Reliable Mathematical Model Research Articles

Hybrid modeling of inulinase bio‐production process

AbstractBACKGROUND: A potential application of inulinase in the food industry is the production of fructooligosaccharides (FOS) through transfructosilation of sucrose. Besides their ability to increase the shelf‐life and flavor of many products, FOS have many interesting functional properties. The use of an industrial medium may represent a good, cost‐effective alternative to produce inulinase, since the activity of the enzyme produced may be improved or at least remain the same compared with that obtained using a synthetic medium. Thus, inulinase production for use in FOS synthesis is of considerable scientific and technological appeal, as is the development of a reliable mathematical model of the process. This paper describes a hybrid neural network approach to model inulinase production in a batch bioreactor using agroindustrial residues as substrate. The hybrid modeling makes use of a series artificial neural network to estimate the kinetic parameters of the process and the mass balance as constitutive equations.RESULTS: The proposed model was shown to be capable of describing the complex behavior of inulinase production employing agroindustrial residues as substrate, so that the mathematical framework developed is a useful tool for simulation of this process.CONCLUSION: The hybrid neural network model developed was shown to be an interesting alternative to estimate model parameters since complete elucidation of the phenomena and mechanisms involved in the fermentation is not required owing to the black‐box nature of the ANN used as parameter estimator. Copyright © 2010 Society of Chemical Industry

Modeling of the anaerobic digestion of sewage sludge: Evaluation of several reactor configurations

Sewage sludge is usually degraded by means of anaerobic digestion in order to produce biogas and stabilized sludge. Several reactor configurations have been implemented or studied intending to optimize the process; however, there is a lack of reliable mathematical models that can be used for this purpose. This paper deals with that issue by using a simplified model for the anaerobic treatment of sewage sludge. The performance of a conventional continuous digester was compared with a plug-flow reactor and the influence of the recycle ratio, a two-phase system and the reactor size effect and the influence of the temperature in a thermophilic-mesophilic operation were evaluated.

Desidratação osmótica de frutículos de jaca (Artocarpus integrifólia L.): aplicação de modelos matemáticos

Osmotic dehydration has been suggested as an important unitary operation in the processing of perishable fruit into new products with greater shelf live and aggregate value. The application of reliable mathematical models makes it possible to predict the behavior of several phenomena that occur in the process, enabling the reduction of operational cost as well. The objective of this paper was to study the application of mathematical models to water loss, solid gain, pH and titratable acidity (TA) variables during osmotic dehydration of jackfruit in sucrose solution at 64°brix and at different concentrations of sucrose and different solution temperatures (40, 50, 60 and 70°C), for 2,880 minutes. The exponential decay model 2 was better adjusted to water loss experimental data, with the determination coefficient ranging from 76.73% to 97.16%, whereas for the variables total soluble solids (TSS) and TA, the logistic model was better adjusted to the experimental data, obtaining a variation from 80.5 to 98.2% and from 89.5 to 99.4%. For pH, the exponential decay model 1 obtained a good adjustment to the experimental data, with determination coefficients ranging from 80.5 to 98.2%.

An overview of the mathematical modelling of liquid membrane separation processes in hollow fibre contactors

AbstractLiquid membranes have traditionally been employed for liquid/liquid mass transfer and have found applications in industrial, biomedical and analytical fields as well as in hydrometallurgical processes, wastewater treatment and remediation of polluted groundwater. However, in spite of the known advantages of liquid membranes, there are few examples of industrial application. The development of reliable mathematical models and design parameters (mass transport coefficients and equilibrium or kinetic parameters associated with the interfacial reactions) is a necessary step for design, cost estimation, process optimisation and scale‐up. This work reports an overview of the different approaches that have been proposed in the literature to the mathematical modelling of liquid membrane separation processes in hollow fibre contactors providing, at the same time, a useful guideline to characterise the mass transport phenomena and a tool for the optimal design and intensification of separation processes. Copyright © 2009 Society of Chemical Industry

