Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

电力系统能量与备用联合优化与精确调度

随着能源与环境危机日益严重,如何建立精确调度模型成为电力市场逐步完善过程中的一个迫切需要研究的课题.目前广泛采用的建模方式是将时间离散化,建立离散时间调度模型,本文首先举例说明离散时间调度模型中所定义的备用容量上、下限存在不可达的情况,即离散时间调度模型中的备用容量上、下限约束条件不严格,从而造成实际调度时存在旋转备用容量无法满足实际需求的情况.通过对机组出力方式与爬坡率关系的详细分析,证明了任意调度时段内机组精确可达的备用容量上、下限与该时段首末时刻机组输出功率相关,并给出了精确可达备用上、下限的计算方法.基于上面的分析结果,建立了能量与备用联合优化与精确调度模型,该模型将能量与备用联合精确调度这样一个连续时间最优控制问题建模成一个非线性规划问题,从而极大地降低了问题的复杂性,避免连续时间最优控制问题所存在的求解困难.应用序列二次规划法对模型进行了数值求解,并对结果进行了讨论,进而验证了模型的有效性.