利用貝氏分析預測土壤參數之案例

On the use of Bayesian analysis to predict soil parameters and case studies

李沅羲(Yuan-Hsi Li)

指導教授 ： 卿建業

國立臺灣大學/工學院/土木工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201802402

摘要

在大地工程設計中，工程師通常需要透過現地試驗或實驗室試驗得到現地的黏土參數值，但往往現地試驗及實驗室試驗所得到的資料並不完整，且可能資料數較少，由於要得到完整且夠多的現地資料所需的成本可能會太高，此時工程師會藉由前人所得到的經驗公式來推估所需要的黏土參數值，但往往這些經驗公式存在著較大的轉換不確定問題，故為了降低轉換不確定性造成參數預估不準確，本研究建立一個適用於特定場址的機率密度函數，但特定場址的數據通常不夠完整會有缺失，或數據點也有可能不夠多可以建立一個有效的現地機率密度函數，因此現地模型會有較大的統計不確定的問題，貝氏分析可以用來量化統計不確定的問題，而為了縮小統計不確定性問題，本研究會把現地的機率密度函數與通用機率密度函數相乘，得到一個混合的機率密度函數，這個混合的機率密度函數的效果，當現地資料量多的時候，混合機率密度函數會比較傾向現地機率密度函數
的結果，當現地資料少的時候會比較傾向通用機率密度函數的結果。當現地資料不論多或少的時候皆可使用混合機率密度函數來預測，但有一例外是現地的機率密度函數與通用機率密度函數所模擬出來的資料點分布範圍差不多，且現地資料點有部分分布在全球資料的邊緣時，此時混合機率密度函數效果會不好。本研究做了八個案例來驗證混合機率密度函數的效果，這八個案例分別位於巴西、中國、加拿大、韓國、美國、澳洲、新加坡，每個案例皆有缺失的資料。

關鍵字

機率密度函數 ； 轉換不確定性 ； 統計不確定性 ； 貝氏分析

並列摘要

In the design of geotechnical engineering, engineers usually need to obtain local clay parameters from in-situ tests or laboratory tests. However, the data are obtained
from in-situ tests and laboratory tests are incomplete because complete local data are expensive. At this time, the engineer will estimate the clay parameters by the empirical formula which is obtained by the predecessors, but these empirical formulas have large transformation uncertainty. Therefore, a probability density function is found to reduce inaccuracy when the parameter is estimated. In this study, a probability density function
is constructed of site-specific data, but site-specific data are incomplete and sparse. As a result, there is large statistical uncertainty in site-specific model. Bayesian analysis can be used to quantify statistical uncertainty. In order to reduce statistical uncertainty, site-specific probability density function and the generic probability density function are hybridized. There is an effect that the hybrid probability density function is governed by the site-specific probability density function, when the site-specific data are abundant. The hybrid probability density function is governed by the generic probability density function, when the site-specific data are sparse. In this study, eight cases were used to verify the effect of the hybrid probability density function and each case has missing data. The eight cases are located in Brazil, China, Canada, South Korea, the United States, Australia, and Singapore.

並列關鍵字

probability density function ； transformation uncertainty ； statistical uncertainty ； Bayesian analysis

參考文獻

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