隨著科學和工程技術的進步，數值模擬在各個領域中變得越來越重要。然而，因為模型誤差和測量誤差的存在，使數據和真值產生差異。模型誤差源自於設計和分析所使用的數學模型與實際情況間的差異。測量誤差源自於在收集數據時，由於測量儀器的精確度、人為操作的不確定性以及環境條件的變化。在營建領域中，數值模擬和真值產生偏差的來源，除了上面提到輸入進模型的測量誤差，模型本身可能因為數學模型選擇不當、過擬合或欠擬合、假設錯誤或者參數估計錯誤等原因，導致產生模型誤差。現今已發展出許多方法減少誤差，像是集成學習的模型融合技術，還有卡爾曼濾波器。
本研究引入混合比例的概念，假設資料由兩組分別包含模型誤差之常態分佈混合包含測量誤差之常態分佈。並分別使用最大期望值演算法(Expectation-maximization algorithm)和基因演算法(Genetic algorithm)進行估算，得到兩分佈相關參數的最適估計。結果發現可以一定程度的分離模型誤差和測量誤差分布，達到減少誤差的最終目的。

With the advancement of technology, numerical simulations have become crucial in various fields. However, both model errors and measurement errors lead to disparities between data and actual values. Model errors arise from mathematical models used for predictions not aligning with real situations, while measurement errors stem from instrument accuracy, operational uncertainties, and environmental changes. In the realm of construction, sources of discrepancies between numerical simulations and actual outcomes are not only rooted in the aforementioned measurement errors incorporated into the model inputs, but also in the model itself. Model errors can arise due to improper mathematical model selection, overfitting or underfitting, erroneous assumptions, or inaccurate parameter estimations. Nowadays, several methods have been developed to mitigate these errors, such as model fusion techniques through integrated learning and the utilization of Kalman filters.
This study introduces the concept of mixed proportions, assuming data originates from two normal distributions encompassing both model and measurement errors. The parameters of these two normal distributions are estimated using Expectation-Maximization (EM) and Genetic Algorithms (GA). The results reveal a certain level of separation between the two error distributions, thereby achieving the goal of error reduction.

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