Dynamic Modeling and Identification of an Axial Flow Ventricular Assist Device

An accurate characterization of the hemodynamic behavior of ventricular assist devices (VADs) is of paramount importance for proper modeling of the heart-pump interaction and the validation of control strategies. This paper describes an advanced test bench, which is able to generate complex hydraulic loads, and a procedure to characterize rotary blood pump performance in a pulsatile environment. Special focus was laid on model parameter identifiability in the frequency domain and the correlation between dynamic and steady-state models. Twelve combinations of different flow/head/speed signals, which covered the clinical VAD working conditions, were generated for the pump characterization. Root mean square error (RMSE) between predicted and measured flow was used to evaluate the VAD model. The found parameters were then validated with broadband random signals. In the experiments the optimization process always successfully converged. Even in the most demanding dynamic conditions the RMSE was 7.4 ml/sec and the absolute error never exceeded 24.9 ml/sec. Validity ranges for the identified VAD model were: flow 0-180 ml/sec; head 0-120 mmHg; speed 7.5-12.5 krpm. In conclusion, a universal test bench and a characterization procedure to describe the hydrodynamic properties of rotary blood pumps were established. For a particular pump, a reliable mathematical model was identified that correctly reproduced the relationship between instantaneous VAD flow, head and impeller speed.

Experimental Uncertainties in Volumetric Methods for Measuring Equilibrium Adsorption

Knowledge of adsorption equilibrium is essential in many industrial processes, including increasingly important technologies such as fuel cells and CO2 sequestration. Developing reliable mathematical models for adsorption requires accurate experimental data. Experimental methods based on volumetric, gravimetric, and chromatographic techniques have all been used to obtain such data. Currently, two volumetric methods are widely used to measure supercritical gas adsorption on heterogeneous matrices such as activated carbon and coal. These two methods differ in the manner in which the gas is injected into the equilibrium cell for adsorption. The methods are referred to as “fixed-pressure” and “fixed-volume.” In this paper, we discuss the details of these experimental designs and error analyses for these two volumetric techniques. Case studies involving pure-fluid adsorption measurements are used to demonstrate both the efficacy and pitfalls of these volumetric methods. Further, case studies are also used to highlight differences in the uncertainties associated with calculation of excess adsorption from the experimentally measured quantities. The results indicate that the fixed-volume method is susceptible to larger experimental errors than the fixed-pressure method for equivalent experimental setups. Specifically, for the case study reported here, the average experimental uncertainties in the amount adsorbed for the fixed-pressure and fixed-volume method were 12% and 42%, respectively. These large experimental uncertainties for the fixed-volume method at the higher pressures result mainly from the uncertainty in the amount injected. Further, Monte Carlo analysis was used to validate these findings, yielding comparable results, thus providing confirmation of the analytical expressions used in the error analysis. Our analysis indicates a significant reduction in expected uncertainties of the fixed-volume injection method may be realized by utilizing an optimized ratio of cell volumes (reference and sample cells) and by having the least possible void fraction in the sample cell.

Phenolic and antioxidant composition of by-products from the cider industry: Apple pomace

Abstract Eleven different cider apple pomaces (six single-cultivar and five from the cider-making industry) have been analysed for low molecular phenolic profiles and antioxidant capacity. The Folin index ranged between 2.3 and 15.1 g gallic acid per kg of dry matter. Major phenols were flavanols, dihydrochalcones (phloridzin and phloretin-2′-xyloglucoside), flavonols and cinnamic acids (chlorogenic and caffeic acids). The group of single-cultivar pomaces had higher contents of chlorogenic acid, (-)-epicatechin, procyanidin B2 and dihydrochalcones, whereas the industrial samples presented higher amounts of up to four unknown compounds, with absorption maxima between 256 and 284 nm. The antioxidant capacity of apple pomace, as determined by the DPPH and FRAP assays, was between 4.4 and 16.0 g ascorbic acid per kg of dry matter, thus confirming that apple pomace is a valuable source of antioxidants. PLSR analysis gave reliable mathematical models which allowed to predict the antioxidant activity of apple pomace as a function of the phenolic profile. The variables with the higher modelling power were phloridzin > procyanidin B2 > rutin + isoquercitrin > protocatechuic acid > hyperin.

