Pham Luu Trung Duong

Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach

Abstract Uncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol’s sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.

Multi-model PID controller design: Polynomial chaos approach

The dynamic behavior of many systems can be approximated by a linear model at each operating point. Therefore, if the process works in several operating points, a set of linear models can be constructed to represent the system behavior. Those multi-models can be viewed as a system with random uncertain bounded parameters with definite influence over the behavior of the solution. Stability and performance of a system can be inferred from the evolution of statistical characteristic of system states with random parameters. The polynomial chaos of Wiener provides a framework for the statistical analysis of dynamical systems, with computational cost far superior to Monte Carlo simulations. Hence, in this work, we design robust integer and fractional order PID controller for multi-model systems by using Legendre Chaos.

Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method

The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem.

Measuring the reliability of a natural gas refrigeration plant: Uncertainty propagation and quantification with polynomial chaos expansion based sensitivity analysis

Abstract The practical quantification of a models ability to describe information is extremely important for the practical estimation of model parameters. Hence, in this study, a complex sweet natural gas refrigeration chemical process was selected for uncertainty quantification (UQ) and sensitivity analysis (SA). A computer code was generated to create a hybrid digital simulation system (HDSS) to connect two commercially important software programs, namely Matlab and Aspen Hysys. Monte Carlo (MC) and Halton based quasi-MC (QMC) methods were used for uncertainty propagation (UP) and uncertainty quantification (UQ). A surrogate model based on the polynomial chaos expansions (PCE) approach was applied for SA. Sobol′ sensitivity indices were evaluated to identify influential input parameters. The proposed PCE methodology was compared with a traditional MC based approach to illustrate its advantages in terms of computational efficiency and acceptable accuracy. The results indicated that UQ and SA help in an in-depth understanding of the chemical process determining the feasibility and improving the operation based on reliability and consumer demands. This study used in the robust design by evaluating the bounds and reliability based on confidence levels and thereby increasing the reliance of the process at hand.

Robust PI controller design for integrator plus dead-time process with stochastic uncertainties using operational matrix

To increase the precision and reliability of process control, random uncertainty factors affecting the control system must be accounted for. We propose a novel approach based on the operational matrix technique for robust PI controller design for dead-time processes with stochastic uncertainties in both process parameters and inputs. The use of the operational matrix drastically reduces computational time in controller design and statistical analysis with a desired accuracy over that of the traditional Monte-Carlo method. Examples with deterministic and stochastic inputs were considered to demonstrate the validity of the proposed method. The computational effectiveness of the proposed method was shown by comparison with the Monte-Carlo method. The proposed approach was mainly derived based on the integrator plus dead-time process, but can be easily extended to other types of more complex stochastic systems with dead-time, such as a first-order plus dead-time or a second-order plus dead-time system.

Uncertainty quantification for fractional order PI control system: Polynomial chaos approach

Abstract Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance…) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fractional order PI control system under the uncertainties both in parameters and additive stochastic disturbance.

Design of robust PID controller for processes with stochastic uncertainties

Abstract Stability and performance of a system can be inferred from the evolution of statistical characteristic of system states. The polynomial chaos of Wiener provides an efficient framework for the statistical analysis of dynamic systems, with computational cost far superior to Monte Carlo simulations. In this work, we design a robust PID controller for systems with stochastic uncertainties by using a generalized polynomial chaos.