Process System Optimization Based On Automatic Differentiation

Process system optimization (PSO) has become a major technology that helps companies in process industry to remain competitive. Numerical derivatives play an important role in mathematical programming, which is the core area in PSO. On one hand, numerical derivatives provide proper search directions in optimization, therefore their accuracy is of great importance for fast convergency. On the other hand, derivative evaluation is one of the most time-consuming steps in optimization. Improving the efficiency of the evaluation of derivatives is an effective way to reduce the time for optimization, and is of significant help to real-time optimization.Automatic differentiation (AD), which is well recognized as the most promising differentiation algorithm in PSO and has been developed rapidly in recent twenty years, is a technique for augmenting computer programs with derivative computations. It exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations such as additions or elementary functions such as exponential function. By applying the chain rule of derivative calculus repeatedly to these operations, derivatives of arbitrary order can be computed automatically, and accurate to working precision. However, AD has some limitations when applied to complicated process models. The research work in this thesis is focused on AD-based differentiation methodology that can fully exploit the structure of the objective model to greatly reduce the time for Jacobian evaluation and improve the efficiency of optimization. The main contributions are as follows:Applications of optimization in process engineering are introduced and the mathematical programming problems related to them are indicated. Then solution methods of the major types of optimization problems are reviewed, based on which the importance of derivative evaluation in optimization is analyzed and summarized. After that, the principle and technique of AD are systematically discussed meanwhile the advantages and disadvantages of AD are pointed out to give hint on more efficient differentiation approach.Symbolic Differentiation (SD) and AD are compared in details and then a novel SD algorithm, Symbolic Automatic Differentiation (SAD), is presented. SAD is able to differentiate models in form of subroutines, fully exploit the sparsity of the models and need few additional operations. It is concluded that SAD is verysuitable for the process models that have relatively simple computational structure and consist mainly of polynomials. An extended AD tool XADMAT, which is derived from ADMAT, the operator-overloading AD tool in MATLAB, is developed to realize both numerical and symbolical AD. XADMAT is successfully applied to an alkylation process optimization problem.The influence of process modeling approaches on optimization and differentiation is studied. It is concluded that a combination of the two main modeling approaches, the sequential modular approach and the equation-oriented approach, can keep a good balance between flexibility and efficiency. So-obtained process model, called composite model in this paper, contains hidden variables that can not be observed externally. Accordingly, traditional algorithms are not able to fully exploit the structure of complex composite model so as to highly improve the efficiency of optimization. It is pointed out that applying different differentiation algorithm to different parts of the model might be the recipe to conquer the difficulty.Module-oriented Automatic Differentiation (MAD), a new AD approach that can employ current differentiation algorithms flexibly to differentiate each module of the process model, is presented to achieve more efficient Jacobian evaluation in optimization. In MAD, the model of interest is partitioned into a series of modules, just as in AD the function of interest is divided into a sequence of elementary functions. Two modes for accumulating the Jacobians of the modules, direct mode and indirect mode are discusse...