基于智能计算的系统动态优化方法及应用
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摘要
严格意义上来说,任何一个化工过程都是动态的过程,状态变量总是会随着时间的演变或者空间的转移而发生改变。系统状态随时间而变化的系统或者按确定性规律随时间演化的系统,称为动态系统,通常可以由微分方程或者差分方程来描述,描述动态系统特征的模型称为动态模型。动态优化就是通过控制动态模型中的控制变量,使得过程中的某个或者某些性能指标达到最优。对于稍许复杂的动态优化问题,通常无法得到解析解,一般是在庞特里亚金极大值原理或者贝尔曼最佳原理的基础上,采用数值求解的方法以分段常数来逼进最优控制曲线,常用的方法包括最速下降法、共轭梯度法和动态规划法等等。随着智能计算的发展,新型的智能计算在动态优化问题中的应用越来越广泛,尤其是在梯度信息不可得的情况下。本文旨在对基于智能计算的动态优化问题的求解展开研究,主要研究内容概括如下：
1.为了求解最简单的单控制变量、状态变量无约束的动态优化问题,对基本的遗传算法进行了改进,引入单纯形算法进行局部寻优,采用遗传算法进行全局寻优,并采用了自适应交叉和高斯变异操作,将单纯形算法的局部寻优能力和遗传算法的全局寻优能力相结合。通过求解动态优化问题实例,表明改进的混合遗传算法在求解动态优化问题时比基本遗传算法的搜索速度和结果准确度都有了提高。由于常用的分段常数法在求解动态优化问题时存在求解准确度不高的问题,为了提高动态优化问题的求解准确度,将控制变量参数化方法与混合遗传算法相结合来求解动态优化问题。在提出的控制变量参数化方法中,控制策略表示为时间和状态变量组成的多项式,将动态优化问题转化为一个非线性规划问题,然后可以通过混合遗传算法来求解未知参数。为了快速地收敛得到参数的最优值,在混合遗传算法中还采用了迭代的方法逐步缩小搜索空间。通过与CACA、SA以及IACA等方法的比较,结果表明提出的基于迭代混合遗传算法的控制变量参数化方法在求解动态优化问题时,在准确度方面有很大优势,求解结果较稳定,并且需要求解的参数个数也较少,计算代价较小。
2.为了提高控制变量参数化方法求解动态优化问题的准确度,提出了分段线性函数参数化方法。在分段线性函数参数化方法中,分别采用了等时间区间和时间区间可变两种方法。为了解决遗传算法和粒子群算法在求解动态优化问题时的早熟收敛问题,采用了一种新的混合进化算法HEA,结合了遗传算法和粒子群算法的性能,提高了求解效率。另外,为了改进收敛速度,提高算法在进化后期的求解速率,结合动态优化问题本身的特点,提出了“收缩搜索域”的概念。通过求解几个动态优化实例,HEA与其它一些算法进行了对比,结果显示,HEA算法易执行,求解速度较快,求解精度较高。基于等时间区间分段线性函数参数化方法的HEA-D算法应用于外源蛋白质生产的补料流率优化,取得了满意的效果。基于时间区间可变的分段线性函数参数化方法的HEA-N算法成功应用于两个生化过程反应器的动态优化,实验结果表明,HEA-N在优化结果和计算代价方面都有一定的优势。
3.针对动态优化问题中的多控制变量以及状态变量有约束的问题,分别提出了多控制变量的求解方法和约束的处理机制。针对前两部分提出的基于混合遗传算法的控制变量参数化方法和基于混合进化算法的分段线性函数参数化方法,分别给出了不同方法用于求解多控制变量动态优化问题时的控制策略编码方式。在状态变量有约束的动态优化问题的求解中,提出了一种新的目标函数评估方法,将可行解和不可行解的信息同时嵌入到目标函数的评估公式中,可以同时求解等式约束和不等式约束,并且能够同时求解路径约束和终端约束,通过将算法应用在测试实例中,表明提出的方法可以有效求解多控制变量和状态变量有约束的动态优化问题。
4.建立了环氧乙烷水合反应器的机理模型,并采用基于混合进化算法的分段线性函数参数化方法对反应器的温度分布进行了优化。环氧乙烷水合反应器是乙二醇生产中的一个重要装置,但是关于水合反应的机理和工业模型的研究和报道却较为少见。考虑到实验室数据与实际工业生产状况存在差距,首先根据实验室数据提出动力学模型,然后根据工业数据进行动力学参数的校正,建立了环氧乙烷水合反应器的数学模型,并将动态优化算法应用于模型中进行优化求解,得到了各反应物沿管长的最优浓度分布以及环氧乙烷水合反应器内的最优温度分布。
Chemical processes strictly are the dynamic processes, where the state variables vary with the time and the position. Dynamic processes are often described by the dynamic model of a group of differential equations. Dynamic optimization is to make a performance index optimal by controlling operational variables in dynamic model. For complex dynamic optimization problems, it is difficult to obtain analytic solution. The general method, including steepest descent method, conjugate gradient method and dynamic programming, is to search piecewise functions as the approximation with numerical methods on the base of Bellman's principle of optimality or the Hamiltonian function. In recent years, the novel intelligent algorithms based on bionics become more and more popular for solving dynamic optimization problems. The intelligent algorithms are applicable especially for the cases that the gradients are not available. This thesis aims at solving dynamic optimization problems using control vector parameterization (CVP) method based on intelligent evolutionary algorithm. The main contributions can be summarized as follows:
1. For solving dynamic optimization problems with single control variable and no constraint, a hybrid genetic algorithm (HGA) is proposed. Genetic algorithm (GA) has been proved to be a feasible method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously. However, in the later period of evolution, GA has a very slow convergence speed. Simplex method (SM) is used to perform the local search in the neighborhoods of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved.In HGA, some improvements like employing adaptive crossover and Gaussian mutation operators are also presented. The efficiency of the proposed algorithm is demonstrated with solving several dynamic optimization problems. An approach that combines HGA and CVP is also proposed to solve the dynamic optimization problems of chemical processes using numerical methods. In the new CVP method, control variables are approximated with polynomials based on state variables and time in the entire time interval. The iterative method, which reduces redundant expense and improves computing efficiency, is used with HGA to reduce the width of the search region. Results demonstrated the feasibility and robustness of the proposed methods.
