改进的Bayes砂土液化判别模型

Improved Bayes Discriminant Analysis Model for Sand Liquefaction

基于Bayes判别分析理论,根据唐山大地震和广东三水地震中40组砂土液化样本构建数据库,本文选取其中30组数据作为训练样本,建立了Bayes判别分析(BDA)函数,并根据该函数对另外10组待测样本进行了液化判别研究。首先,基于震级M、地面加速度最大值gmax、标准贯入击数N63.5、比贯入阻力Ps、相对密实度Dr、平均粒径D50和地下水位深度dw七个评价指标,建立七因素Bayes判别分析模型。继而,依据各评价指标的影响权重,提出了以M、gmax、Ps、Dr和D50五个评价指标为主的五因素Bayes判别分析模型。对比五因素和七因素模型的砂土液化判别结果,可以发现:改进的五因素模型的平均判别准确率高达为90%,而七因素模型准确率为80%,即本文所提出的五因素BDA模型用更少的评价指标可以达到更高的液化判别准确率,既避免了次要因素影响判别函数的稳定性,又节约了建设成本,更有利于实际工程中的液化判别。

Based on Bayes discriminant theory and 40 groups of typical sand samples collected from Tangshan and Sanshui earthquakes, Bayes discriminant analysis (BDA) model of sand liquefaction is constructed with 30 groups among them as training samples and the other 10 groups as test samples. Firstly, taken the earthquake magnitude, the peak ground acceleration, the value of standard penetration test, the specific penetration resistance, the relative density, the mean granular diameter and the depth of groundwater table as the evaluation indexes, seven-factor-BDA model is constructed. According to the weight of seven evaluation indexes, furthermore, a five-factor-BDA model, including the earthquake magnitude, the peak ground acceleration, the specific penetration resistance, the relative density and the mean granular diameter, is presented. Compared with the results from the seven-factor-BDA and the five-factor-BDA models, it can be obtained that the average accuracy of the five-factor-BDA model is as high as 90% while one of the seven-factor-BDA model 80%. Thus, the five-factor-BDA model with fewer indicators can reach the higher accuracy than the seven-factor-BDA model, which reduces the affect of the secondary factors on the stability of the discriminant function, and also saves the cost of construction. It will be more convenient for the application of the five-factor-BDA in civil engineering.