Search results for: direct and inverse technique

Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness

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Authors: Sumei Cai, Hong Li

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Either during water or gas injection into reservoir, in order to understand the areal flow pressure distribution underground, associated bounding deformation is prevalently monitored by ground or downhole tiltmeters. In this paper, an inverse solution to elastic response of far field displacements induced by reservoir pressure change due to flow injection was studied. Furthermore, the fundamental theory on inverse solution to elastic problem as well as its spatial smoothing approach is presented. Taking advantage of source code development based on Boundary Element Method, numerical analysis on the monitoring data of ground surface displacements to further understand the behavior of reservoir process was developed. Numerical examples were also conducted to verify the effectiveness.

Keywords: remote displacement, inverse problem, boundary element method, BEM, reservoir process

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Authors: Mor Diama L. O., Matthieu Davy, Laurent Ferro-Famil

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In this article, inverse synthetic aperture radar (ISAR) is combined with compressive imaging techniques in order to perform 3D interferometric imaging. Interferometric ISAR (InISAR) imaging relies on a two-dimensional antenna array providing diversities in the elevation and azimuth directions. However, the signals measured over several antennas must be acquired by coherent receivers resulting in costly and complex hardware. This paper proposes to use a chaotic cavity as a compressive device to encode the signals arising from several antennas into a single output port. These signals are then reconstructed by solving an inverse problem. Our approach is demonstrated experimentally with a 3-elements L-shape array connected to a metallic compressive enclosure. The interferometric phases estimated from a unique broadband signal are used to jointly estimate the target’s effective rotation rate and the height of the dominant scattering centers of our target. Our experimental results show that the use of the compressive device does not adversely affect the performance of our imaging process. This study opens new perspectives to reduce the hardware complexity of high-resolution ISAR systems.

Keywords: interferometric imaging, inverse synthetic aperture radar, compressive device, computational imaging

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Authors: Gertrude Nkechi Okenwa

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Higher institutions, especially the universities that are saddled with the responsibilities of teaching, learning, research, publications and social services for the production of graduates that are worthy in learning and character, and the creation of up-to-date knowledge and innovations for the total socio-economic and even political development of a given nation. Therefore, the purpose of the study was to identify the teaching, learning techniques used in the Enugu State University of Science and Technology to ensure or ascertain students’ perception on these techniques. To guide the study, survey research method was used. The population for the study was made up of second and final year students which summed up to one hundred and twenty-six students in the faculty of education. Stratified random sampling technique was adopted. A sample size of sixty (60) students was drawn for the study. The instrument used for data collection was questionnaire. To analyze the data, mean and standard deviation were used to answers the research questions. The findings revealed that direct instruction and construction techniques are used in the university. On the whole, it was observed that the students perceived constructivist techniques to be more useful and effective than direct instruction technique. Based on the findings recommendations were made to include diversification of teaching techniques among others.

Keywords: Strategies, Teaching and Learning, Constructive Technique, Direct Instructional Technique

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Authors: Y. N. Phang, E. F. Loh

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Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling over-dispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling over-dispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling over-dispersed medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling over-dispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian, and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling over-dispersed medical count data when ZIP and ZINB are inadequate.

Keywords: zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit

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Authors: Ajay R, Rammohan B, Sridhar K S S, Gurusharan N

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The objective of the work is to develop a numerical method to solve the inverse mode shape problem by determining the cross-sectional area of a structure for the desired mode shape via the vibration response study of the humerus bone, which is in the form of a cantilever beam with anisotropic material properties. The humerus bone is the long bone in the arm that connects the shoulder to the elbow. The mode shape is assumed to be a higher-order polynomial satisfying a prescribed set of boundary conditions to converge the numerical algorithm. The natural frequency and the mode shapes are calculated for different boundary conditions to find the cross-sectional area of humerus bone from Eigenmode shape with the aid of the inverse mode shape algorithm. The cross-sectional area of humerus bone validates the mode shapes of specific boundary conditions. The numerical method to solve the inverse mode shape problem is validated in the biomedical application by finding the cross-sectional area of a humerus bone in the human arm.