Modeling of an Industrial Vibrating Double-Deck Screen of a Urea Granulation Circuit

A reliable mathematical model to predict the performance of double-deck screens from an industrial urea granulation circuit is provided in this work. The classification in each deck was described by the empirical model reported by Karra [Karra, V. K. Development of a Model for Predicting the Screening Performance of a Vibrating Screen. CIM Bull. 1979, 72, 804.] for the mining industry. The estimation of model parameters was based on industrial data collected from two large-scale double-deck screens belonging to a urea granulation plant. Prior to parameter fitting, data reconciliation of the solid streams was performed, with the aim of determining the unmeasured mass flows and the reconciled particle size distributions that fulfill the material balances for every size class. The results indicate that the fitted model reproduces in an accurate way the performance of the urea granules classification device. Thus, the screen mathematical representation can be used as a module of a plant simulator for many existing urea granulation circuits, which (independently of the technology) have similar industrial vibrating double-deck screens to attain the marketable product granulometry. In addition, the fitted model allows finding the optimal screen apertures to achieve the desired product attributes and recycle ratios.

ADSORPTION CHARACTERISTICS OF CROCIN IN THE EXTRACT OF GARDENIA FRUITS (GARDENIA JASMINOIDES ELLIS) ON MACROPOROUS RESINS

ABSTRACT To study resin adsorptions and investigate the differences between processes in crude extracts and microfiltrates, the adsorption characteristics of crocin in the extract of Gardenia jasminoides Ellis on 10 macroporous styrene‐divinylbenzene (SDVB) resins were investigated. Ground gardenia fruit was extracted with water and the crude extract was partially purified by microfiltration. The crude extract and microfiltrate were mixed with the 10 resins until the adsorption of crocin reached equilibrium on resins. The adsorption followed the pseudo‐second‐order kinetics closely, but the data also fitted the first‐order and intraparticle diffusion models. Furthermore, the Freundlich isotherm was found suitable for describing the equilibrate adsorption data. XAD‐1180, HP20, HPD‐100A and AB‐8 stood out as the best performing resins in terms of their adsorptive capacities and selectivities for crocin. The thermodynamics of the adsorption process was shown to be spontaneous and exothermal in nature, and controlled by physical rather than chemical mechanisms. Adsorption with SDVB resins in conjunction with microfiltration was found to be an efficient process for the purification of crocin in gardenia extract.PRACTICAL APPLICATIONSMacroporous resins have been industrially applied in the recovery and purification of some products from plant extracts. However, there is a lack of understanding of the adsorption process and many of the applications are based on empirical data rather than on predicable models. Therefore, the development of reliable mathematical models that can accurately describe and predicate experimental data of adsorption would be extremely helpful in understanding the adsorption process as well as optimizing the design of adsorption systems.

Beating to time: calcium clocks, voltage clocks, and cardiac pacemaker activity

the heartbeat arises in the sinoatrial node (SAN) and then spreads throughout the heart. SAN function is therefore essential for normal cardiac physiology. The function of the SAN decreases with age, and this has been correlated with changes of ion channel expression ([12][1]). It is therefore of

Quality of seamless hot-rolled pipe, taking account of mandrel oscillations

In the piercing and rolling of pipe, dynamic loads of considerable magnitude arise in the rod that retains the mandrel. These loads, which vary over time, are associated with fluctuation in rod shape over the rolling axis. The considerable forces associated with rod oscillation impair pipe quality. To improve pipe quality with intensification of the technological process, the design of the piercing and rolling mills of the pipe-rolling system must be modified. It is important to establish the qualitative and quantitative influence of the technological parameters on the behavior of the rod system and the pipe quality. In order to provide a basis for modernization of the mills and improvement in the production technology, we need a reliable mathematical model. In the present work, we consider the rod system of the mandrel-retention mechanism in the piercing and rolling mills, taking account of the aspects of the technology and the dynamic parameters of the system that differ from those in [1] (Fig. 1). The oscillation of the rod system is transmitted to the mandrel, impairing pipe quality. The dynamic processes are considerably complicated by variation in the contact mass of the blank as it moves along the rod during piercing or rolling. Dynamic analysis calls for a mathematical model of the mill in the pipe-rolling system. By studying the dynamic behavior of the rod system, we may evaluate the dynamic state of the system together with the mandrel during piercing or rolling. The proposed dynamic model of the rod system takes the form of a rod of constant cross section with hinged supports at the ends and with elastic supports (centering units) between them. This model adequately reflects the processes in the initial system. The rod, rotating at speed ω around the rolling axis x , is subject to the action of longitudinal force ( t ). At constant rolling speed , the rod is subject to the distributed load of the rolled pipe, characterized by inten

