Search results for: nonlinear-coupled mode equations

Authors: Abolfazl Mohammadijoo

Abstract:

In this paper, we are investigating the sliding mode control approach for trajectory tracking of a two-link-manipulator with a wheeled mobile robot in its base. The main challenge of this work is the dynamic interaction between mobile base and manipulator, which makes trajectory tracking more difficult than n-link manipulators with a fixed base. Another challenging part of this work is to avoid from chattering phenomenon of sliding mode control that makes lots of damages for actuators in real industrial cases. The results show the effectiveness of the sliding mode control approach for the desired trajectory.

Keywords: mobile manipulator, sliding mode control, dynamic interaction, mobile robotics

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Authors: Nouby M. Ghazaly, Ahmed O. Moaaz, Mostafa Makrahy

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The main purpose of a car suspension system is to reduce the vibrations resulting from road roughness. The main objective of this research paper is to decrease vibration and improve passenger comfort through controlling car suspension system using sliding mode control techniques. The mathematical model for passive and active suspensions systems for quarter car model which subject to excitation from different road profiles is obtained. The active suspension system is synthesized based on sliding mode control for a quarter car model. The performance of the sliding mode control is determined through computer simulations using MATLAB and SIMULINK toolbox. The simulated results plotted in time domain, and root mean square values. It is found that active suspension system using sliding mode control improves the ride comfort and decrease vibration.

Keywords: quarter car model, active suspension system, sliding mode control, road profile

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Kholod Mohammad Abualnaja

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

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

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Authors: Abdallah Ghoul, Bachir Ouamri, Ismail Khalil Bousserhane

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In this paper, we have developed a sliding mode controller for PUMA 600 manipulator robot, to control the remote robot a teleoperation system was developed. This system includes two sites, local and remote. The sliding mode controller is installed at the remote site. The client asks for a position through an interface and receives the real positions after running of the task by the remote robot. Both sites are interconnected via the Internet. In order to verify the effectiveness of the sliding mode controller, that is compared with a classic PID controller. The developed approach is tested on a virtual robot. The results confirmed the high performance of this approach.

Keywords: internet, manipulator robot, PID controller, remote control, sliding mode, teleoperation

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Authors: Anton V. Bourdine, Vladimir A. Burdin, Oleg R. Delmukhametov

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This work presents a fast and simple method for the design of large core silica optical fibers with differential mode delay (DMD) management. Some results are reported concerned with refractive index profile optimization for 42 µm core 16-LP-mode optical fiber for next-generation optical networks. Here special refractive index profile form provides total DMD reducing over all mode staff under desired enhanced mode effective area. Method for the simulation of 'real manufactured' few-mode optical fiber (FMF) core geometry differing from the desired optimized structure by core non-symmetrical ellipticity and refractive index profile deviation including local fluctuations is proposed. Results of the following analysis of optimized FMF with inserted geometry distortions performed by earlier on developed modification of rigorous mixed finite-element method showed strong DMD degradation that requires additional higher-order mode management. In addition, this work also presents a method for design mode division multiplexer channel precision spatial positioning scheme at FMF core end that provides one of the potentiality solutions of described DMD degradation problem concerned with 'distorted' core geometry due to features of optical fiber manufacturing techniques.

Keywords: differential mode delay, few-mode optical fibers, nonlinear Shannon limit, optical fiber non-circularity, ‘real manufactured’ optical fiber core geometry simulation, refractive index profile optimization

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Reyhaneh Hashemi, Shahrooz Saviz

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In his study, we have survey the theory of gyrotron amplifier in a vane-loaded waveguide with inner dielectric material. Dispersion relation for electromagnetic waves emitted by a cylindrical waveguide that provided with wedge-shaped metal vanes projecting radially inward from the wall of the guide and exited in the transverse-electric mode was analysed. From numerical analysis of this dispersion relation, it is shown that the stability behavior of the fast-wave mode is dependent of the dielectric constant. With a small axial momentum spreed, a super bandwidth is shown to be attainable by a mixed mode operation. Also, with the utilization from the numeric analysis of relation dispersion. We show that in the –speed mode, the constant is independent de-electric. With the ratio of dispersion of smell, high –bandwith was obtained for the combined mode. And at the end, we were comparing the result of our work (vane-loaded) by the waveguide with a smooth wall.

