以模擬退火演算法最佳化推估地下水污染源

Optimized Identification of the Groundwater Contaminant Source Using Simulated Annealing Algorithm

林淇平(Chi-Ping Lin) ； 倪春發(Chuen-Fa Ni) ； 李唯祺(Wei-Ci Li) ； 張俼瑍(Yu-Huan Chang)

《土壤及地下水污染整治》 6卷2期 (2021/12) Pp. 81-100

https://doi.org/10.6499/JSGR.202112_6(2).0001

摘要

地下水被視為穩定且可靠的用水來源，卻也因其不可見及水循環更新速度慢這兩特性，一旦受到污染，管理單位難以在第一時間發現，也導致污染源會隨時間推移而擴大其分布範圍，直接或間接增加民眾用水品質風險。在面對受污染的水體，需要瞭解污染傳輸歷程。要瞭解污染物之傳輸歷程，須瞭解該地區的水文地質條件及地下水污染傳輸等機制，方得以數值模式進行相關推估，基於各項參數取得條件之不易、監測井數量有限，推估的工作變得相當困難。為解決現地觀測資料的不足所帶來之影響，本研究開發出以python介接數值模式與啟發式演算法（heuristic algorithm）推估污染傳輸之方法，其中水文及污染傳輸數值模式分別使用Modf low-2005與MT3DMS，用於生成測試案例與當作最佳化問題的數值模式。啟發式演算法則採用退火演算法（simulated annealing（SA）algorithm），用於求解最佳化問題之演算法。為減少推估誤差與提升系統之穩健性，本研究將數值模式中所使用的參數設定成一特定範圍並離散化，降低因固定參數所產生之誤差；對於SA及動力系統所帶來的不確定性，利用系集（ensemble）與空間分析之概念，降低單一次模擬所帶來的誤差，提高推估系統穩健性。為驗證推估方法，研究中使用均質地質條件與單一且持續性的污染點源釋放，合成兩假想之污染傳輸案例作為推估方法的驗證，經測試案例驗證後，推估方法除能夠有效推估污染源之點位、傳輸方向，本研究於方法建立後，探討並量化不同數量的觀測點對於此方法的適用性與不確定性，結果顯示在監測井數量為6以上時，點源推估之誤差皆小於1 m，傳輸方向誤差為5°以內。

關鍵字

污染傳輸歷程 ； 污染源 ； 傳輸方向 ； 啟發式演算法 ； 退火演算法

並列摘要

Groundwater is a stable and reliable water resource, but due to the natural complexity of aquifer systems, early detection of contaminants can be challenging. The spread of such contaminants in groundwater systems might directly or indirectly influence residents near the sources of contamination. A typical approach to predict the migration of contamination plumes involves numerical models, which allow transport processes to be simulated and concentration distributions of contaminants to be quantified. However, the complexity of site-specific conditions and limited model parameters have made the numerical models difficult for practical implementations. In this study, we introduce a heuristic algorithm to estimate the flow and transport parameters for a contaminant at a given synthetic site. The model tests included two numerical examples, which differed in the flow directions and number of observations in the designed scenarios. Specifically, Modflow-2005 and MT3DMS models were used to generate observations at synthetic sites. The Modflow-2005 and MT3DMS models associated with a simulated annealing (SA) algorithm were developed and systematically tested to quantify the accuracy of the estimated flow and transport parameters. The parameters of the numerical model were fixed within a specific range and discretized to minimize estimation errors and improve system robustness. Additionally, an ensemble approach and spatial analysis were used to minimize errors caused by individual simulations. The results showed that the developed model could effectively locate the origin of the contaminant source and track its dispersal. The model enables the evaluation of observation wells at suitable sites and quantifies any uncertainties associated with limited observations. The numerical examples showed that the number of monitoring wells needed to be higher than six and that the source point estimation and transport direction errors can be less than 1 m and five degrees, respectively.

並列關鍵字

transport processes ； contamination sources ； transport direction ； heuristic algorithm ； simulated annealing algorithm

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