Search results for: moment

Authors: Jan Flusser

Abstract:

This paper aims to present a survey of object recognition/classification methods based on image moments. We review various types of moments (geometric moments, complex moments) and moment-based invariants with respect to various image degradations and distortions (rotation, scaling, affine transform, image blurring, etc.) which can be used as shape descriptors for classification. We explain a general theory how to construct these invariants and show also a few of them in explicit forms. We review efficient numerical algorithms that can be used for moment computation and demonstrate practical examples of using moment invariants in real applications.

Keywords: Object recognition, degraded images, moments, moment invariants, geometric invariants, invariants to convolution, moment computation.

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Authors: S. Joshi, D. Pant

Abstract:

Absorption and fluorescence spectra of quinine sulphate (QSD) have been recorded at room temperature in wide range of solvents of different polarities. The ground-state dipole moment of QSD was obtained from quantum mechanical calculations and the excited state dipole moment of QSD was estimated from Bakhshiev-s and Kawski-Chamma-Viallet-s equations by means of solvatochromic shift method. Higher value of dipole moment is observed for excited state as compared to the corresponding ground state value and this is attributed to the more polar excited state of QSD.

Keywords: Dipole moment, Quinine sulphate dication, Solvatochromic shift

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Authors: Marinka Baghdasaryan, Tigran Mnoyan

Abstract:

The pertinence of modeling the moment of resistance generated by the ore-grinding mill is substantiated. Based on the ranking of technological indices obtained in the result of the survey among the specialists of several beneficiating plants, the factors determining the level of the moment of resistance generated by the mill are revealed. A priori diagram of the ranks is obtained in which the factors are arranged in the descending order of the impact degree on the level of the moment. The obtained model of the moment of resistance shows the technological character of the operation modes of the ore-grinding mill and can be used for improving the operation modes of the system motor-mill and preventing the abnormal mode of the drive synchronous motor.

Keywords: Model, abnormal mode, mill, correlation, moment of resistance, rotational speed.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

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Authors: Mahmoud Miri, Morteza Naghipour, Amir Kashiryfar

Abstract:

The unanticipated destruct of more of the steel moment frames in Northridge earthquake, altered class of regard to the beamto- column connections in moment frames. Panel zone is one the significant part of joints which, it-s stiffness and rigidity has an important effect on the behavior and ductility of the frame. Specifically that behavior of panel zone has a very significant effect on the special moment frames. In this paper , meanwhile the relations for modeling of panel zone in frames are expressed , special moment frames with different spans and stories were studied in the way of performance-based design. The frames designed in according with Iranian steel building code. The effect of panel zone is also considered and in the case of non-existence of performance level, by changing in intimacies and parameter of panel zone, performance level is considered.

Keywords: steel moment frame, panel zone, performance based design

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Authors: Mahvash Zandy Navgaran, Maryam Momeni Feili

Abstract:

The bag radius of the nucleon can be determined by MIT bag model based on electric and magnetic form factors of the nucleon. Also we determined the masses and magnetic moment of the nucleon with MIT bag model, using bag radius and compared with other results, suggests a suitable compatibility.

Keywords: MIT bag model, masses and magnetic moment of thenucleon, bag radius of the nucleon.

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Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: Gökhan Yüksel, Serdar Akça, İlker Kalkan

Abstract:

The present study is an attempt to demonstrate the significant levels of contribution of the moment-resisting beam-column connections with side plates to the earthquake behavior of special steel moment frames. To this end, the moment-curvature relationships of a regular beam-column connection and its SidePlate counterpart were determined with the help of finite element analyses. The connection stiffness and deformability values from these finite element analyses were used in the linear time-history analyses of an example structural steel frame under three different seismic excitations. The top-story lateral drift, base shear, and overturning moment values in two orthogonal directions were obtained from these time-history analyses and compared to each other. The results revealed the improvements in the system response with the use of SidePlate connections. The paper ends with crucial recommendations for the plan and design of further studies on this very topic.

Keywords: Seismic detailing, special moment frame, steel structures, beam-column connection, earthquake-resistant design.