Model-based fault diagnosis of induction motor eccentricity using particle swarm optimization

Much research works address model-free or signal processing and spectral analysis-based fault detection schemes for rotor eccentricity fault in induction motors. Nevertheless, despite existing reliable fault-embedded eccentricity mathematical models such as the winding function method an integrated model-based fault detection algorithm for detecting this fault yet has not been fully explored. This article presents model-based mixed-eccentricity fault detection and diagnosis for induction motors. The proposed algorithm can successfully detect faults and their severity using stator currents. To determine the values of the fault-related parameters, an adaptive synchronization-based parameter estimation algorithm is introduced using particle swarm optimization. Simulation and experiments demonstrate the ability of the algorithm to detect and diagnose these faults. The proposed algorithm can be employed to estimate the parameters, in addition to slowly time varying and abruptly changing parameters.

A kinetic study of the depolymerisation of poly(ethylene terephthalate) by phase transfer catalysed alkaline hydrolysis

AbstractBACKGROUND: Chemical or tertiary recycling of waste polymers including PET, poly(ethylene terephthalate), leads to the formation of raw starting monomers by different depolymerisation routes. This work was focused on the identification of the catalytic behaviour, if any, of a series of quaternary phosphonium and ammonium salts as phase transfer catalysts for the alkaline hydrolysis of PET, and on the determination of the kinetics of the phase transfer catalysed process.RESULTS: Among the salts examined tributylhexadecylphosphonium bromide was found to be the most effective catalyst. The proposed kinetic model accounted for the uncatalysed and catalysed reactions and predicted a linear correlation for the reaction rate with the concentration of the quaternary salt. The notable increase in the phase transfer catalysed reaction rate was related mainly to the greater value of the pre‐exponential factor while the value of the activation energy was hardly modified by the presence of the quaternary phosphonium salt, thereby suggesting a similar mechanism for the alkaline hydrolysis with or without phase transfer catalyst.CONCLUSIONS: The use of selected phosphonium quaternary salts exhibited a remarkably positive effect on the experimental conditions under which the depolymerisation of poly(ethylene terephthalate) by alkaline hydrolysis can be carried out, especially in terms of low operating temperature. Kinetic correlations provided a reliable mathematical reaction model for this recycling process, which is in agreement with the principles of sustainable development. Copyright © 2008 Society of Chemical Industry

The influence of mesoscale porosity on cortical bone anisotropy. Investigations via asymptotic homogenization

Recently, the mesoscale of cortical bone has been given particular attention in association with novel experimental techniques such as nanoindentation, micro-computed X-ray tomography and quantitative scanning acoustic microscopy (SAM). A need has emerged for reliable mathematical models to interpret the related microscopic and mesoscopic data in terms of effective elastic properties. In this work, a new model of cortical bone elasticity is developed and used to assess the influence of mesoscale porosity on the induced anisotropy of the material. Only the largest pores (Haversian canals and resorption cavities), characteristic of the mesoscale, are considered. The input parameters of the model are derived from typical mesoscale experimental data (e.g. SAM data). We use the method of asymptotic homogenization to determine the local effective elastic properties by modelling the propagation of low-frequency elastic waves through an idealized material that models the local mesostructure. We use a novel solution of the cell problem developed by Parnell & Abrahams. This solution is stable for the physiological range of variation of mesoscopic porosity and elasticity found in bone. Results are computed efficiently (in seconds) and the solutions can be implemented easily by other workers. Parametric studies are performed in order to assess the influence of mesoscopic porosity, the assumptions regarding the material inside the mesoscale pores (drained or undrained bone) and the shape of pores. Results are shown to be in good qualitative agreement with existing schemes and we describe the potential of the scheme for future use in modelling more complex microstructures for cortical bone. In particular, the scheme is shown to be a useful tool with which to predict the qualitative changes in anisotropy due to variations in the structure at the mesoscale.

