Search results for: Particle Swarm Optimization

Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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Authors: B. Rajesh Kamath, J. Sundara Rajan, M. K. Veeraiah, M. Z. Kurian

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Insulation performance of a gas insulated system is severely affected by particle contaminants. These metallic particles adversely affect the characteristics of insulating system. These particles can produce surface charges due to partial discharge activities. These particles which are free to move enhance the local electric fields. This paper deals with the influence of conducting particle placed in a co-axial duct on the discharge characteristics of gas mixtures. Co-axial duct placed in a high pressure chamber is used for the purpose. A gas pressure of 0.1, 0.2 and 0.3 MPa have been considered with a 10:90 SF₆ and N₂ gas mixtures. The 2D and 3D histograms of clean duct and duct with copper particle are discussed in this paper.

Keywords: B. Rajesh Kamath, J. Sundara Rajan, M. K. Veeraiah, M. Z. Kurian

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Authors: Muniyasamy Kalanchiam, Baskar Mannai

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Topology Optimization is a defined as the method of determining optimal distribution of material for the assumed design space with functionality, loads and boundary conditions [1]. Topology optimization can be used to optimize shape for the purposes of weight reduction, minimizing material requirements or selecting cost effective materials [2]. Topology optimization has been implemented through the use of finite element methods for the analysis, and optimization techniques based on the method of moving asymptotes, genetic algorithms, optimality criteria method, level sets and topological derivatives. Case study of Typical “Fuselage design" is considered for this paper to explain the benefits of Topology Optimization in the design cycle. A cylindrical shell is assumed as the design space and aerospace standard pay loads were applied on the fuselage with wing attachments as constraints. Then topological optimization is done using Finite Element (FE) based software. This optimization results in the structural concept design which satisfies all the design constraints using minimum material.

Keywords: Fuselage, Topology optimization, payloads, designoptimization, Finite Element Analysis.

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Authors: Muhammad Haroon Siddiqui, Muhammad Rehan Khalid

Abstract:

This paper evaluates the performance of a novel algorithm for tracking of a mobile node, interms of execution time and root mean square error (RMSE). Particle Filter algorithm is used to track the mobile node, however a new technique in particle filter algorithm is also proposed to reduce the execution time. The stationary points were calculated through trilateration and finally by averaging the number of points collected for a specific time, whereas tracking is done through trilateration as well as particle filter algorithm. Wi-Fi signal is used to get initial guess of the position of mobile node in x-y coordinates system. Commercially available software “Wireless Mon" was used to read the WiFi signal strength from the WiFi card. Visual Cµ version 6 was used to interact with this software to read only the required data from the log-file generated by “Wireless Mon" software. Results are evaluated through mathematical modeling and MATLAB simulation.

Keywords: Particle Filter, Tracking, Wireless Local Area Network, WiFi, Trilateration

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Authors: M. Jalali Azizpour, H. Mohammadi Majd

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In this paper, the effect of WC-12Co particle velocity in HVOF thermal spraying process on the coating thickness has been studied. The statistical results show that the spray distance and oxygen-to-fuel ratio are more effective factors on particle characterization and thickness of HVOF thermal spraying coatings. Spray Watch diagnostic system, scanning electron microscopy (SEM), X-ray diffraction and thickness measuring system were used for this purpose.

Keywords: Grinding, HVOF, Thermal spray, WC-Co.

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Authors: Pavel Y. Tabakov

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An accurate optimal design of laminated composite structures may present considerable difficulties due to the complexity and multi-modality of the functional design space. The Big Bang – Big Crunch (BB-BC) optimization method is a relatively new technique and has already proved to be a valuable tool for structural optimization. In the present study the exceptional efficiency of the method is demonstrated by an example of the lay-up optimization of multilayered anisotropic cylinders based on a three-dimensional elasticity solution. It is shown that, due to its simplicity and speed, the BB-BC is much more efficient for this class of problems when compared to the genetic algorithms.

Keywords: Big Bang – Big Crunch method, optimization, composite laminates, pressure vessel.

