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

in Computers and Chemical Engineering (2016), 90(7), 23-30

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 ... [more ▼]

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. [less ▲]

Design of an Extractive Distillation Column for the Environmentally Benign Separation of Zirconium and Hafnium Tetrachloride for Nuclear Power Reactor Applications

in Energies (2015), 8(9),

Nuclear power with strengthened safety regulations continues to be used as an important resource in the world for managing atmospheric greenhouse gases and associated climate change. This study examined ... [more ▼]

Nuclear power with strengthened safety regulations continues to be used as an important resource in the world for managing atmospheric greenhouse gases and associated climate change. This study examined the environmentally benign separation of zirconium tetrachloride (ZrCl4) and hafnium tetrachloride (HfCl4) for nuclear power reactor applications through extractive distillation using a NaCl-KCl molten salt mixture. The vapor–liquid equilibrium behavior of ZrCl4 and HfCl4 over the molten salt system was correlated with Raoult’s law. The molten salt-based extractive distillation column was designed optimally using a rigorous commercial simulator for the feasible separation of ZrCl4 and HfCl4. The molten salt-based extractive distillation approach has many potential advantages for the commercial separation of ZrCl4 and HfCl4 compared to the conventional distillation because of its milder temperatures and pressure conditions, smaller number of required separation trays in the column, and lower energy requirement for separation, while still taking the advantage of environmentally benign feature by distillation. A heat-pump-assisted configuration was also explored to improve the energy efficiency of the extractive distillation process. The proposed enhanced configuration reduced the energy requirement drastically. Extractive distillation can be a promising option competing with the existing extraction-based separation process for zirconium purification for nuclear power reactor applications [less ▲]

Stochastic Analysis of Dead-time Systems using a Hybrid Spectral Method

in International Journal of Control, Automation, and Systems (2015), 13(5),

Abstract: Control systems often operate in the presence of dead-time. However, in most works, these dead-time systems are studied in a deterministic manner, which have low precision and reliability. Many ... [more ▼]

Abstract: Control systems often operate in the presence of dead-time. However, in most works, these dead-time systems are studied in a deterministic manner, which have low precision and reliability. Many natural systems often suffer stochastic noise that causes fluctuations in their behavior, making their responses deviate from nominal models. Therefore, it is important to investigate such statistical characteristic of states (mean, variance, etc.) for those stochastic systems. This problem is often called statistical analysis of a system. A hybrid spectral method represents a powerful numerical tool for sta- tistical analysis of stochastic linear system. Thus, a hybrid spectral technique is proposed for statistical analysis of the time delay system under affections of random parameters and inputs. Numerical exam- ples are considered to demonstrate the validity of the proposed method. Comparison with the tradition- al Monte-Carlo and the polynomial chaos methods is made to demonstrate the computationally less- demanding feature of the proposed method. [less ▲]

Probabilistic analysis and control of dynamic systems with uncertain parameters over non-hypercube domain

in Journal Process Control (2014), 22(4), 358-367

Generalised polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a ... [more ▼]

Generalised polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a polynomial chaos-based method was proposed for an analysis and design of control systems with para-metric uncertainty over a non-hypercube support domain. In the proposed method, the polynomial chaosfor the hypercube domain was extended to non-hypercube domains through proper parameterizationto transform the non-hypercube domains to hypercube domains. Based on the proposed polynomialchaos framework, a constrained optimization problem minimizing the mean under the maximum allow-able variance was formulated for a robust controller design of dynamic systems with the parametricuncertainties of the non-hypercube domain. Several numerical examples ranging from integer to frac-tional order systems were considered to validate the proposed method. The proposed method providedsuperior control performance by avoiding the over-bounds from a hypercube assumption in a compu-tationally efficient manner. From the simulation examples, the computation time by gPC analysis was approximately 10–100 times lower than the traditional approach. [less ▲]

Uncertainty propagation in stochastic fractional order processes using spectral methods: A hybrid approach

in Communications in Nonlinear Science and Numerical Simulation (2012), 17(11), 4262-4273

Stochastic spectral methods are widely used in uncertainty propagation thanks to its ability to obtain highly accurate solution with less computational demand. A novel hybrid spectral method is proposed ... [more ▼]

Stochastic spectral methods are widely used in uncertainty propagation thanks to its ability to obtain highly accurate solution with less computational demand. A novel hybrid spectral method is proposed here that combines generalized polynomial chaos (gPC) and operational matrix approaches. The hybrid method takes advantage of gPC’s efficient handling of large parameter uncertainties and overcomes its limited applicability to systems with relatively highly correlated inputs. The hybrid method’s use of operational matrices allows analyses of systems with low input correlations without suffering its restriction to small parameter uncertainties. The hybrid method is aimed to propagate uncertainties in fractional order systems with random parameters and random inputs with low correlation lengths. It is validated through several examples with different stochastic uncertainties.Comparison with Monte Carlo and gPC demonstrates the superior computational efficiency of the proposed method. [less ▲]

Statistical Analysis of Dead-time System using a Deterministic Equivalent Modeling Method

in Asia-Pacific Journal of Chemical Engineering (2011), 6(2), 369378

To increase precision and reliability of automatic control systems, random factors affecting the controlsystem have to be taken into account. In this article, the deterministic equivalent modelling method ... [more ▼]

To increase precision and reliability of automatic control systems, random factors affecting the controlsystem have to be taken into account. In this article, the deterministic equivalent modelling method (DEMM) is used for statistical analysis of time delay systems with random parameters. The proposed method is compared with several existing methods such as the Monte Carlo, Latin-Hypercube, and Quasi Monte Carlo method, to demonstrate its validity and effectiveness. The result shows that the proposed DEMM-based approach drastically reduces computational time with a desired accuracy over traditional methods. [less ▲]