Keywords: Cross-sectional area, Humerus bone, Inverse mode shape problem, Mode shape

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Kyugneun Lee, Ikjin Lee

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Parameter estimation with inverse problem often suffers from unfavorable conditions in the real world. Useless data and many input parameters make the problem complicated or insoluble. Data refinement and reformulation of the problem can solve that kind of difficulties. In this research, a method to solve the rank deficient inverse problem is suggested. A multi-physics system which has rank deficiency caused by response correlation is treated. Impeditive information is removed and the problem is reformulated to sequential estimations using Bayesian network (BN) and subset groups. At first, subset grouping of the responses is performed. Feature selection with singular value decomposition (SVD) is used for the grouping. Next, BN inference is used for sequential conditional estimation according to the group hierarchy. Directed acyclic graph (DAG) structure is organized to maximize the estimation ability. Variance ratio of response to noise is used to pairing the estimable parameters by each response.

Keywords: Bayesian network, feature selection, rank deficiency, statistical inverse analysis

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Authors: Maatoug Hassine, Mourad Hrizi

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In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: geometric inverse source problem, heat equation, topological optimization, topological sensitivity, Kohn-Vogelius formulation

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Authors: S. S. Sathiesh

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The aim of this project is to study the radiation mechanism synchrotron and Inverse Compton scattering. Theoretically, we discussed spectral energy distribution for both. Programming is done for plotting the graph of Power-law spectrum for synchrotron Radiation using fortran90. The importance of power law spectrum was discussed and studied to infer its physical parameters from the model fitting. We also discussed how to infer the physical parameters from the theoretically drawn graph, we have seen how one can infer B (magnetic field of the source), γ min, γ max, spectral indices (p1, p2) while fitting the curve to the observed data.

Keywords: blazars/quasars, beaming, synchrotron radiation, Synchrotron Self Compton, inverse Compton scattering, mrk421

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Authors: Funda Kul, İsmail Gür

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Pension scheme providers have to price mortality risk by accurate mortality forecasting method. There are many mortality-forecasting methods constructed and used in literature. The Lee-Carter model is the first model to consider stochastic improvement trends in life expectancy. It is still precisely used. Mortality forecasting is done by mortality index in the Lee-Carter model. It is assumed that mortality index fits ARIMA time series model. In this paper, we propose and use dynamic normal inverse gaussian distribution to modeling mortality indes in the Lee-Carter model. Using population mortality data for Italy, France, and Turkey, the model is forecasting capability is investigated, and a comparative analysis with other models is ensured by some well-known benchmarking criterions.

Keywords: mortality, forecasting, lee-carter model, normal inverse gaussian distribution

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: Nasiru Inuwa, Haruna Usman Modibbo, Yahya Zakari Abdullahi

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The purpose of this paper is to investigate the effects of foreign direct investment (FDI), economic growth on carbon emissions in context of WAIFEM member countries. The Im-Pesaran-Shin panel unit root test, Kao residual based test panel cointegration technique and panel Granger causality tests over the period 1980-2012 within a multivariate framework were applied. The results of cointegration test revealed a long run equilibrium relationship among CO2 emissions, economic growth and foreign direct investment. The results of Granger causality tests revealed a unidirectional causality running from economic growth to CO2 emissions for the panel of WAIFEM countries at the 5% level. Also, Granger causality runs from economic growth to foreign direct investment without feedback. However, no causality relationship between foreign direct investment and CO2 emissions for the panel of WAIFEM countries was observed. The study therefore, suggest that policy makers from WAIFEM member countries should design policies aim at attracting more foreign direct investments inflow as well the adoption of cleaner production technologies in order to reduce CO2 emissions.

Keywords: economic growth, CO2 emissions, causality, WAIFEM

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Avelino Marques, Diamantino Freitas

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Some important electroacoustic systems, like loudspeaker systems, exhibit a nonminimum phase behavior that poses considerable effort when applying advanced digital signal processing techniques, such as linear equalization. In this paper, the position and the number of zeros and poles of the inverse filter, FIR type or IIR type, designed using time domain techniques, are studied, compared and related to the nonminimum phase zeros of system to be equalized. Conclusions about the impact of the position of the system non-minimum phase zeros, on the length/order of the inverse filter and on the delay of the equalized system are outlined as a guide to previously decide which type of filter will be more adequate.

