臺灣博碩士論文加值系統

膜過濾的通量會隨著操作時間增加而減少，這是由於薄膜表面與膜孔受到污垢附著而產生阻力。為了改善膜過濾的操作設計，過去研究對其膜結垢變化進行辨識，並進行系統的分析，包括使用過部分最小二乘(PLS)與類神經網路(ANN)模型。然而前者為一線性模型，對於複雜的非線性結垢機制進行辨識效果有限；後者雖可以辨識非線性系統，但其模型結構並不易確定。而且，PLS和ANN模型都是確定性的模型，即無法提供其輸出估測值的可信程度。本研究使用一種新的具有概率意義的高斯過程模型(GPR)對結垢機制進行辨識，此GPR模型除了估測輸出值外，還提供輸出值的估測變異量。並且，將估測變異量延伸使用在挑選數據與更新模型的判別標準，避免加入多餘的數據使模型保持健全。
由於膜表面受到汙染所產生的膜阻力會受到操作通量、操作時間與其他因素所影響，必須在適當的時候對膜進行清洗，且膜並不會因清洗而回復到原來的狀態，因此膜過濾為一衰退程序，如在過大的操作通量或是過長的操作時間才進行膜的清洗，會造成膜表面汙染速度加快，導致操作能耗增高，且因阻塞嚴重使得膜的汰換次數增加，因此發展一套控制設計的方法減少操作能耗與膜損耗有其必要性。傳統的控制設計只根據模型所提供的輸出進行設計，因此可能沒辦法使模型足夠健全，本研究將利用GPRM帶有分布的預測值，發展在基理模型與混GPR模型所結合的混合模型為基礎，進行主動式控制設計，特別是針對健全性不夠充足的基理模型，不同於過去一般的研究設計方法，此設計策略是根據預期的改善程度，利用當前的數據來探索數據不夠充足的位置，使得操作成本盡可能的保持在最低，並且能夠維持操作性能。
混合模型的好處以及主動式學習設計將採用模型以及真實實驗操作來驗證，驗證結果將會說明本研究方法有較好的預測性能以及降低操作成本，且比其他常規的方法來得有效。

The membrane permeate flux will decrease with the increasing operating time mainly because of the resistance generated by fouling on the membrane surface and pore. In order to identify the change of membrane fouling, several data-driven modeling methods, such as partial least squares (PLS) and artificial neural networks (ANNs), have been used to identify the fouling change. However, the PLS model is linear, so it is insufficient to capture the nonlinear relationship in the fouling mechanism. Although ANN is able to model the nonlinear relationship, it is still difficult to determine the network topology for a complex modeling task. Additionally, both PLS and ANN models are deterministic, which means that the probabilistic information for its prediction is not provided. In this work, a novel probabilistic method named Gaussian process regression (GPR) is proposed to model the complex nonlinear fouling mechanism. The GPR model can simultaneously provide the prediction uncertainty, e.g., the prediction variance. As a result, the model can be updated in a simple and efficient manner without adding unnecessary data samples when the fouling changes. The superiority of the proposed method is demonstrated through several experiments.

The membrane fouling will be influenced by operation flux, operation time and other factors. The membrane fouling should be cleaned up at the appropriate time. However, membrane filtration is a decay procedure because feed materials may adhere to the pores of the membrane and the membrane would be not completely cleaned up. The membrane operation leads to a significant loss in separation performance and the high energy increases the operation cost if operation flux or time is not proper. The traditional method designs the operation condition only based on the physical models. The models may not be adequately built in advance. In this work, the distributed prediction of the GPR model is utilized to develop an active design based on the combination of the physical and the GPR model, especially for incomplete models. Unlike most of the past research, the design is based on the expected improvement strategy which is able to exploit information from the current data as well as to explore uncharted regions. The cost of the operations would be kept as low as possible while the favorable design performance can be guaranteed.

The superiority of the hybrid models and the active learning design is demonstrated using simulation and experiments. The results show the proposed methods yield better prediction performance and lower operation costs and they are more efficient than the other conventional methods.

摘要 I
Abstract II
致謝 IV
目錄 V
圖目錄 VII
第1章 前言 1
1.1 背景 1
1.2 膜結垢的處理 1
1.3 膜過濾程序設計 2
1.4 研究動機 6
第2章 高斯建模理論 8
2.1 貝氏定理 8
2.2 高斯過程理論 8
第3章 膜過濾程序的混合模型建立 13
3.1 膜過濾機制 13
3.2 膜過濾程序的混合模型 15
3.2.1 物理基理模型的建立 16
3.2.2 基於數據的GPRM經驗模型建立 24
3.2.3 混合模型的建立 26
3.2.4 混合模型的更新方法 35
3.3 膜過濾實驗操作 41
3.3.1 實驗操作方法與前置作業 41
3.3.2 混合模型於實驗操作驗證 44
第4章 以重覆式學習方法進行膜過濾程序設計 49
4.1 膜過濾程序設計的目標函數 49
4.2 CtC設計理論 51
4.2.1 期望改善量(Expected Improvement) 55
4.3 CtC設計於實際膜過濾操作 66
4.4 WC設計理論 69
4.5 WC線上設計於實際膜過濾操作 76
第5章 結論 79
參考文獻 80

