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Article

Yuan Fangyang and Chen Zhongli

The purpose of this paper is to develop new types of direct expansion method of moments (DEMM) by using the n/3th moments for simulating nanoparticle Brownian coagulation…

Abstract

Purpose

The purpose of this paper is to develop new types of direct expansion method of moments (DEMM) by using the n/3th moments for simulating nanoparticle Brownian coagulation in the free molecule regime. The feasibilities of new proposed DEMMs with n/3th moments are investigated to describe the evolution of aerosol size distribution, and some of the models will be applied to further simulation of physical processes.

Design/methodology/approach

The accuracy and efficiency of some kinds of methods of moments are mainly compared including the quadrature method of moments (QMOM), Taylor-expansion method of moments (TEMOM), the log-normal preserving method of moments proposed by Lee (LMM) and the derived DEMM in this paper. QMOM with 12 quadrature approximation points is taken as a reference to evaluate other methods.

Findings

The newly derived models, namely DEMM(4/3,4) and DEMM(2,6), as well as the previous DEMM(2,4), are considered to be qualified models due to their high accuracy and efficiency. They are confirmed to be valid and alternative models to describe the evolution of aerosol size distribution for particle dynamical process involving the n/3th moments.

Originality/value

The n/3th moments, which have clear physical interpretations when n stands for first several integers, are first introduced in the DEMM method for simulating nanoparticle Brownian coagulation in the free molecule regime.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Xi Luo, Yingjie Zhang and Lin Zhang

The purpose of this paper is to improve the positioning accuracy of 6-Dof serial robot by the way of error compensation and sensitivity analysis.

Abstract

Purpose

The purpose of this paper is to improve the positioning accuracy of 6-Dof serial robot by the way of error compensation and sensitivity analysis.

Design/methodology/approach

In this paper, the Denavit–Hartenberg matrix is used to construct the kinematics models of the robot; the effects from individual joint and several joints on the end effector are estimated by simulation. Then, an error model based on joint clearance is proposed so that the positioning accuracy at any position of joints can be predicted for compensation. Through the simulation of the curve path, the validity of the error compensation model is verified. Finally, the experimental results show that the error compensation method can improve the positioning accuracy of a two joint exoskeleton robot by nearly 76.46%.

Findings

Through the analysis of joint error sensitivity, it is found that the first three joints, especially joint 2, contribute a lot to the positioning accuracy of the robot, which provides guidance for the accuracy allocation of the robot. In addition, this paper creatively puts forward the error model based on joint clearance, and the error compensation method which decouples the positioning accuracy into joint errors.

Originality/value

It provides a new idea for error modeling and error compensation of 6-Dof serial robot. Combining sensitivity analysis results with error compensation can effectively improve the positioning accuracy of the robot, and provide convenience for welding robot and other robots that need high positioning accuracy.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article

Mohammad Tabatabaei

– The purpose of this paper is to present a two-loop approach for velocity control of a permanent magnet synchronous motor (PMSM) under mechanical uncertainties.

Abstract

Purpose

The purpose of this paper is to present a two-loop approach for velocity control of a permanent magnet synchronous motor (PMSM) under mechanical uncertainties.

Design/methodology/approach

The inner loop calculates the two-axis stator reference voltages through a feedback linearization method. The outer loop employs an RST control structure to compute the q-axis stator reference current. To increase the robustness of the proposed method, the RST controller parameters are adapted through a fractional order model reference adaptive system (FO-MRAS). The fractional order gradient and Lyapunov methods are utilized as adaptation mechanisms.

Findings

The effect of the fractional order derivative in the load disturbance rejection, transient response speed and the robustness is verified through computer simulations. The simulation results show the effectiveness of the proposed method against the external torque and mechanical parameters uncertainties.

Originality/value

The proposed FO-MRAS based on Lyapunov adaptation mechanism is proposed for the first time. Moreover, application of the FO-MRAS for velocity control of PMSM is presented for the first time.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

Rajneesh Kumar, Kulwinder Singh and Devinder Pathania

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of…

Abstract

Purpose

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined effects of hall current and rotation subjected to ramp-type heating.

Design/methodology/approach

The fractional order theory of thermoelasticity with one relaxation time derived by Sherief et al. (2010) has been used to investigate the problem. Laplace and Fourier transform technique has been used to solve the resulting non-dimensional coupled field equations to obtain displacement, stress components and temperature distribution. A numerical inversion technique has been applied to obtain the solution in the physical domain.

Findings

Numerical computed results of all the considered variables have been shown graphically to depict the combined effect of hall current and rotation. Some particular cases of interest are also deduced from the present study.

