Search results for: fuzzy integrodifferential equation

Authors: Pejman Hosseinioun, Hasan Shakeri, Ghasem Ghorbanirostam

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In recent years, we have seen an increasing importance of research and study on knowledge source, decision support systems, data mining and procedure of knowledge discovery in data bases and it is considered that each of these aspects affects the others. In this article, we have merged information source and knowledge source to suggest a knowledge based system within limits of management based on storing and restoring of knowledge to manage information and improve decision making and resources. In this article, we have used method of data mining and Apriori algorithm in procedure of knowledge discovery one of the problems of Apriori algorithm is that, a user should specify the minimum threshold for supporting the regularity. Imagine that a user wants to apply Apriori algorithm for a database with millions of transactions. Definitely, the user does not have necessary knowledge of all existing transactions in that database, and therefore cannot specify a suitable threshold. Our purpose in this article is to improve Apriori algorithm. To achieve our goal, we tried using fuzzy logic to put data in different clusters before applying the Apriori algorithm for existing data in the database and we also try to suggest the most suitable threshold to the user automatically.

Keywords: decision support system, data mining, knowledge discovery, data discovery, fuzzy logic

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Authors: Shahrokh Barati

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In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Agung Budi Muljono, I Made Ginarsa, I Made Ari Nrartha

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A large-scale power system (LSPS) consists of two or more sub-systems connected by inter-connecting transmission. Loading pattern on an LSPS always changes from time to time and varies depend on consumer need. The serious instability problem is appeared in an LSPS due to load fluctuation in all of the bus. Adaptive neuro-fuzzy inference system (ANFIS)-based power system stabilizer (PSS) is presented to cover the stability problem and to enhance the stability of an LSPS. The ANFIS control is presented because the ANFIS control is more effective than Mamdani fuzzy control in the computation aspect. Simulation results show that the presented PSS is able to maintain the stability by decreasing peak overshoot to the value of −2.56 × 10−5 pu for rotor speed deviation Δω2−3. The presented PSS also makes the settling time to achieve at 3.78 s on local mode oscillation. Furthermore, the presented PSS is able to improve the peak overshoot and settling time of Δω3−9 to the value of −0.868 × 10−5 pu and at the time of 3.50 s for inter-area oscillation.

Keywords: ANFIS, large-scale, power system, PSS, stability enhancement

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Authors: Roberto Cabezas H

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The current work shows the methodology developed to create narrative lighting spaces for the multimedia performance piece 'cluster: the vanished paradise.' This empirical research is focused on exploring unconventional roles for machines in subjective creative processes, by delving into the semantics of data and machine intelligence algorithms in hybrid technological, creative contexts to expand epistemic domains trough human-machine cooperation. The creative process in scenic and performing arts is guided mostly by intuition; from that idea, we developed an approach to embed collective intuition in computational creative systems, by joining the properties of Generative Adversarial Networks (GAN’s) and Fuzzy Clustering based on a semi-supervised data creation and analysis pipeline. The model makes use of GAN’s to learn from phenomenological data (data generated from experience with lighting scenography) and algorithmic design data (augmented data by procedural design methods), fuzzy logic clustering is then applied to artificially created data from GAN’s to define narrative transitions built on membership index; this process allowed for the creation of simple and complex spaces with expressive capabilities based on position and light intensity as the parameters to guide the narrative. Hybridization comes not only from the human-machine symbiosis but also on the integration of different techniques for the implementation of the aided design system. Machine intelligence tools as proposed in this work are well suited to redefine collaborative creation by learning to express and expand a conglomerate of ideas and a wide range of opinions for the creation of sensory experiences. We found in GAN’s and Fuzzy Logic an ideal tool to develop new computational models based on interaction, learning, emotion and imagination to expand the traditional algorithmic model of computation.

