Parallel simulation and state estimation algorithms for dynamic systems on multicomputers.

Abstract

The problem of parallel dynamic simulation and state estimation for large-scale dynamic systems is investigated. Parallelization is based on partitioning of the overall large-scale dynamic system into a number of loosely coupled interconnected subsystems of smaller dimension. Model equations for each subsystem are solved concurrently over a certain time horizon on multiple computer nodes interconnected via a network (multicomputer). Interaction effects among the subsystems are taken into account with a dynamic block Jacobi-like iteration via a coordination routine. A general framework for parallel implementation of the modular integration approach for dynamic process simulation on multicomputers is developed. Using the contraction mapping theorem, a set of sufficient conditions for convergence of the parallel solution scheme for both linear and nonlinear systems is established. These conditions are shown to be very useful in quantifying the convergence rate that can be used as a basis for adjusting the integration time horizon and selection of the best process model partitioning strategy. Timing results from simulation of the dynamics of a multicomponent distillation column on a distributed memory message-passing multicomputer demonstrate the potential of the proposed parallel implementation. Numerical testing indicates that the parallel-modular multirate integration approach (in which equations for each subsystem are integrated by a method best-suited to its dynamic behavior) enhances computational speedup and produces satisfactory convergence and accuracy properties. On the basis of the structural properties of the dynamic system and the parallel processing considerations, a new graph partitioning method is proposed. In particular, this algorithm is aimed at reducing the inter-modal communication overhead and at the same time achieving computational load balance. The application of the graph-theoretic concepts and the structural properties to the problem of process model partitioning is demonstrated on a double-effect evaporator. A partially decentralized model-based control structure that can be implemented on network-based parallel computers is developed. A new state observer design methodology is addressed which accounts for the parallel nature of the implementation and also guarantees stability and optimal performance of the parallel observer. Simulation results on a message-passing multicomputer for a class of chemical engineering applications demonstrate the potential of parallel processing for state estimation in the context of model-based control.