Search results for: Critical trajectory method

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

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 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: A. Morsli, A.Tlemçani, N. Ould Cherchali, M. S. Boucherit

Abstract:

This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to a shunt Active Power Filter (sAPF) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: Fuzzy logic controller, P-Q method, Pulse Width Modulation (PWM), shunt Active Power Filter (sAPF), Total Harmonic Distortion (THD).

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Authors: P. Phokharatkul, S. Chaisriya, S. Somkuarnpanit, S. Phaiboon, C. Kimpan

Abstract:

This paper proposes a new method for image searches and image indexing in databases with a color temperature histogram. The color temperature histogram can be used for performance improvement of content–based image retrieval by using a combination of color temperature and histogram. The color temperature histogram can be represented by a range of 46 colors. That is more than the color histogram and the dominant color temperature. Moreover, with our method the colors that have the same color temperature can be separated while the dominant color temperature can not. The results showed that the color temperature histogram retrieved an accurate image more often than the dominant color temperature method or color histogram method. This also took less time so the color temperature can be used for indexing and searching for images.

Keywords: Color temperature histogram, color temperature, animage retrieval and content-based image retrieval.

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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: Wen-Haw Chen

Abstract:

This paper proposes a method to improve the shortest path problem on a NURBS (Non-uniform rational basis spline) surfaces. It comes from an application of the theory in classic differential geometry on surfaces and can improve the distance problem not only on surfaces but in the Euclidean 3-space R3 .

Keywords: shortest paths, geodesic-like method, NURBS surfaces.

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

Abstract:

Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R color component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: Chromaticity, Feature Extraction, Remote Sensing, Spectral library, Water Index.

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Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj

Abstract:

In this paper, we propose a solution to the motion planning and control problem for a swarm of three-dimensional boids. The swarm exhibit collective emergent behaviors within the vicinity of the workspace. The capability of biological systems to autonomously maneuver, track and pursue evasive targets in a cluttered environment is vastly superior to any engineered system. It is considered an emergent behavior arising from simple rules that are followed by individuals and may not involve any central coordination. A generalized, yet scalable algorithm for attraction to the centroid and inter-individual swarm avoidance is proposed. We present a set of new continuous time-invariant velocity control laws, formulated via the Lyapunov-based control scheme for target attraction and collision avoidance. The controllers provide a collision-free trajectory. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the control laws is demonstrated via computer simulations.

Keywords: Swarm, Practical stability, Motion planning.

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

Abstract:

In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: Azad A. Mohammed, Gulan B. Hassan

Abstract:

Analytical procedure was carried out in this paper to calculate the ultimate load capacity of reinforced concrete corbels strengthened or repaired externally with CFRP sheets. Strut and tie method and shear friction method proposed earlier for analyzing reinforced concrete corbels were modified to incorporate the effect of external CFRP sheets bonded to the corbel. The points of weakness of any method that lead to an inaccuracy, especially when overestimating test results were checked and discussed. Comparison of prediction with the test data indicates that the ratio of test / calculated ultimate load is 0.82 and 1.17 using strut and tie method and shear friction method, respectively. If the limits of maximum shear stress is followed, the calculated ultimate load capacity using shear friction method was found to underestimates test data considerably.

Keywords: Corbel, Strengthening, Strut and Tie Model, Shear Friction

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Authors: R. Sharma, M. Gopal

Abstract:

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).

Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.

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Authors: Chutchada Nusai, Yoshimi Suzuki, Haruaki Yamazaki

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Selecting the word translation from a set of target language words, one that conveys the correct sense of source word and makes more fluent target language output, is one of core problems in machine translation. In this paper we compare the 3 methods of estimating word translation probabilities for selecting the translation word in Thai – English Machine Translation. The 3 methods are (1) Method based on frequency of word translation, (2) Method based on collocation of word translation, and (3) Method based on Expectation Maximization (EM) algorithm. For evaluation we used Thai – English parallel sentences generated by NECTEC. The method based on EM algorithm is the best method in comparison to the other methods and gives the satisfying results.

Keywords: Machine translation, EM algorithm.

