Search results for: iterative root-finding technique

Authors: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

Procedia PDF Downloads 97

Authors: Y. Wang

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The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

Procedia PDF Downloads 194

Authors: Veronica S. Moertini, Vinsensius Kevin, Gede Karya

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Customer reviews have been collected by many kinds of e-commerce websites selling products, services, hotel rooms, tickets and so on. Each website collects its own customer reviews. The reviews can be crawled, collected from those websites and stored as big data. Text analysis techniques can be used to analyze that data to produce summarized information, such as customer opinions. Then, these opinions can be published by independent service provider websites and used to help customers in choosing the most suitable products or services. As the opinions are analyzed from big data of reviews originated from many websites, it is expected that the results are more trusted and accurate. Indonesian customers write reviews in Indonesian language, which comes with its own structures and uniqueness. We found that most of the reviews are expressed with “daily language”, which is informal, do not follow the correct grammar, have many abbreviations and slangs or non-formal words. Hadoop is an emerging platform aimed for storing and analyzing big data in distributed systems. A Hadoop cluster consists of master and slave nodes/computers operated in a network. Hadoop comes with distributed file system (HDFS) and MapReduce framework for supporting parallel computation. However, MapReduce has weakness (i.e. inefficient) for iterative computations, specifically, the cost of reading/writing data (I/O cost) is high. Given this fact, we conclude that MapReduce function is best adapted for “one-pass” computation. In this research, we develop an efficient technique for extracting or mining opinions from big data of Indonesian reviews, which is based on MapReduce with one-pass computation. In designing the algorithm, we avoid iterative computation and instead adopt a “look up table” technique. The stages of the proposed technique are: (1) Crawling the data reviews from websites; (2) cleaning and finding root words from the raw reviews; (3) computing the frequency of the meaningful opinion words; (4) analyzing customers sentiments towards defined objects. The experiments for evaluating the performance of the technique were conducted on a Hadoop cluster with 14 slave nodes. The results show that the proposed technique (stage 2 to 4) discovers useful opinions, is capable of processing big data efficiently and scalable.

Keywords: big data analysis, Hadoop MapReduce, analyzing text data, mining Indonesian reviews

Procedia PDF Downloads 181

Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

Procedia PDF Downloads 511

Authors: Kawser Ahmed, K. Bousson, Milca F. Coelho

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4D flight trajectory optimization is one of the key ingredients to improve flight efficiency and to enhance the air traffic capacity in the current air traffic management (ATM). The present paper explores the iterative dynamic programming (IDP) as a potential numerical optimization method for 4D flight trajectory optimization. IDP is an iterative version of the Dynamic programming (DP) method. Due to the numerical framework, DP is very suitable to deal with nonlinear discrete dynamic systems. The 4D waypoint representation of the flight trajectory is similar to the discretization by a grid system; thus DP is a natural method to deal with the 4D flight trajectory optimization. However, the computational time and space complexity demanded by the DP is enormous due to the immense number of grid points required to find the optimum, which prevents the use of the DP in many practical high dimension problems. On the other hand, the IDP has shown potentials to deal successfully with high dimension optimal control problems even with a few numbers of grid points at each stage, which reduces the computational effort over the traditional DP approach. Although the IDP has been applied successfully in chemical engineering problems, IDP is yet to be validated in 4D flight trajectory optimization problems. In this paper, the IDP has been successfully used to generate minimum length 4D optimal trajectory avoiding any obstacle in its path, such as a no-fly zone or residential areas when flying in low altitude to reduce noise pollution.

Keywords: 4D waypoint navigation, iterative dynamic programming, obstacle avoidance, trajectory optimization

Procedia PDF Downloads 130

Authors: Thorsten Prante, Robert Schöch, Ruth Fleisch, Vaheh Khachatouri, Alexander Walch

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The development of industrial plant control software is a complex and often very expensive task. One of the core problems is that a lot of the implementation and adaptation work can only be done after the plant hardware has been installed. In this paper, we present our approach to virtually developing and validating plant-level control software of production plants. This way, plant control software can be virtually commissioned before actual ramp-up of a plant, reducing actual commissioning costs and time. Technically, this is achieved by linking the actual plant-wide process control software (often called plant server) and an elaborate virtual plant model together to form an emulation system. Method-wise, we are suggesting a four-step iterative process with well-defined increments and time frame. Our work is based on practical experiences from planning to commissioning and start-up of several cut-to-size plants.

