Search results for: 7A6 series manipulator.

Authors: Nikolay Nikolaev, Evgueni Smirnov

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This paper develops an unscented grid-based filter and a smoother for accurate nonlinear modeling and analysis of time series. The filter uses unscented deterministic sampling during both the time and measurement updating phases, to approximate directly the distributions of the latent state variable. A complementary grid smoother is also made to enable computing of the likelihood. This helps us to formulate an expectation maximisation algorithm for maximum likelihood estimation of the state noise and the observation noise. Empirical investigations show that the proposed unscented grid filter/smoother compares favourably to other similar filters on nonlinear estimation tasks.

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Authors: Ming Cong, Yinghua Wu, Dong Liu, Haiying Wen, Junfa Yu

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In order to improve control performance and eliminate steady, a coupling compensation for 6-DOF parallel robot is presented. Taking dynamic load Tank Simulator as the research object, this paper analyzes the coupling of 6-DOC parallel robot considering the degree of freedom of the 6-DOF parallel manipulator. The coupling angle and coupling velocity are derived based on inverse kinematics model. It uses the mechanism-model combined method which takes practical moving track that considering the performance of motion controller and motor as its input to make the study. Experimental results show that the coupling compensation improves motion stability as well as accuracy. Besides, it decreases the dither amplitude of dynamic load Tank Simulator.

Keywords: coupling compensation, screw theory, parallel robot, mechanism-model combined motion

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Authors: Hossein Jafari, Xiangfang Li, Lijun Qian, Alexander Aved, Timothy Kroecker

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Traditionally in sensor networks and recently in the Internet of Things, numerous heterogeneous sensors are deployed in distributed manner to monitor a phenomenon that often can be model by an underlying stochastic process. The big time-series data collected by the sensors must be analyzed to detect change in the stochastic process as quickly as possible with tolerable false alarm rate. However, sensors may have different accuracy and sensitivity range, and they decay along time. As a result, the big time-series data collected by the sensors will contain uncertainties and sometimes they are conflicting. In this study, we present a framework to take advantage of Evidence Theory (a.k.a. Dempster-Shafer and Dezert-Smarandache Theories) capabilities of representing and managing uncertainty and conflict to fast change detection and effectively deal with complementary hypotheses. Specifically, Kullback-Leibler divergence is used as the similarity metric to calculate the distances between the estimated current distribution with the pre- and post-change distributions. Then mass functions are calculated and related combination rules are applied to combine the mass values among all sensors. Furthermore, we applied the method to estimate the minimum number of sensors needed to combine, so computational efficiency could be improved. Cumulative sum test is then applied on the ratio of pignistic probability to detect and declare the change for decision making purpose. Simulation results using both synthetic data and real data from experimental setup demonstrate the effectiveness of the presented schemes.

Keywords: CUSUM, evidence theory, KL divergence, quickest change detection, time series data.

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Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim

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It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

Existence of plastic equation of state has been investigated by performing a series of load relaxation tests at various temperatures using an Al-Li alloy. A plastic equation of state is first developed from a simple kinetics consideration for a mechanical activation process of a leading dislocation piled up against grain boundaries. A series of load relaxation test has been conducted at temperatures ranging from 200 to 530^oC to obtain the stress-strain rate curves. A plastic equation of state has been derived from a simple consideration of dislocation kinetics and confirmed by experimental results.

Keywords: Plastic equation of state, Dislocation kinetics, Load relaxation test, Al-Li alloy, Microstructure.

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Authors: Prakash Persad, Kelvin Loutan, Jr., Trichelle Seepersad

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The Finite Element Method is commonly used in the analysis of flexible manipulators to predict elastic displacements and develop joint control schemes for reducing positioning error. In order to preserve simplicity, regular geometries, ideal joints and connections are assumed. This paper presents the dynamic FE analysis of a 4- degrees of freedom open chain manipulator, intended for striking a curved 3D surface percussion musical instrument. This was done utilizing the new MultiBody Dynamics Module in COMSOL, capable of modeling the elastic behavior of a body undergoing rigid body type motion.

Keywords: Dynamic modeling, Entertainment robots, Finite element method, Flexible robot manipulators, Multibody dynamics, Musical robots.

