Search results for: semi-parametric group-based modeling

Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: dynamic system modeling, neural network, normal equation, second order gradient descent

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Authors: Amin Eslami, Jafar Bolouri Bazaz

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Under active stress conditions, a rigid cantilever retaining wall tends to rotate about a pivot point located within the embedded depth of the wall. For purely granular and cohesive soils, a methodology was previously reported called minimization of moment ratio to determine the location of the pivot point of rotation. The usage of this new methodology is to estimate the rotational stability safety factor. Moreover, the degree of improvement required in a backfill to get a desired safety factor can be estimated by the concept of the shear strength demand. In this article, the accuracy of this method for another type of cantilever walls called Contiguous Bored Pile (CBP) retaining wall is evaluated by using physical modeling technique. Based on observations, the results of moment ratio minimization method are in good agreement with the results of the carried out physical modeling.

Keywords: cantilever retaining wall, physical modeling, minimization of moment ratio method, pivot point

Procedia PDF Downloads 331

Authors: Z. Hormozi Moghaddam, M. Mokhtari-Dizaji, M. Movahedin, M. E. Ravari

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Mechanical index (MI) is used for quantifying acoustic cavitation and the relationship between acoustic pressure and the frequency. In this study, modeling of the MI was applied to provide treatment protocol and to understand the effective physical processes on reproducibility of stem cells. The acoustic pressure and MI equations are modeled and solved to estimate optimal MI for 28, 40, 150 kHz and 1 MHz frequencies. Radial and axial acoustic pressure distribution was extracted. To validate the results of the modeling, the acoustic pressure in the water and near field depth was measured by a piston hydrophone. Results of modeling and experiments show that the model is consistent well to experimental results with 0.91 and 0.90 correlation of coefficient (p<0.05) for 1 MHz and 40 kHz. Low intensity ultrasound with 0.40 MI is more effective on the proliferation rate of the spermatogonial stem cells during the seven days of culture, in contrast, high MI has a harmful effect on the spermatogonial stem cells. This model provides proper treatment planning in vitro and in vivo by estimating the cavitation phenomenon.

Keywords: ultrasound, mechanical index, modeling, stem cell

Procedia PDF Downloads 334

Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

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Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: monomial forms, rectangular surfaces, CAGD curves, monomial matrix applications

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Authors: Melih Cattik

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The present study investigate effectiveness of video modeling procedures on request an item behavior of children with ASD. Two male and a female children with ASD participated in the study. A multiple baseline across participant single-subject design was used to evaluate the effects of the video modeling procedures on request an item behavior. During baseline, no prompts were presented to participants. In the intervention phase, the teacher gave video model to the participant and than created opportunity for request an item to him/her. When the first participant reached to criterion, the second participant began intervention. This procedure continued till all participants completed intervention. Finally, all three participants learned to request an item behavior. Based upon findings of this study, it will make suggestions to future researches.

Keywords: autism spectrum disorders, video modeling procedures, request an item behavior, single subject design

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Authors: Rafayel Azizyan, Valeri Arakelyan, Aram Gevorgyan, Varduhi Balayan, Emil Gevorgyan

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Currently, mathematical and computer modeling are widely used in different biological studies to predict or assess behavior of such complex systems as biological ones. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions, which play an important role in different biochemical pathways. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions in the presence of uncompetitive inhibitors, as well as to describe in details the inhibition effects. Four models of uncompetitive inhibition were designed using different software packages. Particularly, uncompetitive inhibitor to the first [ES1] and the second ([ES1S2]; [FS2]) enzyme-substrate complexes have been studied. The simulation, using the same kinetic parameters for all models allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of uncompetitive inhibition. Besides that shown, that uncompetitive inhibitors exhibit specific selectivity depending on mechanism of bi-substrate enzymatic reaction.

Keywords: mathematical modeling, bi-substrate enzymatic reactions, reversible inhibition

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Authors: Rushiraj Heshi, Smriti Bhandari

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Master Data Management requires creation of Central repository, applying constraints on Repository and designing processes to manage data. Designing of Repository, constraints on repository and business processes is very tedious and time consuming task for large Enterprise. Hence Visual Repository, constraints and Process (Workflow) modeling is the most critical step in Master Data Management.In this paper, we realize a Visual Modeling tool for implementing Repositories, Constraints and Processes based on Eclipse Plugin using GMF/EMF which follows principles of Model Driven Engineering (MDE).