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: M. Hossain, H. P. Zhu, A. B. Yu

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This paper presents a numerical investigation of regime transition of flow of ellipsoidal particles and a comparison with that of spherical particle assembly. Particle assemblies constituting spherical and ellipsoidal particle of 2.5:1 aspect ratio are examined at separate instances in similar flow conditions in a shear cell model that is numerically developed based on the discrete element method. Correlations among elastically scaled stress, kinetically scaled stress, coordination number and volume fraction are investigated, and show important similarities and differences for the spherical and ellipsoidal particle assemblies. In particular, volume fractions at points of regime transition are identified for both types of particles. It is found that compared with spherical particle assembly, ellipsoidal particle assembly has higher volume fraction for the quasistatic to intermediate regime transition and lower volume fraction for the intermediate to inertial regime transition. Finally, the relationship between coordination number and volume fraction shows strikingly distinct features for the two cases, suggesting that different from spherical particles, the effect of the shear rate on the coordination number is not significant for ellipsoidal particles. This work provides a glimpse of currently running work on one of the most attractive scopes of research in this field and has a wide prospect in understanding rheology of more complex shaped particles in light of the strong basis of simpler spherical particle rheology.

Keywords: Discrete element method, granular rheology, non-spherical particles, regime transition

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Authors: Barzin Gavtash, Khalid Hussain, Mohammad Layeghi, Saeed Sadeghi Lafmejani

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This research aims at modeling and simulating the effects of nanofluids on cylindrical heat pipes thermal performance using the ANSYS-FLUENT CFD commercial software. The heat pipe outer wall temperature distribution, thermal resistance, liquid pressure and axial velocity in presence of suspended nano-scaled solid particle (i.e. Cu, Al2O3 and TiO2) within the fluid (water) were investigated. The effect of particle concentration and size were explored and it is concluded that the thermal performance of the heat pipe is improved when using nanofluid as the system working fluid. Additionally, it was observed that the thermal resistance of the heat pipe drops as the particle concentration level increases and particle radius decreases.

Keywords: CFD, Heat Pipe, Nanofluid, Thermal resistance

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Authors: Akbar H. Borzabadi, Omid S. Fard

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In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: Wu Qinglong, Zhou Qicai, Xiong Xiaolei, Zhang Richeng

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In order to achieve the layout and size optimization of the web members of tower crane boom, a truss topology and cross section size optimization method based on continuum is proposed considering three typical working conditions. Firstly, the optimization model is established by replacing web members with web plates. And the web plates are divided into several sub-domains so that periodic soft kill option (SKO) method can be carried out for topology optimization of the slender boom. After getting the optimized topology of web plates, the optimized layout of web members is formed through extracting the principal stress distribution. Finally, using the web member radius as design variable, the boom compliance as objective and the material volume of the boom as constraint, the cross section size optimization mathematical model is established. The size optimization criterion is deduced from the mathematical model by Lagrange multiplier method and Kuhn-Tucker condition. By comparing the original boom with the optimal boom, it is identified that this optimization method can effectively lighten the boom and improve its performance.

Keywords: Tower crane boom, topology optimization, size optimization, periodic, soft kill option, optimization criterion.

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Authors: Yi Liu

Abstract:

In this paper, computational fluid dynamics (CFD) is utilized to characterize a prototype biolistic delivery system, the biomedical device based on the contoured-shock-tube design (CST), with the aim at investigating shocks induced flow instabilities within the contoured shock tube. The shock/interface interactions, the growth of perturbation at an interface between two fluids of different density are interrogated. The key features of the gas dynamics and gas-particle interaction are discussed

Keywords: Simulation, Shock wave, Particle, Interface, Supersonic, Richtmyer-Meshkov Instability

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Authors: Tadaaki Sato, Ryo Ohmura

Abstract:

This paper reports the influence of sucrose on the preservation of CO2 hydrate crystal samples. The particle diameter of hydrate samples were 1.0 and 5.6-8.0 mm. Mass fraction of sucrose in the sample was 0.16. The samples were stored at the aerated condition under atmospheric pressure and at the temperature of 253 or 258 K. The results indicated that the mass fractions of CO2 hydrate in the samples with sucrose were 0.10 ± 0.03 at the end of 3-week preservation, regardless of temperature and particle diameter. Mass fraction of CO2 hydrate in the samples with sucrose was higher than that of pure CO2 hydrate for 1.0 mm particle diameter, while was lower than that of pure CO2 hydrate for 5.6-8.0 mm particle diameter. Discussion is made on the influence of sucrose on the dissociation of CO2 hydrate and the resulting formation of ice.