Keywords: iterative system design, virtual plant engineering, plant control software, simulation and emulation, virtual commissioning

Procedia PDF Downloads 457

Authors: Brahmi Brahim, Mohammad Habibur Rahman, Maarouf Saad, Cristóbal Ochoa Luna

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A repetitive training movement is an efficient method to improve the ability and movement performance of stroke survivors and help them to recover their lost motor function and acquire new skills. The ETS-MARSE is seven degrees of freedom (DOF) exoskeleton robot developed to be worn on the lateral side of the right upper-extremity to assist and rehabilitate the patients with upper-extremity dysfunction resulting from stroke. Practically, rehabilitation activities are repetitive tasks, which make the assistive/robotic systems to suffer from repetitive/periodic uncertainties and external perturbations induced by the high-order dynamic model (seven DOF) and interaction with human muscle which impact on the tracking performance and even on the stability of the exoskeleton. To ensure the robustness and the stability of the robot, a new nonlinear backstepping control was implemented with designed tests performed by healthy subjects. In order to limit and to reject the periodic/repetitive disturbances, an iterative estimator was integrated into the control of the system. The estimator does not need the precise dynamic model of the exoskeleton. Experimental results confirm the robustness and accuracy of the controller performance to deal with the external perturbation, and the effectiveness of the iterative estimator to reject the repetitive/periodic disturbances.

Keywords: backstepping control, iterative control, Rehabilitation, ETS-MARSE

Procedia PDF Downloads 253

Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

Procedia PDF Downloads 174

Authors: Rupu Yang, Cong Toan Tran, Assaad Zoughaib

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The work provides an iterative nonlinear programming method to synthesize a heat exchanger network by manipulating the trade-offs between the heat load of process heat exchangers (HEs) and utilities. We consider for the synthesis problem two cases, the first one without fixed cost for HEs, and the second one with fixed cost. For the no fixed cost problem, the nonlinear programming (NLP) model with all the potential HEs is optimized to obtain the global optimum. For the case with fixed cost, the NLP model is iterated through adding/removing HEs. The method was applied in five case studies and illustrated quite well effectiveness. Among which, the approach reaches the lowest TAC (2,904,026$/year) compared with the best record for the famous Aromatic plants problem. It also locates a slightly better design than records in literature for a 10 streams case without fixed cost with only 1/9 computational time. Moreover, compared to the traditional mixed-integer nonlinear programming approach, the iterative NLP method opens a possibility to consider constraints (such as controllability or dynamic performances) that require knowing the structure of the network to be calculated.

Keywords: heat exchanger network, synthesis, NLP, optimization

Procedia PDF Downloads 134

Authors: Nisar Ahmed Memon

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A new medical image watermarking scheme delivering high embedding capacity is presented in this paper. Integer Wavelet Transform (IWT), Companding technique and adaptive thresholding are used in this scheme. The proposed scheme implants, recovers the hidden information and restores the input image to its pristine state at the receiving end. Magnetic Resonance Imaging (MRI) images are used for experimental purposes. The scheme first segment the MRI medical image into non-overlapping blocks and then inserts watermark into wavelet coefficients having a high frequency of each block. The scheme uses block-based watermarking adopting iterative optimization of threshold for companding in order to avoid the histogram pre and post processing. Results show that proposed scheme performs better than other reversible medical image watermarking schemes available in literature for MRI medical images.

Keywords: adaptive thresholding, companding technique, data authentication, reversible watermarking

Procedia PDF Downloads 269

Authors: Adarsh Shroff

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Big data is a collection of dataset so large and complex that it becomes difficult to process using data base management tools. To perform operations like search, analysis, visualization on big data by using data mining; which is the process of extraction of patterns or knowledge from large data set. In recent years, the data mining applications become stale and obsolete over time. Incremental processing is a promising approach to refreshing mining results. It utilizes previously saved states to avoid the expense of re-computation from scratch. This project uses i2MapReduce, an incremental processing extension to Map Reduce, the most widely used framework for mining big data. I2MapReduce performs key-value pair level incremental processing rather than task level re-computation, supports not only one-step computation but also more sophisticated iterative computation, which is widely used in data mining applications, and incorporates a set of novel techniques to reduce I/O overhead for accessing preserved fine-grain computation states. To optimize the mining results, evaluate i2MapReduce using a one-step algorithm and three iterative algorithms with diverse computation characteristics for efficient mining.

