Search results for: nonlinear processes

Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Yosra Baaziz, Moez Labidi

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Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: Ju-young Hwang, Hyo-Gyoung Kwak, Hong Jae Yim

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This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical non-linearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, Prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC structures, heat transfer analysis, nonlinear analysis, after-cooling concrete model

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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: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: V. Tabrizi, A. Vali, R. GHasemi, V. Behnamgol

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In this article, a nonlinear model of an under actuated six degrees of freedom (6 DOF) quadrotor UAV is derived on the basis of the Newton-Euler formula. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The robust nonlinear control strategy includes a smooth second order non-singular terminal sliding mode control which is applied to stabilizing this model. The control method is on the basis of super twisting algorithm for removing the chattering and producing smooth control signal. Also, nonsingular terminal sliding mode idea is used for introducing a nonlinear sliding variable that guarantees the finite time convergence in sliding phase. Simulation results show that the proposed algorithm is robust against uncertainty or disturbance and guarantees a fast and precise control signal.

Keywords: quadrotor UAV, nonsingular terminal sliding mode, second order sliding mode t, electronics, control, signal processing

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: J.P. Henriques, E. R. Neto, G. Almeida, G. Ribeiro, J.V. Coutinho, A.B. Lugli

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Industry 4.0, or the Fourth Industrial Revolution, is transforming the relationship between people and machines. In this scenario, some technologies such as Cloud Computing, Internet of Things, Augmented Reality, Artificial Intelligence, Additive Manufacturing, among others, are making industries and devices increasingly intelligent. One of the most powerful technologies of this new revolution is the Digital Twin, which allows the virtualization of a real system or process. In this context, the present paper addresses the linear and nonlinear dynamic study of a didactic level plant using Digital Twin. In the first part of the work, the level plant is identified at a fixed point of operation, BY using the existing method of least squares means. The linearized model is embedded in a Digital Twin using Automation Studio® from Famous Technologies. Finally, in order to validate the usage of the Digital Twin in the linearized study of the plant, the dynamic response of the real system is compared to the Digital Twin. Furthermore, in order to develop the nonlinear model on a Digital Twin, the didactic level plant is identified by using the method proposed by Hammerstein. Different steps are applied to the plant, and from the Hammerstein algorithm, the nonlinear model is obtained for all operating ranges of the plant. As for the linear approach, the nonlinear model is embedded in the Digital Twin, and the dynamic response is compared to the real system in different points of operation. Finally, yet importantly, from the practical results obtained, one can conclude that the usage of Digital Twin to study the dynamic systems is extremely useful in the industrial environment, taking into account that it is possible to develop and tune controllers BY using the virtual model of the real systems.

Keywords: industry 4.0, digital twin, system identification, linear and nonlinear models

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Authors: Habib Akbarzadeh Bengar, Mohammad Asadi Kiadehi, Ali Rameeh

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The result of the past earthquakes has shown that insufficient amount of stirrups and brittle behavior of concrete lead to the shear and flexural failure in reinforced concrete (RC) members. In this paper, an analytical model proposed to predict the nonlinear behavior of RC and SFRC elements and frames. In this model, some important parameter such as shear effect, varying axial load, and longitudinal bar buckling are considered. The results of analytical model were verified with experimental tests. The results of verification have shown that the proposed analytical model can predict the nonlinear behavior of RC and SFRC members and also frames accurately. In addition, the results have shown that use of steel fibers increased bearing capacity and ductility of RC frame. Due to this enhancement in shear strength and ductility, insufficient amount of stirrups, which resulted in shear failure, can be offset with usage of the steel fibers. In addition to the steps taken, to analyze the effects of fibers percentages on the bearing capacity and ductility of frames parametric studies have been performed to investigate of these effects.