Keywords: fuzzy clustering, generative adversarial networks, human-machine cooperation, hybrid collective data, multimedia performance

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Authors: O. Poleshchuk, E. Komarov

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In this paper, semantic spaces with the properties of completeness and orthogonality (complete orthogonal semantic spaces) were chosen as models of expert evaluations. As the theoretical and practical studies have shown all the properties of complete orthogonal semantic spaces correspond to the thinking activity of experts that is why these semantic spaces were chosen for modeling. Two methods of construction such spaces were proposed. Models of comparative and fuzzy cluster analysis of expert evaluations were developed. The practical application of the developed methods has demonstrated their viability and validity.

Keywords: expert evaluation, comparative analysis, fuzzy cluster analysis, theoretical and practical studies

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Authors: Arup K. Sarma, Jayshree Hazarika

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The North-eastern part of India, which receives heavier rainfall than other parts of the subcontinent, is of great concern now-a-days with regard to climate change. High intensity rainfall for short duration and longer dry spell, occurring due to impact of climate change, affects river morphology too. In the present study, an attempt is made to delineate the North-Eastern region of India into some homogeneous clusters based on the Fuzzy Clustering concept and to compare the resulting clusters obtained by using conventional methods and non conventional methods of clustering. The concept of clustering is adapted in view of the fact that, impact of climate change can be studied in a homogeneous region without much variation, which can be helpful in studies related to water resources planning and management. 10 IMD (Indian Meteorological Department) stations, situated in various regions of the North-east, have been selected for making the clusters. The results of the Fuzzy C-Means (FCM) analysis show different clustering patterns for different conditions. From the analysis and comparison it can be concluded that non conventional method of using GCM data is somehow giving better results than the others. However, further analysis can be done by taking daily data instead of monthly means to reduce the effect of standardization.

Keywords: climate change, conventional and nonconventional methods of clustering, FCM analysis, homogeneous regions

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Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

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A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

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Authors: S. S. Abas, Y. M. Yatim

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In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Jialin Wu, Zhiwei Lian, Jieyu Tang, Jingyun Shen

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Tornado is a serious and unpredictable natural disaster, which has an important impact on people's production and life. The probability of being hit by tornadoes in China was analyzed considering the principles of tornado formation. Then some suggestions on layout and shapes for newly-built buildings were provided combined with the characteristics of tornado wind fields. Fuzzy clustering and inverse closeness methods were used to evaluate the probability levels of tornado risks in various provinces based on classification and ranking. GIS was adopted to display the results. Finally, wind field single-vortex tornado was studied to discuss the optimized design of rural low-rise houses in Yancheng, Jiangsu as an example. This paper may provide enough data to support building and urban design in some specific regions.

Keywords: tornado probability, computational fluid dynamics, fuzzy mathematics, optimal design

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Authors: Saidu Ibrahim, Winston M. W. Shakantu

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The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.

Keywords: conceptual framework, cost overrun, material waste, project stags

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Authors: S. Valarmathi, P. B. Harathi, R. Sridhar, S. Balasubramanian

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Machine learning tools in medical diagnosis is increasing due to the improved effectiveness of classification and recognition systems to help medical experts in diagnosing breast cancer. In this study, ID3 chooses the splitting attribute with the highest gain in information, where gain is defined as the difference between before the split versus after the split. It is applied for age, location, taluk, stage, year, period, martial status, treatment, heredity, sex, and habitat against Very Serious (VS), Very Serious Moderate (VSM), Serious (S) and Not Serious (NS) to calculate the gain of information. The ranked histogram gives the gain of each field for the breast cancer data. The doctors use TNM staging which will decide the risk level of the breast cancer and play an important decision making field in fuzzy logic for perception based measurement. Spatial risk area (taluk) of the breast cancer is calculated. Result clearly states that Coimbatore (North and South) was found to be risk region to the breast cancer than other areas at 20% criteria. Weighted value of taluk was compared with criterion value and integrated with Map Object to visualize the results. ID3 algorithm shows the high breast cancer risk regions in the study area. The study has outlined, discussed and resolved the algorithms, techniques / methods adopted through soft computing methodology like ID3 algorithm for prognostic decision making in the seriousness of the breast cancer.

