Search results for: optimal size

Authors: S.A.M. Yatim, Z.B. Ibrahim, K.I. Othman, F. Ismail

Abstract:

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precision and computation time. The strategy involves constant, halving or increasing the step size by 1.9 times the previous step size. Decision of changing the step size is determined by the local truncation error (LTE). Numerical results are provided to support the enhancement of method applied.

Keywords: Backward differentiation formulae, block backwarddifferentiation formulae, stiff ordinary differential equation, variablestep size.

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Authors: N. K. Sharma, J. Nayak, D. K. Sehgal, R. K. Pandey

Abstract:

Bone material is treated as heterogeneous and hierarchical in nature therefore appropriate size of bone specimen is required to analyze its tensile properties at a particular hierarchical level. Tensile properties of cortical bone are important to investigate the effect of drug treatment, disease and aging as well as for development of computational and analytical models. In the present study tensile properties of buffalo as well as goat femoral and tibiae cortical bone are analyzed using sub-size tensile specimens. Femoral cortical bone was found to be stronger in tension as compared to the tibiae cortical bone and the tensile properties obtained using sub-size specimens show close resemblance with the tensile properties of full-size cortical specimens. A two dimensional finite element (FE) modal was also applied to simulate the tensile behavior of sub-size specimens. Good agreement between experimental and FE model was obtained for sub-size tensile specimens of cortical bone.

Keywords: Cortical bone, sub-size specimen, full size specimen, finite element modeling.

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.

Keywords: Parking system, optimal location, response time, S/R machine.

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Authors: Jeffrey L. Duffany

Abstract:

Graph coloring is an important problem in computer science and many algorithms are known for obtaining reasonably good solutions in polynomial time. One method of comparing different algorithms is to test them on a set of standard graphs where the optimal solution is already known. This investigation analyzes a set of 50 well known graph coloring instances according to a set of complexity measures. These instances come from a variety of sources some representing actual applications of graph coloring (register allocation) and others (mycieleski and leighton graphs) that are theoretically designed to be difficult to solve. The size of the graphs ranged from ranged from a low of 11 variables to a high of 864 variables. The method used to solve the coloring problem was the square of the adjacency (i.e., correlation) matrix. The results show that the most difficult graphs to solve were the leighton and the queen graphs. Complexity measures such as density, mobility, deviation from uniform color class size and number of block diagonal zeros are calculated for each graph. The results showed that the most difficult problems have low mobility (in the range of .2-.5) and relatively little deviation from uniform color class size.

Keywords: graph coloring, complexity, algorithm.

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Authors: Ehab F. Badran, Guoxiang Gu

Abstract:

We consider optimal channel equalization for MIMO (multi-input/multi-output) time-varying channels in the sense of MMSE (minimum mean-squared-error), where the observation noise can be non-stationary. We show that all ZF (zero-forcing) receivers can be parameterized in an affine form which eliminates completely the ISI (inter-symbol-interference), and optimal channel equalizers can be designed through minimization of the MSE (mean-squarederror) between the detected signals and the transmitted signals, among all ZF receivers. We demonstrate that the optimal channel equalizer is a modified Kalman filter, and show that under the AWGN (additive white Gaussian noise) assumption, the proposed optimal channel equalizer minimizes the BER (bit error rate) among all possible ZF receivers. Our results are applicable to optimal channel equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers, OFDM (orthogonal frequency division multiplexing), and DS (direct sequence) CDMA (code division multiple access) wireless data communication systems. A design algorithm for optimal channel equalization is developed, and several simulation examples are worked out to illustrate the proposed design algorithm.

Keywords: Channel equalization, Kalman filtering, Time-varying systems.

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Authors: Ekow A. Kwofie, Emmanuel K. Anto, Godfred Mensah

Abstract:

In this paper, CYME Distribution software has been used to assess the impacts of solar Photovoltaic (PV) distributed generation (DG) plant on the Electricity Company of Ghana (ECG) 33 kV sub-transmission network at different PV penetration levels. As ECG begins to encourage DG PV interconnections within its network, there has been the need to assess the impacts on the sub-transmission losses and voltage contribution. In Tema, a city in Accra - Ghana, ECG has a 33 kV sub-transmission network made up of 20 No. 33 kV buses that was modeled. Three different locations were chosen: The source bus, a bus along the sub-transmission radial network and a bus at the tail end to determine the optimal location for DG PV interconnection. The optimal location was determined based on sub-transmission technical losses and voltage impact. PV capacities at different penetration levels were modeled at each location and simulations performed to determine the optimal PV penetration level. Interconnection at a bus along (or in the middle of) the sub-transmission network offered the highest benefits at an optimal PV penetration level of 80%. At that location, the maximum voltage improvement of 0.789% on the neighboring 33 kV buses and maximum loss reduction of 6.033% over the base case scenario were recorded. Hence, the optimal location for DG PV integration within the 33 kV sub-transmission utility network is at a bus along the sub-transmission radial network.