Keywords: nonlinear analysis, SFRC frame, shear failure, varying an axial load

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Markéta Gregušová, Vladimíra Schindlerová, Ivana Šajdlerová, Petr Mohyla, Jan Kedroň

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Company managers are always looking for more and more opportunities to succeed in today's fiercely competitive market. To maintain your place among the successful companies on the market today or to come up with a revolutionary business idea is much more difficult than before. Each new or improved method, tool, or approach that can improve the functioning of business processes or even of the entire system is worth checking and verification. The use of simulation in the design of manufacturing systems and their management in practice is one of the ways without increased risk, which makes it possible to find the optimal parameters of manufacturing processes and systems. The paper presents an example of use of simulation for solution of the bottleneck problem in the concrete company.

Keywords: practical applications, business processes, systems, simulation

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Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi

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The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Keywords: active magnetic bearing, three pole AMB, hybrid control, Lyapunov function

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Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous

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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization

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Authors: Biaou Jean-Baptiste Kouchoro, Anissa Meziane, Philippe Micheau, Mathieu Renier, Nicolas Quaegebeur

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Numerous experimental and numerical studies have shown the interest of the local defects resonance (LDR) for the Non-Destructive Testing of metallic and composite plates. Indeed, guided ultrasonic waves such as Lamb waves, which are increasingly used for the inspection of these flat structures, enable the generation of local resonance phenomena by their interaction with a damaged area, allowing the detection of defects. When subjected to a large amplitude motion, a nonlinear behavior can predominate in the damaged area. This work presents a 2D Finite Element Model of the local resonance of a 12 mm long and 5 mm deep Flat Bottom Hole (FBH) in a 6 mm thick aluminum plate under the excitation induced by an incident A0 Lamb mode. The analysis of the transient response of the FBH enables the precise determination of its resonance frequencies and the associate modal deformations. Then, a linear parametric study varying the geometrical properties of the FBH highlights the sensitivity of the resonance frequency with respect to the plate thickness. It is demonstrated that the resonance effect disappears when the ratio of thicknesses between the FBH and the plate is below 0.1. Finally, the nonlinear behavior of the FBH is considered and studied introducing geometrical (taken into account the nonlinear component of the strain tensor) nonlinearities that occur at large vibration amplitudes. Experimental analysis allows observation of the resonance effects and nonlinear response of the FBH. The differences between these experimental results and the numerical results will be commented on. The results of this study are promising and allow to consider more realistic defects such as delamination in composite materials.

Keywords: guided waves, non-destructive testing, dynamic field testing, non-linear ultrasound/vibration

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Authors: Younghoo Choi, Yong Jun, Jinkoo Kim

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In this study seismic performance of typical reinforced concrete staggered wall system structures was evaluated through nonlinear static and incremental dynamic analyses. To this end, and 15-story SWS structures were designed and were analyzed to obtain their nonlinear force-displacement relationships. The analysis results showed that the 5-story SWS structures failed due to yielding of columns and walls located in the lower stories, whereas in the 15-story structures plastic hinges were more widely distributed throughout the stories.

Keywords: staggered wall systems, reinforced concrete, seismic performance

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Khalil Aghapouramin, Mostafa Ranjbar

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Run- to- Run (R2 R) control was developed in order to monitor and control different semiconductor manufacturing processes based upon the fundamental engineering frameworks. This technology allows rectification in the optimum direction. This control always had a significant potency in which was appeared in a variety of processes. The term run to run refers to the case where the act of control would take with the aim of getting batches of silicon wafers which produced in a manufacturing process. In the present work, a brief review about run-to-run control investigated which mainly is effective in the manufacturing process.

Keywords: Run-to-Run (R2R) control, manufacturing, process in engineering, manufacturing controls

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Authors: Dehini Rachid, Ferdi Brahim

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The shunt active power filter (SAPF) is not destined only to improve the power factor, but also to compensate the unwanted harmonic currents produced by nonlinear loads. This paper presents a SAPF with identification and control method based on artificial neural network (ANN). To identify harmonics, many techniques are used, among them the conventional p-q theory and the relatively recent one the artificial neural network method. It is difficult to get satisfied identification and control characteristics by using a normal (ANN) due to the nonlinearity of the system (SAPF + fast nonlinear load variations). This work is an attempt to undertake a systematic study of the problem to equip the (SAPF) with the harmonics identification and DC link voltage control method based on (ANN). The latter has been applied to the (SAPF) with fast nonlinear load variations. The results of computer simulations and experiments are given, which can confirm the feasibility of the proposed active power filter.

