考量非常態分佈資訊於水利系統不確定性分析之研究

Abstract

在工程設計與分析過程中，必然有不確定性的引入。因電腦模式在工程上 的普遍應用，引用電腦模式進行設計，必須考慮隱含在模式輸入與控制參 數的不確定性，及其所產生模式輸出的不確定性。電腦模式之不確定性分 析有許多適用方法，譬如壹階變方估計法(First-order variance estimation)，蒙地卡羅模擬法 (Monte Carlo simulation)，以及點估 法 (Point estimates methods) 等。然而，這些方法應用於含有非常態 分佈的多變數問題時，都有許多的限制與考慮。本研究主要針對蒙地卡羅 模擬法與點估法進行修正，以併入所有的邊際分佈資訊，克服前述問題。 經過數值上的驗證，除了隨機變數的邊際分佈在不確定性分析過程中可有 效地被保存外，兩種修正方法均能獲致合理精度，並保持適當計算量。為 求說明邊際分佈資訊在實際問題之不確定性分析中的必要性，研究中另舉 橋基刷深模式為應用例，採用上述兩種修正方法，進行不確定性分析及風 險機率評估。 In modern engineering designs and analyese, computer models are frequently used. Due to the presence of uncertainty associated with the model inputs and parameters, proper assessment of model output uncertainty is essential. Several algorithms such as first-order variance estimation (FOVE), Monte Carlo simulation, and point estimates (PE) methods have been developed to implement the uncertainty analysis of a computer model. However, limitation is imposed on these algorithms when the problem is multivariate along with mixture distribution types. With the goal of incorporating non-normal marginal distributions of random variables, the two proposed methods yielded results with reasonable accuracy and remain acceptable computational effort. For demonstration, the two proposed methods were applied to a pier scouring model in uncertainty analysis and in failure probability evaluation.