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Authors: N. Cetinkaya

Abstract:

The objective of the present study is to determine the critical control points during the production, transportation and storage conditions of compound feeds to be used in the Hazard Analysis Critical Control Point (HACCP) feed safety management system. A total of 40 feed samples were taken after 20 and 40 days of storage periods from the 10 dairy and 10 beef cattle farms following the transportation of the compound feeds from the factory. In addition, before transporting the feeds from factory immediately after production of dairy and beef cattle compound feeds, 10 from each total 20 samples were taken as 0 day. In all feed samples, chemical composition and total aflatoxin levels were determined. The aflatoxin levels in all feed samples with the exception of 2 dairy cattle feeds were below the maximum acceptable level. With the increase in storage period in dairy feeds, the aflatoxin levels were increased to 4.96 ppb only in a BS8 dairy farm. This value is below the maximum permissible level (10 ppb) in beef cattle feed. The aflatoxin levels of dairy feed samples taken after production varied between 0.44 and 2.01 ppb. Aflatoxin levels were found to be between 0.89 and 3.01 ppb in dairy cattle feeds taken on the 20^th day of storage at 10 dairy cattle farm. On the 40^th day, feed aflatoxin levels in the same dairy cattle farm were found between 1.12 and 7.83 ppb. The aflatoxin levels were increased to 7.83 and 6.31 ppb in 2 dairy farms, after a storage period of 40 days. These obtained aflatoxin values are above the maximum permissible level in dairy cattle feeds. The 40 days storage in pellet form in the HACCP feed safety management system can be considered as a critical control point.

Keywords: Aflatoxin, beef cattle feed, compound feed, dairy cattle feed, HACCP.

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Authors: V. Geetha, K. S. Aprameya

Abstract:

Early diagnosis of dental caries is essential for maintaining dental health. In this paper, method for diagnosis of dental caries is proposed using Laplacian filter, adaptive thresholding, texture analysis and Support Vector Machine (SVM) classifier. Analysis of the proposed method is compared with Otsu thresholding, watershed segmentation and active contouring method. Adaptive thresholding has comparatively better performance with 96.9% accuracy and 96.1% precision. The results are validated using statistical method, two-way ANOVA, at significant level of 5%, that shows the interaction of proposed method on performance parameter measures are significant. Hence the proposed technique could be used for detection of dental caries in automated computer assisted diagnosis system.

Keywords: Computer assisted diagnosis, dental caries, dental radiography, image segmentation.

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Authors: Yuichiro Kanzaki, Akito Monden, Masahide Nakamura, Ken-ichi Matsumoto

Abstract:

This paper proposes an easy-to-use instruction hiding method to protect software from malicious reverse engineering attacks. Given a source program (original) to be protected, the proposed method (1) takes its modified version (fake) as an input, (2) differences in assembly code instructions between original and fake are analyzed, and, (3) self-modification routines are introduced so that fake instructions become correct (i.e., original instructions) before they are executed and that they go back to fake ones after they are executed. The proposed method can add a certain amount of security to a program since the fake instructions in the resultant program confuse attackers and it requires significant effort to discover and remove all the fake instructions and self-modification routines. Also, this method is easy to use (with little effort) because all a user (who uses the proposed method) has to do is to prepare a fake source code by modifying the original source code.

Keywords: Copyright protection, program encryption, program obfuscation, self-modification, software protection.

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Authors: Anon Yantarasri, Yachai Limpiyakorn

Abstract:

Decisions are regularly made during a project or daily life. Some decisions are critical and have a direct impact on project or human success. Formal evaluation is thus required, especially for crucial decisions, to arrive at the optimal solution among alternatives to address issues. According to microeconomic theory, all people-s decisions can be modeled as indifference curves. The proposed approach supports formal analysis and decision by constructing indifference curve model from the previous experts- decision criteria. These knowledge embedded in the system can be reused or help naïve users select alternative solution of the similar problem. Moreover, the method is flexible to cope with unlimited number of factors influencing the decision-making. The preliminary experimental results of the alternative selection are accurately matched with the expert-s decisions.

Keywords: Decision Analysis and Resolution, Indifference Curve, Multi-criteria Decision Making.

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Authors: A. Alrasheed, I. Connerton

Abstract:

Daily provision of high quality food and hygiene to patients is a challenging goal of the healthcare. In Saudi Arabia, matters related to food safety and hygiene are regulated by the Ministry of Health (MOH) and the Saudi Food and Drugs Authority (SFDA). The purpose of this research is to discuss the food safety management inconsistencies and flaws, in particular the ones related to Hazard Analysis and Critical Control Points (HACCP) in Riyadh’s MOH hospitals. As required by law, written HACCP regulations must be implemented, and food handlers need to receive the training accordingly. However, in Saudi hospitals, this is not a requirement, and the food handlers do not need to hold training certificates in food safety or HACCP. Nowadays, the matter of food safety and hygiene have become increasingly important since the decision makers want to align these regulations with the majority of the world and to implement HACCP fully and for this purpose, the SFDA was established. 