Keywords: ID3 algorithm, breast cancer, fuzzy logic, MATLAB

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Authors: Nigina Toktasynova, Sholpan Sagyndykova, Zhanat Kenzhebayeva, Maksat Kalimoldayev, Mariya Ishimova, Irbulat Utepbergenov

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Any business needs a stable operation and continuous improvement, therefore it is necessary to constantly interact with the environment, to analyze the work of the enterprise in terms of employees, executives and consumers, as well as to correct any inconsistencies of certain types of processes and their aggregate. In the case of heat supply organizations, in addition to suppliers, local legislation must be considered which often is the main regulator of pricing of services. In this case, the process approach used to build a functional organizational structure in these types of businesses in Kazakhstan is a challenge not only in the implementation, but also in ways of analyzing the employee's salary. To solve these problems, we investigated the management system of heating enterprise, including strategic planning based on the balanced scorecard (BSC), quality management in accordance with the standards of the Quality Management System (QMS) ISO 9001 and analysis of the system based on expert judgment using fuzzy inference. To carry out our work we used the theory of fuzzy sets, the QMS in accordance with ISO 9001, BSC according to the method of Kaplan and Norton, method of construction of business processes according to the notation IDEF0, theory of modeling using Matlab software simulation tools and graphical programming LabVIEW. The results of the work are as follows: We determined possibilities of improving the management of heat-supply plant-based on QMS; after the justification and adaptation of software tool it has been used to automate a series of functions for the management and reduction of resources and for the maintenance of the system up to date; an application for the analysis of the QMS based on fuzzy inference has been created with novel organization of communication software with the application enabling the analysis of relevant data of enterprise management system.

Keywords: balanced scorecard, heat supply, quality management system, the theory of fuzzy sets

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Fatéma Zahra Benchara, Mohamed Youssfi, Omar Bouattane, Hassan Ouajji, Mohamed Ouadi Bensalah

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The aim of this paper is to present a distributed implementation of the Type-2 Fuzzy algorithm in a parallel and distributed computing environment based on mobile agents. The proposed algorithm is assigned to be implemented on a SPMD (Single Program Multiple Data) architecture which is based on cooperative mobile agents as AVPE (Agent Virtual Processing Element) model in order to improve the processing resources needed for performing the big data image segmentation. In this work we focused on the application of this algorithm in order to process the big data MRI (Magnetic Resonance Images) image of size (n x m). It is encapsulated on the Mobile agent team leader in order to be split into (m x n) pixels one per AVPE. Each AVPE perform and exchange the segmentation results and maintain asynchronous communication with their team leader until the convergence of this algorithm. Some interesting experimental results are obtained in terms of accuracy and efficiency analysis of the proposed implementation, thanks to the mobile agents several interesting skills introduced in this distributed computational model.

Keywords: distributed type-2 fuzzy algorithm, image processing, mobile agents, parallel and distributed computing

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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

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

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Authors: Soumava Boral, Sanjay K. Chaturvedi, Ian Howard, Kristoffer McKee, V. N. A. Naikan