Keywords: Clathrate hydrates, Carbon dioxide

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Authors: M. Suresh Kumar, K. Ramani

Abstract:

This paper proposed the comparison made between Multi-Carrier Pulse Width Modulation, Sinusoidal Pulse Width Modulation and Selective Harmonic Elimination Pulse Width Modulation technique for minimization of Total Harmonic Distortion in Cascaded H-Bridge Multi-Level Inverter. In Multicarrier Pulse Width Modulation method by using Alternate Position of Disposition scheme for switching pulse generation to Multi-Level Inverter. Another carrier based approach; Sinusoidal Pulse Width Modulation method is also implemented to define the switching pulse generation system in the multi-level inverter. In Selective Harmonic Elimination method using Genetic Algorithm and Particle Swarm Optimization algorithm for define the required switching angles to eliminate low order harmonics from the inverter output voltage waveform and reduce the total harmonic distortion value. So, the results validate that the Selective Harmonic Elimination Pulse Width Modulation method does capably eliminate a great number of precise harmonics and minimize the Total Harmonic Distortion value in output voltage waveform in compared with Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method. In this paper, comparison of simulation results shows that the Selective Harmonic Elimination method can attain optimal harmonic minimization solution better than Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method.

Keywords: Multi-level inverter, Selective Harmonic Elimination Pulse Width Modulation, Multi-Carrier Pulse Width Modulation, Total Harmonic Distortion, Genetic Algorithm.

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Authors: K. Divya, G. Sugumaran

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This paper proposes an improved Maximum Power Point Tracking of PhotoVoltaic system using Deterministic Partical Swarm Optimization technique. This method has the ability to track the maximum power under varying environmental conditions i.e. partial shading conditions. The advantage of this method, particles moves in the restricted value of velocity to achieve the maximum power. SEPIC converter is employed to boost up the voltage of PV system. To estimate the value of the proposed method, MATLAB simulation carried out under partial shading condition.

Keywords: DPSO, Partial shading condition, P&O, PV, SEPIC.

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Authors: Ahmed Al-Ani

Abstract:

The Ant Colony Optimization (ACO) is a metaheuristic inspired by the behavior of real ants in their search for the shortest paths to food sources. It has recently attracted a lot of attention and has been successfully applied to a number of different optimization problems. Due to the importance of the feature selection problem and the potential of ACO, this paper presents a novel method that utilizes the ACO algorithm to implement a feature subset search procedure. Initial results obtained using the classification of speech segments are very promising.

Keywords: Ant Colony Optimization, ant systems, feature selection, pattern recognition.

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Authors: E. Petrakis, V. Karmali, K. Komnitsas

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In this study grinding experiments were performed in a laboratory ball mill using Polish ferronickel slag in order to study the effect of the particle size on alkali activation and the properties of the produced alkali activated materials (AAMs). In this regard, the particle size distribution and the specific surface area of the grinding products in relation to grinding time were assessed. The experimental results show that products with high compressive strength, e.g. higher than 60 MPa, can be produced when the slag median size decreased from 39.9 μm to 11.9 μm. Also, finer fractions are characterized by higher reactivity and result in the production of AAMs with lower porosity and better mechanical properties.

Keywords: Alkali activated materials, compressive strength, particle size distribution, slag.

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Authors: M. S. Salwani, B. B. Sahari, Aidy Ali, A. A. Nuraini

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In this study, optimization is carried out to find the optimized design of a foam-filled column for the best Specific Energy Absorption (SEA) and Crush Force Efficiency (CFE). In order to maximize SEA, the optimization gives the value of 2.3 for column thickness and 151.7 for foam length. On the other hand to maximize CFE, the optimization gives the value of 1.1 for column thickness and 200 for foam length. Finite Element simulation is run by using this value and the SEA and CFE obtained 1237.76 J/kg and 0.92.

Keywords: Crash, foam, oblique loading.

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Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

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A new algorithm based on the lattice Boltzmann method (LBM) is proposed as a potential solver for one-dimensional heat and mass transfer for isothermal carbonization of wood particles. To check the validity of this algorithm, the LBM results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and particle size on the evolution of the local temperature and mass loss inside the wood particle.

Keywords: Lattice Boltzmann Method, pyrolysis, conduction, carbonization.

