建議

本研究為有效提升管網損壞分析與管理決策效益，而提出許多分析程 序、優選模式並發展一可有效輔助決策的管網決策支援系統。以下說明本 研究已進行的各項管網分析與管理相關課題中，仍待克服或改善之處，以 供後續研究參考：

(1) 本研究所提出的制水閥關鍵性分析程序，可在複雜的管網系統中有效

為基礎架構，發展各類決策程序與優選管理模組，便利自來水公司執 行各類複雜的管網分析工作，與應用事業人員較難實作的優選決策模 式，以有效提升自來水管網系統的管理效能。

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附錄 A 管網供水分區劃分模式

當管網損壞發生在主要供水幹管損壞而執行停水維護，將因供水幹管 為管網中重要的供水管線，而影響管網整體的供水能力，造成管壓不足或 出水量不夠等影響可供用戶使用的用水量(Mays, 2000; Gupta and Bhave, 1996)，或者因應幹管執行維護更新操作需要，進行重大的供水系統維護工 程，亦將無法完全供應用戶需水量。且台灣受到季風氣候的影響，而有明 顯的季節變化，水庫集水區集水量有豐枯兩個明顯的供水季節性。當極端 氣候發生時，甚至可能發生乾旱等水資源缺乏的狀況，而無法充足供應供 水區域內的需求水量，比如九十一年時翡翠水庫因為長時間的乾旱，造成 蓄水量不足，而必須在大台北地區執行分區供水(中國時報, 2002/5/12)。因 此水公司面對各種操作需求與供水狀態，必須以分區供水或者分區停水的 方式因應無法充足供水的狀況，以節省出水量。此外，在某些發展中國家 如印度，因其氣候條件造成水資源匱乏或經費限制，無法連續供水，而執 行間歇性供水措施(intermittent water supply) (Ingeduld et al., 2006; Batish, 2003)，亦需將整個管網系統劃分為幾個適當的供水區域，以利節省可供水 量。因此水公司必須彈性的根據維護工程的狀況評估可能缺水狀態，規劃 合理的供水分區，便利在此非常狀況時，有效的調配有限的供水量。然而，

水公司一般在進行供水分區的劃分時，因缺乏一個合理的規劃模式，僅多 依賴操作人員的經驗，依據行政區域或道路等來劃分供水區域，然而管網 連通關係並不盡然會與這些劃分邊界吻合，並可能因為忽略管網連通關 係，造成無法預期的關閉區域，所劃分區域可能比規劃停水量更大，而擴 大影響用戶範圍。且不同的缺水狀態其應停水的量亦會不同，因此有必要 發展一個停水供水分區劃分模式，以提升水公司在缺水調配與操作維護上 的彈性，盡可能減少用水戶的影響衝擊。本研究因而以制水閥分區為單

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位，根據其連通關係，發展停水量與規劃缺水量差異最小，且關閉制水閥 數最少的停水區域劃分模式，並以發展恰當的啟發式演算程序，以供後續 相關研究決策盡可能減少缺水分區調配影響的參考。

本研究提出的管網供水分區劃分決策流程如圖 A.1 所示，包括先估算 管網系統供水需要節省的每日供水量、轉換為制水閥分區輔助網路以及利 用基因演算法(Genetic Algorithm)求解管網供水分區優選模式，以下則針對 各項程序詳細說明之。

1 缺水量估算

在執行管網供水分區之前應該要先估算出管網的減供水量，以作為後 續決策供水分區的合理依據。以乾旱缺水來說，減供水量應該要考量目前 可得水資源、近期可得水資源以及預估乾旱期等眾多複雜因素來決定。本 研究假設管理者已依據這些因素決定了擬減供水量值以作為後續分析的 依據。

圖 A.1 管網供水分區劃分決策流程圖

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初步找出此類制水閥分區，由於目前僅以連通關閉判斷供水影響程度，因

147

水量盡可能接近事先設定的減供水量，且同時盡可能使需要操作關閉的分 區邊界制水閥數量盡可能少，以降低分區供水的影響，並提升操作效率。

5 基因演算法

雖然實際管網系統經制水閥分區判識轉換之後可有效簡化原始系統的 複雜度，不過由於實際系統的管件數量龐大，所轉換建立的制水閥分區輔 助網路系統中的制水閥分區節點數與制水閥連線數量仍然相當可觀。因 此，在求解供水分區決策目標式(A-1)時，將因其決策變數選取的邊界制水 閥連線的組合數量過大，造成較不易以簡易的線性規劃模式求解，另方面 在選取邊界制水閥連線之後，必需要判斷劃分出的供水分區以及其內所包 含的總用戶需水量，以利判斷與設定減供目標的差異量，然而在供水分區 判斷過程中需考量所劃分供水分區內組成制水閥分區間的連接性，若是關 閉分區周圍制水閥之後，使得某些其他下游供水區的用水一併關閉，則此 時應同時將該區域歸入該關閉供水分區內。然而此類制水閥分區間的連通 關係很難以一般的優選模式來表示求解。因此，本研究採用基因演算法來 協助求解，並在基因演算的 fitness function 中結合本研究前章所發展改善 的非預期關閉區域演算程序，判斷供水分區關閉所造成的總減供用戶用水 量，以計算目標函數值提供基因演算所需的搜尋驅動力。

基因演算所設計的決策基因如下式所示：

l1 l2 lK1 lK

(A-2) 其中_li 為一 0,1 整數變數，表示制水閥分區間的連線 i 是否被選擇為供水 分區的邊界連線，若為 1 則該連線被選取為邊界連線，反之則未被選擇。

其中 K 為制水閥分區間連線的總數。

本研究所應用的基因演算程序如圖 A.2 所示，各程序說明如下：

STEP 1: 首先以隨機的方式產生一組足夠數量的基因組，以提供基因演算 組合足夠的求解搜尋空間。

STEP 2: 而對於每一個在群組中的基因，必需根據其對應目標值的優劣結

STEP 2: 而對於每一個在群組中的基因，必需根據其對應目標值的優劣結