Nonlinear and Non-Gaussian Process Monitoring Based on Simplified R‑Vine Copula

In the field of chemical process monitoring, the vine copula model provides a new idea for describing the interdependence between high-dimensional complex variables, and directly characterizes the correlation without dimensional reduction. However, in actual industrial processes, the number of pair copulas to be optimized and the parameters to be estimated increase rapidly when the dimensionality of the variables is large. This greatly increases the computational load and reduces the detection efficiency. In this paper, a fault diagnosis method based on a simplified R-vine (SRV) model is proposed. Without reducing the precision of the model significantly, the simplified level is set to reduce the complexity of the workload and calculations. The simplified level of an R-vine model is obtained by a Vuong test. Then, the generalized local probability (GLP) of the non-Gaussian state is constructed by using the theory of highest density region (HDR) and a density quantile table. The monitoring results of the Tennessee Eastman (TE) process and a real acetic acid dehydration distillation system show that the proposed SRV approach achieves good performance in monitoring results and computational load for chemical process fault monitoring

Vine Copula-Based Dependence Description for Multivariate Multimode Process Monitoring

A novel vine copula-based dependence description (VCDD) process monitoring approach is proposed. The main contribution is to extract the complex dependence among process variables rather than perform dimensionality reduction or other decoupling processes. For a multimode chemical process, the C-vine copula model of each mode is initially created, in which a multivariate optimization problem is simplified as coping with a series of bivariate copulas listed in a sparse matrix. To measure the distance of the process data from each non-Gaussian mode, a generalized local probability (GLP) index is defined. Consequently, the generalized Bayesian inference-based probability (GBIP) index under a given control limit can be further calculated in real time via searching the density quantile table created offline. The validity and effectiveness of the proposed approach are illustrated using a numerical example and the Tennessee Eastman benchmark process. The results show that the proposed VCDD approach achieves good performance in both monitoring results and computation load

Lubricating and Waxy Esters, V: Synthesis, Crystallization, and Melt and Flow Behaviors of Branched Monoesters Incorporating 9‑Decenol and 9‑Decenoic Acid

Branched derivatives of waxy monoesters incorporating 9-decenol and 9-decenoic acid were synthesized using epoxidation and ring-opening esterification. The reactions were conducted at two different temperatures and monitored over time. The crystallization, melting, and viscosity of the compounds were all controlled strongly as a function of incremental branching. Isomerism was shown to be critically important: an OH group at the end of the hydrocarbon chain completely suppressed crystallization, whereas its isomer with a terminal acyl chain did not. The structure of the linear monoesters were shown to provide the templates for crystallization, melting, and flow behavior, whereas the branching effect extended but could not erase the effect of the base molecular architecture. These compounds present a large range of properties that are suitable for a variety of applications ranging from waxes to lubricants

Synthesis, Crystallization, and Melting Behavior of Metathesis-like Triacylglycerol Oligomers: Effects of Saturation, Isomerism, and Size

Oligomers of triacylglycerols (TAGs) are derived from the self-metathesis of vegetable oils and are sought for a variety of applications, in particular waxes. A series of model dimers and quatrimers of TAGs with controlled structures were synthesized and characterized by ¹H NMR and ¹³C NMR. Their thermal stability, crystallization, and melting behavior were investigated using TGA and DSC. The relationship of oligomeric structure to thermal properties was found to adhere well to predictive trends. Although the effect of saturation on the phase behavior was the most dramatic, with differences in crystallization temperature up to 62 °C, isomerism and molecular mass were shown to affect crystallization significantly, leading to differences of up to 30 °C. The findings of the study show that the thermal parameters of the oligomers can be adjusted in a very broad range by saturation, isomerism, and size, making the development of a large variety of biosourced functional lubricants and waxes possible

Synthesis and Physical Properties of Triacylglycerol Oligomers: Examining the Physical Functionality Potential of Self-Metathesized Highly Unsaturated Vegetable Oils

Seven model oligomers (from dimer to octamer) of the triacylglycerol (TAG) triolein were synthesized from oleic acid and fully characterized by ¹H NMR, ¹³C NMR, mass spectroscopy, and gel permeation chromatography (GPC). The thermal stability of the oligomers as determined by TGA was excellent, with degradation beginning at 342 °C for the most thermally labile samples. The samples all presented glass transitions at low temperatures, with <i>T</i>_g continuously shifting to higher temperatures with increasing numbers of monomers. The crystallization and melting behavior scaled with molecular size and relative number of double bonds in the trans- configuration. Flow behavior was investigated over a large range of temperatures (−10 to 110 °C), and application of the Herschel–Bulkey model to shear stress versus shear rate data evidenced a flow behavior dependent on molecular size and temperature. The oligomers presented a thinning to Newtonian flow transition temperature proportional to molecular size. The viscosity versus temperature data, fitted with a generalized van Velzen equation, suggested that it is the competition between the trans- character and size of the molecules which determines the rheology of these molecules. Overall, all the investigated properties plateaued at the hexamer, suggesting that no further marginal utility can be obtained with larger oligomers

Lubricating and Waxy Esters. 6. Synthesis and Physical Properties of (<i>E</i>)‑Didec-9-enyl Octadec-9-enedioate and Branched Derivatives