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Authors: Mohamed A. G. H. Abdalsadig, Amir Nourian, G. G. Nasr, Meisam Babaie

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Gas lift optimization is becoming more important now a day in petroleum industry. A proper lift optimization can reduce the operating cost, increase the net present value (NPV) and maximize the recovery from the asset. A widely accepted definition of gas lift optimization is to obtain the maximum output under specified operating conditions. In addition, gas lift, a costly and indispensable means to recover oil from high depth reservoir entails solving the gas lift optimization problems. Gas lift optimization is a continuous process; there are two levels of production optimization. The total field optimization involves optimizing the surface facilities and the injection rate that can be achieved by standard tools softwares. Well level optimization can be achieved by optimizing the well parameters such as point of injection, injection rate, and injection pressure. All these aspects have been investigated and presented in this study by using experimental data and PROSPER simulation program. The results show that the well head pressure has a large influence on the gas lift performance and also proved that smart gas lift valve can be used to improve gas lift performance by controlling gas injection from down hole. Obtaining the optimum gas injection rate is important because excessive gas injection reduces production rate and consequently increases the operation cost.

Keywords: Optimization, production rate, reservoir pressure effect, gas injection rate effect, gas injection pressure.

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Authors: M. H. Narasingha, K. Pana-Suppamassadu, P. Narataruksa

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The separation efficiency of a hydrocyclone has extensively been considered on the rigid particle assumption. A collection of experimental studies have demonstrated their discrepancies from the modeling and simulation results. These discrepancies caused by the actual particle elasticity have generally led to a larger amount of energy consumption in the separation process. In this paper, the influence of particle elasticity on the separation efficiency of a hydrocyclone system was investigated through the Finite Element (FE) simulations using crude oil droplets as the elastic particles. A Reitema-s design hydrocyclone with a diameter of 8 mm was employed to investigate the separation mechanism of the crude oil droplets from water. The cut-size diameter eter of the crude oil was 10 - Ðçm in order to fit with the operating range of the adopted hydrocylone model. Typical parameters influencing the performance of hydrocyclone were varied with the feed pressure in the range of 0.3 - 0.6 MPa and feed concentration between 0.05 – 0.1 w%. In the simulation, the Finite Element scheme was applied to investigate the particle-flow interaction occurred in the crude oil system during the process. The interaction of a single oil droplet at the size of 10 - Ðçm to the flow field was observed. The feed concentration fell in the dilute flow regime so the particle-particle interaction was ignored in the study. The results exhibited the higher power requirement for the separation of the elastic particulate system when compared with the rigid particulate system.

Keywords: Hydrocyclone, separation efficiency, strain energy density, strain rate.

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Authors: Jana Puchyova

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In recent years a number of applications with multirobot systems (MRS) is growing in various areas. But their design is in practice often difficult and algorithms are proposed for the theoretical background and do not consider errors and noise in real conditions, so they are not usable in real environment. These errors are visible also in task of target localization enough, when robots try to find and estimate the position of the target by the sensors. Localization of target is possible also with one robot but as it was examined target finding and localization with group of mobile robots can estimate the target position more accurately and faster. The accuracy of target position estimation is made by cooperation of MRS and particle filtering. Advantage of usage the MRS with particle filtering was tested on task of fixed target localization by group of mobile robots.

Keywords: Multi-robot system, particle filter, position estimation, target localization.

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Authors: Kouamana Bousson, Paulo Machado

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The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials.

Keywords: Pseudospectral Methods, Trajectory Optimization, 4DTrajectories

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Authors: Alireza Sadrmomtaz

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Positron emission particle tracking (PEPT) is a technique in which a single radioactive tracer particle can be accurately tracked as it moves. A limitation of PET is that in order to reconstruct a tomographic image it is necessary to acquire a large volume of data (millions of events), so it is difficult to study rapidly changing systems. By considering this fact, PEPT is a very fast process compared with PET. In PEPT detecting both photons defines a line and the annihilation is assumed to have occurred somewhere along this line. The location of the tracer can be determined to within a few mm from coincident detection of a small number of pairs of back-to-back gamma rays and using triangulation. This can be achieved many times per second and the track of a moving particle can be reliably followed. This technique was invented at the University of Birmingham [1]. The attempt in PEPT is not to form an image of the tracer particle but simply to determine its location with time. If this tracer is followed for a long enough period within a closed, circulating system it explores all possible types of motion. The application of PEPT to industrial process systems carried out at the University of Birmingham is categorized in two subjects: the behaviour of granular materials and viscous fluids. Granular materials are processed in industry for example in the manufacture of pharmaceuticals, ceramics, food, polymers and PEPT has been used in a number of ways to study the behaviour of these systems [2]. PEPT allows the possibility of tracking a single particle within the bed [3]. Also PEPT has been used for studying systems such as: fluid flow, viscous fluids in mixers [4], using a neutrally-buoyant tracer particle [5].

