Robust control of discrete minimum and non-minimum phase systems via data-driven virtual reference feedback tuning and IMC

In this paper, we develop a novel robust control approach for discrete minimum and non-minimum phase systems via a combined data-driven virtual reference feedback tuning ($\text{VRFT}$) and internal model control (IMC) scheme. The first step in the conventional $\text{VRFT}$ method controller design is the selection of the closed-loop reference model ($M\left(z\right)$), and $M\left(z\right)$ selection is still an open problem. The integration of the $\mathrm{IMC}$ scheme and the VRFT method provides the advantage of flexibility in controller design due to the incorporation of the $\mathrm{IMC}$ filter. As a result, the proposed design method begins with the selection of $M\left(z\right)$ and $\mathrm{IMC}$ filter. Unlike the standard $\text{VRFT}$ method, the proposed combined $\text{VRFT}$ and $\mathrm{IMC}$ design approach has the unique feature of taking into account a robustness property of dynamics, namely, maximum sensitivity ($M_{\mathrm{s}}$) as the design specification for the $M\left(z\right)$ and IMC filter selection. Moreover, the proposed approach includes a robustness specification that resolves the trade-off between performance and robustness in real-time controller design. Furthermore, the robustness guarantee with plant uncertainties and controller fragility is elucidated. The proposed approach is validated using numerical simulations and experimental validation through the temperature control process. Compared to conventional $\text{VRFT}$ controllers, experimental and simulation results show that the proposed controllers have less tracking error, minimize control effort, and improve robustness.     

Convective heat transfer coefficient for the side-wall in a fixed bed

Fixed beds are widely used in the chemical and process industry due to their relatively simple yet effective performance. Determining the radial heat transfer at the wall in a fixed bed is crucial to predict the performance of columns. Heat transfer parameters often need to be obtained experimentally. Various Nusselt ${\mathrm{Nu}}_w$ versus Reynolds ${Re}_p$ correlations in literature show considerable scatter and discrepancies. The tube-to-particle diameter ratio $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ and boundary conditions on the particle surface have been understood to affect heat transfer near the wall by virtue of influence on the near-wall porosity and mixing. In this work, a fixed bed consisting of mono-disperse particles is generated via gravity-forced sedimentation modelling utilizing the discrete element method for a $\frac{D_{\mathrm{t}}}{D_{\mathrm{p}}}$ ratio of 3.3. The system is meshed and imported in a computational fluid dynamics (CFD) solver. Fluid inlet velocity is varied to get ${Re}_p\in \left[1,1500\right]$ corresponding to the laminar and turbulent flow regimes. The particles are treated as boundaries with Dirichlet, Neumann, and Robin boundary conditions applied for the closure of energy balance. Another set of simulations is run with particles modelled as solids with varying thermal conductivities ($k_s/k_f$). The heat flux and volume-averaged fluid temperature calculated during post-processing are used to determine the wall heat transfer coefficient and, subsequently, the wall Nu number. Fifteen ${\mathrm{Nu}}_w$ versus ${Re}_p$ correlations are compiled and analyzed. A new semi-empirical correlation for the wall Nusselt number has been developed for a fixed bed packed with monodisperse spheres for $\frac{D_t}{D_p}=3.3$ and results compared with data published in literature. Additionally, the impact of buoyancy effect on the wall Nusselt number has been studied.     

Artificial neural network to predict the power number of agitated tanks fed by CFD simulations

The power consumption of the agitator is a critical variable to consider in the design of a mixing system. It is generally evaluated through a dimensionless number known as the power number $N_p$. Multiple empirical equations exist to calculate the power number based on the Reynolds number $Re$ and dimensionless geometrical variables that characterize the tank, the impeller, and the height of the fluid. However, correlations perform poorly outside of the conditions in which they were established. We create a rich database of 100 k computational fluid dynamics (CFD) simulations. We simulate paddle and pitched blade turbines in unbaffled tanks from $Re$ 1 to 100 and use an artificial neural network (ANN) to create a robust and accurate predictor of the power number. We perform a mesh sensitivity analysis to verify the precision of the $N_p$ values given by the CFD simulations. To sample the 100 k mixers by their geometrical and physical properties, we use the Latin hypercube sampling (LHS) method. We then normalize the data with a MinMax transformation to put all features in the same scale and thus avoid bias during the ANN's training. Using a grid search cross-validation, we find the best architecture of the ANN that prevents overfitting and underfitting. Finally, we quantify the performance of the ANN by extracting 30% of the database, predicting the $N_p$ using the ANN, and evaluating the mean absolute percentage error. The mean absolute error in the ANN prediction is 0.5%, and its accuracy surpasses correlations even for untrained geometries.     

