Central Difference Method

The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987(Wind Load), IS: 802:1995(Structural steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

This paper presented a new method to guide and control a space robot for capturing an uncooperative target. The dynamic model of a target is unknown and estimated with the help of vision system. This methodology has three different steps. First, the feature points of a space target were extracted using the vision system, then the pose of the target (position and orientation) relative to the space robot was determined based on Homography method. Second, because of an unknown model of the target, the location of the center of mass is calculated using kinematic equations and Iterative Closest Point (ICP) algorithm. This would help tracking moving target. Third, a new Adaptive Unscented Kalman Filter (AUKF) was introduced to estimate the dynamic state vector (position, orientation, linear and angular velocities) of an arbitrary space target. The error in AUKF estimation was prevented from divergence by using Fuzzy Logic Adaptive System (FLAS). Finally, a new trajectory method for planning the end-effector velocities of the space robot arm was implemented based on the measurement information from the vision system and estimation a target state using AUKF. The results from simulation experiments were presented and discussed.

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In Numerical analysis, interpolation is a manner of calculating the unknown values of a function for any conferred value of argument within the limit of the arguments. It provides basically a concept of estimating unknown data with the aid of relating acquainted data. The main goal of this research is to constitute a central difference interpolation method which is derived from the combination of Gauss's third formula, Gauss's Backward formula and Gauss's forward formula. We have also demonstrated the graphical presentations as well as comparison through all the existing interpolation formulas with our propound method of central difference interpolation. By the comparison and graphical presentation, the new method gives the best result with the lowest error from another existing interpolation formula.

An enhanced Fault Detection and Isolation (FDI) technique based on 't' statistical test is presented here employing a residual based R-Adaptive Unscented Kalman Filter (AUKF). Although the use of AUKF is common for estimation problem, employing AUKF for FDI duty is quite rare. Adaptive Unscented Kalman filtering framework is chosen here due to its derivative free calculations in the algorithm and reportedly better accuracy. Monitoring the 't' statistic of the innovation sequence, measurement faults are detected and corresponding alarm signals are generated here. The presented 't' statistic based FDI technique comprising of consistency checking and abruptness checking is straight forward, demands less computational burden and minimizes false alarms. The superiority of the proposed AUKF based FDI method compared to non adaptive, nonlinear filtering based FDI techniques is demonstrated here by an extensive simulation study executed on a nonlinear LEO satellite planar model. The use of AUKF has provided faster convergence speed and is also found to be advantageous for the situations where the measurement noise statistics are unknown.

Unscented Kalman filter (UKF) is a filtering algorithm that gives sufficiently good estimation results for the estimation problems of nonlinear systems even when high nonlinearity is in question. However, in case of system uncertainty or measurement malfunctions, the UKF becomes inaccurate and diverges by time. This study introduces a fault-tolerant attitude estimation algorithm for pico satellites. The algorithm uses a robust adaptive UKF, which performs correction for the process noise covariance (Q-adaptation) or measurement noise covariance (R-adaptation) depending on the type of the fault. By the use of a newly proposed adaptation scheme for the conventional UKF algorithm, the fault is detected and isolated, and the essential adaptation procedure is followed in accordance with the fault type. The proposed algorithm is tested as a part of the attitude estimation algorithm of a pico satellite.

A reconfigurable unscented Kalman filter (UKF)-based estimation algorithm for magnetometer biases and scale factors is proposed as a part of the attitude estimation scheme of a pico satellite. Unlike existing algorithms, in this paper, scale factors are not treated, together with other parameters, as part of the state vector; they are estimated separately. After satisfying the conditions of the proposed stopping rule for bias estimation, UKF reconfigures itself for estimation of attitude parameters alone.

In this paper an unscented Kalman filter based procedure for the bias estimation of both the magnetometers and the gyros carried onboard a pico satellite, is proposed. At the initial phase, biases of three orthogonally located magnetometers are estimated as well as the attitude and attitude rates of the satellite. During the initial period after the orbit injection, gyro measurements are accepted as bias free since the precise gyros are working accurately and the accumulated gyro biases are negligible. At the second phase estimated constant magnetometer bias components are taken into account and the algorithm is run for the estimation of the gyro biases that are cumulatively increased by time. As a result, six different bias terms for two different sensors are obtained in two stages, where attitude and attitude rates are estimated regularly. For both estimation phases of the procedure an unscented Kalman filter is used as the estimation algorithm.

