Evaluation of process systems operating envelopes
Evaluation of process systems operating envelopes
复制标题
过程系统操作范围的评估
DOI：
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发表时间：
2013
期刊：
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通讯作者：
M. D. Stuber
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文献类型：
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作者：
M. D. Stuber
本文研究不确定条件下过程系统的最坏情况稳态设计问题，也称为鲁棒设计。当考虑在极端和恶劣环境中部署系统时，为最坏情况设计是非常重要的，因为在极端和恶劣环境中，由于极高的经济和/或环境成本，不能冒操作失败的风险。对于这种独特的场景，“过度设计”流程的成本远远超过与操作失败相关的成本。因此，必须保证流程足够健壮，以避免操作失败。许多工程、经济和运筹学应用都与最坏情况有关。通常，这些问题会产生一种领导者-追随者博弈或Stackelberg博弈，通常被称为“极小-极大”问题，或者更准确地说是最大-最小或最小-最大优化问题。然而，由于这里的应用是稳态设计，问题的表述结果是一个更一般的非凸等式约束的最小-最大规划，以前没有可用的算法可以有效地解决。在一定的假设条件下，将状态变量求解为控制变量和不确定性参数的隐式函数，可以消除与稳态模型相对应的等式约束。这种方法消除了对状态变量的显式函数依赖，从而降低了原始问题的维数。然而，这在程序中嵌入了隐函数，它没有显式的代数形式，只能用数值方法近似。通过这样做，最大-最小程序可以被重新表述为更易于计算的半无限程序，需要注意的是，其中有嵌入的隐式函数。嵌入隐函数的半无限规划是求解最坏情况设计问题的一种新方法。此外，建模过程系统-特别是与化学工程相关的过程系统-通常会产生高度非凸函数。本论文的主要贡献是一个数学工具，用于求解隐式半无限规划，并使用严格的基于模型的方法评估过程系统的鲁棒可行性。该工具能够通过考虑模型参数的不确定性和环境的不确定性，以数学确定性确定基于所建议设计的物理过程系统是否会在最坏情况下失败。
This thesis addresses the problem of worst-case steady-state design of process systems under uncertainty, also known as robust design. Designing for the worst case is of great importance when considering systems for deployment in extreme and hostile environments, where operational failures cannot be risked due to extraordinarily high economic and/or environmental expense. For this unique scenario, the cost of “overdesigning” the process far outweighs the cost associated with operational failure. Hence, it must be guaranteed that the process is sufficiently robust in order to avoid operational failures. Many engineering, economic, and operations research applications are concerned with worst-case scenarios. Classically, these problems give rise to a type of leader-follower game, or Stackelberg game, commonly known as the “minimax” problem, or more precisely as a max-min or min-max optimization problem. However, since the application here is to steady-state design, the problem formulation results in a more general nonconvex equality-constrained min-max program, for which no previously available algorithm can solve effectively. Under certain assumptions, the equality constraints, which correspond to the steady-state model, can be eliminated from the problem by solving them for the state variables as implicit functions of the control variables and uncertainty parameters. This approach eliminates explicit functional dependence on the state variables, and in turn reduces the dimensionality of the original problem. However, this embeds implicit functions in the program, which have no explicit algebraic form and can only be approximated using numerical methods. By doing this, the max-min program can be reformulated as a more computationally tractable semi-infinite program, with the caveat that there are embedded implicit functions. Semi-infinite programming with embedded implicit functions is a new approach to modeling worst-case design problems. Furthermore, modeling process systems—especially those associated with chemical engineering—often results in highly nonconvex functions. The primary contribution of this thesis is a mathematical tool for solving implicit semi-infinite programs and assessing robust feasibility of process systems using a rigorous model-based approach. This tool has the ability to determine, with mathematical certainty, whether or not a physical process system based on the proposed design will fail in the worst case by taking into account uncertainty in the model parameters and uncertainty in the environment.