Real-time control of a magnetic levitation device based on instantaneous modeling of magnetic field

This paper presents an approximation method to simplify the magnetic field calculation for real-time control in a magnetic levitation device. Conventional field modeling methods generally involve the numerical solution of highly nonlinear differential equations of the field. The solution of these equations will take enormous computational time and disqualifies these methods for real-time control applications. In this paper, a fast and reliable mathematical model, called pivot point, is developed for the prediction of the magnetic field distribution and verified experimentally. This model is developed based on the geometry of a magnetic stator and its magnetization pattern. The model is then used in a magnetic levitation experiment to prove its real-time capabilities in position control operations. Experiments showed that application of the pivot point method improved the positioning accuracy of the levitation system in step response and trajectory tracking and reduced the settling time.

Prediction of antifreeze critical strength of infant age concrete

The rule of infant age concrete strength development under low temperature and complex affecting factors is researched. An efficient and reliable mathematical forecast model is set up to predict the infant age concrete antifreeze critical strength under low temperature at construction site. On the basis of the revision of concrete equivalent coefficient under complex influencing factors, least-squares curve-fitting method is applied to approximate the concrete strength under standard curing and the forecast formula of concrete compressive strength could be obtained under natural temperature condition by various effects. When the amounts of double-doped are 10% fly ashes and 4% silica fumes as cement replacement, the antifreeze critical strength changes form 3.5–4.1MPa under different low temperature curing. The equivalent coefficient correction formula of concrete under low temperature affected by various factors could be obtained. The obtained equivalent coefficient is suitable for calculating the strength which is between 10% to 40% of standard strength and the curing temperature from 5–20 °C. The forecast value of concrete antifreeze critical strength under low temperature could be achieved by combining the concrete antifreeze critical strength value with the compressive strength forecast of infant age concrete under low temperature. Then the theory for construction quality control under low temperature is provided.

High-resolution monitoring of biogeochemical gradients in a tar oil-contaminated aquifer

The detailed understanding of in situ biodegradation of petroleum hydrocarbons in porous aquifers requires knowledge on biogeochemical gradients, the distribution of individual redox species and microorganisms. The generally limited spatial resolution of conventional monitoring wells, however, hampers appropriate characterization of small-scale gradients and thus localization of the relevant processes. Groundwater sampling across a BTEX plume in a sandy aquifer by means of a novel high-resolution multi-level well (HR-MLW) is presented here. The presence of distinct and steep biogeochemical gradients is demonstrated in the centimeter and decimeter scale, which could not be resolved with a conventional multi-level well. The thin BTEX plume with a vertical extension of only 80 cm exhibited a decline of contaminant concentrations by two orders of magnitude within a few centimeters in the upper and lower fringe zone. The small-scale distribution of sulfate, sulfide and Fe(II) in relation to the contaminants and elevated δ34S and δ18O values of groundwater sulfate strongly indicated sulfate and iron reduction to be the dominant redox processes involved in biodegradation. High microbial activities and biomass especially at the plume fringes and the slope of chemical gradients supported the concept that the latter are regulated by microbial processes and transverse dispersion, i.e. vertical mixing of electron donors and acceptors. Transverse dispersion therefore was suggested to be a driving factor controlling biodegradation in porous aquifers, but not exclusively limiting natural attenuation processes at this site. Broad overlapping zones of electron donors and electron acceptors point towards additional factors limiting anaerobic biodegradation in situ. The identification of small-scale gradients substantially contributed to a better understanding of biodegradation processes and hence is a prerequisite for the development of reliable predictive mathematical models and future remediation strategies.