Keywords: EMF, GMF, GEF, repository, constraint, process

Procedia PDF Downloads 497

Authors: J. Fernandez de Canete, P. Del Saz Orozco, I. Garcia-Moral, A. Akhrymenka

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Object-oriented modeling is spreading in current simulation of wastewater treatments plants through the use of the individual components of the process and its relations to define the underlying dynamic equations. In this paper, we describe the use of the free-software OpenModelica simulation environment for the object-oriented modeling of an activated sludge process under feedback control. The performance of the controlled system was analyzed both under normal conditions and in the presence of disturbances. The object-oriented described approach represents a valuable tool in teaching provides a practical insight in wastewater process control field.

Keywords: object-oriented programming, activated sludge process, OpenModelica, feedback control

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Authors: Erzen Muharemi, Emmanuel De Jaeger, Jos Knockaert

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The work presented here investigates the modeling of power electronics converters in terms of their harmonic production. Specifically, it addresses high-frequency emissions in the range of 2-150 kHz, referred to as supraharmonics. This paper models a conventional converter, namely the boost converter used as an active power factor corrector (APFC). Furthermore, the modeling is extended to the case of the interleaved boost converter, which offers advantages such as halving the emissions. Finally, a comparison between the theoretical, numerical, and experimental results will be provided.

Keywords: APFC, boost converter, converter modeling, double fourier series, supraharmonics

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Authors: Bothinah Altaf, Gary Montague, Elaine B. Martin

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This study involves the modeling and monitoring of an ammonia synthesis fixed-bed reactor using partial least squares (PLS) and its variants. The process exhibits complex dynamic behavior due to the presence of heat recycling and feed quench. One limitation of static PLS model in this situation is that it does not take account of the process dynamics and hence dynamic PLS was used. Although it showed, superior performance to static PLS in terms of prediction, the monitoring scheme was inappropriate hence adaptive PLS was considered. A limitation of adaptive PLS is that non-conforming observations also contribute to the model, therefore, a new adaptive approach was developed, robust adaptive dynamic PLS. This approach updates a dynamic PLS model and is robust to non-representative data. The developed methodology showed a clear improvement over existing approaches in terms of the modeling of the reactor and the detection of faults.

Keywords: ammonia synthesis fixed-bed reactor, dynamic partial least squares modeling, recursive partial least squares, robust modeling

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Authors: Yousef Abu Nahleh, Arun Kumar, Fugen Daver, Reham Al-Hindawi

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Despite the availability of natural disaster related time series data for last 110 years, there is no forecasting tool available to humanitarian relief organizations to determine forecasts for emergency logistics planning. This study develops a forecasting tool based on identifying probability of disaster for each country in the world by using decision tree modeling. Further, the determination of aggregate forecasts leads to efficient pre-disaster planning. Based on the research findings, the relief agencies can optimize the various resources allocation in emergency logistics planning.

Keywords: decision tree modeling, forecasting, humanitarian relief, emergency supply chain

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Authors: Jamil Khalil Izraqi

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This paper investigates the transition of a 1970 Volkswagen Beetle from an internal combustion engine (ICE) to an EV using Matlab/Simulink modeling and simulation. The performance of the EV drivetrain system was simulated under various operating conditions, including standard and custom driving cycles in Turkey and Jordan (Amman), respectively. The results of this paper indicate that the transition is viable and that modeling and simulation can help in understanding the performance and efficiency of the electric drivetrain system, including battery pack, power electronics, and brushless direct current (BLDC) Motor.