Keywords: big data, map reduce, incremental processing, iterative computation

Procedia PDF Downloads 315

Authors: Lourenço Bastos, Filipa Carneiro, Bruno Vale, Rita Marques Joana Silva, Ricardo Freitas, Ângelo Marques, Sara Cortez, Alberta Coelho, Pedro Parreira, Liliana Sousa, Anabela Salgueiro, Bruno Silva

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The process of flushing is considered to be an adequate technique to reduce the risk of infection during the clinical practice of venous catheterization. Nonetheless, there is still a lack of adhesion to this method, in part due to the complexity of this procedure. The project SeringaDuo aimed to develop an innovative double-chamber syringe for intravenous sequential administration of drugs and serums. This device served the purpose of improving the adherence to the practice, through the reduction of manipulations needed, which also improves patient safety, and though the promotion of flushing practice by health professionals, by simplifying this task. To assist on the development of this innovative syringe, a numerical methodology was developed and validated in order to predict the syringe’s mechanical and flow behavior during the fluids’ loading and administration phases, as well as to allow the material behavior evaluation during its production. For this, three commercial numerical simulation software was used, namely ABAQUS, ANSYS/FLUENT, and MOLDFLOW. This methodology aimed to evaluate the concepts feasibility and to optimize the geometries of the syringe’s components, creating this way an iterative process for product development based on numerical simulations, validated by the production of prototypes. Through this methodology, it was possible to achieve a final design that fulfils all the characteristics and specifications defined. This iterative process based on numerical simulations is a powerful tool for product development that allows obtaining fast and accurate results without the strict need for prototypes. An iterative process can be implemented, consisting of consecutive constructions and evaluations of new concepts, to obtain an optimized solution, which fulfils all the predefined specifications and requirements.

Keywords: Venous catheterization, flushing, syringe, numerical simulation

Procedia PDF Downloads 135

Authors: Hudson Akewe

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We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality.

Keywords: multistep iterative procedures, multivalued mappings, equivalence results, fixed point

Procedia PDF Downloads 96

Authors: Onur Onder, Celal Tanuca, Mahir Ozil, Halil Sen, Alkım Ozkan, Engin Ceylan, Ali Istek, Ozgur Saglam

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White balance adjustment of LCD TVs is an important procedure which has a direct influence on quality perception. Existing methods adjust RGB gain and offset values in different white levels during production. This paper suggests an iterative method in which the gamma is pre-adjusted during the design stage, and only 80% white is adjusted during production by modifying only RGB gain values (offset values are not modified). This method reduces the white balance adjustment time, contributing to the total efficiency of the production. Experiment shows that the adjustment results are well within requirements.

Keywords: color temperature, LCD panel deviation, LCD TV manufacturing, white balance

Procedia PDF Downloads 186

Authors: Muhammad A. Alsubaie

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An iterative learning control framework designed in state feedback structure suffers a lack in investigating load disturbance considerations. The presented work discusses the controller previously designed, highlights the disturbance problem, finds new conditions using singular value principle to assure safe operation conditions with error convergence and reference tracking under the influence of load disturbance. It is known that periodic disturbances can be represented by a delay model in a positive feedback loop acting on the system input. This model can be manipulated by isolating the delay model and finding a controller for the overall system around the delay model to remedy the periodic disturbances using the small signal theorem. The overall system is the base for control design and load disturbance investigation. The major finding of this work is the load disturbance condition found which clearly sets safe operation condition under the influence of load disturbances such that the error tends to nearly zero as the system keeps operating trial after trial.

Keywords: iterative learning control, singular values, state feedback, load disturbance

Procedia PDF Downloads 142

Authors: Shryas Bhurat, Aryan Vashistha, Sampreet Dinakar Nayak, Ayush Gupta

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As the technology is advancing more towards high computational resources, there is a paradigm shift in the usage of these resources to optimize the design process. This paper discusses the usage of ‘Generative Design using Artificial Intelligence’ to build better models that adapt the operations like selection, mutation, and crossover to generate results. The human mind thinks of the simplest approach while designing an object, but the intelligence learns from the past & designs the complex optimized CAD Models. Generative Design takes the boundary conditions and comes up with multiple solutions with iterations to come up with a sturdy design with the most optimal parameter that is given, saving huge amounts of time & resources. The new production techniques that are at our disposal allow us to use additive manufacturing, 3D printing, and other innovative manufacturing techniques to save resources and design artistically engineered CAD Models. Also, this paper discusses the Genetic Algorithm, the Non-Domination technique to choose the right results using biomimicry that has evolved for current habitation for millions of years. The computer uses parametric models to generate newer models using an iterative approach & uses cloud computing to store these iterative designs. The later part of the paper compares the topology optimization technology with Generative Design that is previously being used to generate CAD Models. Finally, this paper shows the performance of algorithms and how these algorithms help in designing resource-efficient models.

