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精馏过程优化存在许多不确定变量,其对优化结果的影响是不可忽略的,所以需要找到真实反映不确定变量的数学模型,找到最优的求解方法得到精确解,进而得到最优的优化结果。本研究通过分析随机规划策略和不确定因素的特性及其对精馏优化过程的影响,对不确定因素进行分类,应用带补偿的随机规划和机会约束规划实现不确定因素对优化目标和约束的影响。对于模型中的机会约束,由于不确定输入变量和不确定输出变量间存在单调关系,所以可以通过对不确定输入变量的多重积分将机会约束转化为等价地确定性非线性约束,此时模型转化为含有非线性约束的带补偿的随机规划模型,此模型通过改进的蒙特卡罗(MonteCarlo)积分和含有序列2次规划(SQP)的Benders分解相结合的混合算法有效的求解。所提出的求解方法借助于Matlab软件能够得到比较精确的结果。采用本文所提出的模型及求解方法对精馏塔操作的模拟实验过程进行优化研究,可以看出带补偿的机会约束规划模型能够很好地反映不确定变量对优化过程的影响。所以本文提出的模型和求解方法是有效可行的,且对于以后的不确定优化研究具有很好的指导意义。
There are many uncertain variables in the optimization of the distillation process. The influence on the optimization results can not be neglected. Therefore, it is necessary to find the mathematical model which can truly reflect the uncertain variables, find the optimal solution to get the exact solution, and get the optimal optimization result . In this study, by analyzing the characteristics of stochastic programming strategies and uncertainties and their impact on the distillation optimization process, the study classified the uncertainties and applied the stochastic programming with compensation and the chance-constrained programming to realize the optimization of the optimization objectives and constraints influences. Due to the monotonic relationship between the uncertain input variables and the uncertain output variables, chance constraints can be converted into equivalent deterministic nonlinear constraints by multiple integrals of uncertain input variables. In the model, Is transformed into a stochastic programming model with compensation with nonlinear constraints. This model is effectively solved by a hybrid algorithm that combines Monte Carlo integration and Benders decomposition with sequence quadratic programming (SQP). The proposed method can get more accurate results by means of Matlab software. By using the model proposed in this paper and the solution method to optimize the simulated experimental process of distillation column operation, it can be seen that the model of chance constrained programming with compensation can well reflect the influence of uncertain variables on the optimization process. Therefore, the proposed model and solution method are effective and feasible, and have a good guiding significance for the future research of uncertain optimization.