A fatty aliphatic “Jojoba-like” ester, didec-9-enyl octadec-9-enedioate, was synthesized by Steglish esterification, and C3-branched derivatives were prepared from its epoxide by a solvent-free epoxide ring-opening and one-pot normal condensation reaction. The thermal stability, phase transition behavior, solid fat content, and flow behavior were investigated using thermogravimetric analysis, differential scanning calorimetry, p-NMR, and rotational rheometry, respectively. These properties were predictably varied as a function of branching, explained by the combined effects of mass, hydroxyl groups, and geometric steric hindrances imposed by the protuberant branches. The compounds demonstrated high thermal stability (>230 °C), competitive flow characteristics (210–773 cP at 40 °C and 31–66 cP at 100 °C) and superior low-temperature performance properties (−27 to −70 °C) suitable for exploitation in various applications such as lubricants, cosmetics, and pharmaceuticals

Fault Detection and Diagnosis for Nonlinear and Non-Gaussian Processes Based on Copula Subspace Division

A novel copula subspace division strategy is proposed for fault detection and diagnosis. High-dimensional industrial data are analyzed in two elemental subspaces: margin distribution subspace (MDS) modeled by joint margin distribution, and dependence structure subspace (DSS) modeled by copula. The highest density regions of two submodels are introduced and quantified using probability indices. To improve the robustness of the monitoring index, a hyperrectangular control boundary in MDS is designed, and the equivalent univariate control limits are estimated. Two associated contribution indices are also constructed for fault diagnosis. The interactive relationships among the root-cause variables are investigated via a proposed state chart. The effectiveness and superiority of the proposed approaches (double-subspace and multisubspace) are validated using a numerical example and the Tennessee Eastman chemical process. Better monitoring performance is achieved compared with some conventional approaches such as principal component analysis, independent component analysis, kernel principal component analysis and vine copula-based dependence description. The proposed multisubspace approach fully utilizes univariate-based alarm data with a dependence restriction modulus, which is promising for industrial application

Glucose deprivation activates Nrf1 through TADs other than the NST domain.

<p>(<b>A</b>) Cells expressing wild-type Nrf1 were allowed to recover from transfection in fresh 5.5 mM-glucose-containing-medium for 8 h, and were thereafter cultured for a further 18 h in media containing 0, 1.1 or 25 mM glucose. The cell lysates were resolved by 4-12% LDS/NuPAGE, followed by immunoblotting with V5 antibodies to detect ectopic Nrf1 protein. (<b>B</b>) Increased activity of ectopic wild-type Nrf1 resulting from exposure to glucose deprivation (i.e. ‘no-glucose’) conditions (, p<0.001, n = 9) was determined by reporter gene assays, in which the transfected cells were allowed to recover for 8 h in medium containing 5.5 mM glucose before they were subjected to an additional 18-h culture in either glucose-free or 25-mM glucose medium. (C) Transactivation of an ARE-driven luciferase gene by Nrf1 or mutants, following 18-h no-glucose starvation, was calculated from three independent reporter gene assays. Significant increases in transactivation activity ($, p<0.05; , p<0.001, n = 9) and significant decreases (*, p<0.05; **, p<0.001, n = 9) are shown.</p

Fault Detection and Diagnosis for Nonlinear and Non-Gaussian Processes Based on Copula Subspace Division

A novel copula subspace division strategy is proposed for fault detection and diagnosis. High-dimensional industrial data are analyzed in two elemental subspaces: margin distribution subspace (MDS) modeled by joint margin distribution, and dependence structure subspace (DSS) modeled by copula. The highest density regions of two submodels are introduced and quantified using probability indices. To improve the robustness of the monitoring index, a hyperrectangular control boundary in MDS is designed, and the equivalent univariate control limits are estimated. Two associated contribution indices are also constructed for fault diagnosis. The interactive relationships among the root-cause variables are investigated via a proposed state chart. The effectiveness and superiority of the proposed approaches (double-subspace and multisubspace) are validated using a numerical example and the Tennessee Eastman chemical process. Better monitoring performance is achieved compared with some conventional approaches such as principal component analysis, independent component analysis, kernel principal component analysis and vine copula-based dependence description. The proposed multisubspace approach fully utilizes univariate-based alarm data with a dependence restriction modulus, which is promising for industrial application

Sequential Dependence Modeling Using Bayesian Theory and D‑Vine Copula and Its Application on Chemical Process Risk Prediction

An emerging kind of prediction model for sequential data with multiple time series is proposed. Because D-vine copula provides more flexibility in dependence modeling, accounting for conditional dependence, asymmetries, and tail dependence, it is employed to describe sequential dependence between variables in the sample data. A D-vine model with the form of a time window is created to fit the correlation of variables well. To describe the randomness dynamically, Bayesian theory is also applied. As an application, a detailed modeling of prediction of abnormal events in a chemical process is given. Statistics (e.g., mean, variance, skewness, kurtosis, confidence interval, etc.) of the posterior predictive distribution are obtained by Markov chain Monte Carlo simulation. It is shown that the model created in this paper achieves a prediction performance better than that of some other system identification methods, e.g., autoregressive moving average model and back propagation neural network