Keywords: genetic algorithm, bio mimicry, generative modeling, non-dominant techniques

Procedia PDF Downloads 118

Authors: N. Dahraoui, M. Boulakroune, D. Benatia

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In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov-Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.

Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage

Procedia PDF Downloads 386

Authors: Umar Yusuf Batsari

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Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

Procedia PDF Downloads 393

Authors: Chae Hoon Park, Jong Kang Park, Jong Tae Kim

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Electrical characteristics of capacitive touchscreen need to be accurately analyzed to result in better performance for multi-channel capacitance sensing. In this paper, we extracted the panel resistances and capacitances of the touchscreen by comparing measurement data and model data. By employing a lumped RC model for driver-to-receiver paths in touchscreen, we estimated resistance and capacitance values according to the physical lengths of channel paths which are proportional to the RC model. As a result, we obtained the model having 95.54% accuracy of the measurement data.

Keywords: electrical characteristics of capacitive touchscreen, iterative extraction, lumped RC model, physical lengths of channel paths

Procedia PDF Downloads 310

Authors: Anteneh Getachew Gebrie, Rabian Wangkeeree

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The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

Keywords: Hilbert Space, minimization problems, Moreau-Yosida approximate, split feasibility problem

Procedia PDF Downloads 107

Authors: Chia-Yu Lin, Yu-Hsiang Shen, Cing-Ciao Ke, Chia-Hao Chang, Fan-Pin Tseng, Yu-Ching Ni, Sheng-Pin Tseng

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Tomosynthesis is an imaging system that generates a 3D image by scanning in a limited angular range. It could provide more depth information than traditional 2D X-ray single projection. Radiation dose in tomosynthesis is less than computed tomography (CT). Because of limited angular range scanning, there are many properties depending on scanning direction. Therefore, non-coplanar imaging technique was developed to improve image quality in traditional tomosynthesis. The purpose of this study was to establish the non-coplanar imaging technique of tomosynthesis system and evaluate this technique by the reconstructed image. INER prototype tomosynthesis system contains an X-ray tube, a flat panel detector, and a motion machine. This system could move X-ray tube in multiple directions during the acquisition. In this study, we investigated three different imaging techniques that were 2D X-ray single projection, traditional tomosynthesis, and non-coplanar tomosynthesis. An anthropopathic chest phantom was used to evaluate the image quality. It contained three different size lesions (3 mm, 5 mm and, 8 mm diameter). The traditional tomosynthesis acquired 61 projections over a 30 degrees angular range in one scanning direction. The non-coplanar tomosynthesis acquired 62 projections over 30 degrees angular range in two scanning directions. A 3D image was reconstructed by iterative image reconstruction algorithm (ML-EM). Our qualitative method was to evaluate artifacts in tomosynthesis reconstructed image. The quantitative method was used to calculate a peak-to-valley ratio (PVR) that means the intensity ratio of the lesion to the background. We used PVRs to evaluate the contrast of lesions. The qualitative results showed that in the reconstructed image of non-coplanar scanning, anatomic structures of chest and lesions could be identified clearly and no significant artifacts of scanning direction dependent could be discovered. In 2D X-ray single projection, anatomic structures overlapped and lesions could not be discovered. In traditional tomosynthesis image, anatomic structures and lesions could be identified clearly, but there were many artifacts of scanning direction dependent. The quantitative results of PVRs show that there were no significant differences between non-coplanar tomosynthesis and traditional tomosynthesis. The PVRs of the non-coplanar technique were slightly higher than traditional technique in 5 mm and 8 mm lesions. In non-coplanar tomosynthesis, artifacts of scanning direction dependent could be reduced and PVRs of lesions were not decreased. The reconstructed image was more isotropic uniformity in non-coplanar tomosynthesis than in traditional tomosynthesis. In the future, scan strategy and scan time will be the challenges of non-coplanar imaging technique.