The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987(Wind Load), IS: 802:1995(Structural steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

An improved fault detection scheme for a non-linear hybrid system with delayed measurement by using a modified non-linear adaptive state estimator is proposed. The proposed estimator performs acceptably even when the (i) covariance of the measurement noise is unknown and also (ii) when the measurements are delayed. The algorithm for the proposed estimator called time-delayed R-adaptive central difference Kalman filter (TD-RACDKF) uses a modified R-adaptive 2nd order Central Difference estimator, also called Central Difference Kalman Filter (CDKF) in some literature. Algorithm for the proposed TD-RACDKF has been presented and its performance evaluated as well as characterised with Monte Carlo simulation on two standard non-linear systems with delayed measurements. The characterisation includes comparison with existing estimators. Having demonstrated the improved performance of the proposed state estimator, its use for fault detection of non-linear hybrid systems was investigated. The performance of the fault detection scheme has been illustrated with the help of a benchmark non-linear hybrid system, namely 'three tank system' and by comparison with a previously available extended KF-based estimator.

In the paper some interval methods for solving the generalized Poisson equation (GPE) are presented. The main aim of this work is focused on providing such algorithms for solving this type of equation that are able to store information about potentially made numerical errors inside the results. In order to cope with these assumptions the floating-point interval arithmetic is used. We proposed to use interval versions of the central-difference method for two types of interval arithmetic: proper and directed. In the experimental part of this paper both arithmetics for three examples of GPE are compared.

The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987(Wind Load), IS: 802:1995(Structural steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h 2 + k 2), where h and k are mesh constants. Using this method in conventional floating-point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose interval versions of the central-difference method in proper and directed interval arithmetic. Applying such methods in floating-point interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented interval method in directed interval arithmetic is a little bit better than the one in proper interval arithmetic, i.e. the intervals of solutions are smaller. It appears that applying both proper and directed interval arithmetic the exact solutions belong to the interval solutions obtained.

The paper presents three-and four-stage implicit interval methods of Runge-Kutta type and is a continuation of our previous paper [6] dealing with one-and two-stage methods of this kind. It is shown that the exact solution of the initial value problem belongs to interval-solutions obtained by both kinds of these methods (three-and four-stage). We also present some approximations of the widths of interval-solutions.

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented.

The paper presents one-and two-stage implicit interval methods of Runge-Kutta type. It is shown that the exact solution of the initial value problem belongs to interval-solutions obtained by both kinds of these methods. Moreover, some approximations of the widths of interval-solutions are given.

In the paper some interval methods for solving the generalized Poisson equation (GPE) are presented. The main aim of this work is focused on providing such algorithms for solving this type of equation that are able to store information about potentially made numerical errors inside the results. In order to cope with these assumptions the floating-point interval arithmetic is used. We proposed to use interval versions of the central-difference method for two types of interval arithmetic: proper and directed. In the experimental part of this paper both arithmetics for three examples of GPE are compared.

To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are mesh constants. Using this method in conventional floating-point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose interval versions of the central-difference method in proper and directed interval arithmetic. Applying such methods in floating-point interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented interval method in directed interval arithmetic is a little bit better than the one in proper interval arithmetic, i.e. the intervals of solutions are smaller. It appears that applying both proper and directed interval arithmetic the exact solutions belong to the interval solutions obtained.

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented.

In the paper some interval methods for solving the generalized Poisson equation (GPE) are presented. The main aim of this work is focused on providing such algorithms for solving this type of equation that are able to store information about potentially made numerical errors inside the results. In order to cope with these assumptions the floating-point interval arithmetic is used. We proposed to use interval versions of the central-difference method for two types of interval arithmetic: proper and directed. In the experimental part of this paper both arithmetics for three examples of GPE are compared.

In the article we present an interval difference scheme for solving a general elliptic boundary value problem with Dirichlet’ boundary conditions. The obtained interval enclosure of the solution contains all possible numerical errors. A numerical example we present confirms that the exact solution belongs to the resulting interval enclosure

: In the paper some interval methods for solving the generalized Poisson equation (GPE) are presented. The main
aim of this work is focused on providing such algorithms for solving this type of equation that are able to store information
about potentially made numerical errors inside the results. In order to cope with these assumptions the floating-point interval
arithmetic is used. We proposed to use interval versions of the central-difference method for two types of interval arithmetic:
proper and directed. In the experimental part of this paper both arithmetics for three examples of GPE are compared.