Keywords: PET, BGO, Particle Tracking, ECAT 931, List mode, PEPT.

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Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte, V. Grincas

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This paper deals with advanced state estimation algorithms for estimation of biomass concentration and specific growth rate in a typical fed-batch biotechnological process. This biotechnological process was represented by a nonlinear mass-balance based process model. Extended Kalman Filter (EKF) and Particle Filter (PF) was used to estimate the unmeasured state variables from oxygen uptake rate (OUR) and base consumption (BC) measurements. To obtain more general results, a simplified process model was involved in EKF and PF estimation algorithms. This model doesn’t require any special growth kinetic equations and could be applied for state estimation in various bioprocesses. The focus of this investigation was concentrated on the comparison of the estimation quality of the EKF and PF estimators by applying different measurement noises. The simulation results show that Particle Filter algorithm requires significantly more computation time for state estimation but gives lower estimation errors both for biomass concentration and specific growth rate. Also the tuning procedure for Particle Filter is simpler than for EKF. Consequently, Particle Filter should be preferred in real applications, especially for monitoring of industrial bioprocesses where the simplified implementation procedures are always desirable.

Keywords: Biomass concentration, Extended Kalman Filter, Particle Filter, State estimation, Specific growth rate.

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Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

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Erosion in a pipe bends caused by particles is a major concern in the oil and gas fields and might cause breakdown to production equipment. This work investigates the effect of sand particle transport in an elbow using computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model is employed to calculate the air/solid particle flow in the elbow. Generic erosion model in Ansys fluent and three particle rebound models are used to predict the erosion rate on the 90° elbows. The model result is compared with experimental data from the open literature validating the CFD-based predictions which reveals that due to the sand particles impinging on the wall of the elbow at high velocity, a point on the pipe elbow were observed to have started turning red due to velocity increase and the maximum erosion locations occur at 48°.

Keywords: Erosion, prediction, elbow, computational fluid dynamics, CFD.

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Authors: Samindi Samarakoon, Ørjan Sletbakk Vie, Remi Kleiven Fjelldal

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White concrete facade elements are widely used in construction industry. It is challenging to achieve the desired workability in casting of white concrete elements. Particle Matrix model was used for proportioning the self-compacting white concrete (SCWC) to control segregation and bleeding and to improve workability. The paper presents how to reach the target slump flow while controlling bleeding and segregation in SCWC. The amount of aggregates, binders and mixing water, as well as type and dosage of superplasticizer (SP) to be used are the major factors influencing the properties of SCWC. Slump flow and compressive strength tests were carried out to examine the performance of SCWC, and the results indicate that the particle matrix model could produce successfully SCWC controlling segregation and bleeding.

Keywords: Mix design, particle, matrix model, white concrete.

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Authors: M. A. Rubio, A. Urquia

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Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.

Keywords: Optimization, sensitivity, genetic algorithms, model calibration.

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Authors: R. Alias, A. Kasa, M. R. Taha

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The effect of particle size on shear strength of granular materials are investigated using direct shear tests. Small direct shear test (60 mm by 60 mm by 24 mm deep) were conducted for particles passing the sieves with opening size of 2.36 mm. Meanwhile, particles passing the standard 20 mm sieves were tested using large direct shear test (300 mm by 300 mm by 200 mm deep). The large direct shear tests and the small direct shear tests carried out using the same shearing rate of 0.09 mm/min and similar normal stresses of 100, 200 and 300 kPa. The results show that the peak and residual shear strength increases as particle size increases.

Keywords: Particle size, shear strength, granular material, direct shear test.

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Authors: Buntara Sthenly Gan, Naohiro Kawada

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A simple and easy algorithm is presented for a fast calculation of kernel functions which required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. Present proposed algorithm improves the Linked-list algorithm and adopts the Pair-Wise Interaction technique, which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The algorithm is easy to be implemented without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, smoothing length and total amount of particles are conducted to show the effectiveness of the present technique. A compact formulation is proposed for practical usage.

Keywords: Technique, fluid simulation, smoothing particle hydrodynamic (SPH), particle interaction.

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