結合最劣化參數、共變異數分析與啟發式演算法於參數結構辨識之研究

Abstract

不確定性的由來是因為人類對於眼前的事件所擁有的相關資訊不夠充分，因此對未知的結果感到迷惑，而不確定性的來源會根據各種領域的問題特性而有所差異，但共同點是不確定性的存在的確會對決策結果造成不可避免之影響。本研究之目的在探討模式應用於河川水質管理時所可能產生之不確定性來源與其影響機制，主要分成模擬歷程不確定性、模式參數不確定性、以及輸入資料不確定性三方面進行討論。為了在研究過程中有效結合利用之方法理論與工具，修正Streeter-Phelps方程式將會被用來進行水質模擬，並與QUAL2E模式之模擬結果進行比較，用以探討並量化不同水質模式模擬結果之差異性。模式參數方面則有別於過去不確定性分析，能在既定的模式應用精度下利用簡單的結構辨識出參數，該方法論的內容包括反向問題的分類、可辨識性之定義、最劣化參數之計算、廣義式反向問題之求解等，藉由上述理論能夠評估事前資訊是否充分，而共變異數分析則是用來協助了解參數結構複雜度、模式模擬誤差、以及參數不確定性之關係。過程中所有最佳化問題將會利用啟發式演算法進行求解，而上述方法將會藉由案例設計來驗證其可行性。

The origin of uncertainty comes from that people don’t have sufficient information and thus feel ambiguous about unknown future results. Sources of uncertainty would be different according to the characteristic of problems at different fields, but the common point is that the existence of uncertainty indeed would have inevitable impacts to the decision-making results. The purpose of this study is to discuss how uncertainty occurs and how uncertainty influences when water quality models are applied to river quality management. Three types of uncertainty are discussed, including process uncertainty, input data uncertainty, and parameter uncertainty. In order to effectively combine the methodologies and tools used in this study, the modified Streeter-Phelps equation would be used to simulate water quality, and the simulation results would be compared with those from QUAL2E for discussing and quantifying differences when different water quality models are used. Unlike traditional parameter uncertainty analysis, this study uses an approach that can identify parameter with a simplified structure and assure its accuracy requirement for predetermined model application. The content of this methodology includes the classification of inverse problems, the definition of identifiability, the calculation of the worst-case parameter, the solution of a generalized inverse problem and so forth. From the above theories, prior information could be assessed whether it is sufficient or not, and covariance analysis is used to help understand the relationship among parameter structure complexity, modeling error, and parameter uncertainty. In this study, all optimization problems are solved by heuristic algorithms. A case would be designed to confirm the above methodologies.