Keywords: gyrotron amplifier, waveguide, vane-loaded waveguide, dielectric material, dispersion relation, cylindrical waveguide, fast-wave mode, mixed mode operation

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Authors: Abderraouf Gaaloul, Faouzi Msahli

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The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Leah Wright, Trevor Townsend

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Mode choice models are crucial instruments in the analysis of travel behaviour. These models show the relationship between an individual’s choice of transportation mode for a given O-D pair and the individual’s socioeconomic characteristics such as household size and income level, age and/or gender, and the features of the transportation system. The most popular functional forms of these models are based on Utility-Based Choice Theory, which addresses the uncertainty in the decision-making process with the use of an error term. However, with the development of artificial intelligence, many researchers have started to take a different approach to travel demand modelling. In recent times, researchers have looked at using neural networks, fuzzy logic and rough set theory to develop improved mode choice formulas. The concept of cloud theory has recently been introduced to model decision-making under uncertainty. Unlike the previously mentioned theories, cloud theory recognises a relationship between randomness and fuzziness, two of the most common types of uncertainty. This research aims to investigate the use of cloud theory in mode choice models. This paper highlights the conceptual framework of the mode choice model using cloud theory. Merging decision-making under uncertainty and mode choice models is state of the art. The cloud theory model is expected to address the issues and concerns with the nested logit and improve the design of mode choice models and their use in travel demand.

Keywords: Cloud theory, decision-making, mode choice models, travel behaviour, uncertainty

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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Authors: Elhadj Bounadja, Mohand Oulhadj Mahmoudi, Abdelkader Djahbar, Zinelaabidine Boudjema

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In this paper we present a novel fuzzy second-order sliding mode control (FSOSMC) for wind energy conversion system based on a doubly-fed induction generator (DFIG). The proposed control strategy combines a fuzzy logic and a second-order sliding mode for the DFIG control. This strategy presents attractive features such as chattering-free, compared to the conventional first and second order sliding mode techniques. The use of this method provides very satisfactory performance for the DFIG control. The overall strategy has been validated on a 1.5-MW wind turbine driven a DFIG using the Matlab/Simulink.

Keywords: doubly fed induction generator, fuzzy second-order sliding mode controller, wind energy

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Authors: Liang Zhang, Yuanfu Lu, Yuming Dong, Guohua Jiao, Wei Chen, Jiancheng Lv

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We demonstrated an interferometric demodulation scheme using a mode-locked fiber laser. The mode-locked fiber laser is launched into a two-beam interferometer. When the ratio between the fiber path imbalance of interferometer and the laser cavity length is close to an integer, an interferometric fringe emerges as a result of vernier effect, and then the phase shift of the interferometer can be demodulated. The mode-locked fiber laser provides a large bandwidth and reduces the cost for wavelength division multiplexion (WDM). The proposed interferometric demodulation scheme can be further applied in multi-point sensing system such as fiber optics hydrophone array, seismic wave detection network with high sensitivity and low cost.

Keywords: fiber sensing, interferometric demodulation, mode-locked fiber laser, vernier effect

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Authors: Matevž Breška, Iztok Peruš, Vlado Stankovski

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Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database, peak ground acceleration

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Authors: Zhanna Yermekova, Sergey Roslyakov

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Solution combustion synthesis (SCS) is the unique method which multiple times has proved itself as an effective and efficient approach for the versatile synthesis of a variety of materials. It has significant advantages such as relatively simple handling process, high rates of product synthesis, mixing of the precursors on a molecular level, and fabrication of the nanoproducts as a result. Nowadays, an overwhelming majority of solution combustion investigations performed through the volume combustion synthesis (VCS) where the entire liquid precursor is heated until the combustion self-initiates throughout the volume. Less amount of the experiments devoted to the steady-state self-propagating mode of SCS. Under the beforementioned regime, the precursor solution is dried until the gel-like media, and later on, the gel substance is locally ignited. In such a case, a combustion wave propagates in a self-sustaining mode as in conventional solid combustion synthesis. Even less attention is given to the impregnated active layer (IAL) mode of solution combustion. An IAL approach to the synthesis is implying that the solution combustion of the precursors should be initiated on the surface of the third chemical or inside the third substance. This work is aiming to emphasize an underestimated role of the impregnated active layer mode of the solution combustion synthesis for the fundamental studies of the combustion mechanisms. It also serves the purpose of popularizing the technical terms and clarifying the difference between them. In order to do so, the solution combustion synthesis of γ-FeNi (PDF#47-1417) alloy has been accomplished within short (seconds) one-step reaction of metal precursors with hexamethylenetetramine (HTMA) fuel. An idea of the special role of the Ni in a process of alloy formation was suggested and confirmed with the particularly organized set of experiments. The first set of experiments were conducted in a conventional steady-state self-propagating mode of SCS. An alloy was synthesized as a single monophasic product. In two other experiments, the synthesis was divided into two independent processes which are possible under the IAL mode of solution combustion. The sequence of the process was changed according to the equations which are describing an Experiment A and B below: Experiment A: Step 1. Fe(NO₃)₃*9H₂O + HMTA = FeO + gas products; Step 2. FeO + Ni(NO₃)₂*6H₂O + HMTA = Ni + FeO + gas products; Experiment B: Step 1. Ni(NO₃)₂*6H₂O + HMTA = Ni + gas products; Step 2. Ni + Fe(NO₃)₃*9H₂O + HMTA = Fe₃Ni₂+ traces (Ni + FeO). Based on the IAL experiment results, one can see that combustion of the Fe(NO₃)₃9H₂O on the surface of the Ni is leading to the alloy formation while presence of the already formed FeO does not affect the Ni(NO₃)₂*6H₂O + HMTA reaction in any way and Ni is the main product of the synthesis.