Keywords: loudspeaker systems, nonminimum phase system, FIR and IIR filter, delay

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Authors: Ruqiya Anwar

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The present study is aimed to find out the Impact of Foreign direct Investment on lifestyle of working women in Rawalpindi and Islamabad (Pakistan). It was hypothesized that easy access to consumer loans uplifts the lifestyle of women. First part of the research study was aimed at developing a tool to measure the Impact of FDI on living pattern of women in Rawalpindi and Islamabad. Purposive sampling technique was used to collect the more reliable and valid data.81 females working in different banks of Rawalpindi and Islamabad (Pakistan) were included in the sample. The value of Alpha Reliability coefficient is .774 for the tool of study. Which was found satisfactory and indicated that tool is reliable to measure the study objectives. Finding of the study showed that foreign direct investment has significant and positive impact on lifestyle of women in Rawalpindi and Islamabad (Pakistan). Study also revealed that there is moderate and high level of consumption power women have through foreign direct investment, which supports the hypothesis.

Keywords: foreign direct investment, lifestyle of women, consumption power, consumer loans

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Authors: Inuwa Abdu Ibrahim

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The research assessed representative democracy as an administrative system in Nigeria, by highlighting the failure of the state. It also looked at some components of direct democracy in Switzerland. Therefore, the paper focused on direct democracy, using secondary sources of data. In conclusion, the research offers direct democracy as a solution to the failure of the Nigerian administrative system especially as it affects participation, developmental programmes and institutionalized corruption.

Keywords: corruption, direct democracy, national development, Nigeria, participation

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Authors: Arunee Wongkhao, Suparat Niwitpong, Sa-aat Niwitpong

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In this paper, we propose two new confidence intervals for the difference between the inverse of normal means with known coefficients of variation. One of these two confidence intervals for this problem is constructed based on the generalized confidence interval and the other confidence interval is constructed based on the closed form method of variance estimation. We examine the performance of these confidence intervals in terms of coverage probabilities and expected lengths via Monte Carlo simulation.

Keywords: coverage probability, expected length, inverse of normal mean, coefficient of variation, generalized confidence interval, closed form method of variance estimation

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Authors: Marulasiddappa H. B., Pushparajesh Viswanathan

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Day by day, the uses of internal combustion engines (ICE) are deteriorating because of pollution and less fuel availability. In the present scenario, the electric vehicle (EV) plays a major role in the place of an ICE vehicle. The performance of EVs can be improved by the proper selection of electric motors. Initially, EV preferred induction motors for traction purposes, but due to complexity in controlling induction motor, permanent magnet synchronous motor (PMSM) is replacing induction motor in EV due to its advantages. Direct torque control (DTC) is one of the known techniques for PMSM drive in EV to control the torque and speed. However, the presence of torque ripple is the main drawback of this technique. Many control strategies are followed to reduce the torque ripples in PMSM. In this paper, the adaptive neuro-fuzzy inference system (ANFIS) controller technique is proposed to reduce torque ripples and settling time. Here the performance parameters like torque, speed and settling time are compared between conventional proportional-integral (PI) controller with ANFIS controller.

Keywords: direct torque control, electric vehicle, torque ripple, PMSM

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Authors: Yakin Hajlaoui, Richard Labib, Jean-François Plante, Michel Gamache

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This study introduces the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs' processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW's ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. it employ gradient descent and backpropagation to train ML-IDW, comparing its performance against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. the results highlight the efficacy of ML-IDW, particularly in handling complex spatial datasets, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: deep learning, multi-layer neural networks, gradient descent, spatial interpolation, inverse distance weighting

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Authors: J. Suwanprateeb, F. Thammarakcharoen

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Calcium phosphate coating (CaP) has been employed for protein delivery, but the typical direct protein adsorption on the coating led to low incorporation content and fast release of the protein from the coating. By using bovine serum albumin (BSA) as a model protein, rapid biomimetic co-precipitation between calcium phosphate and BSA was employed to control the distribution of BSA within calcium phosphate coating during biomimetic formation on titanium surface for only 6 h at 50 oC in an accelerated calcium phosphate solution. As a result, the amount of BSA incorporation and release duration could be increased by using a rapid biomimetic co-precipitation technique. Up to 43 fold increases in the BSA incorporation content and the increase from 6 h to more than 360 h in release duration compared to typical direct adsorption technique were observed depending on the initial BSA concentration used during co-precipitation (1, 10, and 100 microgram/ml). From X-ray diffraction and Fourier transform infrared spectroscopy studies, the coating composition was not altered with the incorporation of BSA by this rapid biomimetic co-precipitation and mainly comprised octacalcium phosphate and hydroxyapatite. However, the microstructure of calcium phosphate crystals changed from straight, plate-like units to curved, plate-like units with increasing BSA content.