圖1 1膜過濾程序示意圖 4
圖2 1 : 單輸入與單輸出GPRM預測示意圖 11
圖 3 1: 膜過濾裝置簡易流程圖 13
圖3 2 : 膜過濾程序跨膜壓差變化示意圖 14
圖3 3 : 膜表面過濾結垢與回洗示意圖， 膜孔未結垢的過濾操作狀況， 膜孔開始堵塞的過濾操作狀況， 膜孔堵塞嚴重過濾操作狀況， 膜孔經過回洗操作狀況。 15
圖3 4 :膜過濾過濾與回洗壓力變化圖 20
圖3 5 : Cycle 7至Cycle 8膜過濾過濾與回洗壓力變化，並以建立在Cycle 7的基理模型進行Cycle 7的估測與Cycle 8的預測結果 21
圖3 6 : 過濾模型起始膜阻力在21個Cycle的變化 22
圖3 7 : 回洗模型不可逆膜阻力在21個Cycle的變化 22
圖3 8 : 過濾模型參數 在21個Cycle中的數值 23
圖3 9 : 回洗模型參數 在21個Cycle中的數值 23
圖3 10 :回洗模型參數 在21個Cycle中的數值 24
圖3 11 : 建立在Cycle 6至7過濾操作的GPRM 驗證Cycle 7跨膜壓差變化與 預測Cycle 8跨膜壓差變化 25
圖3 12 : 建立在Cycle 6至7回洗操作的GPRM 驗證Cycle 7跨膜壓差變化與 預 測Cycle 8跨膜壓差變化 26
圖3 13 : 過濾GPRM在給定範圍內預測的 平均值與 變異量 29
圖3 14 : 回洗GPRM在給定範圍內預測的 平均值與 變異量 30
圖 3 15 : 以混合模型預測Cycle 22至27跨膜壓差變化 過濾與 回洗 32
圖3 16 : 過濾混合模型預測 Cycle 24與 Cycle 26跨膜壓差變化 33
圖3 17 : 回洗混合模型預測 Cycle 24與 Cycle 25跨膜壓差變化 34
圖3 18 : 45個Cycle 過濾與 回洗的操作時間與操作通量 36
圖3 19 : GPRM在主動式更新(實線)與不更新(虛線)狀況下預測 過濾與 回洗未來跨膜壓差的差值 37
圖3 20 : 過濾與 回洗利用變異輛挑選訓練數據的結果 39
圖3 21 : 被動式模型更新(實線)與主動式模型更新(虛線)預測 過濾壓差變化差值與 回洗壓差變化差值 40
圖3 22 : 膜過濾設備儀控圖 42
圖3 23 : 膜過濾裝置 42
圖3 24 : 實際膜過濾實驗於三種不同操作通量與操作時間的過濾跨膜壓差變化 44
圖3 25 : 實際膜過濾實驗的Cycle 19 過濾跨膜壓差變化與辨識結果以及 設定的過濾操作通量 45
圖3 26 : 基理模型辨識Cycle 16至25的估測起始膜阻力變化 46
圖3 27 : 建立於Cycle 19基理模型預測Cycle 20過濾跨膜壓差變化 47
圖3 28 : 主動式模型更新後過濾訓練數據分布 47
圖3 29 : 主動式模型更新於Cycle 21至Cycle 25預測過濾跨膜壓差變化的結果 48
圖3 30 : 非主動式模型更新於Cycle 21至Cycle 25預測過濾跨膜壓差變化的結果 48
圖4 1 : 膜過濾程序跨膜壓差變化示意圖 50
圖4 2 : 式(4-16)的GPRM預測結果與改善因子示意圖 56
圖4 3 : 扣掉GPRM以輸入值 所預測機率密度分布與積分面積 57
圖4 4 : 在不同輸入值 所估算出的EI值 58
圖4 5 : CtC EI設計於膜過濾的設計流程 61
圖4 6 : Cycle 21至Cycle 35在無設計、基理模型設計、以及CtC EI設計的能量消耗 63
圖4 7 : Cycle 22至Cycle 35在基理模型設計與CtC EI設計下的 操作通量與 操作時間 64
圖4 8 : Cycle 21至Cycle 27設計能耗比較 65
圖4 9: 過濾與 回洗疊代學習的估測變異量變化 66
圖4 10 : 固定條件與CtC EI設計的過濾操作跨模壓差比較圖 68
圖4 11 : 固定條件與CtC EI設計的過濾操作能耗比較圖 69
圖4 12 : CtC EI設計的過濾操作通量與操作時間 69
圖4 13 : WC EI設計於膜過濾的設計流程 73
圖4 14 : CtC EI設計與WC EI設計的能耗變化比較 74
圖4 15 : WC EI設計在Cycle22至24過濾與回洗的操作中及時進行調整， 操作通量以及 操作時間的設計過程 75
圖4 16 : CtC EI設計與WC EI設計所消耗的能耗變化 76
圖4 17 : CtC EI設計與WC EI設計的過濾操作跨模壓差比較圖 77
圖4 18 : CtC EI設計與WC EI設計的過濾操作能耗比較圖 77
圖4 19 : CtC EI設計(實線)與WC EI設計(虛線)在Cycle3的過濾操作跨膜壓差變化 78
圖4 20 : CtC EI設計與WC EI設計的過濾操作通量與操作時間 78

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