Search results for: normalized normal constraint method

Authors: Ahmad Darabi, Hassan Moradi, Hossein Azarinfar

Abstract:

In this paper presented initial design of Low Speed Axial Flux Permanent Magnet (AFPM) Machine with Non-Slotted TORUS topology type by use of certain algorithm (Appendix). Validation of design algorithm studied by means of selected data of an initial prototype machine. Analytically design calculation carried out by means of design algorithm and obtained results compared with results of Finite Element Method (FEM).

Keywords: Axial Flux Permanent Magnet (AFPM) Machine, Design Algorithm, Finite Element Method (FEM), TORUS

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: Nhat Linh Ho, Thanh-Phong Dao, Shyh-Chour Huang, Hieu Giang Le

Abstract:

This paper presents a design and optimization for a compliant gripper. The gripper is constructed based on the concept of compliant mechanism with flexure hinge. A passive force regulation mechanism is presented to control the grasping force a micro-sized object instead of using a sensor force. The force regulation mechanism is designed using the planar springs. The gripper is expected to obtain a large range of displacement to handle various sized objects. First of all, the statics and dynamics of the gripper are investigated by using the finite element analysis in ANSYS software. And then, the design parameters of the gripper are optimized via Taguchi method. An orthogonal array L₉ is used to establish an experimental matrix. Subsequently, the signal to noise ratio is analyzed to find the optimal solution. Finally, the response surface methodology is employed to model the relationship between the design parameters and the output displacement of the gripper. The design of experiment method is then used to analyze the sensitivity so as to determine the effect of each parameter on the displacement. The results showed that the compliant gripper can move with a large displacement of 213.51 mm and the force regulation mechanism is expected to be used for high precision positioning systems.

Keywords: Flexure hinge, compliant mechanism, compliant gripper, force regulation mechanism, Taguchi method, response surface methodology, design of experiment.

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Authors: Farhad Asadi, Hossein Sadati

Abstract:

In fields such as neuroscience and especially in cognition modeling of mental processes, uncertainty processing in temporal zone of signal is vital. In this paper, Bayesian online inferences in estimation of change-points location in signal are constructed. This method separated the observed signal into independent series and studies the change and variation of the regime of data locally with related statistical characteristics. We give conditions on simulations of the method when the data characteristics of signals vary, and provide empirical evidence to show the performance of method. It is verified that correlation between series around the change point location and its characteristics such as Signal to Noise Ratios and mean value of signal has important factor on fluctuating in finding proper location of change point. And one of the main contributions of this study is related to representing of these influences of signal statistical characteristics for finding abrupt variation in signal. There are two different structures for simulations which in first case one abrupt change in temporal section of signal is considered with variable position and secondly multiple variations are considered. Finally, influence of statistical characteristic for changing the location of change point is explained in details in simulation results with different artificial signals.

Keywords: Time series, fluctuation in statistical characteristics, optimal learning.

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Authors: Ali Nouri Emamzadeh, Akbar Yaghobfar

Abstract:

The experiment was conducted to evaluate digestibility quantities of protein in Canola Meals (CMs) between caecectomised and intact adult Rhode Island Red (RIR) cockerels with using conventional addition method (CAM) for 7 d: a 4-d adaptation and a 3-d experiment period on the basis of a completely randomized design with 4 replicates. Results indicated that caecectomy decreased (P<0.05) apparent and true digestibility quantities of protein for CMs, except for CMs 2 and 3. The mean apparent and true digestibility quantities for all CMs in caecectomised (80.5 and 81.4%, respectively) were (3.1 and 3.3%, respectively) less (P<0.05) than intact cockerels (83.6 and 84.7%, respectively). Therefore, the caecectomy method increases accuracy of the digestibility measurements of protein for this meal in bioassays based on excreta collection in adult cockerels.

Keywords: Adult cockerels, caecectomy, canola meals, proteindigestibility.

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

Abstract:

The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: Optical soliton, soliton interaction, soliton switching, WDM.

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Authors: Dayananda Pai, Shrikantha S. Rao, Savitha G.Kini

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In this study, the effects of machining parameters on specific energy during surface grinding of 6061Al-SiC35P composites are investigated. Vol% of SiC, feed and depth of cut were chosen as process variables. The power needed for the calculation of the specific energy is measured from the two watt meter method. Experiments are conducted using standard RSM design called Central composite design (CCD). A second order response surface model was developed for specific energy. The results identify the significant influence factors to minimize the specific energy. The confirmation results demonstrate the practicability and effectiveness of the proposed approach.

Keywords: ANOVA, Metal matrix composites, Response surface methodology, Specific energy, Two watt meter method.