Keywords: BLDC, buck-boost, inverter, SOC, drive-cycle

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Authors: Jiaqi Yan, Yani Shi

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The blockchain technology is regarded as the most promising technology that has the potential to trigger a technological revolution. However, besides the bitcoin industry, we have not yet seen a large-scale application of blockchain in those domains that are supposed to be impacted, such as supply chain, financial network, and intelligent manufacturing. The reasons not only lie in the difficulties of blockchain implementation, but are also root in the challenges of blockchain-oriented information systems design. As the blockchain members are self-interest actors that belong to organizations with different existing information systems. As they expect different information inputs and outputs of the blockchain application, a common language protocol is needed to facilitate communications between blockchain members. Second, considering the decentralization of blockchain organization, there is not any central authority to organize and coordinate the business processes. Thus, the information systems built on blockchain should support more adaptive business process. This paper aims to address these difficulties by providing a modeling approach for blockchain-oriented information systems design. We will investigate the information structure of distributed-ledger data with conceptual modeling techniques and ontology theories, and build an effective ontology mapping method for the inter-organization information flow and blockchain information records. Further, we will study the distributed-ledger-ontology based business process modeling to support adaptive enterprise on blockchain.

Keywords: blockchain, ontology, information systems modeling, business process

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Authors: K. D. Sharma, M. Parida, S. S. Jain, Anju Saini, V. K. Katiyar

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Air quality models form one of the most important components of an urban air quality management plan. Various statistical modeling techniques (regression, multiple regression and time series analysis) have been used to predict air pollution concentrations in the urban environment. These models calculate pollution concentrations due to observed traffic, meteorological and pollution data after an appropriate relationship has been obtained empirically between these parameters. Artificial neural network (ANN) is increasingly used as an alternative tool for modeling the pollutants from vehicular traffic particularly in urban areas. In the present paper, an attempt has been made to model traffic air pollution, specifically CO concentration using neural networks. In case of CO concentration, two scenarios were considered. First, with only classified traffic volume input and the second with both classified traffic volume and meteorological variables. The results showed that CO concentration can be predicted with good accuracy using artificial neural network (ANN).

Keywords: air quality management, artificial neural network, meteorological variables, statistical modeling

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Authors: Reza Yadollahi, Arash Hejazi, Dante Savasta

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Building Information Modeling (BIM) is growing so fast in construction projects around the world. Considering BIM's weaknesses in implementing existing heritage and historical buildings, it is critical to facilitate BIM application for such structures. One of the pieces of information to build a model in BIM is to import material and its characteristics. Material library is essential to speed up the entry of project information. To save time and prevent cost overrun, a BIM object material library should be provided. However, historical buildings' lack of information and documents is typically a challenge in renovation and retrofitting projects. Due to the lack of case documents for historic buildings, importing data is a time-consuming task, which can be improved by creating BIM libraries. Based on previous research, this paper reviews the complexities and challenges in BIM modeling for heritage, historic, and architectural buildings. Through identifying the strengths and weaknesses of the standard BIM systems, recommendations are provided to enhance the modeling platform.

Keywords: building Information modeling, historic, heritage buildings, material library

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Authors: Oumaima Lahmar

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This paper aims to define a structured topography for finance researchers seeking to navigate the body of knowledge in their extrapolation of finance phenomena. To make sense of the body of knowledge in finance, a probabilistic topic modeling approach is applied on 6000 abstracts of academic articles published in three top journals in finance between 1976 and 2020. This approach combines both machine learning techniques and natural language processing to statistically identify the conjunctions between research articles and their shared topics described each by relevant keywords. The topic modeling analysis reveals 35 coherent topics that can well depict finance literature and provide a comprehensive structure for the ongoing research themes. Comparing the extracted topics to the Journal of Economic Literature (JEL) classification system, a significant similarity was highlighted between the characterizing keywords. On the other hand, we identify other topics that do not match the JEL classification despite being relevant in the finance literature.

Keywords: finance literature, textual analysis, topic modeling, perplexity

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: M. Bassoui, M. Ferfra, M. Chrayagne

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This paper presents a qualitative modeling for the nonlinear B-H curve of the saturable magnetic materials for a transformer with shunts used in the power supply for the magnetron. This power supply is composed of a single phase leakage flux transformer supplying a cell composed of a capacitor and a diode, which double the voltage and stabilize the current, and a single magnetron at the output of the cell. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve.