Mixing rules for high density polyethylene-polypropylene blends

High-density polyethylene (HDPE) and polypropylene (PP) blends of varying composition have been evaluated in an effort to establish a mixing rule for melt flow index (MFI). In addition, a previously established relationship between MFI and $\overline{M_w}$ for linear polymers was also evaluated for these blends. It was found that a parabolic relationship existed between the composition (by weight fraction) and MFI and that the MFI and $\overline{M_w}$ relationship held for this set of polymeric materials. Additionally, all properties and relationships were evaluated over five extrusion cycles, which showed minimal to no deviations over the five cycles.     

Computational fluid dynamic study of polycaprolactone nanoparticles precipitation in a co-flow capillary micro-tube

Polycaprolactone nanoparticles (NPs) were produced in the co-flow glass capillary device with $250\mathrm{\mu m}$ tip dimension. NPs size was 990 nm for continuous phase velocity, and $u_c=0.05\mathrm{m}/\mathrm{s}$ and 426 nm for $u_c=0.2\mathrm{m}/\mathrm{s}$. The droplet formation process in the co-flow microchannel was also simulated using computational fluid dynamic (CFD). Employing a digital image analysis technique, a cut-off value of 0.81 for the dispersed phase volume fraction was proposed for the determination of droplet size. A scenario was expressed for NP formation from micro-droplets. Moreover, after conducting 27 CFD simulations, a dimensionless exponential form correlation was proposed for droplet size estimation. In this generalized map, there were three distinct regions based on the relative capillary numbers of continuous to dispersed phases. It was revealed that at a constant dispersed phase velocity, by increasing the continuous phase velocity, more small NPs are formed. The results show that the ratio of micro-droplets to NPs size was between 735 and 755.     

Drawbacks of phase change models in simulating flashing of steam with a subsaturation downstream boundary condition

The development of phase change models applicable to a wide range of temperatures, pressures, and mass flow rates is primarily limited by the metastable or partially stable behaviour of the fluid. Due to this, the fluid does not change phase even after crossing saturation conditions. Most liquid–vapour phase change models have been developed primarily for the cavitation process where the phase change is not sustained, occurs in a very narrow region of space, or occurs under equilibrium conditions. In this paper, the mechanism of phase change is discussed along with the review of three different computational fluid dynamics (CFD)-based phase change methods available in OpenFOAM, which are used to simulate flashing of steam, in applications related to steam assisted gravity drainage (SAGD) systems. The first method is based on barotropic compressibility (BC) used with the realizable $k-\epsilon$ turbulence model, the second combination is of mass transfer model (MTM) with the realizable $k-\epsilon$ turbulence model, and the third one is based on two fluid (TF) method along with a family of $k-\omega$ turbulence models. These methods are tested on a converging–diverging nozzle with pressure driven phase change. It is demonstrated that these methods are not able to adjust their physics to different depressurization rates, do not account for liquid to be in superheated conditions, and have significant discrepancies with experimental results. In the end, better approaches to model this category of phase change are discussed.     

A modified fuzzy clustering framework for catalyst activity monitoring in the selective catalytic reduction system

The catalyst activity monitoring in the selective catalytic reduction (SCR) system is of great importance for safety and economic operation in the power plant. To address the problem, a framework based on clustering considering time delay has been proposed. A compound parameter, $q$, is put forward in this paper as a strategy to remove the influences from gas volume (power output), inlet NO_x concentration, and outlet NO_x concentration to the ammonia amount. A modified entropy-based fuzzy clustering (EFC) method is proposed by a threshold varying model and then tested for its efficiency by four datasets from the University of California, Irvine (UCI) machine learning repository. With the maximum mutual information entropy coefficient (MIC) method for detecting time delay and the modified EFC method, process data from three working levels are handled for automatically obtained clustering centres. The proposed activity value, $\mu$, is then calculated based on 1440 process data before and after the catalyst replacement shown in boxplot figures. The results of the framework are analyzed to be in accordance with the real working conditions, with $\mu$ values and fluctuation ranges starting to fall near first from the 721st sample in the 24th box.     