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Authors: Walenty Oniszczuk

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The use of buffer thresholds, blocking and adequate service strategies are well-known techniques for computer networks traffic congestion control. This motivates the study of series queues with blocking, feedback (service under Head of Line (HoL) priority discipline) and finite capacity buffers with thresholds. In this paper, the external traffic is modelled using the Poisson process and the service times have been modelled using the exponential distribution. We consider a three-station network with two finite buffers, for which a set of thresholds (tm1 and tm2) is defined. This computer network behaves as follows. A task, which finishes its service at station B, gets sent back to station A for re-processing with probability o. When the number of tasks in the second buffer exceeds a threshold tm2 and the number of task in the first buffer is less than tm1, the fed back task is served under HoL priority discipline. In opposite case, for fed backed tasks, “no two priority services in succession" procedure (preventing a possible overflow in the first buffer) is applied. Using an open Markovian queuing schema with blocking, priority feedback service and thresholds, a closed form cost-effective analytical solution is obtained. The model of servers linked in series is very accurate. It is derived directly from a twodimensional state graph and a set of steady-state equations, followed by calculations of main measures of effectiveness. Consequently, efficient expressions of the low computational cost are determined. Based on numerical experiments and collected results we conclude that the proposed model with blocking, feedback and thresholds can provide accurate performance estimates of linked in series networks.

Keywords: Blocking, Congestion control, Feedback, Markov chains, Performance evaluation, Threshold-base networks.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi, Abdolrasoul Telvari, Hossein Babazadeh

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Floods have huge environmental and economic impact. Therefore, flood prediction is given a lot of attention due to its importance. This study analysed the annual maximum streamflow (discharge) (AMS or AMD) of Karkheh River in Karkheh River Basin for flood predicting using ARIMA model. For this purpose, we use the Box-Jenkins approach, which contains four-stage method model identification, parameter estimation, diagnostic checking and forecasting (predicting). The main tool used in ARIMA modelling was the SAS and SPSS software. Model identification was done by visual inspection on the ACF and PACF. SAS software computed the model parameters using the ML, CLS and ULS methods. The diagnostic checking tests, AIC criterion, RACF graph and RPACF graphs, were used for selected model verification. In this study, the best ARIMA models for Annual Maximum Discharge (AMD) time series was (4,1,1) with their AIC value of 88.87. The RACF and RPACF showed residuals’ independence. To forecast AMD for 10 future years, this model showed the ability of the model to predict floods of the river under study in the Karkheh River Basin. Model accuracy was checked by comparing the predicted and observation series by using coefficient of determination (R²).

Keywords: Time series modelling, stochastic processes, ARIMA model, Karkheh River.

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Authors: Ahmet Denker, Tuğrul Adıgüzel

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In this paper, a solution is presented for a robotic manipulation problem in industrial settings. The problem is sensing objects on a conveyor belt, identifying the target, planning and tracking an interception trajectory between end effector and the target. Such a problem could be formulated as combining object recognition, tracking and interception. For this purpose, we integrated a vision system to the manipulation system and employed tracking algorithms. The control approach is implemented on a real industrial manipulation setting, which consists of a conveyor belt, objects moving on it, a robotic manipulator, and a visual sensor above the conveyor. The trjectory for robotic interception at a rendezvous point on the conveyor belt is analytically calculated. Test results show that tracking the raget along this trajectory results in interception and grabbing of the target object.

Keywords: robotics, robot vision, rendezvous planning, self organizingmaps.

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Authors: Chih-Ling Huang, Wen-Yi Lin, Kuo-Mo Hsiao

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A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.

Keywords: Flapping vibration, Inclination angle, Natural frequency, Rotating beam.

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Authors: Irwin Ma, Tony Wong, Thiagas Sankar

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By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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Authors: Seok Hong Min, Tae Kwon Ha

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In this study, thermal fatigue properties of 400 series ferritic stainless steels have been evaluated in the temperature ranges of 200-800oC and 200-900oC. Systematic methods for control of temperatures within the predetermined range and measurement of load applied to specimens as a function of temperature during thermal cycles have been established. Thermal fatigue tests were conducted under fully constrained condition, where both ends of specimens were completely fixed. It has been revealed that load relaxation behavior at the temperatures of thermal cycle was closely related with the thermal fatigue property. Thermal fatigue resistance of 430J1L stainless steel is found to be superior to the other steels.

