基于MEP法的在役桥梁时变可靠度研究

Time-Dependent Reliability Study for In-Service Bridge Based on MEP Method

基于最大熵原理和概率理论,提出用于分析在役桥梁结构时变可靠度的最大熵概率密度迁移法(MEP法)。采用有限元法求出较为精确的响应量,用数理统计法求得响应量的各阶矩;以4阶原点矩为最大熵约束条件,结合最小二乘法推导结构响应的概率密度函数解析式;基于时变可靠度原理,得出1组迁移的概率密度曲线族;根据"安全—损伤—失效"三级工作模式确定积分限值,计算结构的时变损伤概率与失效概率,进而得到相应的可靠度。运用MEP法和Monte Carlo法对在役桥梁算例可靠度的比较计算结果表明:2种算法结果较为吻合,且符合在役桥梁现状;MEP法可避免Monte Carlo法的大规模取样,并解决数值积分法所面临的复杂结构功能函数难以获得的问题。

Based on maximum entropy principle and probability theory, a maximum entropy-probability density migration combined method （MEP method） for the time-dependent reliability estimation of in-serve bridges was proposed. Finite element method was used to work out more accurate response value, and then each order moment of the response value was worked out by mathematical statistics method. The fourth order origin moment was used as the constraint for the maximum entropy, the analytical expression for the probability density function of structural response was deduced with least square method. Based on time- dependent theory, a group of the migrated probability density curves was obtained. The integral limit was determined according to the three-level working mode of ＂safe-damage-failure＂. Both the time-dependent damage probability and failure probability were calculated, and then the corresponding reliability could be obtained. An in-service bridge example was given and the reliability was calculated by both the proposed MEP method and Monte Carlo method. The calculated results have been compared and showed good agree- ment, and are in accordance with the actual situation of the in-service bridge. Large sampling required by Monte Carlo method can be avoided by MEP method. The problem that it is hard to acquire the performance function of complex structure required by numerical integration method has been solved, which has provided the theoretical basis for the decision-making for the strengthening of in-service bridge.