Keywords: Food safety, patients, hospitals, HACCP, Saudi Arabia.

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Authors: Nina Suszczanska, Przemyslaw Szmal, Slawomir Kulikow

Abstract:

In the paper a method of modeling text for Polish is discussed. The method is aimed at transforming continuous input text into a text consisting of sentences in so called canonical form, whose characteristic is, among others, a complete structure as well as no anaphora or ellipses. The transformation is lossless as to the content of text being transformed. The modeling method has been worked out for the needs of the Thetos system, which translates Polish written texts into the Polish sign language. We believe that the method can be also used in various applications that deal with the natural language, e.g. in a text summary generator for Polish.

Keywords: anaphora, machine translation, NLP, sign language, text syntax.

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Authors: E. Hemmati Vand, R. H. Oskouei, T. N. Chakherlou

Abstract:

In this paper, the details of an experimental method to measure the clamping force value at bolted connections due to application of wrenching torque to tighten the nut have been presented. A simplified bolted joint including a holed plate with a single bolt was considered to carry out the experiments. This method was designed based on Hooke-s law by measuring compressive axial strain of a steel bush placed between the nut and the plate. In the experimental procedure, the values of clamping force were calculated for seven different levels of applied torque, and this process was repeated three times for each level of the torque. Moreover, the effect of lubrication of threads on the clamping value was studied using the same method. In both conditions (dry and lubricated threads), relation between the torque and the clamping force have been displayed in graphs.

Keywords: Clamping force, Bolted joints, Experimental method, Lubrication.

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Authors: Livier Serna, Xavier Fischer, Fouad Bennis

Abstract:

In this paper, a decision aid method for preoptimization is presented. The method is called “negotiation", and it is based on the identification, formulation, modeling and use of indicators defined as “negotiation indicators". These negotiation indicators are used to explore the solution space by means of a classbased approach. The classes are subdomains for the negotiation indicators domain. They represent equivalent cognitive solutions in terms of the negotiation indictors being used. By this method, we reduced the size of the solution space and the criteria, thus aiding the optimization methods. We present an example to show the method.

Keywords: Optimization Model Reduction, Pre-Optimization, Negotiation Process, Class-Making, Cognition Based VirtualExploration.

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Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: Y. T. Boon, M. N. Naim, R. Zakaria, N. F. Abu Bakar, N. Ahmad, I. W. Lenggoro

Abstract:

In this study, encapsulation of agarwood oil with non-ionic surfactant, Tween 80 was prepared at critical micelle concentration of 0.0167 % v/v to produce the most stable nano-emulsion in aqueous. The encapsulation has minimized the bioactive compounds degradation in various pH conditions thus prolong their shelf life and maintained its initial oil grade. The oil grading of the prepared samples were conducted using the gel electrophoresis instead of using common analytical industrial grading such as gas chromatography- mass spectrometry (GC- MS). The grading method was chosen due to their unique zeta potential value after the encapsulation process. This paper demonstrates the feasibility of applying the electrophoresis principles to separate the encapsulated agarwood oil or grading of the emulsified agarwood oil. The results indicated that the grading process are potential to be further investigate based on their droplet size and zeta potential value at various pH condition when the droplet were migrate through polyacrylamide gel.

Keywords: Electrophoretic mobility, essential oil, nanoemulsion, polyacrylamide gel electrophoresis, Tween 80, zeta potential.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: Haydar Teymourlouei

Abstract:

Cybersecurity is one of the greatest challenges society faces in an age revolving around technological development. With cyber-attacks on the continuous rise, the nation needs to understand and learn ways that can prevent such attacks. A major contribution that can change the education system is to implement laboratories and competitions into academia. This method can improve and educate students with more hands-on exercises in a highly motivating setting. Considering the fact that students are the next generation of the nation’s workforce, it is important for students to understand concepts not only through books, but also through actual hands-on experiences in order for them to be prepared for the workforce. An effective cybersecurity education system is critical for creating a strong cyber secure workforce today and for the future. This paper emphasizes the need for awareness and the need for competitions and cybersecurity laboratories to be implemented into the education system.

Keywords: Awareness, competition, cybersecurity, laboratories, workforce.

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Authors: Nurhakimah Ab. Rahman, Lazim Abdullah

Abstract:

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

Keywords: Dual fuzzy polynomial equations, Interval type-2, Ranking method, Value.