Originality/value

Comparison are made in the presence and absence of hall current and rotation in a magneto-micropolar thermoelastic solid with fractional order derivative.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

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Article

Guy Jumarie

To define the main elements of a formal calculus which deals with fractional Brownian motion (fBm), and to examine its prospects of applications in systems science.

Abstract

Purpose

To define the main elements of a formal calculus which deals with fractional Brownian motion (fBm), and to examine its prospects of applications in systems science.

Design/methodology/approach

The approach is based on a generalization of the Maruyama's notation. The key is the new Taylor's series of fractional order f(x+h)=Eα(hαDα)f(x), where Eα( · ) is the Mittag‐Leffler function.

Findings

As illustrative applications of this formal calculus in systems science, one considers the linear quadratic Gaussian problem with fractal noises, the analysis of the equilibrium position of a system disturbed by a local fractal time, and a model of growing which involves fractal noises. And then, one examines what happens when one applies the maximum entropy principle to systems involving fBms (or shortly fractals).

Research limitations/implications

The framework of this paper is applied mathematics and engineering mathematics, and the results so obtained allow the practical analysis of stochastic dynamics subject to fractional noises.

Practical implications

The direct prospect of application of this approach is the analysis of some stock markets dynamics and some biological systems.

Originality/value

The fractional Taylor's series is new and thus so are all its implications.

Details

Kybernetes, vol. 35 no. 9
Type: Research Article
ISSN: 0368-492X

Keywords

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Article

Guishu Liang and Yulan Yang

This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at…

Abstract

Purpose

This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations.

Design/methodology/approach

This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations.

Findings

The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result.

Originality/value

This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

Mohammad Javad Fotuhi and Zafer Bingul

This paper aims to develope a novel fractional hybrid impedance control (FHIC) approach for high-sensitive contact stress force tracking control of the series elastic…

Abstract

Purpose

This paper aims to develope a novel fractional hybrid impedance control (FHIC) approach for high-sensitive contact stress force tracking control of the series elastic muscle-tendon actuator (SEM-TA) in uncertain environments.

Design/methodology/approach

In three different cases, the fractional parameters of the FHIC were optimized with the particle swarm optimization algorithm. Its adaptability to the pressure of the sole of the foot on real environments such as grass (soft), carpet (medium) and solid floors (hard) is far superior to traditional impedance control. The main aim of this paper is to derive the dynamic simulation models of the SEM-TA, to develop a control architecture allowing for high-sensitive contact stress force control in three cases and to verify the simulation models and the proposed controller with experimental results. The performance of the optimized controllers was evaluated according to these parameters, namely, maximum overshoot, steady-state error, settling time and root mean squared errors of the positions. Moreover, the frequency robustness analysis of the controllers was made in three cases.

Findings

Different simulations and experimental results were conducted to verify the control performance of the controllers. According to the comparative results of the performance, the responses of the proposed controller in simulation and experimental works are very similar.

Originality/value

Origin approach and origin experiment.

Details

Industrial Robot: the international journal of robotics research and application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0143-991X

Keywords

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Article

Diptiranjan Behera, Hong-Zhong Huang and Smita Tapaswini

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique…

Abstract

Purpose

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Design/methodology/approach

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

Findings

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Originality/value

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

Sunita Deswal, Devender Sheoran and Kapil Kumar Kalkal

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic…

Abstract

Purpose

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with microtemperatures. The expressions for different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain.

Design/methodology/approach

Normal mode analysis technique is adopted to procure the exact solution of the problem.

Findings

Numerical computations have been carried out with the help of MATLAB programming, and the results are illustrated graphically. Comparisons are made to show the effects of rotation, time and microtemperatures on the resulting quantities. The graphical results indicate that the effects of rotation, microtemperatures and time are very pronounced on the field variables.

Originality/value

In the present work, we have investigated the effects of rotation, time and microtemperature in an initially stressed thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form, i.e. the disturbances in a thermoelastic medium in the presence of angular velocity, initial stress and microtemperature have not been studied till now. The present work is useful and valuable for analysis of problems involving coupled thermal shock, rotation parameter, microtemperatures and elastic deformation.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

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Article

Xiwang Xiang, Xin Ma, Minda Ma, Wenqing Wu and Lang Yu

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for…

Abstract

Purpose

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.

Design/methodology/approach

The grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.

Findings

The introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.

Practical implications

With high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.

Originality/value

This is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

Details

Grey Systems: Theory and Application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2043-9377

Keywords

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