基于PCA-DDA原理的砂土液化预测模型及应用

影响砂土液化的因素有很多，建立多指标的液化预测模型非常有必要。目前所有的多指标砂土液化预测模型，均默认选取的判别因子之间相互独立，不存在相关性，可能导致各判别因子之间存在信息叠加而发生误判。以唐山地震砂土液化的25个案例为样本，选取8个影响因素作为砂土液化预测的初始判别指标，首先采用主成分分析（PCA）对各判别指标进行分析，对存在相关性比较高的指标进行了降维处理。基于降维后的4个主成分换算得到新的样本数据，以18个案例为学习样本，建立主成分分析与距离判别分析（DDA）相结合的砂土液化预测模型。利用建立的预测模型对18个案例进行回判，结果全部正确。对其他7个案例的液化情况进行了预测，并与规范法、Seed方法、BP法、DDA法的判别结果进行分析比较，结果表明基于主成分分析与距离判别方法的砂土液化判别模型预测准确率为100%。将模型应用于工程实例，判别结果也与实际情况一致，表明该模型具有良好的预测功能，可在实际工程中应用。

Discrimination model of sandy soil liquefaction based on PCA-DDA principle and its application

There are a lot of factors that affect sand liquefaction, and then it is necessary to establish a multi-index liquefaction prediction model. At present, all of the multi-index sand liquefaction prediction models based on a hypothesis—the selected discriminant factors are independent and there is no correlation between each other, which may lead to information superimpose between the different factors and mis-discrimination. In this paper, based on 25 cases of sand liquefaction in Tangshan earthquake, eight factors influencing sand liquefaction are selected as the initial discriminant indexes. The principal component analysis(PCA) is introduced in the correlation analysis of initial discriminant indexes and dimension-reduction processing is conducted to some indexes with high correlation. The new sample data are obtained based on the 4 principal component conversions. A predictive model for predicting sand liquefaction is established under the combination of PCA and distance dscriminant analysis(DDA). The forecasting results of 18 training samples are all correct by using the established model. The liquefaction of the other 7 cases is also predicted; and the results are compared with those of the standard, Seed method, BP method and DDA method. The results show that the prediction accuracy of the forecasting model is 100%. The model is applied to a practical engineering example, and the results are consistent with the actual situation, so as to show that the model has good prediction function and can be used in practical engineering.