Search results for: Biogeography based optimization method

Authors: Sanjib Kr Pal, S. Bhattacharyya

Abstract:

Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: Entropy generation, mixed convection, conjugate heat transfer, numerical, nanofluid, wall waviness.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

Abstract:

The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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Authors: Muftah H. El-Naas, Ameera F. Mohammad, Mabruk I. Suleiman, Mohamed Al Musharfy, Ali H. Al-Marzouqi

Abstract:

CO₂ capture and storage technologies play a significant role in contributing to the control of climate change through the reduction of carbon dioxide emissions into the atmosphere. The present study evaluates and optimizes CO₂ capture through a process, where carbon dioxide is passed into pH adjusted high salinity water and reacted with sodium chloride to form a precipitate of sodium bicarbonate. This process is based on a modified Solvay process with higher CO₂ capture efficiency, higher sodium removal, and higher pH level without the use of ammonia. The process was tested in a bubble column semi-batch reactor and was optimized using response surface methodology (RSM). CO₂ capture efficiency and sodium removal were optimized in terms of major operating parameters based on four levels and variables in Central Composite Design (CCD). The operating parameters were gas flow rate (0.5–1.5 L/min), reactor temperature (10 to 50 ^oC), buffer concentration (0.2-2.6%) and water salinity (25-197 g NaCl/L). The experimental data were fitted to a second-order polynomial using multiple regression and analyzed using analysis of variance (ANOVA). The optimum values of the selected variables were obtained using response optimizer. The optimum conditions were tested experimentally using desalination reject brine with salinity ranging from 65,000 to 75,000 mg/L. The CO₂ capture efficiency in 180 min was 99% and the maximum sodium removal was 35%. The experimental and predicted values were within 95% confidence interval, which demonstrates that the developed model can successfully predict the capture efficiency and sodium removal using the modified Solvay method.

Keywords: Bubble column reactor, CO2 capture, Response Surface Methodology, water desalination.

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Authors: Miquel Colobran, Josep M. Basart

Abstract:

One of the most ancient humankind concerns is knowledge formalization i.e. what a concept is. Concept Analysis, a branch of analytical philosophy, relies on the purpose of decompose the elements, relations and meanings of a concept. This paper aims at presenting a method to make a concept analysis obtaining a knowledge representation suitable to be processed by a computer system using either object-oriented or ontology technologies. Security notion is, usually, known as a set of different concepts related to “some kind of protection". Our method concludes that a more general framework for the concept, despite it is dynamic, is possible and any particular definition (instantiation) depends on the elements used by its construction instead of the concept itself.

Keywords: Concept analysis, Knowledge representation, Security, UML.

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Authors: Mohanad Alhabo, Naveed Nawaz, Mahmoud Al-Faris

Abstract:

The dense deployment of small cells is a promising solution to enhance the coverage and capacity of the heterogeneous networks (HetNets). However, the unplanned deployment could bring new challenges to the network ranging from interference, unnecessary handovers and handover failures. This will cause a degradation in the quality of service (QoS) delivered to the end user. In this paper, we propose an integrated Grey Rational Analysis Standard Deviation based handover method (GRA-SD) for HetNet. The proposed method integrates the Standard Deviation (SD) technique to acquire the weight of the handover metrics and the GRA method to select the best handover base station. The performance of the GRA-SD method is evaluated and compared with the traditional Multiple Attribute Decision Making (MADM) methods including Simple Additive Weighting (SAW) and VIKOR methods. Results reveal that the proposed method has outperformed the other methods in terms of minimizing the number of frequent unnecessary handovers and handover failures, in addition to improving the energy efficiency.

Keywords: Energy efficiency, handover, HetNets, MADM, small cells.

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Authors: Jung-Hyun Kim, Jihyung Kim, Kwangjae Lim, Dong Seung Kwon

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In this paper, our focus is to assure a global frequency synchronization in OFDMA-based wireless mesh networks with local information. To acquire the global synchronization in distributed manner, we propose a novel distributed frequency synchronization (DFS) method. DFS is a method that carrier frequencies of distributed nodes converge to a common value by repetitive estimation and averaging step and sharing step. Experimental results show that DFS achieves noteworthy better synchronization success probability than existing schemes in OFDMA-based mesh networks where the estimation error is presented.

Keywords: OFDMA systems, Frequency synchronization, Distributed networks, Multiple groups.