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Authors: Angelo Thurairajah

Abstract:

Sufficient ultimate deformation is necessary to demonstrate the member ductility, which is dependent on the section and the material ductility. The concrete cracking phase of softening prior to the plastic hinge formation is an essential feature as well. The nature of the overload behaviour is studied using the order of the ultimate deflection. The ultimate deflection is primarily dependent on the slenderness (span to depth ratio), the ductility of the reinforcing steel, the degree of moment redistribution, the type of loading, and the support conditions. The ultimate deflection and the degree of moment redistribution from the analytical study are in good agreement with the experimental results and the moment redistribution provisions of the Australian Standards AS3600 Concrete Structures Code.

Keywords: Ductility, softening, ultimate deflection, overload behaviour, moment redistribution.

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Authors: G. Karakaya, C. Türker, M. Anaklı

Abstract:

It is necessary to test to see if optical devices such as camera, night vision devices are working properly. Therefore, a precision biaxial rotary system (gimbal) is required for mounting Unit Under Test, UUT. The Gimbal systems can be utilized for precise positioning of the UUT; hence, optical test can be performed with high accuracy. The weight of UUT, which is placed outside the axis of rotation, causes an off-axis moment to the mounting armature. The off-axis moment can act against the direction of movement for some orientation, thus the electrical motor, which rotates the gimbal axis, has to apply higher level of torque to guide and stabilize the system. Moreover, UUT and its mounting fixture to the gimbal can be changed, which causes change in applied resistance moment to the gimbals electrical motor. In this study, a preloaded spring is added to the gimbal system for minimizing applied off axis moment with the help of four bar mechanism. Two different possible methods for preloading spring are introduced and system optimization is performed to eliminate all moment which is created by off axis weight.

Keywords: Balancing, gimbal, tension, preload, spring.

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Authors: Tudor Barbu

Abstract:

An automatic moment-based texture segmentation approach is proposed in this paper. First, we describe the related work in this computer vision domain. Our texture feature extraction, the first part of the texture recognition process, produces a set of moment-based feature vectors. For each image pixel, a texture feature vector is computed as a sequence of area moments. Then, an automatic pixel classification approach is proposed. The feature vectors are clustered using an unsupervised classification algorithm, the optimal number of clusters being determined using a measure based on validation indexes. From the resulted pixel classes one determines easily the desired texture regions of the image.

Keywords: Image segmentation, moment-based texture analysis, automatic classification, validity indexes.

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Authors: Hamid Reza Boveiri

Abstract:

Classification of Persian printed numeral characters has been considered and a proposed system has been introduced. In representation stage, for the first time in Persian optical character recognition, extended moment invariants has been utilized as characters image descriptor. In classification stage, four different classifiers namely minimum mean distance, nearest neighbor rule, multi layer perceptron, and fuzzy min-max neural network has been used, which first and second are traditional nonparametric statistical classifier. Third is a well-known neural network and forth is a kind of fuzzy neural network that is based on utilizing hyperbox fuzzy sets. Set of different experiments has been done and variety of results has been presented. The results showed that extended moment invariants are qualified as features to classify Persian printed numeral characters.

Keywords: Extended moment invariants, optical characterrecognition, Persian numerals classification.

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Authors: Omar M. Ben-Sasi

Abstract:

A total of fourteen slab-edge beam-column connection specimens were tested gradually to failure under the effect of simultaneous action of shear force and moment. The objective was to investigate the influence of some parameters thought to be important on the behavior and strength of slab-column connections with edge beams encountered in flat slab flooring and roofing systems. The parameters included the existence and strength of edge beam, depth and width of edge beam, steel reinforcement ratio of slab, ratio of moment to shear force, and the existence of openings in the region next to the column.

Results obtained demonstrated the importance of the studied parameters on the strength and behavior of slab-column connections with edge beams.

Keywords: Strength, flat slab, slab-column connections, shear force, moment, behavior.