Keywords: Distributed generation photovoltaic, DG PV, optimal location, penetration level, sub-transmission network.

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Authors: A. Bagheri Garmarudi, M. Khanmohammadi, N. Khoddami, K. Shabani

Abstract:

Determination of nano particle size is substantial since the nano particle size exerts a significant effect on various properties of nano materials. Accordingly, proposing non-destructive, accurate and rapid techniques for this aim is of high interest. There are some conventional techniques to investigate the morphology and grain size of nano particles such as scanning electron microscopy (SEM), atomic force microscopy (AFM) and X-ray diffractometry (XRD). Vibrational spectroscopy is utilized to characterize different compounds and applied for evaluation of the average particle size based on relationship between particle size and near infrared spectra [1,4] , but it has never been applied in quantitative morphological analysis of nano materials. So far, the potential application of nearinfrared (NIR) spectroscopy with its ability in rapid analysis of powdered materials with minimal sample preparation, has been suggested for particle size determination of powdered pharmaceuticals. The relationship between particle size and diffuse reflectance (DR) spectra in near infrared region has been applied to introduce a method for estimation of particle size. Back propagation artificial neural network (BP-ANN) as a nonlinear model was applied to estimate average particle size based on near infrared diffuse reflectance spectra. Thirty five different nano TiO2 samples with different particle size were analyzed by DR-FTNIR spectrometry and the obtained data were processed by BP- ANN.

Keywords: near infrared, particle size, chemometrics, neuralnetwork, nano structure.

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Authors: Reza Sirjani, Nobosse Tafem Bolan

Abstract:

Many optimization techniques available in the literature have been developed in order to solve the problem of voltage stability enhancement in power systems. However, there are a number of drawbacks in the use of previous techniques aimed at determining the optimal location and size of reactive compensators in a network. In this paper, an Improved Cuckoo Search algorithm is applied as an appropriate optimization algorithm to determine the optimum location and size of a Static Var Compensator (SVC) in a transmission network. The main objectives are voltage stability improvement and total cost minimization. The results of the presented technique are then compared with other available optimization techniques.

Keywords: Cuckoo search algorithm, optimization, power system, var compensators, voltage stability.

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

Abstract:

Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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Authors: Zhizhong Jiang, Peter Naudé, Binghua Jiang

Abstract:

Effective evaluation of software development effort is an important issue during project plan. This study provides a model to predict development effort based on the software size estimated with function points. We generalize the average amount of effort spent on each phase of the development, and give the estimates for the effort used in software building, testing, and implementation. Finally, this paper finds a strong correlation between software defects and software size. As the size of software constantly increases, the quality remains to be a matter which requires major concern.

Keywords: Development effort, function points, software quality, software size.

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Authors: R. Oloomi, M. A. Sadrnia

Abstract:

This paper proposes a new optimal feedback controller for voltage source converters VSC's, for current regulated voltage source converters, which allows compensate the harmonics of current produced by nonlinear loads and load reactive power. The aim of the present paper is to describe a novel switching signal generation technique called optimal controller which guarantees that the injected currents follow the reference currents determined by the compensation strategy, with the smallest possible tracking error and fixed switching frequency. It is compared with well-known hysteresis current controller HCC. The validity of presented method and its comparison with HCC is studied through simulation results.

Keywords: Hysteresis Current Controller, Optimal Controller, Switching pattern, Voltage Source Converter.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

Smart Dust particles, are small smart materials used for generating weather maps. We investigate question of the optimal number of Smart Dust particles necessary for generating precise, computationally feasible and cost effective 3–D weather maps. We also give an optimal matching algorithm for the generalized scenario, when there are N Smart Dust particles and M ground receivers.

Keywords: Remote sensing, smart dust, matching, optimization.