2. For solving dynamic optimization more accuratly, the piecewise linear function parameterization method is proposed, including equal time interval distribution and changeable time interval distribution. A novel hybrid evolutionary algorithm (HEA) by combining GA and particle swarm optimization (PSO) is proposed. Based on the characteristics of dynamic optimization problems, the concept of "search region reduction" is integrated into the HEA to improve the convergence rate. The results of the case studies demonstrate the feasibility and efficiency of the proposed methods. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the proposed approach presents the best compromise between robustness and efficiency.
3. For solving dynamic optimization problems with multi control variables and with constraints, the methods for dealing with multi variables and constraints are proposed. Multi control variables dynamic optimization problems and constrained dynamic optimization problems are more difficult than the simple dynamic optimization problems. A new method that embeds the information of infeasible chromosomes into the evaluation function is introduced in this study to solve dynamic optimization problems with or without constraint. The results indicate that the proposed approaches can effectively solve the dynamic optimization problems with multi control variables and with constraints.
4. Focusing on ethylene oxide (EO) hydration reactor industrial equipment, the reaction mechanism model is established. Based on the principle of material balance, energy balance and kinetics of the reactions of ethylene oxide with water, partial least squares regression (PLSR) is used in the model to establish a corresponding relationship between the reaction rate constant and the reaction temperature. With kinetic parameters correction by using field data, the results are more tallies with the actual operation. According to the established model, influences of water/EO molar ratio and inlet temperature on product quality, outlet temperature and energy consumption are analyzed. The results show that the model can preferably reflect the performance of EO hydration reactor and have certain guidance functions to the further advanced control strategies. At last, the dynamic optimization algorithm is used to slove the temperature distribution problem of the EO hydration reactor. The optimal concentration distribution of the product and the optimal temperature distribution of the reactor are obtained.
1.为了求解最简单的单控制变量、状态变量无约束的动态优化问题,对基本的遗传算法进行了改进,引入单纯形算法进行局部寻优,采用遗传算法进行全局寻优,并采用了自适应交叉和高斯变异操作,将单纯形算法的局部寻优能力和遗传算法的全局寻优能力相结合。通过求解动态优化问题实例,表明改进的混合遗传算法在求解动态优化问题时比基本遗传算法的搜索速度和结果准确度都有了提高。由于常用的分段常数法在求解动态优化问题时存在求解准确度不高的问题,为了提高动态优化问题的求解准确度,将控制变量参数化方法与混合遗传算法相结合来求解动态优化问题。在提出的控制变量参数化方法中,控制策略表示为时间和状态变量组成的多项式,将动态优化问题转化为一个非线性规划问题,然后可以通过混合遗传算法来求解未知参数。为了快速地收敛得到参数的最优值,在混合遗传算法中还采用了迭代的方法逐步缩小搜索空间。通过与CACA、SA以及IACA等方法的比较,结果表明提出的基于迭代混合遗传算法的控制变量参数化方法在求解动态优化问题时,在准确度方面有很大优势,求解结果较稳定,并且需要求解的参数个数也较少,计算代价较小。
2.为了提高控制变量参数化方法求解动态优化问题的准确度,提出了分段线性函数参数化方法。在分段线性函数参数化方法中,分别采用了等时间区间和时间区间可变两种方法。为了解决遗传算法和粒子群算法在求解动态优化问题时的早熟收敛问题,采用了一种新的混合进化算法HEA,结合了遗传算法和粒子群算法的性能,提高了求解效率。另外,为了改进收敛速度,提高算法在进化后期的求解速率,结合动态优化问题本身的特点,提出了“收缩搜索域”的概念。通过求解几个动态优化实例,HEA与其它一些算法进行了对比,结果显示,HEA算法易执行,求解速度较快,求解精度较高。基于等时间区间分段线性函数参数化方法的HEA-D算法应用于外源蛋白质生产的补料流率优化,取得了满意的效果。基于时间区间可变的分段线性函数参数化方法的HEA-N算法成功应用于两个生化过程反应器的动态优化,实验结果表明,HEA-N在优化结果和计算代价方面都有一定的优势。
3.针对动态优化问题中的多控制变量以及状态变量有约束的问题,分别提出了多控制变量的求解方法和约束的处理机制。针对前两部分提出的基于混合遗传算法的控制变量参数化方法和基于混合进化算法的分段线性函数参数化方法,分别给出了不同方法用于求解多控制变量动态优化问题时的控制策略编码方式。在状态变量有约束的动态优化问题的求解中,提出了一种新的目标函数评估方法,将可行解和不可行解的信息同时嵌入到目标函数的评估公式中,可以同时求解等式约束和不等式约束,并且能够同时求解路径约束和终端约束,通过将算法应用在测试实例中,表明提出的方法可以有效求解多控制变量和状态变量有约束的动态优化问题。
4.建立了环氧乙烷水合反应器的机理模型,并采用基于混合进化算法的分段线性函数参数化方法对反应器的温度分布进行了优化。环氧乙烷水合反应器是乙二醇生产中的一个重要装置,但是关于水合反应的机理和工业模型的研究和报道却较为少见。考虑到实验室数据与实际工业生产状况存在差距,首先根据实验室数据提出动力学模型,然后根据工业数据进行动力学参数的校正,建立了环氧乙烷水合反应器的数学模型,并将动态优化算法应用于模型中进行优化求解,得到了各反应物沿管长的最优浓度分布以及环氧乙烷水合反应器内的最优温度分布。