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Authors: A. Farshidianfar, P. Oliazadeh, M. H. Farshidianfar

Abstract:

In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.

Keywords: Circular Cylindrical Shell, Free Vibration, Natural Frequency.

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Authors: Hadeer R. M. Tawfik, Rania A. K. Birry, Amani A. Saad

Abstract:

Eyes are considered to be the most sensitive and important organ for human being. Thus, any eye disorder will affect the patient in all aspects of life. Cataract is one of those eye disorders that lead to blindness if not treated correctly and quickly. This paper demonstrates a model for automatic detection, classification, and grading of cataracts based on image processing techniques and artificial intelligence. The proposed system is developed to ease the cataract diagnosis process for both ophthalmologists and patients. The wavelet transform combined with 2D Log Gabor Wavelet transform was used as feature extraction techniques for a dataset of 120 eye images followed by a classification process that classified the image set into three classes; normal, early, and advanced stage. A comparison between the two used classifiers, the support vector machine SVM and the artificial neural network ANN were done for the same dataset of 120 eye images. It was concluded that SVM gave better results than ANN. SVM success rate result was 96.8% accuracy where ANN success rate result was 92.3% accuracy.

Keywords: Cataract, classification, detection, feature extraction, grading, log-gabor, neural networks, support vector machines, wavelet.

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: Alpesh Adeshara, Rajendrasinh Jadeja, Praghnesh Bhatt

Abstract:

Implementation of advanced technologies requires sophisticated instruments that deal with the operation, control, restoration and protection of rapidly growing power system network under normal and abnormal conditions. Presently, the applications of Phasor Measurement Unit (PMU) are widely found in real time operation, monitoring, controlling and analysis of power system network as it eliminates the various limitations of supervisory control and data acquisition system (SCADA) conventionally used in power system. The use of PMU data is very rapidly increasing its importance for online and offline analysis. Wide area measurement system (WAMS) is developed as new technology by use of multiple PMUs in power system. The present paper proposes a model of Matlab based PMU using Discrete Fourier Transform (DFT) algorithm and evaluation of its operation under different contingencies. In this paper, PMU based two bus system having WAMS network is presented as a case study.

Keywords: DFT-Discrete Fourier Transform, GPS-Global Positioning System, PMU-Phasor Measurement System, WAMS-Wide Area Monitoring System.

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Authors: E. Halawa

Abstract:

Solar water heating (SWH) systems are gaining popularity in ASEAN in the midst of increasing number of affluent population in society and environmental concerns from seemingly unchanged reliance on fossil-based fuels. The penetration of these systems and technologies into ASEAN markets is a welcome development; however there is a need for the method of assessment of their thermal performances. This paper discusses the reasons for this need and a suitable method for thermal performance evaluation of SWH systems in ASEAN. The paper also calls on research to be focused on the establishment of reliable data to be entered into the performance rating software. The establishment of accredited solar systems testing facilities can help boost the competitiveness of ASEAN solar industry.

Keywords: ASEAN, solar industry, solar water heating systems, thermal performance rating.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: Jaeho Han, Moonjung Kim, Won-Ho Kim, Chang-Ho Hyun

Abstract:

This paper introduces a high-gain observer based state of charge(SOC) estimator for lithium-Ion batteries. The proposed SOC estimator has a high-gain observer(HGO) structure. The HGO scheme enhances the transient response speed and diminishes the effect of uncertainties. Furthermore, it guarantees that the output feedback controller recovers the performance of the state feedback controller when the observer gain is sufficiently high. In order to show the effectiveness of the proposed method, the linear RC battery model in ADVISOR is used. The performance of the proposed method is compared with that of the conventional linear observer(CLO) and some simulation result is given.

Keywords: SOC, high-gain, observer, uncertainties, robust

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Authors: Hazim J. Al-Daraji

Abstract:

The aim of this study was to investigate the effects of supplementing the diluent of roosters' semen with different levels of olive oil on motility, viability, morphology and acrosome integrity of chicken spermatozoa after in vitro storage for up to 72 h. Semen was collected from 60 White Layer males (62 wk of age) kept in separated floor pens and randomly divided into six treatment groups (10 males in each group). Experimental groups were as follows: T1 :fresh semen, T2 : semen extended 1:1 with Al – Daraji 2 diluent (AD2D) alone, T3 – T6 :semen samples extended 1:1 with AD2D supplemented with 2 ml, 4 ml, 6 ml or 8 ml of olive oil / 100 ml of diluent, respectively. Semen samples were then stored at 5 °C for 24 h, 48 h or 72 h. There was a clear influence of diluent supplementation with olive oil on the spermatozoa motility profile; olive oil groups (T3, T4, T5 and T6) recorded the highest scores of mass activity and individual motility during all storage periods compared to T1 and T2 groups. In addition, the inclusion of olive oil into semen diluent (T3, T4, T5 and T6) gave significantly higher percentages of viable spermatozoa, normal morphologically spermatozoa and intact acrosomes irrespective of storage period. These results clearly show that supplementation the diluent of roosters' semen with olive oil can improve semen quality when semen samples in vitro stored at 5 °C for up to 72 h.