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Authors: A. P. Joshi, H. V. Warrior, J. P. Panda

Abstract:

This paper is a continuation of the work carried out by various turbulence modelers in Oceanography on the topic of oceanic turbulent mixing. It evaluates the evolution of ocean water temperature and salinity by the appropriate modeling of turbulent mixing utilizing proper prescription of eddy viscosity. Many modelers in past have suggested including terms like shear, buoyancy and vorticity to be the parameters that decide the slow pressure strain correlation. We add to it the fact that dissipation anisotropy also modifies the correlation through eddy viscosity parameterization. This recalibrates the established correlation constants slightly and gives improved results. This anisotropization of dissipation implies that the critical Richardson’s number increases much beyond unity (to 1.66) to accommodate enhanced mixing, as is seen in reality. The model is run for a couple of test cases in the General Ocean Turbulence Model (GOTM) and the results are presented here.

Keywords: Anisotropy, GOTM, pressure-strain correlation, Richardson Critical number.

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Authors: M. Nikbakht, N. Choupani

Abstract:

In this study the behavior of interlaminar fracture of carbon-epoxy thermoplastic laminated composite is investigated numerically and experimentally. Tests are performed with Arcan specimens. Testing with Arcan specimen gives the opportunity of utilizing just one kind of specimen for extracting fracture properties for mode I, mode II and different mixed mode ratios of materials with exerting load via different loading angles. Variation of loading angles in range of 0-90° made possible to achieve different mixed mode ratios. Correction factors for various conditions are obtained from ABAQUS 2D finite element models which demonstrate the finite shape of Arcan specimens used in this study. Finally, applying the correction factors to critical loads obtained experimentally, critical interlaminar fracture toughness of this type of carbon- epoxy composite has been attained.

Keywords: Fracture Mechanics, Mixed Mode, Arcan Specimen, Finite Element.

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Authors: Venkatesh C., K. Shanti Swarup

Abstract:

This paper investigates the impact on operating time delay and relay maloperation when 1st,2nd and 3rd order analog antialiasing filters are used in numerical distance protection. RC filter with cut-off frequency 90 Hz is used. Simulations are carried out for different SIR (Source to line Impedance Ratio), load, fault type and fault conditions using SIMULINK, where the voltage and current signals are fed online to the developed numerical distance relay model. Matlab is used for plotting the impedance trajectory. Investigation results shows that, about 75 % of the simulated cases, numerical distance relay operating time is not increased even-though there is a time delay when higher order filters are used. Relay maloperation (selectivity) also reduces (increases) when higher order filters are used in numerical distance protection.

Keywords: Antialiasing, capacitive voltage transformers, delay estimation, discrete Fourier transform (DFT), distance measurement, low-pass filters, source to line impedance ratio (SIR), protective relaying.

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Authors: Karandeep Singh, Baibing Li

Abstract:

Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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Authors: Indu Saini, Phool Singh, Vikas Malik

Abstract:

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Genetic Algorithm is used to calculate shooting angle. The initial value problems arisen during shooting are computed by Runge-Kutta Fehlberg method. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors.

Keywords: Boundary Layer Flow, Falkner–Skan equation, Genetic Algorithm, Shooting method.

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Authors: Nafisur Rahman, Habibur Rahman, Syed Najmul Hejaz Azmi

Abstract:

This paper presents a simple and sensitive kinetic spectrophotometric method for the determination of ramipril in commercial dosage forms. The method is based on the reaction of the drug with 1-chloro-2,4-dinitrobenzene (CDNB) in dimethylsulfoxide (DMSO) at 100 ± 1ºC. The reaction is followed spectrophotometrically by measuring the rate of change of the absorbance at 420 nm. Fixed-time (ΔA) and equilibrium methods are adopted for constructing the calibration curves. Both the calibration curves were found to be linear over the concentration ranges 20 - 220 μg/ml. The regression analysis of calibration data yielded the linear equations: Δ A = 6.30 × 10-4 + 1.54 × 10-3 C and A = 3.62 × 10-4 + 6.35 × 10-3 C for fixed time (Δ A) and equilibrium methods, respectively. The limits of detection (LOD) for fixed time and equilibrium methods are 1.47 and 1.05 μg/ml, respectively. The method has been successfully applied to the determination of ramipril in commercial dosage forms. Statistical comparison of the results shows that there is no significant difference between the proposed methods and Abdellatef-s spectrophotometric method.

Keywords: Equilibrium method, Fixed-time (ΔA) method, Ramipril, Spectrophotometry.

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