Dynamic Behavior Of Process Research Articles

Characteristics of pseudo-second-order kinetic model for liquid-phase adsorption: A mini-review

Since the introduction of pseudo-second-order (PSO) model for the description of adsorption kinetics in 1999, it has been widely applied in liquid-phase adsorption systems. An approaching equilibrium factor ( R w) was defined and deduced from the PSO model in this work. The adsorption characteristic curves were built up, in which three different zones of the PSO model were classified. Activated carbons with various particle sizes were prepared from fir wood with KOH activation for the adsorption of phenol, 4-chlorophenol (4-CP), 2,4-dichlorophenol (2,4-DCP), 2,4,6-trichlorophenol (2,4,6-TCP), and methylene blue (MB) from water. Suitable ranges of the PSO model and the effect of adsorbent particle size on the R w value were analyzed. It was found that the quantity k 2 q e was exactly the inverse of the half-life of adsorption process. It could be used as an indicator of kinetic performance because it was a key parameter affecting the fractional adsorption at any time. That is, k 2 q e, a newly defined rate index, could provide the related information between the static and dynamic behavior of adsorption processes in engineering practice.

Variation of ADM1 by using temperature-phased anaerobic digestion (TPAD) operation

The objective of the study was to examine the application of the Anaerobic Digestion Model No. 1 (ADM1) developed by the IWA task group for mathematical modelling of anaerobic process. Lab-scale temperature-phased anaerobic digestion (TPAD) process were operated continuously, and were fed with co-substrate composed of dog food and flour. The model platform implemented in the simulation was a derivative of the ADM1. Sensitivity analysis showed that k m.process (maximum specific uptake rate) and K S.process (half saturation value) had high sensitivities to model components. Important parameters including maximum uptake rate for propionate utilisers ( k m.pro ) and half saturation constant for acetate utilisers ( K S.ac ) in the thermophilic digester and maximum uptake rate for acetate utilisers ( k m.ac ) in the mesophilic digester were estimated using iterative methods, which optimized the parameters with experimental results. Simulation with estimated parameters showed good agreement with experimental results in the case of methane production, uptake of acetate, soluble chemical oxygen demand (SCOD) and total chemical oxygen demand (TCOD). Under these conditions, the model predicted reasonably well the dynamic behavior of the TPAD process for verifying the model.

Software Reliability Modeling Based on Capture-Recapture Sampling

This paper proposes a dynamic capture-recapture (DCR) model to estimate not only the total number of software faults but also quantitative software reliability from observed data. Compared to conventional static capture-recapture (SCR) model and usual software reliability models (SRMs) in the past literature, the DCR model can handle dynamic behavior of software fault-detection processes and can evaluate quantitative software reliability based on capture-recapture sampling of software fault data. This is regarded as a unified modeling framework of SCR and SRM with the Bayesian estimation. Simulation experiments under some plausible testing scenarios show that our models are superior to SCR and SRMs in terms of estimation accuracy.

Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior

The class of counting processes constitutes a significant part of applied probability. The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes. More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications. These counting processes seem to be quite different on the surface, forcing one to understand each of them separately. The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes. The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior ast→∞is established. As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically.

Investigation of System Dynamics in a Corrosion Process by Optical and Electrochemical Methods

A brief investigation is presented in an electrochemical corrosion cell consisting of 99.5% aluminum sample immersed in 3% NaCl and hydrocarbon-chloride solution emulsion, which reaction processes were optically monitored using Michelson interferometry. An image processing method applied on obtained interferograms allowed to calculate oxide corrosion layer thickness formed over the metal surface. Additionally a theoretical model consisting of a two bi-dimensional difference equation system is proposed, in order to explain evolution of optical interference pattern maxima observed as a function of time for corrosion process, and also to establish a growth-competition model for the maxima fringes evolution and consequently for the oxide layer and corrosion system dynamics. Bifurcation diagrams showing equation system solution regions were additionally obtained based on the nonlinear dynamic behavior of corrosion processes showing chaotic dynamics.