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Authors: Fan Yang, Ye-lu Wang, Yang Zhao

Abstract:

The dynamic load allowance, as an application result of the vehicle-bridge coupled vibration theory, is an important parameter for bridge design and evaluation. Based on the coupled vehicle-bridge vibration theory, the current work establishes a full girder model of a dynamic load allowance, selects a planar five-degree-of-freedom three-axis vehicle model, solves the coupled vehicle-bridge dynamic response using the APDL language in the spatial finite element program ANSYS, selects the pivot point 2 sections as the representative of the negative moment section, and analyzes the effects of parameters such as travel speed, unevenness, vehicle frequency, span diameter, span number and forced displacement of the support on the negative moment dynamic load allowance through orthogonal tests. The influence of parameters such as vehicle speed, unevenness, vehicle frequency, span diameter, span number, and forced displacement of the support on the negative moment dynamic load allowance is analyzed by orthogonal tests, and the influence law of each influencing parameter is summarized. It is found that the effects of vehicle frequency, unevenness, and speed on the negative moment dynamic load allowance are significant, among which vehicle frequency has the greatest effect on the negative moment dynamic load allowance; the effects of span number and span diameter on the negative moment dynamic load allowance are relatively small; the effects of forced displacement of the support on the negative moment dynamic load allowance are negligible.

Keywords: Continuous T-girder bridge, dynamic load allowance, sensitivity analysis, vehicle-bridge coupling.

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Authors: Amin Eslami, Jafar Bolouri Bazaz

Abstract:

Under active stress conditions, a rigid cantilever retaining wall tends to rotate about a pivot point located within the embedded depth of the wall. For purely granular and cohesive soils, a methodology was previously reported called minimization of moment ratio to determine the location of the pivot point of rotation. The usage of this new methodology is to estimate the rotational stability safety factor. Moreover, the degree of improvement required in a backfill to get a desired safety factor can be estimated by the concept of the shear strength demand. In this article, the accuracy of this method for another type of cantilever walls called Contiguous Bored Pile (CBP) retaining wall is evaluated by using physical modeling technique. Based on observations, the results of moment ratio minimization method are in good agreement with the results of the carried out physical modeling.

Keywords: Cantilever Retaining Wall, Physical Modeling, Minimization of Moment Ratio Method, Pivot Point.

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Authors: C. Thassana, W. Techitdheera

Abstract:

This calculation focus on the effect of exchange interaction J and Coulomb interaction U on spin magnetic moments (ms) of MnO by using the local spin density approximation plus the Coulomb interaction (LSDA+U) method within full potential linear muffin-tin orbital (FP-LMTO). Our calculated results indicated that the spin magnetic moments correlated to J and U. The relevant results exhibited the increasing spin magnetic moments with increasing exchange interaction and Coulomb interaction. Furthermore, equations of spin magnetic moment, which h good correspondence to the experimental data 4.58μB, are defined ms = 0.11J +4.52μB and ms = 0.03U+4.52μB. So, the relation of J and U parameter is obtained, it is obviously, J = -0.249U+1.346 eV.

Keywords: exchange interaction J, the Coulomb interaction U, spin magnetic moment, LSDA+U, MnO.

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Authors: Saruhan Kartal, Ilker Kalkan

Abstract:

The present paper reports the cracking moment estimates of a set of steel-reinforced, Fiber Reinforced Polymer (FRP)-reinforced and hybrid steel-FRP reinforced concrete beams, calculated from different analytical formulations in the codes, together with the experimental cracking load values. A total of three steel-reinforced, four FRP-reinforced, 12 hybrid FRP-steel over-reinforced and five hybrid FRP-steel under-reinforced concrete beam tests were analyzed within the scope of the study. Glass FRP (GFRP) and Basalt FRP (BFRP) bars were used in the beams as FRP bars. In under-reinforced hybrid beams, rupture of the FRP bars preceded crushing of concrete, while concrete crushing preceded FRP rupture in over-reinforced beams. In both types, steel yielding took place long before the FRP rupture and concrete crushing. The cracking moment mainly depends on two quantities, namely the moment of inertia of the section at the initiation of cracking and the flexural tensile strength of concrete, i.e. the modulus of rupture. In the present study, two different definitions of uncracked moment of inertia, i.e. the gross and the uncracked transformed moments of inertia, were adopted. Two analytical equations for the modulus of rupture (ACI 318M and Eurocode 2) were utilized in the calculations as well as the experimental tensile strength of concrete from prismatic specimen tests. The ACI 318M modulus of rupture expression produced cracking moment estimates closer to the experimental cracking moments of FRP-reinforced and hybrid FRP-steel reinforced concrete beams when used in combination with the uncracked transformed moment of inertia, yet the Eurocode 2 modulus of rupture expression gave more accurate cracking moment estimates in steel-reinforced concrete beams. All of the analytical definitions produced analytical values considerably different from the experimental cracking load values of the solely FRP-reinforced concrete beam specimens.