Modelling and parameter estimation of trans-β-farnesene coordination polymerization

trans-β-Farnesene is a bio-derived terpene monomer that can polymerize, generating polymers with properties that can be similar to the properties of conventional petroleum-derived polymers. For this reason, in the present study, several coordination polymerizations of trans-β-farnesene are carried out using the Ziegler–Natta catalyst system composed by neodymium versatate (${\mathrm{NdV}}_3$), diisobutylaluminum hidride (DIBAH), and dimethyldichlorosilane (DMDCS) in order to evaluate the influence of key operation variables on the control of average molar masses and monomer conversion. A phenomenological model is proposed to describe the coordination polymerization of trans-β-farnesene, and the kinetic parameters required to simulate the reactions are estimated. The initial concentration of DIBAH used as a chain transfer agent (CTA) is calculated by a data reconciliation procedure since this very active compound can participate in undesired side reactions. It is shown that the initial monomer, DIBAH, and ${\mathrm{NdV}}_3$ concentrations exert strong influences on the monomer conversion and average molar masses of (poly)farnese while the temperature effect is not so pronounced. The proposed kinetic mechanism was able to predict well the experimental data collected during the reactions, with the successful reconciliation of CTA concentrations and estimation of model parameters.     

Recovery of valeric acid using green solvents

In this work, extraction of valeric acid (VA) using tri-n-butyl phosphate (TBP) as a reactive extractant was carried out. To reduce the toxic effects of the conventional diluents on microorganisms, non-toxic and green edible sunflower and soybean oils were tried as the diluents. The high values of the distribution coefficient and extraction efficiency advocated to use them in the bio-refinery industries. Moreover, it shows intensification of the recovery of VA using reactive extraction process. Sunflower oil appeared to be a better diluent than soybean oil. The complexation reaction stoichiometry (m and n) and equilibrium complexation reaction constant $K_{E\left(m:n\right)}$ were estimated by using the differential evolution technique. In spite of the loading ratio being less than 0.5, the estimated m/n was found to be more than 1.0. The higher values of $K_{E\left(m:n\right)}$ occurred due to the 9higher stability of the VA-TBP complex in sunflower oil than in soybean oil. The stoichiometry of VA decreased with increasing TBP concentration. The complex concentration, ${\left[{\left(\mathit{HA}\right)}_m{S}_n\right]}_{\mathrm{org}}$, was found to be higher for soybean oil. It increased with temperature and initial VA concentration but remained invariant with TBP concentration. Due to the decreasing trend of $K_{E\left(m:n\right)}$ with temperature, the complexation reaction became exothermic. The enthalpy changes due to mass transfer stipulated easier mixing of the phases in sunflower oil than in soybean oil.     

Influence of weak electrostatic charges and secondary flows on pneumatic powder transport

The dynamics of the transported powder determines the functionality and safety of pneumatic conveying systems. The relation between the carrier gas flow, induced by the flown-through geometry, and the powder flow pattern is not clear yet for electrostatically charged particles. This paper highlights the influence of relatively minor cross-sectional secondary flows and electrostatic forces on the concentration and dynamics of the particles. To this end, direct numerical simulations (DNS) capture the interaction of the continuous and dispersed phases using a four-way coupled Eulerian–Lagrangian strategy. The transport of weakly charged particles in channel flows, where turbopheresis defines the particle concentration, is compared to duct flows, where additional cross-sectional vortices form. For both geometries, the Stokes number ($St=8,32$) and the electrical Stokes number (${\mathit{St}}_{\mathrm{el}}=\left[0,1,2,4\right]\times {10}^{-3}$) are varied, and the turbulent carrier flow was fixed to ${\mathit{Re}}_{\tau }=360$. The presented simulations demonstrate that secondary flows, for the same ${\mathit{Re}}_{\tau }$, $St$, and $S{t}_{\mathrm{el}}$, dampen the effect of particle charge. In a duct flow, vortical secondary flows enhance the cross-sectional particle mobility against the direction of electrostatic forces. Compared to a duct flow, in a channel, the wall-normal aerodynamic forces are weaker. Thus, electrical forces dominate their transport; the local particle concentration at the walls increases. Further, electrostatic charges cause a stronger correlation between the gas and particle velocities. In conclusion, despite being weak compared to the primary flow forces, secondary flow and electrostatic forces drive particle dynamics during pneumatic transport.     