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Authors: A. Charlangsut, M. Boonthienthong, N. Rugthaicharoencheep

Abstract:

This paper proposes a mathematical model for transmission expansion employing optimization method with scenario analysis approach. Economic transmission planning, on the other hand, seeks investment opportunities so that network expansions can generate more economic benefits than the costs. This approach can be used as a decision model for building new transmission lines added to the existing transmission system minimizing costs of the entire system subject to various system’s constraints and consider of loss value of transmission system and N-1 checking. The results show that the proposed model is efficient to be applied for the larger scale of power system topology.

Keywords: Transmission Expansion Planning, Economic Dispatch, Scenario Analysis, Contingency.

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Authors: Chen Wu, Jingyu Yang

Abstract:

Using maximal consistent blocks of tolerance relation on the universe in incomplete decision table, the concepts of join block and meet block are introduced and studied. Including tolerance class, other blocks such as tolerant kernel and compatible kernel of an object are also discussed at the same time. Upper and lower approximations based on those blocks are also defined. Default definite decision rules acquired from incomplete decision table are proposed in the paper. An incremental algorithm to update default definite decision rules is suggested for effective mining tasks from incomplete decision table into which data is appended. Through an example, we demonstrate how default definite decision rules based on maximal consistent blocks, join blocks and meet blocks are acquired and how optimization is done in support of discernibility matrix and discernibility function in the incomplete decision table.

Keywords: rough set, incomplete decision table, maximalconsistent block, default definite decision rule, join and meet block.

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Authors: Isa Ahmadi, Ramin Khamedi

Abstract:

In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C¹ continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: Cyclic Loading, Finite Element Analysis, Prager Kinematic Hardening Model, Torsion of shaft.

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Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, fluid systems, observer systems, unscented Kalman filter.

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Authors: Attitude Stabilization of Satellites Using Random Dither Quantization

Abstract:

Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: Quantized control, nonlinear systems, random dither quantization.

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Authors: Soroosh Rezazadeh, Mehran Yazdi

Abstract:

In this paper, a robust digital image watermarking scheme for copyright protection applications using the singular value decomposition (SVD) is proposed. In this scheme, an entropy masking model has been applied on the host image for the texture segmentation. Moreover, the local luminance and textures of the host image are considered for watermark embedding procedure to increase the robustness of the watermarking scheme. In contrast to all existing SVD-based watermarking systems that have been designed to embed visual watermarks, our system uses a pseudo-random sequence as a watermark. We have tested the performance of our method using a wide variety of image processing attacks on different test images. A comparison is made between the results of our proposed algorithm with those of a wavelet-based method to demonstrate the superior performance of our algorithm.

Keywords: Watermarking, copyright protection, singular value decomposition, entropy masking, texture segmentation.

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

Multimodal biometric systems integrate the data presented by multiple biometric sources, hence offering a better performance than the systems based on a single biometric modality. Although the coupling of biometric systems can be done at different levels, the fusion at the scores level is the most common since it has been proven effective than the rest of the fusion levels. However, the scores from different modalities are generally heterogeneous. A step of normalizing the scores is needed to transform these scores into a common domain before combining them. In this paper, we study the performance of several normalization techniques with various fusion methods in a context relating to the merger of three unimodal systems based on the face, the palmprint and the fingerprint. We also propose a new adaptive normalization method that takes into account the distribution of client scores and impostor scores. Experiments conducted on a database of 100 people show that the performances of a multimodal system depend on the choice of the normalization method and the fusion technique. The proposed normalization method has given the best results.

Keywords: Multibiometrics, Fusion, Score level, Score normalization, Adaptive normalization.

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Authors: Yong-jun Zhao, Heng-li Zhang, Zong-yun Hu

Abstract:

Based on the sources- smoothed rank profile (SRP) and modified minimum description length (MMDL) principle, a method for estimation of the source coherency structure (SCS) and the number of wideband sources is proposed in this paper. Instead of focusing, we first use a spatial smoothing technique to pre-process the array covariance matrix of each frequency for de-correlating the sources and then use smoothed rank profile to determine the SCS and the number of wideband sources. We demonstrate the availability of the method by numerical simulations.

Keywords: Wideband sources, source coherency structure (SCS), smoothed rank profile (SRP).

