Search results for: NARX (Nonlinear Autoregressive Exogenous Model)

Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Arun Kumar Yadav, Badam Singh Kushvah

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In the present work, we investigated displaced periodic orbits in the linear order in the circular restricted three-body Sun-Jupiter system, where the third mass-less body utilizes solar electric sail. The electric solar sail is a new space propulsion concept which uses the solar wind momentum for producing thrust, and it is somewhat like to the more well-known solar radiation pressure sail which is often called simply the solar sail. Moreover, we implement the feedback linearization control scheme to perform the stabilization and trajectory tracking for the nonlinear system. Further, we derived periodic orbits analytically in linear order by introducing a first order approximation. These approximate analytic solutions are utilized in a numerical search to determine displaced periodic orbit in the full nonlinear model. We found the displaced periodic orbit for the defined non-linear model and stabilized the model.

Keywords: solar electric sail, circular restricted three-body problem (CRTBP), displaced orbit, feedback linearization control

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Authors: Toshinori Nawata

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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Longqing Li

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The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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Authors: Babesse Saad, Ameddah Djemeleddine

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In this paper, a learning algorithm using neuronal networks to improve the roll stability and prevent the rollover in a single unit heavy vehicle is proposed. First, LQR control to keep balanced normalized rollovers, between front and rear axles, below the unity, then a data collected from this controller is used as a training basis of a neuronal regulator. The ANN controller is thereafter applied for the nonlinear side force model, and gives satisfactory results than the LQR one.

Keywords: rollover, single unit heavy vehicle, neural networks, nonlinear side force

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Masood Roohi, Amir Taghavipour

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This paper describes a strategy to develop an energy management system (EMS) for a charge-sustaining power-split hybrid electric vehicle. This kind of hybrid electric vehicles (HEVs) benefit from the advantages of both parallel and series architecture. However, it gets relatively more complicated to manage power flow between the battery and the engine optimally. The applied strategy in this paper is based on nonlinear model predictive control approach. First of all, an appropriate control-oriented model which was accurate enough and simple was derived. Towards utilization of this controller in real-time, the problem was solved off-line for a vast area of reference signals and initial conditions and stored the computed manipulated variables inside look-up tables. Look-up tables take a little amount of memory. Also, the computational load dramatically decreased, because to find required manipulated variables the controller just needed a simple interpolation between tables.

Keywords: hybrid electric vehicles, energy management system, nonlinear model predictive control, real-time

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

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This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Wong Hock Tsen

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This study aims to investigate the impact of exchange rate volatility on real export in Malaysia. The moving standard deviation with order three (MSD(3)) is used for the measurement of exchange rate volatility. The conventional and partially asymmetric autoregressive distributed lag (ARDL) models are used in the estimations. This study finds exchange rate volatility to have significant impact on real total export and some sub-categories of real total export. Moreover, this study finds that the positive or negative exchange rate volatility tends to have positive or negative impact on real export. Exchange rate volatility can be harmful to export of Malaysia.

Keywords: exchange rate volatility, autoregressive distributed lag, export, Malaysia

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Authors: Madhu Aneja, Sapna Sharma

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Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Syed Aziz Rasool, Ayesha Zaman

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Poverty is one of the most important problems for any developing nation. Workers’ remittances and investment plays a crucial role in development of any country by reducing the poverty level in Pakistan. This research studies the relationship between workers’ remittances and poverty alleviation. It also focused the significant effect on poverty reduction. This study uses time series data for the period of 1972-2013. Autoregressive Distributed Lag (ARDL)Model and Error Correction (ECM)Model has been used in order to find out the long run and short run relationship between the worker’s remittances and poverty level respectively. Thus, inflow of remittances showed the significant and negative impact on poverty level. Moreover, coefficient of error correction model explains the adjustment towards convergence and it has highly significant and negative value. According to this research, Policy makers should strongly focus on positive and effective policies to attract more remittances. JELCODE: JEL: J61

Keywords: ECM, ARDL, AIC, SC

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Authors: Armin Rahmatfam, Mohammad Zehsaz, Farid Vakili Tahami, Nasser Ghassembaglou

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In this paper the thermal ratcheting, kinematic hardening parameters C, γ, isotropic hardening parameters and also k, b, Q combined isotropic/kinematic hardening parameters have been obtained experimentally from the monotonic, strain controlled cyclic tests at room and elevated temperatures of 20°C, 100°C, and 400°C. These parameters are used in nonlinear combined isotropic/kinematic hardening model to predict better description of the loading and reloading cycles in the cyclic indentation as well as thermal ratcheting. For this purpose, three groups of specimens made of Aluminum 7075-T6 have been investigated. After each test and using stable hysteretic cycles, material parameters have been obtained for using in combined nonlinear isotropic/kinematic hardening models. Also the methodology of obtaining the correct kinematic/isotropic hardening parameters is presented.