Chemical processes strictly are the dynamic processes, where the state variables vary with the time and the position. Dynamic processes are often described by the dynamic model of a group of differential equations. Dynamic optimization is to make a performance index optimal by controlling operational variables in dynamic model. For complex dynamic optimization problems, it is difficult to obtain analytic solution. The general method, including steepest descent method, conjugate gradient method and dynamic programming, is to search piecewise functions as the approximation with numerical methods on the base of Bellman's principle of optimality or the Hamiltonian function. In recent years, the novel intelligent algorithms based on bionics become more and more popular for solving dynamic optimization problems. The intelligent algorithms are applicable especially for the cases that the gradients are not available. This thesis aims at solving dynamic optimization problems using control vector parameterization (CVP) method based on intelligent evolutionary algorithm. The main contributions can be summarized as follows:
1. For solving dynamic optimization problems with single control variable and no constraint, a hybrid genetic algorithm (HGA) is proposed. Genetic algorithm (GA) has been proved to be a feasible method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously. However, in the later period of evolution, GA has a very slow convergence speed. Simplex method (SM) is used to perform the local search in the neighborhoods of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved.In HGA, some improvements like employing adaptive crossover and Gaussian mutation operators are also presented. The efficiency of the proposed algorithm is demonstrated with solving several dynamic optimization problems. An approach that combines HGA and CVP is also proposed to solve the dynamic optimization problems of chemical processes using numerical methods. In the new CVP method, control variables are approximated with polynomials based on state variables and time in the entire time interval. The iterative method, which reduces redundant expense and improves computing efficiency, is used with HGA to reduce the width of the search region. Results demonstrated the feasibility and robustness of the proposed methods.
2. For solving dynamic optimization more accuratly, the piecewise linear function parameterization method is proposed, including equal time interval distribution and changeable time interval distribution. A novel hybrid evolutionary algorithm (HEA) by combining GA and particle swarm optimization (PSO) is proposed. Based on the characteristics of dynamic optimization problems, the concept of "search region reduction" is integrated into the HEA to improve the convergence rate. The results of the case studies demonstrate the feasibility and efficiency of the proposed methods. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the proposed approach presents the best compromise between robustness and efficiency.
3. For solving dynamic optimization problems with multi control variables and with constraints, the methods for dealing with multi variables and constraints are proposed. Multi control variables dynamic optimization problems and constrained dynamic optimization problems are more difficult than the simple dynamic optimization problems. A new method that embeds the information of infeasible chromosomes into the evaluation function is introduced in this study to solve dynamic optimization problems with or without constraint. The results indicate that the proposed approaches can effectively solve the dynamic optimization problems with multi control variables and with constraints.
4. Focusing on ethylene oxide (EO) hydration reactor industrial equipment, the reaction mechanism model is established. Based on the principle of material balance, energy balance and kinetics of the reactions of ethylene oxide with water, partial least squares regression (PLSR) is used in the model to establish a corresponding relationship between the reaction rate constant and the reaction temperature. With kinetic parameters correction by using field data, the results are more tallies with the actual operation. According to the established model, influences of water/EO molar ratio and inlet temperature on product quality, outlet temperature and energy consumption are analyzed. The results show that the model can preferably reflect the performance of EO hydration reactor and have certain guidance functions to the further advanced control strategies. At last, the dynamic optimization algorithm is used to slove the temperature distribution problem of the EO hydration reactor. The optimal concentration distribution of the product and the optimal temperature distribution of the reactor are obtained.
引文
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