Keywords: Cracking moment, four-point bending, hybrid use of reinforcement, polymer reinforcement.

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Authors: Zhengyi Kong, Seung-Eock Kim

Abstract:

Single angle connections, which are bolted to the beam web and the column flange, are studied to investigate their moment-rotation behavior. Elastic–perfectly plastic material behavior is assumed. ABAQUS software is used to analyze the nonlinear behavior of a single angle connection. The identical geometric and material conditions with Lipson’s test are used for verifying finite element models. Since Kishi and Chen’s Power model and Lee and Moon’s Log model are accurate only for a limited range of mechanism, simpler and more accurate hyperbolic function models are proposed.

Keywords: Single-web angle connections, finite element method, moment and rotation, hyperbolic function models.

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Authors: Mohsen Soori, Fooad Karimi Ghaleh Jough

Abstract:

The integration of Artificial Intelligence (AI) techniques in the optimization of steel moment frame structures represents a transformative approach to enhance the design, analysis, and performance of these critical engineering systems. The review encompasses a wide spectrum of AI methods, including machine learning algorithms, evolutionary algorithms, neural networks, and optimization techniques, applied to address various challenges in the field. The synthesis of research findings highlights the interdisciplinary nature of AI applications in structural engineering, emphasizing the synergy between domain expertise and advanced computational methodologies. This synthesis aims to serve as a valuable resource for researchers, practitioners, and policymakers seeking a comprehensive understanding of the state-of-the-art in AI-driven optimization for steel moment frame structures. The paper commences with an overview of the fundamental principles governing steel moment frame structures and identifies the key optimization objectives, such as efficiency of structures. Subsequently, it delves into the application of AI in the conceptual design phase, where algorithms aid in generating innovative structural configurations and optimizing material utilization. The review also explores the use of AI for real-time structural health monitoring and predictive maintenance, contributing to the long-term sustainability and reliability of steel moment frame structures. Furthermore, the paper investigates how AI-driven algorithms facilitate the calibration of structural models, enabling accurate prediction of dynamic responses and seismic performance. Thus, by reviewing and analyzing the recent achievements in applications artificial intelligent in optimization of steel moment frame structures, the process of designing, analysis, and performance of the structures can be analyzed and modified.

Keywords: Artificial Intelligent, optimization process, steel moment frame, structural engineering.

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Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

Abstract:

The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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Authors: Sajad Farokhi, Siti Mariyam Shamsuddin, Jan Flusser, Usman Ullah Sheikh

Abstract:

Although face recognition seems as an easy task for human, automatic face recognition is a much more challenging task due to variations in time, illumination and pose. In this paper, the influence of time-lapse on visible and thermal images is examined. Orthogonal moment invariants are used as a feature extractor to analyze the effect of time-lapse on thermal and visible images and the results are compared with conventional Principal Component Analysis (PCA). A new triangle square ratio criterion is employed instead of Euclidean distance to enhance the performance of nearest neighbor classifier. The results of this study indicate that the ideal feature vectors can be represented with high discrimination power due to the global characteristic of orthogonal moment invariants. Moreover, the effect of time-lapse has been decreasing and enhancing the accuracy of face recognition considerably in comparison with PCA. Furthermore, our experimental results based on moment invariant and triangle square ratio criterion show that the proposed approach achieves on average 13.6% higher in recognition rate than PCA.

