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This paper presents a process-monitoring method based on multiblock rolling pin vine copula. The multiblock strategy not only reduces the impact of the local errors of the global variable during th...

This paper proposes a robust copula double-subspace (CDS) model based on a sparse robust autoencoder (SRAE) named SRAE-CDS. By reconstructing training data with SRAE, the resulting SRAE-CDS model i...

This paper proposes a process monitoring and fault diagnosis method based on a regular vine (R vine) and Bayesian network. The R vine model structure is determined by searching for the maximum sum ...

Nonlinear processes and non-Gaussian properties are challenging subjects for soft sensor modeling of chemical processes. In this paper, we propose a D-vine copula regression method based on a Hamil...

Soft-sensing methods have been widely used in recent years to predict key variables that are difficult to measure or involve costly and time-consuming in chemical processes. Owing to the increasing complexity of industrial processes, industrial data often exhibit strong nonlinearities and self-correlation, and the data distribution fails to satisfy the Gaussian assumption. To address these problems, a vine copula-based soft-sensor model combined with the rolling pin method is proposed. This approach uses a D-vine copula to model a joint probability distribution of auxiliary variables and a key variable. In accordance with the joint distribution, the predicted value of the key variable can be determined by weighting the training samples. During modeling, the Bayesian information criterion is adopted to select the best-fitted copula pairs. Given the nonmonotonicity between variables of actual industrial data, the rolling pin monotonic transformation is simultaneously introduced to improve the suitability of...

A process monitoring method based on double-model and multi-subspace vine copula (DMVC) is proposed in this paper. To improve the fault detection performance, process variables are divided into two...

This paper proposes a boosting vine copula-based dependence description (BVCDD) method for multivariate and multimode process monitoring. The BVCDD aims to improve the standard vine copula-based de ...

This paper proposes a new process monitoring method based on vine copula and active learning strategy under a limited number of labeled samples. The proposed method uses active learning strategy and the generalized Bayesian inference-based probability (GBIP) index to choose samples that can provide the most significant information for the process monitoring model. An adaptive strategy is used to select the number of training samples in every active learning loop. Then, the vine copula-based dependence description (VCDD) is used to fulfill fault detection for complex chemical processes. The validity and effectiveness of the proposed approach are illustrated using a numerical example and the Tennessee Eastman (TE) benchmark process. The results show that the proposed method can maximize the process monitoring performance while minimizing the number of samples labeled.

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 T...

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 a...

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 ...

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.

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.

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.

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.

Three pure jojoba wax-like esters (JLEs), i.e., octadec-9-enyl dec-9-enoate (JLE 281), dec-9-enyl oleate (JLE 282), and dec-9-enyl dec-9-enoate (JLE-20), were synthesized from fatty acids and fatty alcohols. Calorimetric, solid fat content evolution, and flow data were used to elucidate the phase behavior of the JLEs. It was clearly established that the length of the terminal alkyl chain and orientation of the linking group in the side chains of the bent-core molecules play an important role in the phase development of the JLEs and ultimately their physical properties. Measurable differences in all physical properties investigated were detected between the isomers based on the position of the ester group in the molecule, leading to informed choices on what isomer should be synthesized for similar monoesters for specific applications.

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 Tg 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 ...

A comprehensive study of branched derivatives of four pure jojoba wax-like esters (JLEs), having 36, 40 (two isomers), and 44 carbons was conducted to elucidate their crystallization and melting behavior. Crystallization and melting characteristics depended strongly on the number of branches, molar mass, and symmetry. The derivatives demonstrated a very strong tendency to form glassy liquids rather than crystal phases and remain liquid-like at very low temperatures. As the number of branches increased, their crystallinity decreased drastically while their glassy phase increased concomitantly with the depression of the onset of crystallization and/or glass transition temperature. A variety of possible transformation paths, ranging from very little polymorphic activity to extremely polymorphic behavior, depending on number of branches, mass, and symmetry were revealed. It is shown that asymmetry plays a large role in the low temperature behavior, rendering the branched derivatives of the asymmetrical JLEs much better candidates for lubricant formulations.

In the production of pure terephthalic acid, a tiny amount of reactant p-xylene may enter into the acetic acid dehydration distillation column through the feed stream. In normal operation, p-xylene will not leave the column from the top or bottom product. It will be accumulated in the top of dehydration distillation column and decanter. With the accumulation of p-xylene, the operation cost will be increased gradually, to ensure the purity specifications of the top and bottom products. To reduce the operation cost, it is necessary to cut down the concentration of p-xylene by draining some organic reflux and make up the pure entrainer intermittent. In this paper, reboiler duties at different concentrations of p-xylene in the reflux were analyzed. The optimal operation condition—that the concentration of p-xylene is decreased by draining some organic reflux when the mass fraction of p-xylene accumulation exceeds 0.15—had been suggested. Finally, the residue curves diagram of three key components in the top o...