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Due to strict regulations from government to enhance the possibilities of sustainability practices in industries, and noting the advances in sustainable manufacturing practices, it is necessary that the associated processes are also sustainable. Maintenance of large scale and complex machines is a pivotal task to maintain the uninterrupted flow of manufacturing processes. Appropriate maintenance practices can prolong the lifetime of machines, and prevent associated breakdowns, which subsequently reduces different cost heads. Selection of the best maintenance strategies for such machines are considered as a burdensome task, as they require the consideration of multiple technical criteria, complex mathematical calculations, previous fault data, maintenance records, etc. In the era of the fourth industrial revolution, organizations are rapidly changing their way of business, and they are giving their utmost importance to sensor technologies, artificial intelligence, data analytics, automations, etc. In this work, the effectiveness of several maintenance strategies (e.g., preventive, failure-based, reliability centered, condition based, total productive maintenance, etc.) related to a large scale and complex gearbox, operating in a steel processing plant is evaluated in terms of economic, social, environmental and technical criteria. As it is not possible to obtain/describe some criteria by exact numerical values, these criteria are evaluated linguistically by cross-functional experts. Fuzzy sets are potential soft-computing technique, which has been useful to deal with linguistic data and to provide inferences in many complex situations. To prioritize different maintenance practices based on the identified sustainable criteria, multi-criteria decision making (MCDM) approaches can be considered as potential tools. Multi-Attributive Ideal Real Comparative Analysis (MAIRCA) is a recent addition in the MCDM family and has proven its superiority over some well-known MCDM approaches, like TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and ELECTRE (ELimination Et Choix Traduisant la REalité). It has a simple but robust mathematical approach, which is easy to comprehend. On the other side, due to some inherent drawbacks of Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS), recently, the use of Fermatean Fuzzy Sets (FFSs) has been proposed. In this work, we propose the novel concept of FF-MAIRCA. We obtain the weights of the criteria by experts’ evaluation and use them to prioritize the different maintenance practices according to their suitability by FF-MAIRCA approach. Finally, a sensitivity analysis is carried out to highlight the robustness of the approach.

Keywords: Fermatean fuzzy sets, Fermatean fuzzy MAIRCA, maintenance strategy selection, sustainable manufacturing, MCDM

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Authors: Kamel Al-Khaled

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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: Jiradeach Kalayaruan, Tosawat Seetawan

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This paper studied the energy of the nature systems by looking at the overall image throughout the universe. The energy of the nature systems was developed from the Einstein’s energy equation. The researcher used the new ideas called even 2n and odd 3n light dimension energy states systems, which were developed from Einstein’s relativity energy theory equation. In this study, the major methodology the researchers used was the basic principle ideas or beliefs of some religions such as Buddhism, Christianity, Hinduism, Islam, or Tao in order to get new discoveries. The basic beliefs of each religion - Nivara, God, Ether, Atman, and Tao respectively, were great influential ideas on the researchers to use them greatly in the study to form new ideas from philosophy. Since the philosophy of each religion was alive with deep insight of the physical nature relative energy, it connected the basic beliefs to light dimension energy states systems. Unfortunately, Einstein’s original relative energy equation showed only even 2n light dimension energy states systems (if n = 1,…,∞). But in advance ideas, the researchers multiplied light dimension energy by Einstein’s original relative energy equation and get new idea of theoritical physics in odd 3n light dimension energy states systems (if n = 1,…,∞). Because from basic principle ideas or beliefs of some religions philosophy of each religion, you had to add the media light dimension energy into Einstein’s original relative energy equation. Consequently, the simple meaning picture in deep insight showed that you could touch light dimension energy of Nivara, God, Ether, Atman, and Tao by light dimension energy. Since light dimension energy was transferred by Nivara, God, Ether, Atman and Tao, the researchers got the new equation of odd 3n light dimension energy states systems. Moreover, the researchers expected to be able to solve overview problems of all light dimension energy in all nature relative energy, which are developed from Eistein’s relative energy equation.The finding of the study was called 'super nature relative energy' ( in odd 3n light dimension energy states systems (if n = 1,…,∞)). From the new ideas above you could do the summation of even 2n and odd 3n light dimension energy states systems in all of nature light dimension energy states systems. In the future time, the researchers will expect the new idea to be used in insight theoretical physics, which is very useful to the development of quantum mechanics, all engineering, medical profession, transportation, communication, scientific inventions, and technology, etc.