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented.

In this research, the comparison of Analysis and Design of Monopole and Transmission Tower with the manual calculation and by using STAAD.Pro V8i software for analysis is done. The monopole of 18m height and transmission tower of 20m height are designed by manually calculated terms and the analysis is done by using structural analysis software. For the point of design, a 4-legged transmission tower of double circuited structure with 132KV power and a 16 sided polygonal-shaped of double circuited structure of monopole with 132KV power are considered. The structural and power fields are considered while designing towers for transmission line and monopole for its safe and economic aspects. The design of both monopole and Transmission tower are done manually using LSM (Limit State Method). The acting Loads on the monopole and transmission tower are dead load of the configured structure, braking load of the conductor, earthquake load and wind load are considered as per relevant IS code. The design are based on IS Codes which includes IS 800, IS 875, IS 802, IS 5613, etc. The wind forces are much effective on the transmission line tower and monopole, on their components like conductors and insulators, beside its self weight, hence wind analysis is done by using standard IS code 800-2007 and software. Also, the Earthquake analysis is done out using IS code for earthquake and software. In this research firstly the design of monopole and transmission tower are done with manual calculation and then analysis is carried out in analysis software, finally results are compared. The analysis with compressive stress, tensile stress, bending moment, lateral displacement and resultant displacement respect to three loading condition namely Normal, Vertical and Broken wire condition is compared for the results.

In Numerical analysis, interpolation is a manner of calculating the unknown values of a function for any conferred value of argument within the limit of the arguments. It provides basically a concept of estimating unknown data with the aid of relating acquainted data. The main goal of this research is to constitute a central difference interpolation method which is derived from the combination of Gauss's third formula, Gauss's Backward formula and Gauss's forward formula. We have also demonstrated the graphical presentations as well as comparison through all the existing interpolation formulas with our propound method of central difference interpolation. By the comparison and graphical presentation, the new method gives the best result with the lowest error from another existing interpolation formula.

Unscented Kalman filter (UKF) is a filtering algorithm that gives sufficiently good estimation results for the estimation problems of nonlinear systems even when high nonlinearity is in question. However, in case of system uncertainty or measurement malfunctions, the UKF becomes inaccurate and diverges by time. This study introduces a fault-tolerant attitude estimation algorithm for pico satellites. The algorithm uses a robust adaptive UKF, which performs correction for the process noise covariance (Q-adaptation) or measurement noise covariance (R-adaptation) depending on the type of the fault. By the use of a newly proposed adaptation scheme for the conventional UKF algorithm, the fault is detected and isolated, and the essential adaptation procedure is followed in accordance with the fault type. The proposed algorithm is tested as a part of the attitude estimation algorithm of a pico satellite. it with a time-dependent variable. One of the methods for constructing such algorithm is to use a scale factor as a multiplier to the process or measurement noise covariance matrices . This kind of gain correction-based algorithms can be used when the information about the dynamic or measurement process is absent . Hence, the adaptation against both the system uncertainty and the measurement malfunctions is possible.

The following are the steps involved in design of communication tower. a. Selection of configuration of tower b. Computation of loads acting on tower c. Analysis of tower for above loads d. Design of tower members according to codes of practices. Selection of configuration of a tower involves fixing of top width, bottom width, number of panels and their heights, type of bracing system and slope of tower.

The factor of safety ( f.o.s ) of a conductor ( or ground wire ) is the ratio of the ultimate strength of the conductor ( or ground wire ) to the load imposed under assumed loading condition. Rule 76 (1)(c) of the Indian Electricity Rules, 1956, stipulates as follows:

Over the past 30 years, the growing demand for wireless and broadcast communication has spurred a dramatic increase in communication tower construction and maintenance. Failure of such structures is a major concern. In this paper a comparative analysis is being carried out for different heights of towers using different bracing patterns for Wind zones I to VI and Earthquake zones II to V of India. Gust factor method is used for wind load analysis, modal analysis and response spectrum analysis are used for earthquake loading. The results of displacement at the top of the towers and stresses in the bottom leg of the towers are compared.