Keywords: alloy, hexamethylenetetramine, impregnated active layer mode, mechanism, solution combustion synthesis

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Authors: Moussa Hamdan, Abdulati Abdullah

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This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.

Keywords: surface plasmons, optical waveguides, semiconductor lasers, refractive index, slab dialectical

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Pinghe Wang

Abstract:

In this paper, we demonstrate a tunable long-cavity passive mode-locked fiber laser. The mode locker is a nonlinear amplifying loop mirror (NALM). The cavity frequency of the laser is 465 kHz because that 404m SMF is inserted in the cavity. A tunable bandpass filter with ~1nm 3dB bandwidth is inserted into the cavity to realize tunable mode locking. The passive mode-locked laser at a fixed wavelength is investigated in detail. The experimental results indicate that the laser operates in dissipative soliton resonance (DSR) region. When the pump power is 400mW, the laser generates the rectangular pulses with 10.58 ns pulse duration, 70.28nJ single-pulse energy. When the pump power is 400mW, the laser keeps stable mode locking status in the range from 1523.4nm to 1575nm. During the whole tuning range, the SNR, the pulse duration, the output power and single pulse energy have a little fluctuation because that the gain of the EDF changes with the wavelength.

Keywords: fiber laser, dissipative soliton resonance, mode locking, tunable

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Authors: Devinder Singh, Rajneesh Kumar, Arvind Kumar

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The present investigation deals with generalized model of the equations for a homogeneous isotropic microstretch thermoelastic half space with mass diffusion medium. Theories of generalized thermoelasticity Lord-Shulman (LS) Green-Lindsay (GL) and Coupled Theory (CT) theories are applied to investigate the problem. The stresses in the considered medium have been studied due to normal force and tangential force. The normal mode analysis technique is used to calculate the normal stress, shear stress, couple stresses and microstress. A numerical computation has been performed on the resulting quantity. The computed numerical results are shown graphically.

Keywords: microstretch, thermoelastic, normal mode analysis, normal and tangential force, microstress force

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Authors: Young-Hyun Seo, Hyunwoo Park, Dong-Kyu Kim, Seung-Young Kho

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The purpose of this study is providing an improved mode choice model considering parameters including age grouping of prime-aged and old age. In this study, 2010 Household Travel Survey data were used and improper samples were removed through the analysis. Chosen alternative, date of birth, mode, origin code, destination code, departure time, and arrival time are considered from Household Travel Survey. By preprocessing data, travel time, travel cost, mode, and ratio of people aged 45 to 55 years, 55 to 65 years and over 65 years were calculated. After the manipulation, the mode choice model was constructed using LIMDEP by maximum likelihood estimation. A significance test was conducted for nine parameters, three age groups for three modes. Then the test was conducted again for the mode choice model with significant parameters, travel cost variable and travel time variable. As a result of the model estimation, as the age increases, the preference for the car decreases and the preference for the bus increases. This study is meaningful in that the individual and households characteristics are applied to the aggregate model.

Keywords: age grouping, aging, mode choice model, multinomial logit model

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Authors: B. Mahfoud, A. Bendjagloli

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The effect of an axial magnetic field on the flow produced by co-rotation of the top and bottom disks in a vertical cylindrical heated from below is numerically analyzed. The governing Navier-Stokes, energy, and potential equations are solved by using the finite-volume method. It was observed that the Reynolds number is increased, the axisymmetric basic state loses stability to circular patterns of axisymmetric vortices and spiral waves. In mixed convection case the axisymmetric mode disappears giving an asymmetric mode m=1. It was also found that the primary thresholds Recr corresponding to the modes m=1and 2, increase with increasing of the Hartmann number (Ha). Finally, stability diagrams have been established according to the numerical results of this investigation. These diagrams giving the evolution of the primary thresholds as a function of the Hartmann number for various values of the Richardson number.