Keywords: 2n light dimension energy states systems effect, Ether, even 2n light dimension energy states systems, nature relativity, Nivara, odd 3n light dimension energy states systems, perturbation points energy, relax point energy states systems, stress perturbation energy states systems effect, super relative energy

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Authors: Alireza Abdikian

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By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: Selin Guney, Andres Riquelme

Abstract:

Among the main purposes of optimal and efficient forecasts of agricultural commodity prices is to guide the firms to advance the economic decision making process such as planning business operations and marketing decisions. Governments are also the beneficiaries and suppliers of agricultural price forecasts. They use this information to establish a proper agricultural policy, and hence, the forecasts affect social welfare and systematic errors in forecasts could lead to a misallocation of scarce resources. Various empirical approaches have been applied to forecast commodity prices that have used different methodologies. Most commonly-used approaches to forecast commodity sectors depend on classical time series models that assume values of the response variables are precise which is quite often not true in reality. Recently, this literature has mostly evolved to a consideration of fuzzy time series models that provide more flexibility in terms of the classical time series models assumptions such as stationarity, and large sample size requirement. Besides, fuzzy modeling approach allows decision making with estimated values under incomplete information or uncertainty. A number of fuzzy time series models have been developed and implemented over the last decades; however, most of them are not appropriate for forecasting repeated and nonconsecutive transitions in the data. The modeling scheme used in this paper eliminates this problem by introducing Markov modeling approach that takes into account both the repeated and nonconsecutive transitions. Also, the determination of length of interval is crucial in terms of the accuracy of forecasts. The problem of determining the length of interval arbitrarily is overcome and a methodology to determine the proper length of interval based on the distribution or mean of the first differences of series to improve forecast accuracy is proposed. The specific purpose of this paper is to propose and investigate the potential of a new forecasting model that integrates methodologies for determining the proper length of interval based on the distribution or mean of the first differences of series and Fuzzy Time Series- Markov Chain model. Moreover, the accuracy of the forecasting performance of proposed integrated model is compared to different univariate time series models and the superiority of proposed method over competing methods in respect of modelling and forecasting on the basis of forecast evaluation criteria is demonstrated. The application is to daily corn and soybean prices observed at three commercially important North Carolina markets; Candor, Cofield and Roaring River for corn and Fayetteville, Cofield and Greenville City for soybeans respectively. One main conclusion from this paper is that using fuzzy logic improves the forecast performance and accuracy; the effectiveness and potential benefits of the proposed model is confirmed with small selection criteria value such MAPE. The paper concludes with a discussion of the implications of integrating fuzzy logic and nonarbitrary determination of length of interval for the reliability and accuracy of price forecasts. The empirical results represent a significant contribution to our understanding of the applicability of fuzzy modeling in commodity price forecasts.

Keywords: commodity, forecast, fuzzy, Markov

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Authors: Ingrid Argote, John Archila, Marcelo Becker

Abstract:

In agriculture, intelligent systems applications have generated great advances in automating some of the processes in the production chain. In order to improve the efficiency of those systems is proposed a vision system to estimate the amount of fruits in sweet orange trees. This work presents a system proposal using capture of thermal images and fuzzy logic. A bibliographical review has been done to analyze the state-of-the-art of the different systems used in fruit recognition, and also the different applications of thermography in agricultural systems. The algorithm developed for this project uses the metrics of the fuzzines parameter to the contrast improvement and segmentation of the image, for the counting algorith m was used the Hough transform. In order to validate the proposed algorithm was created a bank of images of sweet orange Citrus (L.) Osbeck acquired in the Maringá Farm. The tests with the algorithm Indicated that the variation of the tree branch temperature and the fruit is not very high, Which makes the process of image segmentation using this differentiates, This Increases the amount of false positives in the fruit counting algorithm. Recognition of fruits isolated with the proposed algorithm present an overall accuracy of 90.5 % and grouped fruits. The accuracy was 81.3 %. The experiments show the need for a more suitable hardware to have a better recognition of small temperature changes in the image.

Keywords: Agricultural systems, Citrus, Fuzzy logic, Thermal images.

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Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

Procedia PDF Downloads 501