Keywords: Olive oil, diluent, liquid storage, semen quality of roosters.

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising operation, this new definition of entropy can be implemented to compare the performance analysis of filtering methods. In the second part, we apply the concept of pure state in quantum formalism to generalize the maximum entropy method for narrowband and farfield source localization problem. Several computer simulation results are illustrated to demonstrate the effectiveness of the proposed techniques.

Keywords: Von Neumann entropy, Filtering, array, DoA, Maximum Entropy Method.

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Authors: H. Chaker, T. Slama, N. Elyétim

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This paper analyzes the effects of gender, affiliation, prior work experience, social work, and vicarious learning through family role models on entrepreneurial skills development by students when they followed the teaching through the entrepreneurship method in Tunisia. We suggest that these variables enhance the development of students’ entrepreneurial skills when combined with teaching through entrepreneurship. The article assesses the impact of these combinations by comparing their effects on the development of thirteen students’ entrepreneurial competencies, namely entrepreneurial mindset, core self-evaluation, entrepreneurial attitude, entrepreneurial knowledge, creativity, financial literacy, managing ambiguity, marshaling of resources, planning, teaching methods, entrepreneurial teachers, innovative employee, and entrepreneurial intention. We use a two-sample independent t-test to make the comparison, and the results indicate that, when combined with teaching through the entrepreneurship method, students with prior work experience developed better six entrepreneurial skills; students with social work developed better three entrepreneurial skills, men developed better four entrepreneurial skills than women. However, all students developed their entrepreneurial skills through this practical method regardless of their affiliation and their vicarious learning through family role models.

Keywords: Affiliation, entrepreneurial skills, gender, role models, social work, teaching through entrepreneurship, vicarious learning, work experience.

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Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

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Authors: Masoud Hekmatpanah, Mohammad Sadroddin, Saeid Shahbaz, Farhad Mokhtari, Farahnaz Fadavinia

Abstract:

The six sigma method is a project-driven management approach to improve the organization-s products, services, and processes by continually reducing defects in the organization. Understanding the key features, obstacles, and shortcomings of the six sigma method allows organizations to better support their strategic directions, and increasing needs for coaching, mentoring, and training. It also provides opportunities to better implement six sigma projects. The purpose of this paper is the survey of six sigma process and its impact on the organizational productivity. So I have studied key concepts , problem solving process of six sigmaas well as the survey of important fields such as: DMAIC, six sigma and productivity applied programme, and other advantages of six sigma. In the end of this paper, present research conclusions. (direct and positive relation between six sigma and productivity)

Keywords: Six sigma, project management, quality, theory, productivity.

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Authors: Abhinav Kumar, Raja Sekhar Bandaru, B Madhusudan Rao, Saket Kulkarni, Nilesh Ghatpande

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This paper proposes an algorithm which automatically aligns and stitches the component medical images (fluoroscopic) with varying degrees of overlap into a single composite image. The alignment method is based on similarity measure between the component images. As applied here the technique is intensity based rather than feature based. It works well in domains where feature based methods have difficulty, yet more robust than traditional correlation. Component images are stitched together using the new triangular averaging based blending algorithm. The quality of the resultant image is tested for photometric inconsistencies and geometric misalignments. This method cannot correct rotational, scale and perspective artifacts.

Keywords: Histogram Matching, Image Alignment, ImageStitching, Medical Imaging.

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Authors: Yong-Quan Zhou, Deng-Xu He, Zheng Nong

Abstract:

In this paper two models using a functional network were employed to solving classification problem. Functional networks are generalized neural networks, which permit the specification of their initial topology using knowledge about the problem at hand. In this case, and after analyzing the available data and their relations, we systematically discuss a numerical analysis method used for functional network, and apply two functional network models to solving XOR problem. The XOR problem that cannot be solved with two-layered neural network can be solved by two-layered functional network, which reveals a potent computational power of functional networks, and the performance of the proposed model was validated using classification problems.

Keywords: Functional network, neural network, XOR problem, classification, numerical analysis method.

