最佳化方法於土壤組成律模式參數校正之應用

Abstract

傳統上作實驗得之實驗數據，若以Mohr-Coulomb Model來描述這些實驗數據，是以線性迴歸的方式找出它的參數，以凝聚力c和角度Φ作表示，但並不是所有的組成律模式都能使用如此線性迴歸的方法找出它的組成律模式參數，這些組成律模式並沒有一個合適的方法，在此希望以一種方法描述實驗數據並得到這些組成律模式參數，以期未來能做其他更進一步的數值模擬。 為了繪製這些曲線並得到這些組成律模式參數，本研究使用數值最佳化方法和定義合適的目標函數，數值最佳化方法有很多，本研究使用三種最佳化方法，分別是直接最佳化演算法 (DIRECT Optimization Algorithm)、非線性最小平方法 (Nonlinear Least Squares Method) 和基因演算法 (Genetic Algorithm)，討論三種最佳化方法的適用性，而目標函數主要是以距離的概念作定義，當用這三種最佳化方法得到目標函數最小值時，可以得到曲線模擬結果和最佳的組成律模式參數。 本研究使用四組實驗數據作模擬，包括了土壤材料的三軸壓縮試驗、岩石材料的三軸壓縮試驗、岩石材料的純剪應力路徑試驗和岩石材料的三軸伸張試驗，使用三種組成律模式，分別是Duncan and Chang Model、Modified Cam Clay Model和Fuzzy Set Plasticity Model來模擬實驗數據，討論三種組成律模式模擬所得的結果。

Traditionally, constitutive model calibration from experimental data is based on the method of linear regression. However, not all constitutive model parameters can be obtained by the method of linear regression. Once these parameters are determined, numerical simulation such as finite element or finite difference analyses can be carried out accordingly. This research used the numerical optimization techniques including DIRECT Optimization Algorithm, Nonlinear Least Squares Method and Genetic Algorithm to evaluate the applicability to constitutive model calibration. The objective function is defined by the distance between the measured and computed data. When a minimum value of the objective function is reached, the corresponding variables are the optimized model parameters. This research used four groups of experimental test results, which are soil triaxial compression tests, rock triaxial compression tests, rock pure shear tests and rock triaxial extension tests. Three constitutive models were used in this study including Duncan and Chang Model, Modified Cam Clay Model and Fuzzy Set Plasticity Model. Genetic Algorithm works effectively in all three constitutive models used in this study. DIRECT Optimization Algorithm works well in calibrating Modified Cam Clay Model and Duncan and Chang Model while Nonlinear Least Squares Method only works in Duncan and Chang Model. In conclusion, Genetic Algorithm works better than DIRECT Optimization Algorithm and Nonlinear Least Squares Method.