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Authors: Kul Pun, F. A. Hamad, T. Ahmed, J. O. Ugwu, J. Eyers, G. Lawson, P. A. Russell

Abstract:

Determining droplet size and distribution is essential when determining the separation efficiency of a two/three-phase separator. This paper investigates the effect of liquid flow and oil pad thickness on the droplet size at the lab scale. The findings show that increasing the inlet flow rates of the oil and water results in size reduction of the droplets and increasing the thickness of the oil pad increases the size of the droplets. The data were fitted with a simple Gaussian model, and the parameters of mean, standard deviation, and amplitude were determined. Trends have been obtained for the fitted parameters as a function of the Reynolds number, which suggest a way forward to better predict the starting parameters for population models when simulating separation using CFD packages. The key parameter to predict to fix the position of the Gaussian distribution was found to be the mean droplet size.

Keywords: Two-phase separator, average bubble droplet, bubble size distribution, liquid-liquid phase.

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Authors: N. Popovich, P. Yan

Abstract:

In this paper a controller for the pitch angle of an aircraft regarding to the elevator deflection angle is designed. The way how the elevator angle affects pitching motion of the aircraft is pointed out, as well as, how a pitch controller can be applied for the aircraft to reach certain pitch angle. In this digital optimal system, the elevator deflection angle and pitching angle of the plane are considered to be input and output respectively. A single input single output (SISO) system is presented. A digital pitch aircraft control is demonstrated. A simulation for the whole system has been performed. The optimal control weighting vectors, Q and R have been determined.

Keywords: Aircraft, control, digital, optimal, Q and Rmatrices.

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Authors: Ho Yuan-Hong, Hunag Chiung-Ju

Abstract:

This study conducts simulation analyses to find the optimal debt ceiling of Taiwan, while factoring in welfare maximization under a dynamic stochastic general equilibrium framework. The simulation is based on Taiwan's 2001 to 2011 economic data and shows that welfare is maximized at a debt/GDP ratio of 0.2, increases in the debt/GDP ratio leads to increases in both tax and interest rates and decreases in the consumption ratio and working hours. The study results indicate that the optimal debt ceiling of Taiwan is 20% of GDP, where if the debt/GDP ratio is greater than 40%, the welfare will be negative and result in welfare loss.

Keywords: Debt sustainability, optimal debt ceiling, dynamic stochastic general equilibrium, welfare maximization.

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Authors: Ziquan Hu, Kun She, Shahzad Ali, Kai Yan

Abstract:

Game theory could be used to analyze the conflicted issues in the field of information hiding. In this paper, 2-phase game can be used to build the embedder-attacker system to analyze the limits of hiding capacity of embedding algorithms: the embedder minimizes the expected damage and the attacker maximizes it. In the system, the embedder first consumes its resource to build embedded units (EU) and insert the secret information into EU. Then the attacker distributes its resource evenly to the attacked EU. The expected equilibrium damage, which is maximum damage in value from the point of view of the attacker and minimum from the embedder against the attacker, is evaluated by the case when the attacker attacks a subset from all the EU. Furthermore, the optimal equilibrium capacity of hiding information is calculated through the optimal number of EU with the embedded secret information. Finally, illustrative examples of the optimal equilibrium capacity are presented.

Keywords: 2-Phase Game, Expected Equilibrium damage, InformationHiding, Optimal Equilibrium Capacity.

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Authors: Afshin Jahangirzadeh, Shatirah Akib, Babak Kamali, Sadia Rahman

Abstract:

Scarcity of water resources and huge costs of establishing new hydraulic installations necessitate optimal exploitation from existing reservoirs. Sustainable management and efficient exploitation from existing finite water resources are important factors in water resource management, particularly in the periods of water insufficiency and in dry regions, and on account of competitive allocations in the view of exploitation management. This study aims to minimize reservoir water release from a determined rate of demand. A numerical model for water optimal exploitation has been developed using GAMS introduced by the World Bank and applied to the case of Meijaran dam, northern Iran. The results indicate that this model can optimize the function of reservoir exploitation while required water for lower parts of the region will be supplied. Further, allocating optimal water from reservoir, the optimal rate of water allocated to any group of the users were specified to increase benefits in curve dam exploitation.

Keywords: Water resource management, water reservoirs, water allocation, GAMS, Meijaran dam

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Authors: Jae Wook Shin, Ju-man Song, Hyun-Taek Choi, Poo Gyeon Park

Abstract:

This paper introduces a new variable step-size APA with decorrelation of AR input process is based on the MSD analysis. To achieve a fast convergence rate and a small steady-state estimation error, he proposed algorithm uses variable step size that is determined by minimising the MSD. In addition, experimental results show that the proposed algorithm is achieved better performance than the other algorithms.