Keywords: B(H) curve, fuzzy clustering, magnetron, power supply

Procedia PDF Downloads 236

Authors: M. Kiran Reddy, K. Sreenivasa Rao

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The conventional Hidden Markov Model (HMM)-based speech synthesis system (HTS) uses only a pulse excitation model, which significantly differs from natural excitation signal. Hence, buzziness can be perceived in the speech generated using HTS. This paper proposes an efficient excitation modeling method that can significantly reduce the buzziness, and improve the quality of HMM-based speech synthesis. The proposed approach models the pitch-synchronous residual frames extracted from the residual excitation signal. Each pitch synchronous residual frame is parameterized using 30 wavelet coefficients. These 30 wavelet coefficients are found to accurately capture the perceptually important information present in the residual waveform. In synthesis phase, the residual frames are reconstructed from the generated wavelet coefficients and are pitch-synchronously overlap-added to generate the excitation signal. The proposed excitation modeling method is integrated into HMM-based speech synthesis system. Evaluation results indicate that the speech synthesized by the proposed excitation model is significantly better than the speech generated using state-of-the-art excitation modeling methods.

Keywords: excitation modeling, hidden Markov models, pitch-synchronous frames, speech synthesis, wavelet coefficients

Procedia PDF Downloads 248

Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Gionata Carmignani, Mario G. C. A. Cimino, Franco Failli

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Business Processes (BPs) are the key instrument to understand how companies operate at an organizational level, taking an as-is view of the workflow, and how to address their issues by identifying a to-be model. In last year’s, the BP Model and Notation (BPMN) has become a de-facto standard for modeling processes. However, this standard does not incorporate explicitly the Problem-Solving (PS) knowledge in the Process Modeling (PM) results. Thus, such knowledge cannot be shared or reused. To narrow this gap is today a challenging research area. In this paper we present a framework able to capture the PS knowledge and to improve a workflow. This framework extends the BPMN specification by incorporating new general-purpose elements. A pilot scenario is also presented and discussed.

Keywords: business process management, BPMN, problem solving, process mapping

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Authors: Gary Miller, Andriy Didenko, David Allison

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The boundary of a region in the plane shrinks according to its curvature. A simple algorithm based upon this motion by curvature performed by a spreadsheet simulates the evaporation/dissipation behavior of oil spill boundaries.

Keywords: mathematical modeling, oil, evaporation, dissipation, boundary

Procedia PDF Downloads 510

Authors: Pierce Radecki, Pulkit Malik, Bharath Ramaswamy, Ben Shapiro

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The ability to effectively design and test magnetic nanoparticles for controlled movement has been an elusive goal in the design of these particles. Magnetic nanoparticles of various characteristics have been created for use towards therapeutic effects, however the challenge of designing for controlled movement remains unmet. A step towards design in this aspect is a first principles model that captures and predicts the behaviors of particles in a magnetic field. The model is governed by four forces acting on the particles, the magnetic gradient, the dipole-dipole forces, the steric forces, and the viscous drag force. The particles are multi-core or single core, and incorporate a preferred magnetization axis. Particles exhibit behaviors, such as chaining, in simulations that are similar to those witnessed through experimentation. Currently, experimental results are being compared to the modeling results for verification of the model, through the analysis of chaining behaviors. This modeling system will be used in designing magnetic nanoparticles for specific chaining and movement behaviors.

Keywords: controlled movement, modeling, magnetic nanoparticles, nanoparticle design

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Authors: Artem Sedov, Aigerim Uyzbayeva, Valeriya Tyo

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The presented article is showing results of dynamic modeling with Mathlab software of optimal automatic room climate control system for two experimental houses in Astana, one of which has circle plan and the other one has square plan. These results are showing that building geometry doesn't influence on climate system PID-controls configuring. This confirms theoretical implication that optimal automatic climate control system parameters configuring should depend on building's internal space volume, envelope heat transfer, number of people inside, supply ventilation air flow and outdoor temperature.

Keywords: climate control system, climate physics, dome-like building, mathematical modeling

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Authors: Nassima Sotehi

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This article presents experimental and numerical results concerning the thermal properties of the porous materials used as heat insulator in the buildings sector. Initially, the thermal conductivity of three types of studied walls (classic concrete, concrete with cork aggregate and polystyrene concrete) was measured in experiments by the method of the boxes. Then a numerical modeling of the heat and mass transfers which occur within porous materials was applied to these walls. This work shows the influence of the presence of water in building materials on their thermophysical properties, as well as influence of the nature of materials and dosage of fibers introduced within these materials on the thermal and mass transfers.

