Lixia Kang

Graph representation and decomposition of ODE/hyperbolic PDE systems

Abstract This paper deals with the decomposition of process networks consisting of distributed parameter systems modeled by first-order hyperbolic partial differential equations (PDEs) and lumped parameter systems modeled by ordinary differential equations (ODEs) into compact, weakly interacting subsystems. A structural interaction parameter (SIP) generalizing the concept of relative degree in ODE systems to first-order hyperbolic PDE systems is defined. An equation graph representation of these systems is developed for efficient calculation of SIPs. An agglomerative (bottom-up) hierarchical clustering algorithm and a divisive (top-down) algorithm are used to obtain hierarchical decompositions based on the SIPs. Modularity maximization is used to select the optimal decomposition. A network of two absorbers and two desorbers serves as a case study. The optimal decompositions of this network obtained from both the algorithms illustrate the effectiveness of the graph-based procedure in capturing key structural connectivity properties of the process network.

Modularity-based control structure selection for process networks: An extension to distributed parameter systems

This paper deals with obtaining the optimal control configuration for process networks comprising lumped and distributed parameter systems. Equation graphs that capture structural interactions among the input and output variables of first-order hyperbolic PDE systems with different types of actuations are proposed, which are combined with equation graphs of lumped parameter systems. Using these equation graphs, parameters that quantify structural coupling (relative degrees, characteristic indices) are calculated, on the basis of which, the optimal decentralized control configuration is identified. Agglomerative hierarchical clustering is then applied to obtain candidates for block-decentralized control configurations. A modularity maximization algorithm is used to select the optimal block-decentralized control configuration.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Abstract To increase computational efficiency and quality of solutions on large-scale mixed- integer nonlinear programming (MINLP) models of heat exchanger network synthesis (HENs), a paralleled sequential quadratic programming (SQP) algorithm based on graphic process unit (GPU) acceleration is proposed. It features that the HENs model is decomposed into independent nonlinear programming (NLP) sub-problems that are simultaneously solved by paralleled SQP algorithm on CPU-GPU heterogeneous architectures. The estimation formulae of speed-up ratios for single-GPU and multi- GPU are derived, and the acceleration performances of the proposed algorithm are demonstrated by two MINLP problems of HENs. Results present the effectiveness and the advantage to solve large-scale MINLP models of HENs problems.

Research on the Solution of Heat Exchanger Network MINLP Problems Based on GPU

The optimization of heat exchanger network can be expressed in a Mixed Integer Non-Linear mathematical Programming (MINLP) model. However, it demands huge computing power to solve a realistic heat exchanger network optimize problem. Nowadays graphic processing unit (GPU) can be very powerful for general purpose computation. Based on the CUDA framework, this paper presents a parallel computing framework for solving the MINLP problem. We concentrate on both parallel computing model and specific GPU programming level optimization. Tests on a simple MINLP problem is conducted and the results show the new solution has 40 times faster than the one running serially on CPU.