Reliability of Conventional Settlement Evaluation for Circular Foundations on Stone Columns

The unit cell idealization has been long adopted in the settlement prediction of stone column-reinforced soils. This paper tests the accuracy of this modeling concept against trusted settlement values of engineering foundations. It is believed that in order to bestow the outcome of this study adequate generality different soil properties and foundation geometries need to be considered. It was, nevertheless, found impracticable to collect field settlement records for all the analyzed cases. The authors, therefore, appealed to the back analysis concept to construct a reliable mathematical model, calibrated against settlement records of full-scale field load test. This model, which is capable of reproducing the real field settlements, is then employed as a generic tool to obtain trusted settlement values for a variety of cases with essential geometrical similarity. The investigation revealed that the unit cell analysis may, in some cases, lead to erroneous estimation for the settlements of foundations with limited extents. Correction factors, dependent on the treated soil properties as well as the foundation size, are introduced.

다층신경망을 이용한 전단모드 회전형 MR 댐퍼의 모델링

자기변성유체(magnetorheological fluid)에 관한 연구는 MR 장치의 개발, MR 장치의 수학적 모델링 및 시뮬레이션, 그리고 MR 장치를 채용한 시스템의 제어 알고리즘 개발에 관한 연구로 구분된다. 시뮬레이션을 통한 제어 알고리즘 개발을 위해서는 MR 장치의 비선형 응답을 예상하기 위한 신뢰성 높은 수학적 모델이 요구된다. 또한 MR 장치 시스템을 제어하기 위해서는 제어기에서 요구하는 댐핑력을 출력하기 위한 MR 장치의 전류(또는 전압) 입력 값이 필요하며, 이 입력값을 얻기 위해서는 역댐퍼 모델이 필요하다. 이러한 이유로 MR 장치의 모델링 및 역댐퍼 모델링은 MR 장치개발의 중요한 역할을 담당하며 이에 관한 많은 연구가 요구되고 있다. 본 연구에서는 전단모드 회전형 MR 댐퍼의 모델링을 위해 개발된 MR 댐퍼를 이용하여 동특성 시험기를 제작하였으며, 전단모드 회전형 MR 댐퍼의 특성을 연구하기 위한 실험을 수행하였다. 시험기 시험결과를 통해 모델링에 필요한 시험 데이터들을 획득하였으며 다층신경망을 이용하여 전단모드 회전형 MR 댐퍼의 모델 및 역모델을 구하였다. Scientific challenges in the field of MR(magnetorheological) fluids and devices consist in the development of MR devices, the mathematical modeling and simulation of MR devices, and the development of (optimal) control algorithm for MR device systems. To take a maximum advantage of MR fluids in control applications a reliable mathematical model, which predicts their nonlinear characteristics, is needed. A inverse model of the MR device is required to calculate current(or voltage) input of MR damper, which generates required damping force. In this paper, we implemented test a bench for shear mode rotary MR damper and laboratory tests were performed to study the characteristics of the prototype shear-mode rotary MR damper. The direct identification and inverse dynamics modeling for shear mode rotary MR dampers using multi-layer neural networks are studied.

Impacts of climate extremes on activity sectors – stakeholders’ perspective

Significant changes in the climatic system have been observed, which may be attributed to human-enhanced greenhouse effect. Even stronger changes are projected for the future, impacting in an increasing way on human activity sectors. The present contribution, prepared in the framework of the MICE (Modelling the Impact of Climate Extremes) Project of the European Union, reviews how climate change may impact on winter tourism in the Alpine region, intense precipitation and flood potential in central Europe, forest damage in Scandinavia and beach holidays in the Mediterranean coast. Impacts are likely to be serious and largely adverse. Due to a lack of adequate information and lack of broadly accepted and reliable mathematical models describing the impact of changes in climate extremes on these activity sectors, it has been found useful to use expert judgement based impact assessment. Accordingly, regional mini-workshops were organized serving as platforms for communication between scientists and stakeholders, vehicles for dissemination of the state-of-the-art of the scientific understanding and for learning stakeholders' view on extreme events, their impacts and the preparedness system. Stakeholders had the opportunity to react to the scientific results and to reflect on their perception of the likely impacts of projected changes in extremes on relevant activity sectors and the potential to adapt and avert adverse consequences. The results reported in this paper present the stakeholders' suggestions for essential information on different extreme event impacts and their needs from science.