Abstract: The utility system design would consider the reliability to respond to boiler failure even shut down. The design would ensure system flexibility for the fluctuation of process steam demand as well. In this work, boiler system design was studied considering both the uncertainty of process steam demand and equipment failure based on mathematical programming. Probability distribution was used for fluctuation of process steam demand and the Markov model was used to deal with boiler failure to express uncertain parameter with probability. The approach of two-stage stochastic programming was to compensate the constraint violations caused by uncertain steam demand and boiler failure to reduce the effect on optimization and constraints. A mixed integer linear programming model (MILP) was formulated with the objective of minimum annual cost to design system configuration, equipment modes and operation of compensating flexible steam demand and equipment failure.

Key words: uncertainty, two-stage stochastic programming, systems engineering, simulation, optimal design

摘要： 公用工程系统中锅炉系统设计不仅要考虑锅炉应对发生的故障的可靠性，还要保证系统具有一定应对蒸汽需求的波动的可操作性。本研究针对满足不确定蒸汽需求和考虑设备故障的锅炉系统设计，提出基于数学规划法的设计模型：对生产过程波动引起的不确定蒸汽需求以概率表达，采用Markov模型分析锅炉故障，表达为以一定概率发生的不确定参数。优化模型采用二阶段随机规划策略对蒸汽需求不确定波动和锅炉故障实现引起的约束违背进行补偿，以降低不确定变量对目标函数和约束条件的影响。以年总费用最小为目标，建立混合整数线性模型（MILP），实现锅炉系统配置，设备模式确定以及应对蒸汽需求波动和设备故障发生的补偿操作的优化设计。

关键词: 不确定性, 两阶段随机规划, 系统工程, 模拟, 优化设计