Keywords: Infrared Face recognition, Time-lapse, Zernike moment invariants

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Authors: Latha Parameswaran, K. Anbumani

Abstract:

Multimedia security is an incredibly significant area of concern. The paper aims to discuss a robust image watermarking scheme, which can withstand geometric attacks. The source image is initially moment normalized in order to make it withstand geometric attacks. The moment normalized image is wavelet transformed. The first level wavelet transformed image is segmented into blocks if size 8x8. The product of mean and standard and standard deviation of each block is computed. The second level wavelet transformed image is divided into 8x8 blocks. The product of block mean and the standard deviation are computed. The difference between products in the two levels forms the watermark. The watermark is inserted by modulating the coefficients of the mid frequencies. The modulated image is inverse wavelet transformed and inverse moment normalized to generate the watermarked image. The watermarked image is now ready for transmission. The proposed scheme can be used to validate identification cards and financial instruments. The performance of this scheme has been evaluated using a set of parameters. Experimental results show the effectiveness of this scheme.

Keywords: Image moments, wavelets, content-based watermarking, moment normalization, geometric attacks.

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Authors: Latha Parameswaran, K. Anbumani

Abstract:

Multimedia security is an incredibly significant area of concern. A number of papers on robust digital watermarking have been presented, but there are no standards that have been defined so far. Thus multimedia security is still a posing problem. The aim of this paper is to design a robust image-watermarking scheme, which can withstand a different set of attacks. The proposed scheme provides a robust solution integrating image moment normalization, content dependent watermark and discrete wavelet transformation. Moment normalization is useful to recover the watermark even in case of geometrical attacks. Content dependent watermarks are a powerful means of authentication as the data is watermarked with its own features. Discrete wavelet transforms have been used as they describe image features in a better manner. The proposed scheme finds its place in validating identification cards and financial instruments.

Keywords: Watermarking, moments, wavelets, content-based, benchmarking.

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Authors: Mahmoud A. Mahmoud, Ashraf Osman

Abstract:

In this study, the different approaches currently followed by design codes to assess the stability of buildings utilizing concrete moment resisting frames structural system are evaluated. For such purpose, a parametric study was performed. It involved analyzing group of concrete moment resisting frames having different slenderness ratios (height/width ratios), designed for different lateral loads to vertical loads ratios and constructed using ordinary reinforced concrete and high strength concrete for stability check and overall buckling using code approaches and computer buckling analysis. The objectives were to examine the influence of such parameters that directly linked to frames’ lateral stiffness on the buildings’ stability and evaluates the code approach in view of buckling analysis results. Based on this study, it was concluded that, the most susceptible buildings to instability and magnification of second order effects are buildings having high aspect ratios (height/width ratio), having low lateral to vertical loads ratio and utilizing construction materials of high strength. In addition, the study showed that the instability limits imposed by codes are mainly mathematical to ensure reliable analysis not a physical ones and that they are in general conservative. Also, it has been shown that the upper limit set by one of the codes that second order moment for structural elements should be limited to 1.4 the first order moment is not justified, instead, the overall story check is more reliable.

Keywords: Buckling, lateral stability, p-delta, second order.

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Authors: Ihsan Al-Abboodi, Tahsin Toma-Sabbagh

Abstract:

Laboratory tests have been carried out to investigate the response of 2x2 pile group subjected to triangular soil movement. The pile group was instrumented with displacement and tilting devices at the pile cap and strain gauges on two piles of the group. In this paper, results from four model tests were presented to study the effects of axial loads and soil density on the lateral behavior of piles. The responses in terms of bending moment, shear force, soil pressure, deflection, and rotation of piles were compared. Test results indicate that increasing the soil strength could increase the measured moment, shear, soil pressure, and pile deformations. Most importantly, adding loads to the pile cap induces additional moment to the head of front-pile row unlike the back-pile row which was influenced insignificantly.

