Monte-Carlo-simulation-based optimization for copolymerization processes with embedded chemical composition distribution

Uncertainty in chemical process systems engineering: a critical review

Uncertainty or error occurs as a result of a lack or misuse of knowledge about specific topics or situations. In this review, we recall the differences between error and uncertainty briefly, first, and then their probable sources. Then, their identifications and management in chemical process design, optimization, control, and fault detection and diagnosis are illustrated. Furthermore, because of the large amount of information that can be obtained in modern plants, accurate analysis and evaluation of those pieces of information have undeniable effects on the uncertainty in the system. Moreover, the origins of uncertainty and error in simulation and modeling are also presented. We show that in a multidisciplinary modeling approach, every single step can be a potential source of uncertainty, which can merge into each other and generate unreliable results. In addition, some uncertainty analysis and evaluation methods are briefly presented. Finally, guidelines for future research are proposed based on existing research gaps, which we believe will pave the way to innovative process designs based on more reliable, efficient, and feasible optimum planning.

Goodness of Fit Tests for the Log-Logistic Distribution Based on Cumulative Entropy under Progressive Type II Censoring

In this paper, we propose two new methods to perform goodness-of-fit tests on the log-logistic distribution under progressive Type II censoring based on the cumulative residual Kullback-Leibler information and cumulative Kullback-Leibler information. Maximum likelihood estimation and the EM algorithm are used for statistical inference of the unknown parameter. The Monte Carlo simulation is conducted to study the power analysis on the alternative distributions of the hazard function monotonically increasing and decreasing. Finally, we present illustrative examples to show the applicability of the proposed methods.

A Framework of Covariance Projection on Constraint Manifold for Data Fusion

A general framework of data fusion is presented based on projecting the probability distribution of true states and measurements around the predicted states and actual measurements onto the constraint manifold. The constraint manifold represents the constraints to be satisfied among true states and measurements, which is defined in the extended space with all the redundant sources of data such as state predictions and measurements considered as independent variables. By the general framework, we mean that it is able to fuse any correlated data sources while directly incorporating constraints and identifying inconsistent data without any prior information. The proposed method, referred to here as the Covariance Projection (CP) method, provides an unbiased and optimal solution in the sense of minimum mean square error (MMSE), if the projection is based on the minimum weighted distance on the constraint manifold. The proposed method not only offers a generalization of the conventional formula for handling constraints and data inconsistency, but also provides a new insight into data fusion in terms of a geometric-algebraic point of view. Simulation results are provided to show the effectiveness of the proposed method in handling constraints and data inconsistency.

Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.