Keywords: combined hardening model, kinematic hardening, isotropic hardening, cyclic tests

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Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Abdelmalek Ouannou, Adil Brouri, Laila Kadi, Tarik

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Switched reluctance motor (SRM) has a major interest in a large domain as in electric vehicle driving because of its wide range of speed operation, high performances, low cost, and robustness to run under degraded conditions. The purpose of the paper is to develop a new analytical approach for modeling SRM parameters. Then, an identification scheme is proposed to obtain the SRM parameters. Since the SRM is featured by a highly nonlinear behavior, modeling these devices is difficult. Then, it is convenient to develop an accurate model describing the SRM. Furthermore, it is always operated in the magnetically saturated mode to maximize the energy transfer. Accordingly, it is shown that the SRM can be accurately described by a generalized polynomial Hammerstein model, i.e., the parallel connection of several Hammerstein models having polynomial nonlinearity. Presently an analytical identification method is developed using a chirp excitation signal. Afterward, the parameters of the obtained model have been determined using Finite Element Method analysis. Finally, in order to show the effectiveness of the proposed method, a comparison between the true and estimate models has been performed. The obtained results show that the output responses are very close.

Keywords: switched reluctance motor, swept-sine signal, generalized Hammerstein model, nonlinear system

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Authors: Yanling Li, Linying Ji, Zita Oravecz, Timothy R. Brick, Michael D. Hunter, Sy-Miin Chow

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Assessing several individuals intensively over time yields intensive longitudinal data (ILD). Even though ILD provide rich information, they also bring other data analytic challenges. One of these is the increased occurrence of missingness with increased study length, possibly under non-ignorable missingness scenarios. Multiple imputation (MI) handles missing data by creating several imputed data sets, and pooling the estimation results across imputed data sets to yield final estimates for inferential purposes. In this article, we introduce dynr.mi(), a function in the R package, Dynamic Modeling in R (dynr). The package dynr provides a suite of fast and accessible functions for estimating and visualizing the results from fitting linear and nonlinear dynamic systems models in discrete as well as continuous time. By integrating the estimation functions in dynr and the MI procedures available from the R package, Multivariate Imputation by Chained Equations (MICE), the dynr.mi() routine is designed to handle possibly non-ignorable missingness in the dependent variables and/or covariates in a user-specified dynamic systems model via MI, with convergence diagnostic check. We utilized dynr.mi() to examine, in the context of a vector autoregressive model, the relationships among individuals’ ambulatory physiological measures, and self-report affect valence and arousal. The results from MI were compared to those from listwise deletion of entries with missingness in the covariates. When we determined the number of iterations based on the convergence diagnostics available from dynr.mi(), differences in the statistical significance of the covariate parameters were observed between the listwise deletion and MI approaches. These results underscore the importance of considering diagnostic information in the implementation of MI procedures.

Keywords: dynamic modeling, missing data, mobility, multiple imputation

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Authors: I. Khabbazi, R. Ghasemi

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This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Shewangizaw Tesfaye Wolde

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The current engineering community has developed a method called performance based seismic design in which we design structures based on predefined performance levels set by the parties. Since we design our structures economically for the maximum actions expected in the life of structures they go beyond their elastic limit, in need of nonlinear analysis. In this paper conventional pushover analysis (nonlinear static analysis) is used for the performance assessment of the case study Reinforced Concrete (RC) Frame building located in Addis Ababa City, Ethiopia where proposed peak ground acceleration value by RADIUS 1999 project and others is more than twice as of EBCS-8:1995 (RADIUS 1999 project) by taking critical planar frame. Fiber beam-column model is used to control material nonlinearity with tension stiffening effect. The reliability of the fiber model and validation of software outputs are checked under verification chapter. Therefore, the aim of this paper is to propose a way for structural performance assessment of existing reinforced concrete frame buildings as well as design check.

