论文部分内容阅读
基于概率理论,对基桩完整性检测的概率分布进行了详细的分析,分析表明抽检结果与总体不合格率和抽检桩数有关,因此建议将总体不合格率作为评价整批桩质量的标准。利用Bayesian方法推导出总体不合格率的先验分布服从标准的Beta分布,由共轭分布原理得出后验分布也服从Beta分布。然后分析了总体不合格率后验分布的期望和方差,得出结论:后验分布的期望是先验分布的期望和当前抽样检测不合格率的加权和;后验分布的方差是当前抽检不合格率及先验分布方差的加权和。通过分析抽检桩数对加权系数和后验分布的期望和方差的影响,结果表明:当抽检桩数小于10时,抽检桩数对检测结果有显著影响;当抽检桩数大于10时,抽检桩数对抽检结果的影响变小;尤其当抽检桩数大于20时,对抽检结果无显著影响。最后利用先验分布的期望和方差与后验分布的期望和方差的关系建立起质量检测的动态评估模型。算例分析表明该动态模型可更准确地估计出总体不合格率,具有较重要的工程实际意义。
Based on the theory of probability, the probability distribution of pile integrity testing is analyzed in detail. The analysis shows that the sampling results are related to the overall failure rate and the number of piles sampled. Therefore, it is suggested that the overall failure rate be used as the standard to evaluate the quality of batch piles. The Bayesian method is used to derive the prior distribution of the overall unqualified rate from the standard Beta distribution, and the posterior distribution derived from the conjugate distribution theory also follows the Beta distribution. Then the expectation and variance of the posterior distribution of the total unqualified rate are analyzed, and the conclusion is drawn that the expectation of the posterior distribution is the weighted sum of the expectation of the prior distribution and the unqualified rate of the current sampling; the variance of the posterior distribution is the difference between the current sampling Pass rate and a priori distribution of the weighted sum of variance. By analyzing the influence of sampling pile number on the expectation and variance of the weighted coefficient and the posterior distribution, the results show that when the sampling pile number is less than 10, the number of pile sampling has a significant effect on the detection result. When the sampling pile number is greater than 10, The number of the sampling results of the impact of smaller; especially when the number of piles is greater than 20, the sampling results no significant impact. Finally, the dynamic assessment model of quality inspection is established by using the relationship between the expectation and variance of prior distribution and the expectation and variance of posterior distribution. The case study shows that the dynamic model can estimate the overall failure rate more accurately and has more important practical significance.