Keywords: adaptive filter, affine projection algorithm, variable step size.

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Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

Abstract:

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

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Authors: Sunglim Lee, Susumu Fujii, Koji Okamura

Abstract:

Smart grid is a new approach for electric power grid that uses information and communications technology to control the electric power grid. Smart grid provides real-time control of the electric power grid, controlling the direction of power flow or time of the flow. Control devices are installed on the power lines of the electric power grid to implement smart grid. The number of the control devices should be determined, in relation with the area one control device covers and the cost associated with the control devices. One approach to determine the number of the control devices is to use the data on the surplus power generated by home solar generators. In current implementations, the surplus power is sent all the way to the power plant, which may cause power loss. To reduce the power loss, the surplus power may be sent to a control device and sent to where the power is needed from the control device. Under assumption that the control devices are installed on a lattice of equal size squares, our goal is to figure out the optimal spacing between the control devices, where the power sharing area (the area covered by one control device) is kept small to avoid power loss, and at the same time the power sharing area is big enough to have no surplus power wasted. To achieve this goal, a simulation using landscape ecology method is conducted on a sample area. First an aerial photograph of the land of interest is turned into a mosaic map where each area is colored according to the ratio of the amount of power production to the amount of power consumption in the area. The amount of power consumption is estimated according to the characteristics of the buildings in the area. The power production is calculated by the sum of the area of the roofs shown in the aerial photograph and assuming that solar panels are installed on all the roofs. The mosaic map is colored in three colors, each color representing producer, consumer, and neither. We started with a mosaic map with 100 m grid size, and the grid size is grown until there is no red grid. One control device is installed on each grid, so that the grid is the area which the control device covers. As the result of this simulation we got 350m as the optimal spacing between the control devices that makes effective use of the surplus power for the sample area.

Keywords: Landscape ecology, IT, smart grid, aerial photograph, simulation.

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Authors: Mohamed Shawki Elamir, Heinrich Gotzig, Raoul Zoellner, Patrick Maeder

Abstract:

In this work, a methodology is presented for identifying the optimal digitization parameters for the analog signal of ultrasonic sensors. These digitization parameters are the resolution of the analog to digital conversion and the sampling rate. This is accomplished though the derivation of characteristic curves based on Fano inequality and the calculation of the mutual information content over a given dataset. The mutual information is calculated between the examples in the dataset and the corresponding variation in the feature that needs to be estimated. The optimal parameters are identified in a manner that ensures optimal estimation performance while preventing inefficiency in using unnecessarily powerful analog to digital converters.

Keywords: Analog to digital conversion, digitization, sampling rate, ultrasonic sensors.

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Authors: R. M. Chandima Ratnayake, Daniel Dyakov

Abstract:

Super steel materials play a vital role in the construction and fabrication of structural, piping and pipeline components. In assuring the integrity of onshore and offshore operating systems, they enable life cycle costs to be minimized. In this context, Duplex stainless steel (DSS) material related welding on constructions and fabrications plays a significant role in maintaining and assuring integrity at an optimal expenditure over the life cycle of production and process systems as well as associated structures. In DSS welding, factors such as gap geometry, shielding gas supply rate, welding current, and type of the welding process are vital to the final joint performance. Hence, an experimental investigation has been performed using an engineering robust design approach (ERDA) to investigate the optimal settings that generate optimal super DSS (i.e. UNS S32750) joint performance. This manuscript illustrates the mathematical approach and experimental design, optimal parameter settings and results of the verification experiment.

Keywords: Duplex stainless steel welding, engineering robust design, mathematical framework, optimal parameter settings.

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Authors: Yuekun Chen, Yousef Sardahi, Salam Hajjar, Christopher Greer

Abstract:

