基于贝叶斯理论不同尺度样本空间下深受弯构件受剪概率模型

Bayesian Theory as an advanced statistical model can systematically consider the sample data and the subjective priori model, and accurately evaluate the research target within the sample space of different scales. Abundant experimental data and various corresponding shear models of deep flexural members provided sufficient priori information for the further understanding of the shear behavior of deep beams. The author introduces the Bayesian posterior edge parameters distribution theory to quantitatively analyze the significance of influence parameters and dynamically identify the properties of prior shear models for deep flexural members. Combining the advantages of both the prior information and the Bayesian dynamic update theory, the shear models with normalweight concrete were probabilistic identified by tests database. Based on the principle of constant precision, dynamically update and optimize the probabilistic model in order to establish a posterior probabilistic model which has a characteristic of clear mechanism concept and high-precision. By utilizing the advanced inherited function of the Bayesian theory, the effects of influence parameters were identified within a small sample space to dynamically update the shear model with lightweight aggregate concrete. Experimental investigation was carried out to verify the accuracy of this model, and the test results were utilized for the secondary optimization of this model. In conclusion, the probabilistic shear strength model was established within the sample space of different scales and the coordinating STM based design method was simultaneously proposed for deep flexural members. These final contributions achieve an effective unification between the Bayesian statistical method and specimen prior information and provide a new thought and method to analyze the shear behavior of deep flexural members.

贝叶斯理论能系统考虑样本数据和主观先验模型，在不同尺度样本空间下对研究目标进行精准预测。深受弯构件受剪试验数据丰富，受剪模型众多，为深入认识剪切问题提供了充足的先验信息。申请人拟采用贝叶斯后验边缘参数分布理论，量化分析影响因素显著性，动态识别深受弯构件受剪先验模型性能；结合先验信息与贝叶斯动态更新思路，在大数据样本空间内概率识别普通混凝土深受弯构件受剪模型，基于精度不变原则动态更新与优化模型，建立高精度且具有明确力学概念的深受弯构件受剪后验概率模型；发挥贝叶斯方法遗传、继承功能，在小样本空间内识别参数影响，动态更新轻骨料混凝土深受弯构件受剪概率模型，通过试验验证、二次优化概率模型。最终在不同尺度样本空间内建立深受弯构件受剪概率模型，提出与概率模型相协调的拉压杆设计法，达到贝叶斯统计方法与深受弯构件先验信息的统一，为受剪问题分析提供新思路、新方法。

因材料的离散性和剪切破坏机理的复杂性，受剪问题始终是混凝土结构基本理论的难点问题，项目引入贝叶斯后验概率统计理论，采用大数据统计、试验研究和理论分析相结合的方法在不同尺度样本空间下系统开展了深受弯构件受剪概率模型研究。建立了普通混凝土深受弯构件受剪试验数据库，量化评估其影响因素的显著性和相关性，完成了基于宏观和细观两个层次的受剪模型分析，建立了深受弯构件受剪分析的先验信息和先验模型；结合先验数据和贝叶斯动态更新思路，动态识别了大样本空间下普通混凝土深受弯构件受剪影响因素显著性，概率识别混凝土深受弯构件受剪模型，基于精度不变原则动态更新与优化模型，分别建立了参数无先验信息、无先验分布和共轭先验分布下深受弯构件受剪后验概率模型，基于随机模拟方式实现高维积分计算，引入马尔科夫链-蒙特卡洛（MCMC）高效采样方法二次优化受剪概率模型，提高其计算精度；先后完成了25根大尺寸轻骨料混凝土深受弯构件受剪性能试验以及11个轻骨料混凝土压杆隔离体轴压性能试验，明确了截面高度、剪跨比、加载板宽度、腹筋配筋率等关键因素对深受弯构件受剪性能的影响，明确了轻骨料混凝土深受弯构件与压杆隔离体的关联性，揭示了其剪切破坏机理和开裂软化特性。优化、修正混凝土弹性模量、软化系数等特征参数，建立了适用于轻骨料混凝土深受弯构件受剪分析的宏观和细观模型；基于贝叶斯方法遗传、继承功能，在小样本空间内深入考虑轻骨料混凝土材料特性与构件受剪特征将概率模型用于预测轻骨料混凝土深受弯构件受剪承载力。最终在不同尺度样本空间内建立了深受弯构件受剪概率模型，实现了贝叶斯统计方法与深受弯构件受剪先验信息的统一。研究成果为解决混凝土结构或构件的受剪问题提供了新思路，为推广轻骨料混凝土的工程应用提供了理论指导。