Keywords: modeling, porous media, thermal materials, thermal properties

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

Procedia PDF Downloads 530

Authors: Benaliouche Hana, Abdessemed Djamal, Meniai Abdessalem, Lesage Geoffroy, Heran Marc

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This paper presents a dynamic mathematical model of activated sludge which is able to predict the formation and degradation kinetics of SMP (Soluble microbial products) in membrane bioreactor systems. The model is based on a calibrated version of ASM1 with the theory of production and degradation of SMP. The model was calibrated on the experimental data from MBR (Mathematical modeling Membrane bioreactor) pilot plant. Analytical expressions have been developed, describing the concentrations of the main state variables present in the sludge matrix, with the inclusion of only six additional linear differential equations. The objective is to present a new dynamic mathematical model of activated sludge capable of predicting the formation and degradation kinetics of SMP (UAP and BAP) from the submerged membrane bioreactor (BRMI), operating at low organic load (C / N = 3.5), for two sludge retention times (SRT) fixed at 40 days and 60 days, to study their impact on membrane fouling, The modeling study was carried out under the steady-state condition. Analytical expressions were then validated by comparing their results with those obtained by simulations using GPS-X-Hydromantis software. These equations made it possible, by means of modeling approaches (ASM1), to identify the operating and kinetic parameters and help to predict membrane fouling.

Keywords: Activated Sludge Model No. 1 (ASM1), mathematical modeling membrane bioreactor, soluble microbial products, UAP, BAP, Modeling SMP, MBR, heterotrophic biomass

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Authors: Roham Rafiee, Hadi Hesamsadat

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In this study, a parametric finite element modeling is developed to analyze failure modes of FRP pipes subjected to internal pressure. First-ply failure pressure and functional failure pressure was determined by a progressive damage modeling and then it is validated using experimental observations. The influence of both winding angle and fiber volume fraction is studied on the functional failure of FRP pipes and it corresponding pressure. It is observed that despite the fact that increasing fiber volume fraction will enhance the mechanical properties, it will be resulted in lower values for functional failure pressure. This shortcoming can be compensated by modifying the winding angle in angle plies of pipe wall structure.

Keywords: composite pipe, functional failure, progressive modeling, winding angle

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Authors: Anwar Jarndal

Abstract:

In this paper, a genetic-neural-network (GNN) based large-signal model for GaN HEMTs is presented along with its parameters extraction procedure. The model is easy to construct and implement in CAD software and requires only DC and S-parameter measurements. An improved decomposition technique is used to model self-heating effect. Two GNN models are constructed to simulate isothermal drain current and power dissipation, respectively. The two model are then composed to simulate the drain current. The modeling procedure was applied to a packaged GaN-on-Si HEMT and the developed model is validated by comparing its large-signal simulation with measured data. A very good agreement between the simulation and measurement is obtained.

Keywords: GaN HEMT, computer-aided design and modeling, neural networks, genetic optimization

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Authors: Endeshaw Assefa Derso, Maria Gabriella Campolo, Angela Alibrandi

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Objectives:Early childhood malnutrition can have long-term and irreversible effects on a child's health and development. This study uses the Bayesian method with spatial variation to investigate the flexible trends of metrical covariates and to identify communities at high risk of injury. Methods: Cross-sectional data on underweight are collected from the 2016 Ethiopian Demographic and Health Survey (EDHS). The Bayesian geo-additive model is performed. Appropriate prior distributions were provided for scall parameters in the models, and the inference is entirely Bayesian, using Monte Carlo Markov chain (MCMC) stimulation. Results: The results show that metrical covariates like child age, maternal body mass index (BMI), and maternal age affect a child's underweight non-linearly. Lower and higher maternal BMI seem to have a significant impact on the child’s high underweight. There was also a significant spatial heterogeneity, and based on IDW interpolation of predictive values, the western, central, and eastern parts of the country are hotspot areas. Conclusion: Socio-demographic and community- based programs development should be considered compressively in Ethiopian policy to combat childhood underweight malnutrition.

Keywords: bayesX, Ethiopia, malnutrition, MCMC, semi-parametric bayesian analysis, spatial distribution, P- splines

Procedia PDF Downloads 87