Numerical study of the mixing characteristics in an air swirling fluidized bed with monodisperse and multi-sized particles

Powder mixers are used in many industries. In the present work, a new type of air swirling mixer was designed and optimized with eight horizontally arranged inlet pipes at the tangential inlet angle of 35°. The mixing of multi-sized spherical particles (2.0, 3.0, 4.0, and 5.0 mm) was numerically investigated in the air swirling mixer by coupled computational fluid dynamics–discrete element method. The numerical results showed that multi-sized particles achieved comparable mixing performance to monodisperse particles. The Lacey index for multi-sized particles increased initially, and then reached a maximum value at 0.824. The upward velocity of the particles, $v_{\mathrm{z}}$, increased initially, and then decreased to zero along the bed height. The maximum value of $v_{\mathrm{z}}$ occurred at a height of 40 mm. Particle radial velocity was larger near the wall than at the mixer tube centre area. The smallest particles aggregated in three layers. The collision number of the particles reached a maximum at bed height of 120 mm, which was consistent with the position of the maximum stress of the particles against the tube wall.     

SSAE-KPLS: A quality-related process monitoring via integrating stacked sparse autoencoder with kernel partial least squares

Kernel partial least squares (KPLS) is widely employed to address the issue of nonlinearity inherent in complex industrial processes. However, KPLS can only extract shallow features from process measurements. This paper proposes a new quality-related process monitoring method via integrating stacked sparse autoencoder (SSAE) with KPLS (SSAE-KPLS). First, an SSAE model is employed to exploit the nonlinearity within process variables. Through SSAE, hierarchical features are learned to extract latent representations of process variables from multiple sparse autoencoder (SAE) layers. Second, the learned hierarchical features from SSAE are used as input, and the final quality variables are used as output. A KPLS model is then built to exploit the nonlinear relationship between the hierarchical features extracted from process variables and the final product quality for process monitoring. Third, Hotelling's $T^2$ and $Q$ statistics are employed to detect the quality-unrelated and quality-related faults, respectively. Finally, experiments on a numerical example and the commonly used industrial benchmark of the Tennessee Eastman process (TEP) are conducted to illustrate the efficacy and merits of the proposed SSAE-KPLS based quality-related process monitoring method by comparing it with other related methods.     

The critical mass for the unconfined vapour cloud explosion of compressed and liquid hydrogen

The (unconfined) vapour cloud explosion (VCE) is a dramatic phenomenon that generates a severe pressure wave with a high potential to damage assets and produce injuries in the far field. This definition applies also to hydrogen. Nevertheless, no clear tools and methodology have been so far developed and tested for this highly reactive gas, and even advanced numerical simulations lack validation and suffer from large uncertainties. In this view, the comprehension of the physic which subtends this dramatic phenomenon for the specific case of hydrogen is still a central issue. This paper revises some of the most adopted theories on VCE based on classical acoustic theory and models for pressure wave propagation and provides a consequence-based, threshold (minimum) value for the critical mass of hydrogen $m_f^{\text{crit}}\left(4.0\mathrm{kg}\right)$ which is needed—at a stoichiometric concentration in air—for a vapour cloud to behave as a VCE. To this regard, any non-stoichiometric hydrogen concentration in air or lower amount of hydrogen would decrease either the flame Mach number $M_{\mathrm{f}}$ or the total energy, thus resulting in negligible overpressure. In this sense, the effects of buoyancy, diffusivity, and weather conditions on the dispersion of hydrogen should be taken into account. The results are valid either for compressed or cryogenic liquid tanks and can be adopted for the sake of distinction between hydrogen flash fire and VCE; for the hazard analysis of hydrogen production and storage; and more in general for the risk assessment of hydrogen systems.     

An effective characterization procedure for petroleum reservoir fluids using molecular type methods and cubic equations of state

Two eminent molecular type composition methods (paraffins, naphthenes, and aromatics [PNA] and saturates, aromatics, and polynuclear aromatics [SAP]) are employed to construct new characterization procedures for predicting the phase behaviour of petroleum fluids using a modified Peng–Robinson equation of state. The PNA and SAP methods divide a petroleum fraction into (PNA) and (SAP) homologous groups, respectively. Two generalized models are developed to predict the physical properties ($\mathrm{Mw},\mathrm{SG},T_b$) and equation of state (EOS) parameters ($T_c,P_c,\omega$) for both PNA and SAP sub-fractions. Each generalized model covers 18 different correlations in a single mathematical form that enables the model to return 18 outputs for PNA and SAP sub-fraction parameters. A new lumping method is also developed to convert triple PNA or SAP pseudo-components into single characterized fractions. Accordingly, seven different characterization procedures are introduced and compared with one another. The first two procedures are completely constructed based on the proposed models, and the other procedures encompass the models already developed. The results obtained from the simulation of the differential liberation test for 12 diverse reservoir fluids and bubble pressure prediction for 40 oil samples revealed that the first two methods (1 and 2) could enhance the abilities of the traditional characterization procedures for reservoir fluid modelling. The mean value of average absolute relative deviations (AARDs) over a total of 52 oil samples is about 6.5% for the proposed methods and is about 13.2% for the best previously existing methods. Moreover, an efficient workflow is provided for the parameter tuning process, which is notably capable of reducing the level of prediction errors using only three adjustable parameters.     