Formulation of transmission towers is tendered in a perspective of confronting high voltage transmitting conductors and insulators to stand in need of altitude from the ground level. For the same purpose a transmission tower is replicated with similar context of height 49m and fetching a 220KV double circuit conductor, maneuvered with STAAD PRO. The contemplations from both structural and electrical fields are viewed in designing transmission line towers, for safe and economic aspects. According to IS 800-2007, the wind forces are much prominent on the tower, conductors and insulators, besides the self-weight. This work is focused in optimizing the transmission tower with employing the 'X' and 'K' bracings, and by varying the sections, examined using Static analysis. The upshots of using 'X' bracing to 'K' bracing are the appraisable reduction in the weight of the structure by 6% and having the displacement values supplemented.

A new algorithm for adaptive non-linear filter suitable for signal models with unknown measurement noise covariance is presented here. The proposed adaptive filter is based on numerically efficient central difference algorithm which is potentially suitable for on board implementation. Unlike some competing adaptation scheme the proposed method guarantees positive definiteness of the estimated covariance matrix and avoids consequent singularity. Superiority of the proposed filter in comparison with non-adaptive central difference filter (CDF), an adaptive unscented Kalman filter and also another CDF based adaptive filter with alternative adaptation scheme has been demonstrated by Monte Carlo simulations. The signal models used are a well-known reentry ballistic target tracking problem and a high dimensional, relatively complex spacecraft attitude determination problem. The algorithm has provisions for (i) iterative refinement, (ii) modulating the degree of adaptation and also (iii) for incorporating tradeoff mechanisms between computational load and estimation error.

The following are the steps involved in design of communication tower. a. Selection of configuration of tower b. Computation of loads acting on tower c. Analysis of tower for above loads d. Design of tower members according to codes of practices. Selection of configuration of a tower involves fixing of top width, bottom width, number of panels and their heights, type of bracing system and slope of tower.

In this paper a new Adaptive Unscented Kalman Filter (AUKF) is proposed and applied for the state estimation of a LEO (Low earth Orbit) satellite planar model. The Unscented Kalman Filter (UKF) is preferred here because of its derivative free calculation process and superior performance in highly non linear systems. Further the choice of adaptive filter gives the opportunity to estimate the states without any prior knowledge about the noise covariances. The measurement noise covariance (R) is changed here adaptively. Previously R adaptation techniques have been employed for linear and Extended Kalman Filters (EKF) but the use of R adaptation for sigma point filter is relatively newer trend. Two versions of R-adaptive UKF are presented here depending on the residual sequences and the innovation sequences. Positive definiteness of R is ensured in the proposed algorithm. The R matrix here has been constrained to have a diagonal structure as the measurement noise sources are normally independent of each other. Proposed scheme has also the provision to modulate the speed of adaptation. The simulation results show the superiority of the AUKF compared to the non-adaptive filters like EKF, UKF and CDF (Central Difference Filter). It is also found that the steady state performance of the residual based adaptive filter is robust to the initial value of R.

The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987(Wind Load), IS: 802:1995(Structural steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

In this paper, an explicit time integration scheme is proposed for structural vibration analysis by using wavelet functions. Initially, the differential equation of vibration governing SDOF (single-degree of freedom) systems has been solved by wavelet operators, and later the proposed approach has been generalized for MDOF (multi-degrees of freedom) systems. For this purpose, two different types of wavelet functions have been exemplified including, complex Chebyshev wavelet functions and simple Haar wavelet functions. In the proposed approach, a straightforward formulation has been derived from the numerical approximation of response through the wavelet definition. Emphasizing on frequency-domain approximation, a simple step-by-step algorithm has been implemented and improved to calculate the response of MDOF systems. Moreover, stability and accuracy of results have been evaluated. The effectiveness of the proposed approach is demonstrated using three examples compared with some of the existing numerical integration schemes such as family of Newmark-β, Wilson-θ and central difference method. In all the procedures, computation time involved has also been considered. Finally, it is concluded that the vibration analysis of structures is improved by lesser computation time and high accuracy of proposed approach, particularly, in large-scaled systems. © 2013 Elsevier Inc. All rights reserved.

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