Keywords: Ferritic stainless steel, automotive exhaust, thermal fatigue, microstructure, load relaxation.

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Authors: Ramesh K. Sunkaria

Abstract:

The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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Authors: Yizhi Gai, Yukinori Kobayashi, Yohei Hoshino, Takanori Emaru

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Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

Keywords: Motion control, flexible robotic arm, CEVEPSO, ball throwing robot.

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Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

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In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

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Authors: Farhad Asadi, Hossein Sadati

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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: Tanuj Kumar, Rakesh Kumar Bajaj

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In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

Keywords: Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

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Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

The hydrologic time series data display periodic structure and periodic autoregressive process receives considerable attention in modeling of such series. In this communication long term record of monthly waste flow of Lyari river is utilized to quantify by using PAR modeling technique. The parameters of model are estimated by using Frances & Paap methodology. This study shows that periodic autoregressive model of order 2 is the most parsimonious model for assessing periodicity in waste flow of the river. A careful statistical analysis of residuals of PAR (2) model is used for establishing goodness of fit. The forecast by using proposed model confirms significance and effectiveness of the model.

Keywords: Diagnostic checks, Lyari river, Model selection, Monthly waste flow, Periodicity, Periodic autoregressive model.

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Authors: N. Sopipan

Abstract:

In this paper, we study the rainfall using a time series for weather stations in Nakhon Ratchasima province in Thailand by various statistical methods to enable us to analyse the behaviour of rainfall in the study areas. Time-series analysis is an important tool in modelling and forecasting rainfall. The ARIMA and Holt-Winter models were built on the basis of exponential smoothing. All the models proved to be adequate. Therefore it is possible to give information that can help decision makers establish strategies for the proper planning of agriculture, drainage systems and other water resource applications in Nakhon Ratchasima province. We obtained the best performance from forecasting with the ARIMA Model(1,0,1)(1,0,1)12.

Keywords: ARIMA Models, Exponential Smoothing, Holt- Winter model.

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Authors: Amir Atrian, Javad Jafari Fesharaki, Gh. Hossein Majzoobi, Mahsa Sheidaee

Abstract:

The analytical solution of functionally graded piezoelectric hollow cylinder which is under radial electric potential and non-axisymmetric thermo-mechanical loads, are presented in this paper. Using complex Fourier series and estimation of power law for variations of material characterizations through the thickness, the electro thermo mechanical behavior of the FGPM cylinder is obtained. The stress and displacement distributions and the effect of electric potential field on the cylinder behavior are also presented and some applicable results are offered at the end of the paper.

Keywords: Analytical, FGM, Fourier series, Non-axisymmetric, Piezoelectric, Thermo-elasticity

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Authors: Tawiwat Veeraklaew, Nathasit Phathana-im, Songkit Heama

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Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting relationship between the minimum direct and indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of direct and indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of control inputs employed by minimum direct and indirect jerk designs. By considering minimum indirect jerk problem, the numerical solution becomes much easier and yields to the similar results as minimum direct jerk problem.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: V. Tawiwat, P. Jumnong

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting when combining the minimum energy and jerk of indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of the minimum energy, the minimum jerk and combining them together are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of state inputs employed by combining minimum energy and jerk designs. The numerical solution of minimum direct jerk and energy problem are exactly the same solution; however, the solutions from problem of minimum energy yield the similar solution especially in term of tendency.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: S. Salkhordeh, P. Golbazi, H. Amini

Abstract:

In this study two series of self compacting concrete mixtures were prepared with 100% coarse recycled concrete aggregates and different percentages of 0%, 20%, 40%, 60%, 80% and 100% fine recycled concrete aggregates. In series I and II the water to binder ratios were 0.50 and 0.45, respectively. The cement content was kept 350 3 m kg for those mixtures that don't have any Nano-Silica. To improve the compressive strength of samples, Nano- Silica replaced with 10% of cement weight in concrete mixtures. By doing the tests, the results showed that, adding Nano-silica to the samples with less percentage of fine recycled concrete aggregates, lead to more increase on the compressive strength.

