Operational Flexibility Analysis And Design Optimization Of Process Systems Based On Numerical-Symbolic Method

Process Systems Engineering(PSE)is an interdiscipline on the basis of the systems engineering,process control,operation research and computer technology.Based on the process system,it studies process system analysis,process system optimization,process system control,process system synthesis,etc.PSE has gradually transited from theoretical research to industrial applications.It is not only widely used in the traditional fields of chemical,petroleum,metallurgical,food and energy,but also develops rapidly in the emerging fileds such as power grid,transportation,supply chains,logistics and warehousing,robots,etc.Currently,PSE is still in the development stage.With the development of computer technology,artificial intelligence and optimization algorithms,how to make further evolution for the concepts,principles and methods used in PSE has received the great attention.Operational flexibility analysis and design optimization of process systems are the research hotspots in the field of Process System Engineering.The core of operational flexibility analysis and design optimization is to establish and solve the mathematical models.Numerical computation and symbolic computation are two methods to solve mathematical models.The numerical computation is efficient,but the inaccuracy and instability lead to errors or even failures during the computation process.The symbolic computation can ensure the accuracy and completeness of the computation process.However,it suffers from the heavy computational complexity,takes up a lot of memory and the expression form is complex.How to take the advantages of numerical computation and symbolic computation to address traditional problems in the field of PSE is the core goal in this dissertation.This dissertation focuses on the basic theory of PSE from two aspects of operational flexibility analysis and process system design optimization.By using numerical and symbolic computation methods,it aims to address traditional problems in the field of PSE with more effective strategies.The detailed work can be summarized as follows:(1)Quantification of process flexibility via space projection.Flexibility index is an effective indicator to characterize the operational flexibility of a process design model.The traditional approaches to evaluate the flexibility index mainly rely on solving mixed-integer linear programming(MILP)or mixed-integer nonlinear programming(MINLP)problems,which have limitations for non-convex systems.A novel method based on symbolic computation is proposed for directly deducing the flexibility index in this work.First,the flexibility index problem is reformulated as an existential quantifier formula.Then,the projection operator in the cylindrical algebraic decomposition(CAD)method is introduced to eliminate all the state variables and project the original solution space onto the one-dimensional feasible space of the flexibility index.The final flexibility index can be directly determined by two different hyperrectangle checking rules.The optimal flexibility index of convex or nonconvex systems is guaranteed to be found,with no need of solving any optimization problems.(2)Analytical method for operational flexibility analysis of high-dimensional systems.The main purpose of operational flexibility analysis is to determine and describe the flexibility space.The existing methods based on numerical computation can only roughly estimate the envelope of the space.On the other hand,symbolic computation methods are limited by the scale of the model and the heavy burden of the computation.Based on the model reduction,a hybrid iterative method with sampling,surrogate model,symbolic calculation and boundary checking is proposed in this work to describe the flexbility space of high-dimensional systems with analytical expressions and explicitly express the steady-state operations to handle the uncertainties.(3)Parametric and analytical method for flexibility index and design problem.For a given process design,there exists a corresponding flexibility index to indicate the flexbility of the design model.In this work,we lift the flexibility index problem to the dimension of design variables.The solution space is projected into the dimension of design variables,flexibility index and uncertain parameters.The analytical expressions between design variables and flexibility index can be deduced with the inscribed hyperrectangle checking rule.Thus,the flexibility index and design problem is reduced to a simple function evaluation for a given design and enables a designer to know a priori which designs have the desired level of flexibility.(4)Design and operation optimization for cooling water system synthesis.The cooling water system is one of the largest consumers of energy in a power plant,which consists of a cooling water network,a pump network and cooling towers.Due to the interaction between each network,the unnecessary energy loss will occur if we did not consider the system as a whole.In this work,an integrated optimization is presented in which the pump network,cooling water network and cooling tower are designed as a whole system.Mixed-integer nonlinear programming based on a superstructure description is formulated by considering the configuration of the mainauxiliary pump,the location of the cooling towers,and the supply mode of cooling water simultaneously.Relaxation techniques for addressing the nonlinear terms in the model are also presented and good performance in computation speed can be achieved.(5)Robust optimization via space projection for polynomial systems.Robust counterpart reformulation is a common technique used to deal with data uncertainty in robust optimization(RO)problems.The derivation of the robust counterpart formulation using the duality theory is nontrivial,especially for a complex uncertainty set.To reduce the dependence on robust counterparts,a novel method is proposed in this work for RO problems.Based on the feasible space projection,the proposed method can locate robust solutions without formulating the robust counterparts.A modified cylindrical algebraic decomposition method is applied to directly project the high-dimensional feasible space on the low-dimensional space of the objective function and uncertainty parameters.The deduced analytical expressions in the projection result can be used to construct a series of lower profiles of the objective function.By solving the maximization problem for each lower profile and using the max-max decision criterion,the final robust optimal solution can be obtained.