Dynamic Simulation of Phenol Biodegradation in a Fluidized Bed Bioreactor Using Genetic Algorithm Trained Neural Network

The aim of this work is to simulate the dynamic behavior of a phenol biodegradation process in a fluidized bed bioreactor (FBR). Pseudomonas putida is used for the biodegradation of phenol. A mathematical model was developed to describe the dynamic behavior of the biodegradation process. The model equations describing the process have been solved, and the rate of biodegradation and the biofilm thickness at different points of time have been determined. The mathematical model has been directly mapped onto the network architecture. The network is used to find an error function. Minimization of error function with respect to the network parameters (weights and biases) has been considered as training of the network. A real-coded genetic algorithm has been used for training the network in an unsupervised manner. The system is tested for two different inlet concentrations of feed. The results obtained are then compared with the experimental results. It is found that there is a good agreement between the experimental results and the results obtained from the model.

A Control Flow Analysis for Beta-binders with and without static compartments

We introduce a Control Flow Analysis, that statically approximates the dynamic behaviour of processes, expressed in the Beta-binders calculus and in an extended version of the calculus modelling static compartments. Our analysis of a system is able to describe the essential behaviour of each box, tracking all the possible bindings of variables, all the possible intra- and inter-boxes communications, and, finally, all the possible movements across compartments. The analysis offers a basis for establishing static checks of biological dynamic properties. We apply our analysis to an abstract specification of the interaction between a virus and cells of the immune system and to a model of the c A M P -signaling Pathway in Olfactory Sensory Neurons.

Aqueous-based extrusion of high solids loading ceramic pastes: Process modeling and control

A novel fabrication method known as aqueous-based extrusion fabrication (ABEF) has been developed for the manufacture of ceramic-based components in an environmentally friendly fashion. The method is based on the extrusion of ceramic pastes using water as the medium. This paper describes a machine developed for the extrusion of high solids loading ceramic pastes, investigates the dynamic behavior of the extrusion process, and develops and implements a feedback controller to regulate the extrusion force. The results demonstrate that aqueous-based ceramic extrusion processes have a very slow dynamic response, as compared to other non-compressible fluids such as water. A substantial amount of variation exists in aqueous-based ceramic extrusion processes, most notably during the transient period, and a constant ram velocity may either produce a relatively constant steady-state extrusion force or it may cause the extrusion force to steadily increase until the ram motor skips. It is demonstrated that the use of feedback control reduces the effects of process disturbances (i.e., agglomerate breakdown and air bubble release) and variations in the process as the material in the reservoir decreases, substantially decreases the time to obtain a desired extrusion force level, and dramatically improves part quality.

Use of bifurcation analysis for development of nonlinear models for control applications

Nonlinear system identification poses challenging questions because a closed general theory is not available for this field. Particularly, nonlinear models based on neural networks (NN) may present incompatible general dynamic process behavior, leading to improper closed-loop responses, even when they allow for satisfactory one step ahead prediction of process dynamics, as required by traditional validation methods. It is shown here that performing detailed bifurcation and stability analysis may be very helpful for the adequate development and implementation of nonlinear models and model based controllers. The study of many parameters that are defined a priori during the training of the NN shows that the spurious dynamic behavior is related mostly to the use of incomplete data sets during the learning process. This is an indication that, for each kind of process, the number, range and distribution of the data points in the operation region of interest are of paramount importance for proper training of the nonlinear model. Strategies to improve the quality of the training procedure are provided and analyzed both theoretically and experimentally, using the solution polymerization of styrene in a tubular reactor as a case study.

Simulation of styrene polymerization reactors: kinetic and thermodynamic modeling

A mathematical model for the free radical polymerization of styrene is developed to predict the steady-state and dynamic behavior of a continuous process. Special emphasis is given for the kinetic and thermodynamic models, where the most sensitive parameters were estimated using data from an industrial plant. The thermodynamic model is based on a cubic equation of state and a mixing rule applied to the low-pressure vapor-liquid equilibrium of polymeric solutions, suitable for modeling the auto-refrigerated polymerization reactors, which use the vaporization rate to remove the reaction heat from the exothermic reactions. The simulation results show the high predictive capability of the proposed model when compared with plant data for conversion, average molecular weights, polydispersity, melt flow index, and thermal properties for different polymer grades.

An Exact Solution for the Level-Crossing Rate of Shadow Fading Processes Modelled by Using the Sum-of-Sinusoids Principle

The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed out that Gudmundson's correlation model results in an infinite LCR. To avoid this problem, two alternative spatial correlation models are proposed. Illustrative examples of the dynamic behavior of shadow fading processes are presented for all three types of correlation models. Emphasis will be placed on two realistic propagation scenarios capturing the shadowing effects in suburban and urban areas.