This paper presents a multi-objective optimal design of a cascade control system for an underactuated mechanical system. Cascade control structures usually include two control algorithms (inner and outer). To design such a control system properly, the following conflicting objectives should be considered at the same time: 1) the inner closed-loop control must be faster than the outer one, 2) the inner loop should fast reject any disturbance and prevent it from propagating to the outer loop, 3) the controlled system should be insensitive to measurement noise, and 4) the controlled system should be driven by optimal energy. Such a control problem can be formulated as a multi-objective optimization problem such that the optimal trade-offs among these design goals are found. To authors best knowledge, such a problem has not been studied in multi-objective settings so far. In this work, an underactuated mechanical system consisting of a rotary servo motor and a ball and beam is used for the computer simulations, the setup parameters of the inner and outer control systems are tuned by NSGA-II (Non-dominated Sorting Genetic Algorithm), and the dominancy concept is used to find the optimal design points. The solution of this problem is not a single optimal cascade control, but rather a set of optimal cascade controllers (called Pareto set) which represent the optimal trade-offs among the selected design criteria. The function evaluation of the Pareto set is called the Pareto front. The solution set is introduced to the decision-maker who can choose any point to implement. The simulation results in terms of Pareto front and time responses to external signals show the competing nature among the design objectives. The presented study may become the basis for multi-objective optimal design of multi-loop control systems.

Keywords: Cascade control, multi-loop control systems, multi-objective optimization, optimal control.

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Authors: M. Saravanan, J. Raja Murugadoss, V. Jayanthi

Abstract:

Optimal design of structure has a main role in reduction of material usage which leads to deduction in the final cost of construction projects. Evolutionary approaches are found to be more successful techniques for solving size and shape structural optimization problem since it uses a stochastic random search instead of a gradient search. By reviewing the recent literature works the problem found was the optimization of weight. A new meta-heuristic algorithm called as Cuckoo Search (CS) Algorithm has used for the optimization of the total weight of the truss structures. This paper has used set of 10 bars and 25 bars trusses for the testing purpose. The main objective of this work is to reduce the number of iterations, weight and the total time consumption. In order to demonstrate the effectiveness of the present method, minimum weight design of truss structures is performed and the results of the CS are compared with other algorithms.

Keywords: Cuckoo search algorithm, levy’s flight, meta-heuristic, optimal weight.

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Authors: Haider A Ramadhan, Khalil Shihab

Abstract:

Clustering techniques have been used by many intelligent software agents to group similar access patterns of the Web users into high level themes which express users intentions and interests. However, such techniques have been mostly focusing on one salient feature of the Web document visited by the user, namely the extracted keywords. The major aim of these techniques is to come up with an optimal threshold for the number of keywords needed to produce more focused themes. In this paper we focus on both keyword and similarity thresholds to generate themes with concentrated themes, and hence build a more sound model of the user behavior. The purpose of this paper is two fold: use distance based clustering methods to recognize overall themes from the Proxy log file, and suggest an efficient cut off levels for the keyword and similarity thresholds which tend to produce more optimal clusters with better focus and efficient size.

Keywords: Data mining, knowledge discovery, clustering, dataanalysis, Web log analysis, theme based searching.

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Authors: T. Sattarpour, D. Nazarpour

Abstract:

This paper investigates the effect of simultaneous placement of DGs and smart meters (SMs), on voltage profile improvement in active distribution networks (ADNs). A substantial center of attention has recently been on responsive loads initiated in power system problem studies such as distributed generations (DGs). Existence of responsive loads in active distribution networks (ADNs) would have undeniable effect on sizing and siting of DGs. For this reason, an optimal framework is proposed for sizing and siting of DGs and SMs in ADNs. SMs are taken into consideration for the sake of successful implementing of demand response programs (DRPs) such as direct load control (DLC) with end-side consumers. Looking for voltage profile improvement, the optimization procedure is solved by genetic algorithm (GA) and tested on IEEE 33-bus distribution test system. Different scenarios with variations in the number of DG units, individual or simultaneous placing of DGs and SMs, and adaptive power factor (APF) mode for DGs to support reactive power have been established. The obtained results confirm the significant effect of DRPs and APF mode in determining the optimal size and site of DGs to be connected in ADN resulting to the improvement of voltage profile as well.

Keywords: Active distribution network (ADN), distributed generations (DGs), smart meters (SMs), demand response programs (DRPs), adaptive power factor (APF).

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Authors: Shyam S.N. Perera

Abstract:

The optimal control problem for the viscoelastic melt spinning process has not been reported yet in the literature. In this study, an optimal control problem for a mathematical model of a viscoelastic melt spinning process is considered. Maxwell-Oldroyd model is used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and the temperature of the quench air and the fiber length serve as control variables. A constrained optimization problem is derived and the first–order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. A computer program in MATLAB is developed for simulations.

Keywords: Fiber spinning, Maxwell-Oldroyd, Optimal control, First-order optimality system, Adjoint system

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

Abstract:

The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: Wire coating die, Corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method.

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