利用卷積神經網路與水力掃描推估水力與熱傳參數異質場

Abstract

地源熱泵(Ground Source Heat Pump, GSHP)是一種高效的熱交換系統，利用自然環境中的能量進行供暖和制冷。熱交換效率不僅取決於熱交換管材質和管徑等因素，更受地下水流場和熱傳參數的影響。為了有效地推估地下水流與熱傳參數異質場，以之作為熱交換井群最佳化設計之依據，本研究提出利用卷積編碼解碼器(Encoder-Decoder)架構的神經網絡結合水力掃描(Hydraulic Tomography，HT)，推估水力與熱傳參數異質場，並將此神經網路命名為THT-NN(Thermal and Hydraulic Tomography Neural Network)，並透過數值試驗檢驗THT-NN的效能。在數值試驗的設計上，本研究使用TOUGH2創建了一個二維異質地下水與熱傳模式，並生成了20000組給定統計條件下的水力與熱傳參數異質場，再以之建立神經網路的訓練、驗證與測試資料集。THT-NN的建立流程首先從數值模式的觀測位置中收集溫度與水位資料建立輸入檔，再透過編碼與解碼提取水位與溫度特徵轉換成水力(Permeability and porosity, kp and n)與熱傳(Thermal conductivity and specific heat, kt and Sp)參數異質場。隨後，本研究通過均方根誤差(RMSE)、平均絕對誤差(MAE)和判定係數(R²)來檢驗估算結果的正確性與可行性。在數值試驗設計部分，本研究分別探討(1)檢驗THT-NN推估參數之可行性、(2)討論噪訊(noise)對THT-NN推估結果之影響，並檢驗其強健性(robustness)、(3)探討邊界條件引起的平流(advection)對THT-NN推估結果之影響，並檢驗其強健性。研究結果顯示，THT-NN具備同時推估kp場、n場、kt場、Sp場之能力；噪訊會影響THT-NN之表現，因此本研究提出加入具噪訊之資料重新訓練THT-NN，使THT-NN適應噪訊，有效的降低噪訊之影響；邊界條件引起的平流會改變水位與溫度分布，進而改變觀測資料的數值，導致資料特徵不足，使得THT-NN推估表現下降，因此本研究利用不同強度之邊界平流下產生之資料訓練THT-NN，使THT-NN掌握不同觀測資料的特徵，提升此情況下THT-NN推估表現。研究結果證實THT-NN在考慮輸入資料有噪訊與平流的影響下，依然能夠準確推估參數，顯示THT-NN可以作為強健且有效的水力與熱傳參數推估方法。

The ground source heat pump (GSHP) is an efficient thermal exchange system that utilizes natural environmental heat for heating and cooling. The heat exchange efficiency depends not only on factors such as the material and diameter of the heat exchange pipes but also on groundwater flow fields and thermal parameters. To effectively estimate the heterogeneous fields of hydraulic and thermal parameters, which are critical for optimizing the design of heat exchange well groups, this study proposes using a neural network, THT-NN (Thermal and Hydraulic Tomography Neural Network), with an encoder-decoder architecture combined with hydraulic tomography (HT). To evaluate the parameter estimation capabilities of THT-NN, numerical experiments were conducted, using a two-dimensional heterogeneous groundwater and heat transfer model created with TOUGH2, generating 20,000 data sets and divided into training, validation, and testing. The process of establishing THT-NN begins with collecting temperature and water level data from observation points in the numerical model to create the input files. Features of the water level and temperature are then extracted through encoding and decoding, transforming them into heterogeneous hydraulic (permeability and porosity, kp and n) and thermal (thermal conductivity and specific heat, kt and Sp) parameter fields. Subsequently, the accuracy and feasibility of the estimated results were verified using root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2). The numerical experiments were designed to explore (1) the feasibility of THT-NN in estimating parameters, (2) the impact of noise on the estimation results of THT-NN and examining its robustness, and (3) the effect of advection on the estimation results of THT-NN and examining its robustness. The results show that THT-NN is capable of simultaneously estimating kp, n, kt, and Sp fields. Noise affects the performance of THT-NN, so this study proposes retraining THT-NN with noisy data to adapt to the noise and effectively reduce impact of noise. Advection changes the distribution of water levels and temperatures, altering the patterns of observation data, which hinders THT-NN's data analysis and reduces its estimation performance. Therefore, data generated under different advection strengths were used to train THT-NN, allowing it to capture the features of various observation data and improve its estimation performance under these conditions. The results confirm that THT-NN can accurately estimate parameters despite the influence of noisy input data and advection, demonstrating that THT-NN can be a robust and effective method for estimating hydraulic and thermal parameters.