Keywords: Compressive Strength, Nano-Silica, RecycledConcrete Aggregates, Self Compacting Concrete.

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Authors: Ju Young Lee, Jung-Seok Yang, Jaeyoung Choi

Abstract:

The purpose of this paper primarily intends to develop GIS interface for estimating sequences of stream-flows at ungauged stations based on known flows at gauged stations. The integrated GIS interface is composed of three major steps. The first, precipitation characteristics using statistical analysis is the procedure for making multiple linear regression equation to get the long term mean daily flow at ungauged stations. The independent variables in regression equation are mean daily flow and drainage area. Traditionally, mean flow data are generated by using Thissen polygon method. However, method for obtaining mean flow data can be selected by user such as Kriging, IDW (Inverse Distance Weighted), Spline methods as well as other traditional methods. At the second, flow duration curve (FDC) is computing at unguaged station by FDCs in gauged stations. Finally, the mean annual daily flow is computed by spatial interpolation algorithm. The third step is to obtain watershed/topographic characteristics. They are the most important factors which govern stream-flows. In summary, the simulated daily flow time series are compared with observed times series. The results using integrated GIS interface are closely similar and are well fitted each other. Also, the relationship between the topographic/watershed characteristics and stream flow time series is highly correlated.

Keywords: Integrated GIS interface, spatial interpolation algorithm, FDC.

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Authors: Samir Brahim Belhaouari

Abstract:

By taking advantage of both k-NN which is highly accurate and K-means cluster which is able to reduce the time of classification, we can introduce Cluster-k-Nearest Neighbor as "variable k"-NN dealing with the centroid or mean point of all subclasses generated by clustering algorithm. In general the algorithm of K-means cluster is not stable, in term of accuracy, for that reason we develop another algorithm for clustering our space which gives a higher accuracy than K-means cluster, less subclass number, stability and bounded time of classification with respect to the variable data size. We find between 96% and 99.7 % of accuracy in the lassification of 6 different types of Time series by using K-means cluster algorithm and we find 99.7% by using the new clustering algorithm.

Keywords: Pattern recognition, Time series, k-Nearest Neighbor, k-means cluster, Gaussian Mixture Model, Classification

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Authors: Mohamed T. Sorour, Mohamed A. Abdellatif, Ahmed A. Ramadan, Ahmed A. Abo-Ismail

Abstract:

This paper describes the development of an autonomous robot for painting the interior walls of buildings. The robot consists of a painting arm with an end effector roller that scans the walls vertically and a mobile platform to give horizontal feed to paint the whole area of the wall. The painting arm has a planar twolink mechanism with two joints. Joints are driven from a stepping motor through a ball screw-nut mechanism. Four ultrasonic sensors are attached to the mobile platform and used to maintain a certain distance from the facing wall and to avoid collision with side walls. When settled on adjusted distance from the wall, the controller starts the painting process autonomously. Simplicity, relatively low weight and short painting time were considered in our design. Different modules constituting the robot have been separately tested then integrated. Experiments have shown successfulness of the robot in its intended tasks.

Keywords: Automated roller painting, Construction robots, Mobile robots, service robots, two link planar manipulator

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Authors: Sandra Baßler, Peter Dünow, Mathias Marquardt

Abstract:

A Fourier series based learning control (FSBLC) algorithm for tracking trajectories of mechanical systems with unknown nonlinearities is presented. Two processes are introduced to which the FSBLC with PD controller is applied. One is a simplified service robot capable of climbing stairs due to special wheels and the other is a propeller driven pendulum with nearly the same requirements on control. Additionally to the investigation of learning the feed forward for the desired trajectories some considerations on the implementation of such an algorithm on low cost microcontroller hardware are made. Simulations of the service robot as well as practical experiments on the pendulum show the capability of the used FSBLC algorithm to perform the task of improving control behavior for repetitive task of such mechanical systems.

Keywords: Climbing stairs, FSBLC, ILC, Service robot.

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Authors: Ahmed M. Mansour, Ali M. El-Sawy, Ahmed T Sayed

Abstract:

Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving insights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

Keywords: Logarithms, log2, floor, iterative, CORDIC, Taylor series.

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