial foraging (IBFO). In this strategy, the individual and population extremum of quantum particle swarmoptimizationwere used to update the bacterial positions in the chemotaxis process for BFO. The chemotaxis operator wasupgraded through bacteria synergy to improve the optimization accuracy. The reproduction operator was improved with difference method to solve the problem of partial dimension degradation. The roulette measure was applied as the selection mechanism to perfect the migration operator, which could overcome the disadvantage of the disappearance for the excellent solutions in the optimization process. Finally, the weights and thresholds of BP neural network were optimized to work out the coagulant dosage. Off-line training andtesting fordata model of one waterworks in Yunnan showed that the mean square error (MSE) of the prediction results of the proposed algorithm was 0.0116mg/L, and the mean absolute percentageerror (MAPE) was 1.36%, which weresuperior toBFO-BPNN and PSO-BPNN models in prediction accuracy and stability.

coagulation dosing；prediction model；BPNN；BFO；QPSO

TP273

A

1000-6923(2021)10-4616-08

張長勝(1970-),男,陜西平利人,昆明理工大學(xué)副教授,主要研究方向復(fù)雜工業(yè)過程建模、智能優(yōu)化算法.發(fā)表論文50余篇.

2021-02-22

國家自然科學(xué)基金資助項(xiàng)目(51665025,61963022)

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