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Authors: Guguloth Ramesh, T. K. Sunil Kumar

Abstract:

This paper presents congestion management in deregulated power systems. In a deregulated environment, every buyer wants to buy power from the cheapest generator available, irrespective of relative geographical location of buyer and seller. As a consequence of this, the transmission corridors evacuating the power of cheaper generators would get overloaded if all such transactions are approved. Congestion management is a mechanism to prioritize the transactions and commit to such a schedule which would not overload the network. The congestions in the transmission lines are determined by Optimal Power Flow (OPF) solution, which is carried by primal liner programming method. Congestion in the transmission lines are alleviated by connected Distributed Generation (DG) of micro grid at load bus. A method to determine the optimal location of DG unit has been suggested based on transmission line relief sensitivity based approach. The effectiveness of proposed method has been demonstrated on modified IEEE-14 and 30 bus test systems.

Keywords: Congestion management, Distribution Generation (DG), Transmission Line Relief (TLR) sensitivity index, OPF.

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Authors: Rashid S S, Alam M Z, Karim M I A, Salleh, M H

Abstract:

A statistical optimization was studied to design a media composition to produce optimum cellulolytic enzyme where palm oil mill effluent (POME) as a basal medium and filamentous fungus, Trichoderma reesei RUT-C30 were used in the liquid state bioconversion(LSB). 2% (w/v) total suspended solid, TSS, of the POME supplemented with 1% (w/v) cellulose, 0.5%(w/v) peptone and 0.02% (v/v) Tween 80 was estimated to produce the optimum CMCase activity of 18.53 U/ml through the statistical analysis followed by the faced centered central composite design(FCCCD). The probability values of cellulose (<0.0011) and peptone (0.0021) indicated the significant effect on the production of cellulase with the determination coefficient (R2) of 0.995.

Keywords: Face centered central composite design (FCCCD), Liquid state bioconversion (LSB), Palm oil mill effluent, Trichoderma reesei RUT C-30.

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Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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Authors: Mohammad Al-Fayoumi, Soumya Banerjee, Jr., P. K. Mahanti

Abstract:

A social network is a set of people or organization or other social entities connected by some form of relationships. Analysis of social network broadly elaborates visual and mathematical representation of that relationship. Web can also be considered as a social network. This paper presents an innovative approach to analyze a social network using a variant of existing ant colony optimization algorithm called as Clever Ant Colony Metaphor. Experiments are performed and interesting findings and observations have been inferred based on the proposed model.

Keywords: Social Network, Ant Colony, Maximum Clique, Sub graph, Clever Ant colony.

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Authors: Cheng-Lung Huang, Cheng-Wei Lin

Abstract:

This study proposes a new recommender system based on the collaborative folksonomy. The purpose of the proposed system is to recommend Internet resources (such as books, articles, documents, pictures, audio and video) to users. The proposed method includes four steps: creating the user profile based on the tags, grouping the similar users into clusters using an agglomerative hierarchical clustering, finding similar resources based on the user-s past collections by using content-based filtering, and recommending similar items to the target user. This study examines the system-s performance for the dataset collected from “del.icio.us," which is a famous social bookmarking website. Experimental results show that the proposed tag-based collaborative and content-based filtering hybridized recommender system is promising and effectiveness in the folksonomy-based bookmarking website.

Keywords: Collaborative recommendation, Folksonomy, Social tagging

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Authors: Florin Pop

Abstract:

Simulation is a very powerful method used for highperformance and high-quality design in distributed system, and now maybe the only one, considering the heterogeneity, complexity and cost of distributed systems. In Grid environments, foe example, it is hard and even impossible to perform scheduler performance evaluation in a repeatable and controllable manner as resources and users are distributed across multiple organizations with their own policies. In addition, Grid test-beds are limited and creating an adequately-sized test-bed is expensive and time consuming. Scalability, reliability and fault-tolerance become important requirements for distributed systems in order to support distributed computation. A distributed system with such characteristics is called dependable. Large environments, like Cloud, offer unique advantages, such as low cost, dependability and satisfy QoS for all users. Resource management in large environments address performant scheduling algorithm guided by QoS constrains. This paper presents the performance evaluation of scheduling heuristics guided by different optimization criteria. The algorithms for distributed scheduling are analyzed in order to satisfy users constrains considering in the same time independent capabilities of resources. This analysis acts like a profiling step for algorithm calibration. The performance evaluation is based on simulation. The simulator is MONARC, a powerful tool for large scale distributed systems simulation. The novelty of this paper consists in synthetic analysis results that offer guidelines for scheduler service configuration and sustain the empirical-based decision. The results could be used in decisions regarding optimizations to existing Grid DAG Scheduling and for selecting the proper algorithm for DAG scheduling in various actual situations.

Keywords: Scheduling, Simulation, Performance Evaluation, QoS, Distributed Systems, MONARC

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Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.

Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.

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Authors: Kyung Hyun, Choi, Minh Ngoc, Nong, M. Asif Ali, Rehmani

Abstract:

This present paper proposes the modified Elastic Strip method for mobile robot to avoid obstacles with a real time system in an uncertain environment. The method deals with the problem of robot in driving from an initial position to a target position based on elastic force and potential field force. To avoid the obstacles, the robot has to modify the trajectory based on signal received from the sensor system in the sampling times. It was evident that with the combination of Modification Elastic strip and Pseudomedian filter to process the nonlinear data from sensor uncertainties in the data received from the sensor system can be reduced. The simulations and experiments of these methods were carried out.

Keywords: Collision avoidance, Avoidance obstacle, Elastic Strip, Real time collision avoidance.

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Authors: Yury Nikulin

Abstract:

A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.

Keywords: Stability and accuracy, multicriteria optimization, lexicographic optimality.

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Authors: Wenlong Feng, Zhenchun Du, Jianguo Yang

Abstract:

To decrease the grating scale thermal expansion error, a novel method which based on multiple temperature detection is proposed. Several temperature sensors are installed on the grating scale and the temperatures of these sensors are recorded. The temperatures of every point on the grating scale are calculated by interpolating between adjacent sensors. According to the thermal expansion principle, the grating scale thermal expansion error model can be established by doing the integral for the variations of position and temperature. A novel compensation method is proposed in this paper. By applying the established error model, the grating scale thermal expansion error is decreased by 90% compared with no compensation. The residual positioning error of the grating scale is less than 15μm/10m and the accuracy of the machine tool is significant improved.

Keywords: Thermal expansion error of grating scale, error compensation, machine tools, integral method.

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Authors: C. Ardil

Abstract:

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PyFS), Picture fuzzy sets (PFS), q-rung orthopair fuzzy sets (q-ROF), Spherical fuzzy sets (SFS), T-spherical FS, and Neutrosophic sets (NS) are reviewed as multidimensional extensions of fuzzy sets in order to more explicitly and informatively describe the opinions of decision-making experts under uncertainty. To handle operations with standard fuzzy sets (SFS), the necessary operators; weighted arithmetic mean (WAM), weighted geometric mean (WGM), and Minkowski distance function are defined. The algorithm of the proposed proximity measure method (PMM) is provided with a multiple criteria group decision making method (MCDM) for use in a standard fuzzy set environment. To demonstrate the feasibility of the proposed method, the problem of selecting the best drone for an Air Force procurement request is used. The proximity measure method (PMM) based multidimensional standard fuzzy sets (SFS) is introduced to demonstrate its use with an issue involving unmanned combat aircraft selection.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), proximity measure method (PMM).

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Authors: Abdullah Bajelan, Adel Akbarimajd

Abstract:

Object manipulation techniques in robotics can be categorized in two major groups including manipulation with grasp and manipulation without grasp. The original aim of this paper is to develop an object manipulation method where in addition to being grasp-less, the manipulation task is done in a passive approach. In this method, linear and angular positions of the object are changed and its manipulation path is controlled. The manipulation path is a helix track with constant radius and incline. The method presented in this paper proposes a system which has not the actuator and the active controller. So this system requires a passive mechanical intelligence to convey the object from the status of the source along the specified path to the goal state. This intelligent is created based on utilizing the geometry of the system components. A general set up for the components of the system is considered to satisfy the required conditions. Then after kinematical analysis, detailed dimensions and geometry of the mechanism is obtained. The kinematical results are verified by simulation in ADAMS.

Keywords: Mechanical intelligence, Object manipulation, Passive mechanism, Passive non-prehensile manipulation.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

Abstract:

Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: 6-DOF robots, motion planning, trigonometric function, kinematic constraints

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Authors: Dahi Ghareab Abdelsalam Ibrahim

Abstract:

Axial and lateral measurements of a step depth standard are presented. The axial measurement is performed based on the ISO 5436 profile analysis. The lateral measurement is performed based on the Hamming window band-pass filter method. The method is applied to calibrate a groove structure of a step depth standard of 60 nm. For the axial measurement, the computed results show that the depth of the groove structure is 59.7 ± 0.6 nm. For the lateral measurement, the computed results show that the difference between the two line edges of the groove structure is 151.7 ± 2.5 nm. The method can be applied to any step height/depth regardless of the sharpness of the line edges.

Keywords: Hamming window, band-pass filter, metrology, interferometry.

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