Keywords: artificial neural networks (ANN), p-q theory, harmonics, total harmonic distortion

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: Mohamed Belhorma, Aboubakar S. Bouchikhi, Belkacem Bounab

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This paper addresses modeling a Double A-Arm suspension, a three-dimensional nonlinear model has been developed using the multibody systems formalism. Dynamical study of the different components responses was done, particularly for the wheel assembly. To validate those results, the system was constructed and simulated by RecurDyn, a professional multibody dynamics simulation software. The model has been used as the Objectif function in an optimization algorithm for ride quality improvement.

Keywords: double A-Arm suspension, multibody systems, ride quality optimization, dynamic simulation

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Mithil Pandey, Ragunathan Bala Subramanian

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One of the major conversion technologies in the oil refinery industry is Fluid catalytic cracking (FCC) which produces the majority of the world’s gasoline. Some useful products are generated from the vacuum gas oil, heavy gas oil and residue feedstocks by the FCC unit in an oil refinery. Moreover, Zeolite catalysts (zeo-catalysts) have found widespread applications and have proved to be substantial and paradigmatic in oil refining and petrochemical processes, such as FCC because of their porous features. Several famous zeo-catalysts have been fabricated and applied in industrial processes as milestones in history, and have brought on huge changes in petrochemicals. So far, more than twenty types of zeolites have been industrially applied, and their versatile porous architectures with their essential features have contributed to affect the catalytic efficiency. This poster depicts the evolution of pore models in zeolite catalysts which are accompanied by an increase in environmental and demands. The crucial roles of modulating pore models are outlined for zeo-catalysts for the enhancement of their catalytic performances in various industrial processes. The development of industrial processes for the FCC process, aromatic conversions and olefin production, makes it obvious that the pore architecture plays a very important role in zeo-catalysis processes. By looking at the different necessities of industrial processes, rational construction of the pore model is critically essential. Besides, the pore structure of the zeolite would have a substantial and direct effect on the utilization efficiency of the zeo-catalyst.

Keywords: catalysts, fluid catalytic cracking, industrial processes, zeolite

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

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Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: synthetic gene network, network identification, optimization, nonlinear modeling

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Authors: Martin Goubej, Tomas Popule, Alois Krejci

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This paper deals with experimental identification of mechanical systems with nonlinear friction characteristics. Dynamic LuGre friction model is adopted and a systematic approach to parameter identification of both linear and nonlinear subsystems is given. The identification procedure consists of three subsequent experiments which deal with the individual parts of plant dynamics. The proposed method is experimentally verified on an industrial-grade robotic manipulator. Model fidelity is compared with the results achieved with a static friction model.

Keywords: mechanical friction, LuGre model, friction identification, motion control

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Authors: Andre M. Carvalho, Pedro Sebastiao

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This article is based on a dissertation that intends to analyze and make a model, intelligently, algorithms based on stochastic processes of a gamification application applied to marketing. Gamification is used in our daily lives to engage us to perform certain actions in order to achieve goals and gain rewards. This strategy is an increasingly adopted way to encourage and retain customers through game elements. The application of gamification aims to encourage children between 6 and 10 years of age to have healthy habits and the purpose of serving as a model for use in marketing. This application was developed in unity; we implemented intelligent algorithms based on stochastic processes, web services to respond to all requests of the application, a back-office website to manage the application and the database. The behavioral analysis of the use of game elements and stochastic processes in children’s motivation was done. The application of algorithms based on stochastic processes in-game elements is very important to promote cooperation and to ensure fair and friendly competition between users which consequently stimulates the user’s interest and their involvement in the application and organization.

Keywords: engage, games, gamification, randomness, stochastic processes

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: auxiliary variable, dynamic programming technique, nonlinear programming problem, optimum stratification, uniform distribution

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