Keywords: seismic, performance, fiber model, tension stiffening, reinforced concrete

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: non-stationary, BINARMA(1, 1) model, Poisson innovations, conditional maximum likelihood, CML

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Authors: A. Mansouri, F. Krim

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This paper presents two techniques for DC motor parameters identification. We propose a numerical method using the adaptive extensive recursive least squares (AERLS) algorithm for real time parameters estimation. This algorithm, based on minimization of quadratic criterion, is realized in simulation for parameters identification of DC motor autoregressive moving average with extra inputs (ARMAX). As advanced technique, we use genetic algorithms (GA) identification with biased estimation for high dynamic performance speed regulation. DC motors are extensively used in variable speed drives, for robot and solar panel trajectory control. GA effectiveness is derived through comparison of the two approaches.

Keywords: ARMAX model, DC motor, AERLS, GA, optimization, parameter identification, PID speed regulation

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Authors: Francesco Morgan Bono, Simone Cinquemani

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This research aims to enhance bridge monitoring by employing innovative techniques that incorporate exogenous factors into the modeling of sensor signals, thereby improving long-term predictability beyond traditional static methods. Using real datasets from two different bridges equipped with Linear Variable Displacement Transducer (LVDT) sensors, the study investigates the fundamental principles governing sensor behavior for more precise long-term forecasts. Additionally, the research evaluates performance on noisy and synthetically damaged data, proposing a residual-based alarm system to detect anomalies in the bridge. In summary, this novel approach combines advanced modeling, exogenous factors, and anomaly detection to extend prediction horizons and improve preemptive damage recognition, significantly advancing structural health monitoring practices.

Keywords: structural health monitoring, dynamic models, sindy, railway bridges

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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: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

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In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller.

Keywords: the Bouc-Wen hysteresis model, particle swarm optimization, Prandtl-Ishlinskii model, automation engineering

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Authors: Zahid Ahmad, Nosheen Imran, Nauman Ali, Farah Amir

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The objective of the study is to forecast the US Dollar and Pak Rupee exchange rate by using time series models. For this purpose, daily exchange rates of US and Pakistan for the period of January 01, 2007 - June 2, 2017, are employed. The data set is divided into in sample and out of sample data set where in-sample data are used to estimate as well as forecast the models, whereas out-of-sample data set is exercised to forecast the exchange rate. The ADF test and PP test are used to make the time series stationary. To forecast the exchange rate ARIMA model and GARCH model are applied. Among the different Autoregressive Integrated Moving Average (ARIMA) models best model is selected on the basis of selection criteria. Due to the volatility clustering and ARCH effect the GARCH (1, 1) is also applied. Results of analysis showed that ARIMA (0, 1, 1 ) and GARCH (1, 1) are the most suitable models to forecast the future exchange rate. Further the GARCH (1,1) model provided the volatility with non-constant conditional variance in the exchange rate with good forecasting performance. This study is very useful for researchers, policymakers, and businesses for making decisions through accurate and timely forecasting of the exchange rate and helps them in devising their policies.

Keywords: exchange rate, ARIMA, GARCH, PAK/USD

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Krisada Lekdee, Sunee Sammatat, Nittaya Boonsit

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This paper proposes a GLMM with spatial and temporal effects for malaria data in Thailand. A Bayesian method is used for parameter estimation via Gibbs sampling MCMC. A conditional autoregressive (CAR) model is assumed to present the spatial effects. The temporal correlation is presented through the covariance matrix of the random effects. The malaria quarterly data have been extracted from the Bureau of Epidemiology, Ministry of Public Health of Thailand. The factors considered are rainfall and temperature. The result shows that rainfall and temperature are positively related to the malaria morbidity rate. The posterior means of the estimated morbidity rates are used to construct the malaria maps. The top 5 highest morbidity rates (per 100,000 population) are in Trat (Q3, 111.70), Chiang Mai (Q3, 104.70), Narathiwat (Q4, 97.69), Chiang Mai (Q2, 88.51), and Chanthaburi (Q3, 86.82). According to the DIC criterion, the proposed model has a better performance than the GLMM with spatial effects but without temporal terms.

Keywords: Bayesian method, generalized linear mixed model (GLMM), malaria, spatial effects, temporal correlation

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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