Tunable size and shape of conductive poly(N‐methylaniline) based on surfactant template and doping

Poly(N‐methylaniline) (PNMA) is one of the polyaniline derivatives with N‐substituted position. Polyaniline derivatives have attracted attention due to their higher solubility in common solvents than pristine polyaniline, but they still possess lower electrical conductivity. In this work, PNMA was synthesized via chemical oxidative polymerization in an ethanol–water system. The effect of surfactant type, namely anionic sodium dodecylbenzenesulfonate (SDBS), cationic cetyltrimethylammonium bromide and non‐ionic Tween20, on the electrical conductivity, doping level and morphology was investigated. PNMA prepared with the SDBS system possessed the highest electrical conductivity among the obtained PNMAs with and without surfactants. The effect of $N_{{\mathrm{\text{HClO}}}_4}$/N_NMA dopant mole ratios on the re‐doping, crystallinity, morphology and particle size was also examined. Using an $N_{{\mathrm{\text{HClO}}}_4}$/N_NMA mole ratio of 10:1 in the re‐doping process provided the highest electrical conductivity of 15.53 ± 2.5 S cm^?1, a doping level of 55.59%, along with hollow spherical particles with the thinnest membrane. Electron microscopy images revealed that the morphology of PNMA particles depended mainly on the surfactant type but not the $N_{{\mathrm{\text{HClO}}}_4}$/N_NMA mole ratio. © 2019 Society of Chemical Industry     

Mathematical study and simulation on stenosed carotid arteries with the help of a two-phase blood flow model

The present study is focused on a medical problem called stenosed carotid artery. The problem is formulated with the help of a two-phase blood flow model. The non-Newtonian nature of blood is considered that hold power law. Physical quantities were expressed in tensorial form. Analytical and numerical methods are used to solve equations under given boundary conditions. The effects of various parameters on blood flow like stenosis size, flow flux, resistance, haematocrit, pressure drop, etc. were studied and shown through various graphs. Parameter $k$, which ensures that the fluid is Newtonian or non-Newtonian; its impact on pressure drop; resistance to flow; and flow flux were obtained during the disease and presented through the graph. A relationship between pressure drop and haematocrit was obtained, which was helpful to predict fluctuation in blood flow during stenosis. We have also given a medical use for this model with the help of pathological data. We also analyzed steady and laminar flow in a carotid artery for different heights of stenosis. The study of various physiological parameters has been performed on the basis of blockage percentage and concentration of haematocrit. The nature of the red blood corpuscle (RBC) phase is considered liquid packets in a semi-permeable membrane, which makes this model close to reality.     

Colourless distributed combustion effects on a pre-mixed coke oven gas flame

Fuels consisting of high hydrogen concentration can be consumed under colourless distributed combustion (CDC) to suppress flashback tendency in premixed conditions. Higher NO_X challenges can also be overcome through CDC. For those purposes, coke oven gas was consumed under CDC within the scope of this study. To achieve CDC, ${\mathrm{N}}_2$ or ${\mathrm{CO}}_2$ diluents were introduced into the oxidizer so that oxygen concentration in the oxidizer would be decreased from 21% O₂ to its lean blow-off limits. Excess air ratios were determined as λ = 1.2 and λ = 1.5 along with a thermal power of 10 kW under premixed conditions. A commercial computational fluid dynamics code was used to predict temperature distribution and ${\mathrm{NO}}_X$, CO, and ${\mathrm{CO}}_2$ emissions. 162-step reactions created with GRI-Mech 3.0 chemical kinetics was integrated to the eddy dissipation concept combustion model. The temperature and ${\mathrm{NO}}_X$ profiles predicted were compared with the experimental results. Consistency was achieved at ~95% for temperature profiles, and almost 100% for ${\mathrm{NO}}_X$ profiles between the measured and the predicted ones. According to the results, it is concluded that a more homogeneous temperature distribution with the ~21% decrease in the maximum temperature was observed, and there was about 96% decrease in ${\mathrm{NO}}_X$ level. It was also demonstrated that using ${\mathrm{CO}}_2$ as a diluent is more effective in terms of temperature distribution over the combustor and ${\mathrm{NO}}_X$ reduction, while dilution with ${\mathrm{N}}_2$ is more effective in terms about 70% in decrease on CO.     

