地盤反應逆向運算-病態問題

Abstract

大地工程是在做地盤反應逆向運算時，由於不熟悉反算問題的本質，經常求得不合理的結果，所以在本文中我們將釐清正算及反算問題的本質，藉此知道工程上逆向運算為何常屬於病態問題。處理這種問題我們捨棄工程常用的切除頻率法 (如SHAKE程式的cutoff frequency) ，該法係在頻率域上加矩形視窗，而改以再生核 (reproducing kernel) 的加權視窗 (Cesaro視窗或e -ak2高斯視窗) 觀念，將原本會發散之病態問題的解加以正規化，因而求出合理的解，並應用L曲線的觀念來決定最佳視窗之正規化參數。最後我們將以剪刀梁波傳方程(地盤逆向運算)及拉普拉斯方程式兩種給過定邊界條件的兩個算例來驗證本文方法的可行性。In this paper, the regularization techniques (Cesaro and Gaussian windows) are appiled to regularize the divergence problems which occur in ground motion deconvolution and in the Laplace equation with overspecified boundary conditions. To deal with this ill-posed problem, the corner of the L-curve is chosen as the compromise point to determine the optimal window so that the high frequency or high wave-number(k) contents can be suppressed instead of engineering judgement using the cincept of a cutoff wave-number. From the examples shown, it is found that reasonable solutions can be reconstructed, and that both the high frequency and high wave-number content of the divergent results can be avoided by using the proposed regularization techniques.