Keywords: bifurcation, co-rotating end disks, magnetic field, stability diagrams, vortices

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Authors: Jon Cobb, Nasir

Abstract:

Due to higher switching frequencies, the conducted Electromagnetic interference (EMI) noise is generated in a converter. It degrades the performance of a switching converter. Therefore, it is an essential requirement to mitigate EMI noise of high performance converter. Moreover, it includes two types of emission such as common mode (CM) and differential mode (DM) noise. CM noise is due to parasitic capacitance present in a converter and DM noise is caused by switching current. However, there is dire need to understand the main cause of EMI noise. Hence, we propose a novel method to predict conducted EMI noise of different converter topologies during early stage. This paper also presents the comparison of conducted electromagnetic interference (EMI) noise due to different SMPS topologies. We also make an attempt to develop an EMI noise model for a converter which allows detailed performance analysis. The proposed method is applied to different converter, as an example, and experimental results are verified the novel prediction technique.

Keywords: EMI, electromagnetic interference, SMPS, switch-mode power supply, common mode, CM, differential mode, DM, noise

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Authors: M. Bouferhane, A. Boukhebza, L. Hatab

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In this paper, the position control of linear induction motor using fuzzy sliding mode controller design is proposed. First, the indirect field oriented control LIM is derived. Then, a designed sliding mode control system with an integral-operation switching surface is investigated, in which a simple adaptive algorithm is utilized for generalised soft-switching parameter. Finally, a fuzzy sliding mode controller is derived to compensate the uncertainties which occur in the control, in which the fuzzy logic system is used to dynamically control parameter settings of the SMC control law. The effectiveness of the proposed control scheme is verified by numerical simulation. The experimental results of the proposed scheme have presented good performances compared to the conventional sliding mode controller.

Keywords: linear induction motor, vector control, backstepping, fuzzy-sliding mode control

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: William Albeiro Alvarez, Gloria Patricia Jaramillo, Ivan Reinaldo Sarmiento

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Understanding the behavior of individuals and the different human factors that influence the choice when faced with a complex system such as transportation is one of the most complicated aspects of measuring in the components that constitute the modeling of route choice due to that various behaviors and driving mode directly or indirectly affect the choice. During the last two decades, with the development of information and communications technologies, new data collection techniques have emerged such as GPS, geolocation with mobile phones, apps for choosing the route between origin and destination, individual service transport applications among others, where an interest has been generated to improve discrete choice models when considering the incorporation of these developments as well as psychological factors that affect decision making. This paper implements a discrete choice model that proposes and estimates a hybrid model that integrates route choice models and latent variables based on the observation on the route of a sample of public taxi drivers from the city of Medellín, Colombia in relation to its behavior, personality, socioeconomic characteristics, and driving mode. The set of choice options includes the routes generated by the individual service transport applications versus the driver's choice. The hybrid model consists of measurement equations that relate latent variables with measurement indicators and utilities with choice indicators along with structural equations that link the observable characteristics of drivers with latent variables and explanatory variables with utilities.

Keywords: behavior choice model, human factors, hybrid model, real time data

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Chi Zhang, Hua-Peng Chen

Abstract:

With the increasingly demanding resources in the word, renewable and clean energy has been considered as an alternative way to replace traditional ones. Thus, one of practical examples for using wind energy is wind turbine, which has gained more attentions in recent research. Like most offshore structures, the blades, which is the most critical components of the wind turbine, will be subjected to millions of loading cycles during service life. To operate safely in marine environments, the blades are typically made from fibre reinforced composite materials to resist fatigue delamination and harsh environment. The fatigue crack development of blades is uncertain because of indeterminate mechanical properties for composite and uncertainties under offshore environment like wave loads, wind loads, and humid environments. There are three main delamination failure modes for composite blades, and the most common failure type in practices is subjected to mixed mode loading, typically a range of opening (mode 1) and shear (mode 2). However, the fatigue crack development for mixed mode cannot be predicted as deterministic values because of various uncertainties in realistic practical situation. Therefore, selecting an effective stochastic model to evaluate the mixed mode behaviour of wind turbine blades is a critical issue. In previous studies, gamma process has been considered as an appropriate stochastic approach, which simulates the stochastic deterioration process to proceed in one direction such as realistic situation for fatigue damage failure of wind turbine blades. On the basis of existing studies, various Paris Law equations are discussed to simulate the propagation of the fatigue crack growth. This paper develops a Paris model with the stochastic deterioration modelling according to gamma process for predicting fatigue crack performance in design service life. A numerical example of wind turbine composite materials is investigated to predict the mixed mode crack depth by Paris law and the probability of fatigue failure by gamma process. The probability of failure curves under different situations are obtained from the stochastic deterioration model for comparisons. Compared with the results from experiments, the gamma process can take the uncertain values into consideration for crack propagation of mixed mode, and the stochastic deterioration process shows a better agree well with realistic crack process for composite blades. Finally, according to the predicted results from gamma stochastic model, assessment strategies for composite blades are developed to reduce total lifecycle costs and increase resistance for fatigue crack growth.

Keywords: Reinforced fibre composite, Wind turbine blades, Fatigue delamination, Mixed failure mode, Stochastic process.

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