EPIDEMIC PREDICTIONS AND PREDICTABILITY IN COMPLEX ENVIRONMENTS

The spread of epidemics is inevitably entangled with human behavior, social contacts, and population flows among different geographical regions. The collection and analysis of datasets which trace the activities and interactions of individuals, social patterns, transportation infrastructures and travel fluxes, have unveiled the presence of connectivity patterns characterized by complex features encoded in large-scale heterogeneities and unbounded statistical fluctuations. These features dramatically affect the behavior of dynamical processes occurring on networks, and are responsible for the observed statistical properties of the processes' dynamics and evolution patterns. Here we will present a large-scale stochastic computational approach for the study of the global spread of emergent infectious diseases which explicitly incorporates real world transportation networks and census data.

Nucleation and propagation of dislocations during nanopore lattice mending by laser annealing: Modified continuum-atomistic modeling

This paper investigates the atomic-level microscopic dynamic behavior of a solid-state nanopore lattice mending process by femtosecond laser annealing using a modified continuum-atomistic modeling approach. The nucleation and propagation of dislocation are also depicted via quantitative dislocation analyses. Three typical lattice mending phases, including (i) the incubation of dislocation nucleation, (ii) pressure-induced dislocation propagation and plastic deformation, and (iii) lattice recovery and reconstruction via thermal diffusion, are thoroughly characterized by the evolution of microscopic dislocation and the slope change of atomic mean-squared displacement curve. The results of the analyses indicate that the structural mending originated from the heterogeneous nucleation of dislocation from the pore surface. The laser-induced shock waves provide considerable mechanical work and, consequently, are transferred largely to become an equivalent applied stress on the activated glide planes. These pressure-induced multiple glides on a lattice near the pore rapidly and effectively enable the mending operations in solid-state structural transition processes. Subsequently, the relaxation of the compression stress leads to the target material that is rapidly swelled in the $z$ direction with an expansive strain rate of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The expansion dynamics and associated tension stress further induce drastic emissions of dislocation after the pore is completely mended. Moreover, it is also observed that the dislocation of sessile stair rods can act as a strong barrier to prevent further glide on slip planes, thus leading to a local strain-hardening effect. The simulation results presented in this paper provide comprehensive insights for a better understanding of the laser-induced solid-state nanopore mending process. The approach proposed here can also be modified and used to further investigate the mechanisms of laser-induced surface hardening with various advanced functional materials.

Minimizing the effects of unmeasured disturbances in an open-loop unstable chemical plant containing measurement dead times

The dynamic behavior of many processes is characterized by time delays due to measurement delays, which put strict limitations on the performance of the control system. In this paper a time-delay factorization strategy for the nonlinear model predictive control (NMPC) and state estimation of multiple-input multiple-output (MIMO), nonlinear, open-loop unstable processes having output-measurement delays, and subject to unmeasured disturbances is proposed. At first, the NMPC algorithm based on a nonlinear programming approach is presented. Then, on-line parameter-identification and state-estimation schemes are combined with the NMPC algorithm to maintain the process at a steady-state which is unstable for the open-loop system. Finally, the effectiveness of the proposed method is demonstrated via simulation on the control of a catalytic continuous stirred tank reactor (CSTR).

An adaptive model predictive control configuration for production–inventory systems

In this paper, an adaptive model predictive control (MPC) configuration is proposed for the identification and control of production–inventory systems. The time-varying dynamic behavior of the production process is approximated by an adaptive Finite Impulse Response (FIR) model. The well-known recursive least-squares (RLS) method is used for the online identification of the model coefficients. The adapted model along with a smoothed estimation of the future customer demand are used to predict inventory levels over the optimization horizon. The efficiency of the proposed scheme is evaluated regarding its capability to eliminate the inventory drift. The performance of the method with respect to the bullwhip effect is also considered and studied in the paper. Comparison with non-adaptive control approaches illustrates the advantages of the proposed method.

A Static Analysis for Beta-Binders

We introduce a Control Flow Analysis, that statically approximates the dynamic behaviour of processes, expressed in the Beta-Binders calculus. Our analysis of a system is able to describe the essential behaviour of each box, tracking all the possible bindings of variables and all the possible intra- e inter-boxes communications. The analysis offers a basis for establishing static checks of biological dynamic properties. We finally apply our analysis to an example, based on an abstract specification of the interaction between a virus and cells of the immune system.

Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation

In this paper, a continuous time recurrent neural network (CTRNN) is developed to be used in nonlinear model predictive control (NMPC) context. The neural network represented in a general nonlinear state-space form is used to predict the future dynamic behavior of the nonlinear process in real time. An efficient training algorithm for the proposed network is developed using automatic differentiation (AD) techniques. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve the online optimization problem in the predictive controller. The proposed neural network and the nonlinear predictive controller were tested on an evaporation case study. A good model fitting for the nonlinear plant is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The CTRNN trained is used as an internal model in a predictive controller and results in good performance under different operating conditions.

Optimization of a large scale industrial reactor by genetic algorithms

The present work aims to employ genetic algorithms (GAs) to optimize an industrial chemical process, characterized by being difficult to be optimized by conventional methods. The considered chemical process is the three phase catalytic slurry reactor in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol occurs. In order to describe the dynamic behavior of the multivariable process, a non-linear mathematical model is used. Due to the high dimensionality and non-linearity of the model, a rigorous one, the solution of the optimization problem through conventional algorithms does not always lead to convergence. This fact justifies the use of an evolutionary method, based on the GAs, to deal with this process. In this way, in order to optimize the process, the GA code is coupled with the rigorous model of the reactor. The aim of the optimization through GAs is the searching of the process inputs that maximizes the productivity of 2-methyl-cyclohexanol subject to the environmental constraint of conversion. Many simulations are conducted in order to find the maximization of the objective function without violating the constraint. The results show that the GAs are used successfully in the process optimization. The selection of the most important GA parameters making use of a factorial design approach by fractional factorial design is proposed. A factorial design approach by a central composite design is also proposed in order to determine the best values of the GA parameters that lead to the optimal solution of the optimization problem.

Integrated design and control for robust performance: Application to an MSMPR crystallizer

The interplay of different types of performance constraints in an integrated design and control problem is studied by means of a case study. This integrated problem is based on a recent method for robust process design [M. Mönnigmann, W. Marquardt, Normal vectors on manifolds of critical points for parametric robustness of equilibrium solutions of ODE systems, J. Nonlinear Sci. 12 (2002) 85–112; M. Mönnigmann, W. Marquardt, Steady state process optimization with guaranteed robust stability and feasibility, AIChE J. 49 (12) (2003) 3110–3126; M. Mönnigmann, W. Marquardt, Steady state process optimization with guaranteed robust stability and flexibility: application to HDA reaction section, Ind. Eng. Chem. Res. 44 (2005) 2737–2753; W. Marquardt, M. Mönnigmann, Constructive nonlinear dynamics in process systems engineering, Comput. Chem. Eng. 29 (2005) 1265–1275; M. Mönnigmann, Constructive nonlinear dynamics methods for the design of chemical engineering processes, Ph.D. Thesis, RWTH Aachen University, 2003]. The design is found by means of a steady-state optimization problem accounting for process economics and performance requirements. In particular, the latter are represented by constraints which guarantee a user-specified performance of the design in spite of parametric uncertainties. For the first time, two types of dynamic performance constraints are used simultaneously within the adopted framework. These are constraints on time-domain performance indicators as well as on the asymptotic dynamic process behavior. Furthermore, the effect of uncertainty in both, design and model parameters, is accounted for. A key strength of the suggested framework is the direct quantification of the trade-offs between economics and dynamic performance requirements for a selection of uncertainty scenarios. A series of different integrated design and control problems are formulated and solved for a continuous mixed-suspension mixed-product removal (MSMPR) crystallizer. The process exhibits a complex nonlinear behavior and represents a challenging example. The results of the case study allow an in depth understanding of the interactions of design and control for the underlying process.

Differential recurrent neural network based predictive control

In this paper an efficient algorithm to train general differential recurrent neural network (DRNN) is developed. The trained network can be directly used in the nonlinear model predictive control (NMPC) context. The neural network is represented in a general nonlinear state-space form and used to predict the future dynamic behavior of the nonlinear process in real time. In the new training algorithms, the ODEs of the model and the dynamic sensitivity are solved simultaneously using Taylor series expansion and automatic differentiation (AD) techniques. The same approach is also used to solve the online optimization problem in the predictive controller. The efficiency and effectiveness of the DRNN training algorithm and the NMPC approach are demonstrated through a two-CSTR case study. A good model fitting for the nonlinear plant at different sampling rates is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The DRNN based NMPC approach results in good control performance under different operating conditions.