Design and simulation of a novel solar photovoltaic system assisted single-slope solar still distillation unit

Water is an essential component of our lives. Conventional seawater desalination, based on fossil fuel energy, is primary in meeting freshwater demands. Thus, solar desalination still emerged as an alternative technology that employs environmentally friendly renewable energy. Here, we aim to design and simulate a novel hybrid solar photovoltaic (PV) system coupled with a single-slope solar still unit for freshwater production. Various design techniques were utilized to fine-tune the model towards producing 3–4.6 kg/m² · day of distillate water, thereby calculating the design aspects such as tank size, energy, and cost. The results revealed that a conventional solar desalination system had 22% lower efficiency than the proposed novel still distillation unit assisted with a solar PV system (connected to a heating element). The maximum efficiency of 45% has been recorded at the peak solar insolation due to the combination of the solar PV system. According to our design constraints, only a 3 m² basin area was required to achieve a productivity of ${\mathit{P}}_{\mathit{st}}$ = 1–5 kg/day. Design analysis showed that the total capital cost of a conventional still can be significantly reduced from 2600 to 1500 $/unit with PV system integration at the specified productivity and optimal solar radiation of ~17 MJ/m² · day at peak time (02.00 PM). This work paves the way towards maximizing solar energy utilization from PV integration with solar desalination to achieve high freshwater productivity in single-basin solar still systems.     

Degradation of wastewater from carbon capture plants using metal-impregnated TiO2 photocatalyst

Amine-based carbon capture (ABCC) is an advanced and cost-effective technology used to reduce the effects of climate change by capturing ${\mathrm{CO}}_2$ emitted from different sources. Although it has been demonstrated commercially, amine degradation poses a significant threat to humans and aquatic life. Amine degradation produces a wide variety of complex products such as nitrosamines and some organic acids. Some of these products are carcinogenic and mutagenic in nature and have demonstrated acute toxicity for laboratory animals. In order to mitigate the adverse impact of these compounds on human health and aquatic life, heterogeneous photocatalysis, an advanced oxidation process which can degrade a wide variety of chemical species with potent reactive hydroxyl radicals, was considered for the degradation of these compounds. The photocatalytic degradation of N-nitrosodiethylamine (NDEA), acetic acid, and formic acid were tested using TiO₂ and metal-impregnated TiO₂ catalysts such as Fe, Co, Ni, and Cu. Various techniques, such as thermogravimetric analysis (TGA), UV–Vis, X-ray diffraction (XRD), Brunauer–Emmett–Teller (BET), scanning electron microscopy (SEM), and X-ray fluorescence (XRF) were used to characterize these catalysts. The operational parameters for the photocatalytic degradation process were chosen as solution pH, catalyst dose, and metal impregnation percentage (imp%), and they were optimized using response surface methodology (RSM). pH was found as an important factor, and its impact on the photocatalytic degradation efficiency was more significant than the other operational parameters. The average degradation efficiency of the compounds reached 93.1% for Fe-TiO₂, 92.08% for Co-TiO₂, 89.09% for Ni-TiO₂, 88.81% for Cu-TiO₂, and 86.3% for TiO₂ at the optimum conditions.     

Feature learning based on entropy estimation density peak clustering and stacked autoencoder for industrial process monitoring

Recently, stacked autoencoder (SAE)-based deep learning has been widely employed for industrial process fault detection, which can extract representative low-dimensional features. However, SAE fails to take the distribution structure of raw data into consideration in the unsupervised self-reconstruction learning, and this may lead to limited monitoring performance. Focusing on this issue, this paper proposes a new fault detection method based on entropy estimation density peak clustering and stacked autoencoder (EEDPC-SAE) for industrial process monitoring. First, an improved automatic clustering algorithm, namely, entropy estimation density peak clustering (EEDPC), is presented to analyze the distribution structure of process data. Then, the data distribution information is integrated into the learning procedure of SAE to capture the data intrinsic structure. EEDPC-SAE can describe the distribution characteristics of process data, and more informative high-level features can be learned for fault detection. Finally, two statistics, that is, Hotelling's T-squared ($T^2$) and squared prediction error (SPE), are established based on the encoder features and residual features generated by EEDPC-SAE. The effectiveness of the proposed method is evaluated by the Tennessee Eastman (TE) process and fed-batch fermentation penicillin (FBFP) process.