Keywords: Pile group, passive piles, lateral soil movement, soil density, axial loads.

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Authors: Reza Ziaie Moayed, Naeem Gholampoor

Abstract:

Jet grouting strengthened pile (JPP) is one of composite piles used in soft ground improvement. It may improve the vertical and lateral bearing capacity effectively and it has been practically used in a considerable scale. In order to make a further research on load transfer mechanism of single JPP with and without cap under lateral loads, JPP is analyzed by means of FEM analysis. It is resulted that the JPP pile could improve lateral bearing capacity by compared with bored concrete pile which is higher for shorter pile and the biggest bending moment of JPP pile is located in the depth of around 48% of embedded length of the pile. Meanwhile, increase of JPP pile length causes to increase of peak mobilized bending moment. Also, by cap addition, JPP piles will have a much higher lateral bearing capacity and increasing in cohesion of soil layer resulted to increase of lateral bearing capacity of JPP pile. In addition, the numerical results basically coincide with the experimental results presented by other researchers.

Keywords: Bending moment, FEM analysis, JPP pile, lateral bearing capacity.

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Authors: H. R. Kazemi Nia, A. Yeganeh Fallah

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Without uncertainty by applying external loads on beams, bending is created. The created bending in I-beams, puts one of the flanges in tension and the other one in compression. With increasing of bending, compression flange buckled and beam in out of its plane direction twisted, this twisting well-known as Lateral Torsional Buckling. Providing bending moment varieties along the beam, the critical moment is greater than the case its under pure bending. In other words, the value of bending gradient coefficient is always greater than unite. In this article by the use of " ANSYS 10.0" software near 80 3-D finite element models developed for the propose of analyzing beams` lateral torsional buckling and surveying influence of slenderness on beams' bending gradient coefficient. Results show that, presented Cb coefficient via AISC is not correct for some of beams and value of this coefficient is smaller than what proposed by AISC. Therefore instead of using a constant Cb for each case of loading , a function with two criterion for calculation of Cb coefficient for some cases is proposed.

Keywords: Beams critical moment, Bending Gradient Coefficient, finite element, Lateral Torsional Buckling

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Authors: Babak Dizangian, Mohammad Reza Ghasemi, Akram Ghalandari

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Moment frames have considerable ductility against cyclic lateral loads and displacements; however, if this feature causes the relative displacement to exceed the permissible limit, it can impose unfavorable hysteretic behavior on the frame. Therefore, adding a bracing system with the capability of preserving the capacity of high energy absorption and controlling displacements without a considerable increase in the stiffness is quite important. This paper investigates the retrofitting of a single storey steel moment frame through a delayed wire-rope bracing system using a middle steel plate. In this model, the steel plate lies where the wire ropes meet, and the model geometry is such that the cables are continuously under tension so that they can take the most advantage of the inherent potential they have in tolerating tensile stress. Using the steel plate also reduces the system stiffness considerably compared to cross bracing systems and preserves the ductile frame’s energy absorption capacity. In this research, the software models of delayed wire-rope bracing system have been studied, validated, and compared with other researchers’ laboratory test results.

Keywords: Ductile moment frame, delayed wire rope bracing, cyclic loading, hysteresis curve, energy absorption.

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Authors: Abhay Tawalare, Rajesh Lalwani

Abstract:

An attempt in this paper proposes a re-modification to the minimum moment approach of resource leveling which is a modified minimum moment approach to the traditional method by Harris. The method is based on critical path method. The new approach suggests the difference between the methods in the selection criteria of activity which needs to be shifted for leveling resource histogram. In traditional method, the improvement factor found first to select the activity for each possible day of shifting. In modified method maximum value of the product of Resources Rate and Free Float was found first and improvement factor is then calculated for that activity which needs to be shifted. In the proposed method the activity to be selected first for shifting is based on the largest value of resource rate. The process is repeated for all the remaining activities for possible shifting to get updated histogram. The proposed method significantly reduces the number of iterations and is easier for manual computations.

Keywords: Re-Modified, Resource Leveling, Resources Rate, Free Float, Resource Histogram

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