Keywords: image reconstruction, non-coplanar imaging technique, tomosynthesis, X-ray imaging

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Authors: Ghussoun Al-Jeiroudi

Abstract:

Stochastic programming is one of the powerful technique which is used to solve real-life problems. Hence, the data of real-life problems is subject to significant uncertainty. Uncertainty is well studied and modeled by stochastic programming. Each day, problems become bigger and bigger and the need for a tool, which does deal with large scale problems, increase. Interior point method is a perfect tool to solve such problems. Interior point method is widely employed to solve the programs, which arise from stochastic programming. It is an iterative technique, so it is required a starting point. Well design starting point plays an important role in improving the convergence speed. In this paper, we propose a starting point for interior point method for multistage stochastic programming. Usually, the optimal solution of stage k+1 is used as starting point for the stage k. This point has the advantage of being close to the solution of the current program. However, it has a disadvantage; it is not in the feasible region of the current program. So, we suggest to take this point and modifying it. That is by adding to it a vector in the null space of the matrix of the unchanged constraints because the solution will change only in the null space of this matrix.

Keywords: interior point methods, stochastic programming, null space, starting points

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Dalvinder Kaur Mangal

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For the past decade, noise corrupted output measurements have been a fundamental research problem to be investigated. On the other hand, the estimation of the parameters for linear dynamic systems when also the input is affected by noise is recognized as more difficult problem which only recently has received increasing attention. Representations where errors or measurement noises/disturbances are present on both the inputs and outputs are usually called errors-in-variables (EIV) models. These disturbances may also have additive effects which are also considered in this paper. Parameter estimation of false EIV problem using equation error, output error and iterative prefiltering identification schemes with and without additive uncertainty, when only the output observation is corrupted by noise has been dealt in this paper. The comparative study of these three schemes has also been carried out.

Keywords: errors-in-variable (EIV), false EIV, equation error, output error, iterative prefiltering, Gaussian noise

Procedia PDF Downloads 458

Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Rindra Rantoson, Hichem Nouira, Nabil Anwer, Charyar Mehdi-Souzani

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Multiple measurements by means of various data acquisition systems are generally required to measure the shape of freeform workpieces for accuracy, reliability and holisticity. The obtained data are aligned and fused into a common coordinate system within a registration technique involving coarse and fine registrations. Standardized iterative methods have been established for fine registration such as Iterative Closest Points (ICP) and its variants. For coarse registration, no conventional method has been adopted yet despite a significant number of techniques which have been developed in the literature to supply an automatic rough matching between data sets. Two main issues are addressed in this paper: the coarse registration and the fine registration. For coarse registration, two novel automated methods based on the exploitation of discrete curvatures are presented: an enhanced Hough Transformation (HT) and an improved Ransac Transformation. The use of curvature features in both methods aims to reduce computational cost. For fine registration, a new variant of ICP method is proposed in order to reduce registration error using curvature parameters. A specific distance considering the curvature similarity has been combined with Euclidean distance to define the distance criterion used for correspondences searching. Additionally, the objective function has been improved by combining the point-to-point (P-P) minimization and the point-to-plane (P-Pl) minimization with automatic weights. These ones are determined from the preliminary calculated curvature features at each point of the workpiece surface. The algorithms are applied on simulated and real data performed by a computer tomography (CT) system. The obtained results reveal the benefit of the proposed novel curvature-based registration methods.

Keywords: discrete curvature, RANSAC transformation, hough transformation, coarse registration, ICP variant, point-to-point and point-to-plane minimization combination, computer tomography

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Authors: Zhuoran Li, Guan Qin

Abstract:

A robust and efficient compositional equilibrium characterization model for hydrate-containing systems is required, especially for time-critical simulations such as subsea pipeline flow assurance analysis, compositional simulation in hydrate reservoirs etc. A multiphase flash calculation framework, which combines Gibbs energy minimization function and cubic plus association (CPA) EoS, is developed to describe the highly non-ideal phase behavior of hydrate-containing systems. A non-iterative eigenvalue problem-solving approach for the trust-region sub-problem is selected to guarantee efficiency. The developed flash model is based on the state-of-the-art objective function proposed by Michelsen to minimize the Gibbs energy of the multiphase system. It is conceivable that a hydrate-containing system always contains polar components (such as water and hydrate inhibitors), introducing hydrogen bonds to influence phase behavior. Thus, the cubic plus associating (CPA) EoS is utilized to compute the thermodynamic parameters. The solid solution theory proposed by van der Waals and Platteeuw is applied to represent hydrate phase parameters. The trust-region method combined with the trust-region sub-problem non-iterative eigenvalue problem-solving approach is utilized to ensure fast convergence. The developed multiphase flash model's accuracy performance is validated by three available models (one published and two commercial models). Hundreds of published hydrate-containing system equilibrium experimental data are collected to act as the standard group for the accuracy test. The accuracy comparing results show that our model has superior performances over two models and comparable calculation accuracy to CSMGem. Efficiency performance test also has been carried out. Because the trust-region method can determine the optimization step's direction and size simultaneously, fast solution progress can be obtained. The comparison results show that less iteration number is needed to optimize the objective function by utilizing trust-region methods than applying line search methods. The non-iterative eigenvalue problem approach also performs faster computation speed than the conventional iterative solving algorithm for the trust-region sub-problem, further improving the calculation efficiency. A new thermodynamic framework of the multiphase flash model for the hydrate-containing system has been constructed in this work. Sensitive analysis and numerical experiments have been carried out to prove the accuracy and efficiency of this model. Furthermore, based on the current thermodynamic model in the oil and gas industry, implementing this model is simple.

Keywords: equation of state, hydrates, multiphase equilibrium, trust-region method

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Authors: Guenther Schuh, Michael Riesener, Frederic Diels

Abstract:

Nowadays, manufacturing companies are faced with the challenge of meeting heterogeneous customer requirements in short product life cycles with a variety of product functions. So far, some of the functional requirements remain unknown until late stages of the product development. A way to handle these uncertainties is the highly iterative product development (HIP) approach. By structuring the development project as a highly iterative process, this method provides customer oriented and marketable products. There are first approaches for combined, hybrid models comprising deterministic-normative methods like the Stage-Gate process and empirical-adaptive development methods like SCRUM on a project management level. However, almost unconsidered is the question, which development scopes can preferably be realized with either empirical-adaptive or deterministic-normative approaches. In this context, a development scope constitutes a self-contained section of the overall development objective. Therefore, this paper focuses on a methodology that deals with the uncertainty of requirements within the early development stages and the corresponding selection of the most appropriate development approach. For this purpose, internal influencing factors like a company’s technology ability, the prototype manufacturability and the potential solution space as well as external factors like the market accuracy, relevance and volatility will be analyzed and combined into an Agile-Indicator. The Agile-Indicator is derived in three steps. First of all, it is necessary to rate each internal and external factor in terms of the importance for the overall development task. Secondly, each requirement has to be evaluated for every single internal and external factor appropriate to their suitability for empirical-adaptive development. Finally, the total sums of internal and external side are composed in the Agile-Indicator. Thus, the Agile-Indicator constitutes a company-specific and application-related criterion, on which the allocation of empirical-adaptive and deterministic-normative development scopes can be made. In a last step, this indicator will be used for a specific clustering of development scopes by application of the fuzzy c-means (FCM) clustering algorithm. The FCM-method determines sub-clusters within functional clusters based on the empirical-adaptive environmental impact of the Agile-Indicator. By means of the methodology presented in this paper, it is possible to classify requirements, which are uncertainly carried out by the market, into empirical-adaptive or deterministic-normative development scopes.

Keywords: agile, highly iterative development, agile-indicator, product development

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Authors: Belgherbi Aicha, Hadjidj Ismahen, Bessaid Abdelhafid

Abstract:

Interpretation of medical images benefits from anatomical and physiological priors to optimize computer-aided diagnosis applications. Segmentation of liver, spleen and kidneys is regarded as a major primary step in the computer-aided diagnosis of abdominal organ diseases. In this paper, a semi-automated method for medical image data is presented for the abdominal organ segmentation data using mathematical morphology. Our proposed method is based on hierarchical segmentation and watershed algorithm. In our approach, a powerful technique has been designed to suppress over-segmentation based on mosaic image and on the computation of the watershed transform. Our algorithm is currency in two parts. In the first, we seek to improve the quality of the gradient-mosaic image. In this step, we propose a method for improving the gradient-mosaic image by applying the anisotropic diffusion filter followed by the morphological filters. Thereafter, we proceed to the hierarchical segmentation of the liver, spleen and kidney. To validate the segmentation technique proposed, we have tested it on several images. Our segmentation approach is evaluated by comparing our results with the manual segmentation performed by an expert. The experimental results are described in the last part of this work.

Keywords: anisotropic diffusion filter, CT images, morphological filter, mosaic image, simultaneous organ segmentation, the watershed algorithm

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