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Authors: Alexander B. Bichkov, Alla A. Mityureva, Valery V. Smirnov

Abstract:

In present work are considered the scheme of evaluation the transition probability in quantum system. It is based on path integral representation of transition probability amplitude and its evaluation by means of a saddle point method, applied to the part of integration variables. The whole integration process is reduced to initial value problem solutions of Hamilton equations with a random initial phase point. The scheme is related to the semiclassical initial value representation approaches using great number of trajectories. In contrast to them from total set of generated phase paths only one path for each initial coordinate value is selected in Monte Karlo process.

Keywords: Path integral, saddle point method, semiclassical approximation, transition probability

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

Abstract:

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: R. Sadykova

Abstract:

This article analyses the peculiarities of Japan’s policy toward the countries of Central Asia. The increasing role of Central Asia in the system of international relations engendered an objective need for understanding of the policy of leading states, including Japan, in the region in the twenty-first century. The purpose of the study is to investigate the peculiarities of the formation and development of Japan policy in Central Asia and to identify the problems and prospects of Japan’s policy toward the countries of the region on the basis of experts’ opinions. In this article, the method of analysis of the situation and a systematic method were used. Prognostic methods, the collective expert assessment and scenarios were used in the study to determine the prospects of Japan’s policy toward the countries of Central Asia.

Keywords: Japan, Central Asia, the Eurasian concept, ‘Central Asia plus Japan’ Dialogue.

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Authors: Nader Gharibnavaz, Hossein Yazdi

Abstract:

If organizations like Mellat Bank want to identify its customer market completely to reach its specified goals, it can segment the market to offer the product package to the right segment. Our objective is to offer a segmentation model for Iran banking market in Mellat bank view. The methodology of this project is combined by “segmentation on the basis of four part-quality variables" and “segmentation on the basis of different in means". Required data are gathered from E-Systems and researcher personal observation. Finally, the research offers the organization that at first step form a four dimensional matrix with 756 segments using four variables named value-based, behavioral, activity style, and activity level, and at the second step calculate the means of profit for every cell of matrix in two distinguished work level (levels α1:normal condition and α2: high pressure condition) and compare the segments by checking two conditions that are 1- homogeneity every segment with its sub segment and 2- heterogeneity with other segments, and so it can do the necessary segmentation process. After all, the last offer (more explained by an operational example and feedback algorithm) is to test and update the model because of dynamic environment, technology, and banking system.

Keywords: market segmentation model, banking system, Mellat bank

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Authors: Chintanu K. Sarmah, Sandhya Samarasinghe, Don Kulasiri, Daniel Catchpoole

Abstract:

Gene expression profiling is rapidly evolving into a powerful technique for investigating tumor malignancies. The researchers are overwhelmed with the microarray-based platforms and methods that confer them the freedom to conduct large-scale gene expression profiling measurements. Simultaneously, investigations into cross-platform integration methods have started gaining momentum due to their underlying potential to help comprehend a myriad of broad biological issues in tumor diagnosis, prognosis, and therapy. However, comparing results from different platforms remains to be a challenging task as various inherent technical differences exist between the microarray platforms. In this paper, we explain a simple ratio-transformation method, which can provide some common ground for cDNA and Affymetrix platform towards cross-platform integration. The method is based on the characteristic data attributes of Affymetrix- and cDNA- platform. In the work, we considered seven childhood leukemia patients and their gene expression levels in either platform. With a dataset of 822 differentially expressed genes from both these platforms, we carried out a specific ratio-treatment to Affymetrix data, which subsequently showed an improvement in the relationship with the cDNA data.

Keywords: Gene expression profiling, microarray, cDNA, Affymetrix, childhood leukaemia.

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Authors: S. Montenegro, W. Hu

Abstract:

The objective of this paper is to develop a neural network-based residual generator to detect the fault in the actuators for a specific communication satellite in its attitude control system (ACS). First, a dynamic multilayer perceptron network with dynamic neurons is used, those neurons correspond a second order linear Infinite Impulse Response (IIR) filter and a nonlinear activation function with adjustable parameters. Second, the parameters from the network are adjusted to minimize a performance index specified by the output estimated error, with the given input-output data collected from the specific ACS. Then, the proposed dynamic neural network is trained and applied for detecting the faults injected to the wheel, which is the main actuator in the normal mode for the communication satellite. Then the performance and capabilities of the proposed network were tested and compared with a conventional model-based observer residual, showing the differences between these two methods, and indicating the benefit of the proposed algorithm to know the real status of the momentum wheel. Finally, the application of the methods in a satellite ground station is discussed.

Keywords: Satellite, Attitude Control, Momentum Wheel, Neural Network, Fault Detection.

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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