以7種GM (1, 1 ) 模型預測舊濁水溪水質之研究

Using seven types of GM (1, 1) model to predict water quality of Old Zhuoshui River

郭瑞玲(Jui-Ling Kuo)

指導教授 ： 白子易

朝陽科技大學/理工學院/環境工程與管理系在職專班/碩士(2011年)

摘要

本研究採用7種GM (1, 1) 模型，預測舊濁水溪溶氧 (Dissolved Oxygen, DO) 、生化需氧量 (biochemical oxygen demand, BOD) 、化學需氧量(chemical oxygen, COD) 、懸浮固體物 (suspended solids, SS) 及氨氮 (ammonia, NH3-N) 之濃度。灰色系統理論利用系統少數 (至少4個)之輸出資料建立灰色模型 (Grey Model；GM) 近似灰色系統之動態行為，進而對此少量輸出數資料之系統進行灰預測 (Grey Prediction) 。因此可利用灰色系統理論進行灰預測。結果顯示，在預測DO時，建模的均方根誤差 (root mean squared error, RMSE) 介於1.3185至3.9834之間，預測時的RMSE介於1.0890至5.8013之間。對於R值而言，建模時的相關係數 (correlation coefficient, R) 介於-0.01至0.30之間，預測時的R值介於-0.07至0.73之間。在預測BOD時，建模時的RMSE介於7.2444至16.4952之間，預測時的RMSE介於4.0016至6.8901之間。對於R值而言，建模時的R介於0.09至0.50之間，預測時的R值介於-0.46至0.52之間。在預測COD時，建模時的RMSE介於22.5040至161.6450之間，預測時的RMSE介於23.6303至219.9561之間。對於R值而言，建模時的R介於-0.06至0.45之間，預測時的R值介於-0.68至0.46之間。在預測SS時，建模時的RMSE介於16.1784至129.2348之間，預測時的RMSE介於11.6261至50.8907之間。對於R值而言，建模時的R介於-0.11至0.19之間，預測時的R值介於-0.55至0.13之間。在預測NH3-N時，建模時的RMSE介於5.7104至6.9602之間，預測時的RMSE介於2.3144至8.5405之間。對於R值而言，建模時的R介於0.15至0.57之間，預測時的R值介於-0.68至0.37之間。無論預測DO、BOD、COD、SS或NH3-N，皆以GM (1, 1, x(0)) 、GM (1, 1, a) 、GM (1, 1, b) 三種GM (1, 1) 模型較佳。在預測DO時，RMSE介於1.0890至1.1357之間，R值介於0.39至0.73之間。在預測BOD時，RMSE介於4.0016至5.5776之間，R值介於0.02至0.52之間。在預測COD時，RMSE介於23.6303至219.9561之間，R值介於-0.11至0.46之間。在預測SS時，RMSE介於16.8088至29.3383之間，R值介於-0.08至0.13之間。在預測NH3-N時，RMSE介於2.3144至8.3636之間，R值介於0.29至0.37之間。

關鍵字

河川水質 ； 氨氮 ； 懸浮固體 ； 化學需氧量 ； 生化需氧量 ； 溶氧 ； 舊濁水溪 ； 1) 模型 ； GM (1

並列摘要

In this study, seven types of first-order and one-variable grey differential equation model (abbreviated as GM (1, 1) model) were used to predict the water quality of Old Zhuoshui River including dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD), suspended solids (SS), and ammonia (NH3-N). Their prediction performance was also compared. The results indicated that the root mean squared error (RMSE) was between 1.3185 and 3.9834 at constructing models when simulating DO. When predicting, they were between 1.0890 and 5.8013. The correlation coefficient (R) was between -0.01 and 0.30 when constructing models. When predicting, they were between -0.70 and 0.73. In the aspect of BOD, the RMSE was between 7.2444 and 16.4952 when constructing models. When predicting, they were between 4.0016 and 6.8901. The R was between 0.09 and 0.50 when constructing models. When predicting, they were between -0.46 and 0.52. In the aspect of COD, the RMSE was between 22.5040 and 161.6450 when constructing models. When predicting, they were between 23.6303 and 219.9561. The R was between -0.06 and 0.45 when constructing models. When predicting, they were between -0.68 and 0.46. In the aspect f SS, the RMSE was between 16.1784 and 129.2348 when constructing models. When predicting, they were between 11.6261 and 50.8907. The R was between -0.11 and 0.19 when constructing models. When predicting, they were between -0.55 and 0.13. In the aspect of NH3-N, the RMSE was between 5.7104 and 6.9602 when constructing models. When predicting, they were between 2.3144 and 8.5405. The R was between 0.15 and 0.57 when constructing models. When predicting, they were between -0.68 and 0.37. All statistical values revealed that the predicting performance of GM (1, 1, x(0)), GM (1, 1, a), and GM (1, 1, b) outperformed other GM (1, 1) models.

並列關鍵字

River water quality. ； NH3-N ； SS ； BOD ； COD ； DO ； Old Zhuoshui River ； 1) model ； GM (1

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