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NMR求解多孔固體孔徑分布的逐步回歸方法

NMR Technique for the Analysis of Pore Distribution in Porous Solid:The Stepwise Regression Method

  • 摘要: 探討了用NMR方法求解多孔固體孔徑分布中有關病態積分方程的求解問題,借助于數理統計中的逐步回歸分析,加入非負限制,給出了一個新的求解方法.這種方法數值上很穩定,計算量小,可以給出較為連續的f(T1)分布曲線,并采用嶺回歸和Hesse光滑方法抑制噪聲的影響.從所給出的計算實例看出,這種方法有一定的優越性.

     

    Abstract: In view of the multivariate regression analysis,astepwise regression analysis method with non-negative constraint to solve the ill-posed integral equation is proposed,which is required in NMR technique for the analysis of pore structure.This method is numerically stable,easy to implement with less calculations,and a more continuous distribution f(T1) can be obtained.Two ways to reduce the effect of noise are suggested:Marquardt method and the smooth approach proposed by Hesse.From the results of the computed examples this method works quite well.

     

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