Keywords: biomimetic, Calcium Phosphate Coating, protein, titanium

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Authors: Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He

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This study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a closed rectangular enclosure for various values of fin height. The inverse method with the finite difference method and the experimental temperature data is applied to determine the heat transfer coefficient. The k-ε turbulence model is used to obtain the heat transfer and fluid flow characteristics within the fins. To validate the accuracy of the results obtained, the comparison of the average heat transfer coefficient is made. The calculated temperature at selected measurement locations on the plate-fin is also compared with experimental data.

Keywords: inverse method, FLUENT, k-ε model, heat transfer characteristics, plate-fin heat sink

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Authors: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

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In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: inverse analysis, function specification, neural net works, particle swarm, run-out table

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Authors: Haci Mehmet Guzey, Levent Acar

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In this paper, a novel decentralized controller is developed for linear systems with nonlinear unknown interconnections. A model linear decoupled system is assigned for each system. By using the difference actual and model state dynamics, the problem is formulated as inverse problem. Then, the interconnected dynamics are approximated by using Galerkin’s expansion method for inverse problems. Two different sets of orthogonal basis functions are utilized to approximate the interconnected dynamics. Approximated interconnections are utilized in the controller to cancel the interconnections and decouple the systems. Subsequently, the interconnected systems behave as a collection of decoupled systems.

Keywords: decentralized control, inverse problems, large scale systems, nonlinear interconnections, basis functions, system identification

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Authors: M. R. Bengourina, M. Rahli, L. Hassaine, S. Saadi

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In this study, we present a control method entitled virtual flux direct power control of a grid connected photovoltaic system associated with an active power filter. The virtual flux direct control of power (VF-DPC) is employed for the calculation of reference current generation. In this technique, the switches states of inverter are selected from a table of switching based on the immediate errors between the active and reactive powers and their reference values. The objectives of this paper are the reduction of Total Harmonic Distortion (THD) of source current, compensating reactive power and injecting the maximum active power available from the PV array into the load and/or grid. MATLAB/SIMULINK simulations are provided to demonstrate the performance of the proposed approach.

Keywords: shunt active power filter, VF-DPC, photovoltaic, MPPT

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Authors: Vigen Arakelian

Abstract:

This paper deals with the study of devices for displacement of the mould base of blow-molding machines. The displacement of the mould in the studied case is carried out by a linear actuator, which ensures the descent of the mould base and by extension springs, which return the letter in the initial position. The aim of this paper is to study the inverse dynamics of the device for displacement of the mould base of blow-molding machines and to determine its optimum parameters for higher rate of production. In the other words, it is necessary to solve the inverse dynamic problem to find the equation of motion linking applied forces with displacements. This makes it possible to determine the stiffness coefficient of the spring to turn the mold base back to the initial position for a given time. The obtained results are illustrated by a numerical example. It is shown that applying a spring with stiffness returns the mould base of the blow molding machine into the initial position in 0.1 sec.

Keywords: design, mechanisms, dynamics, blow-molding machines

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Authors: Mahboubeh Davoudi Pahnekolayi

Abstract:

Begonia rex cv. DS-EYWA is a rare, unique cultivar of begonia rex with curly colorful leaves. Optimization of an in vitro efficient regeneration protocol by focusing on transverse Thin Cell Layer (tTCL) petiole explants for high-scale production of such a beautiful cultivar was considered as our main purpose in this experiment. Thus, various concentrations of Plant Growth Regulators (PGRs) including 6-Benzylaminopurine (BAP), Thidiazuron (TDY), and –Naphthaleneacetic Acid (NAA), were selected in a Completely Randomized Design (CRD) to establish and optimize the direct organogenesis efficiency of this cultivar. Cultivation of 1 mm tTCL petiole explants in noted treatments showed that 1.5 mgl-1 BAP + 0.5 mgl-1 NAA can induce the highest number of direct regenerated shoots and lower concentration of BAP (0.5 mgl-1) can be suggested for shoot elongation before rooting stage. Elongated shoots were successfully rooted in MS free basal medium and acclimatized in 1:1 peat moss: perlite sterilized pot mixture.

Keywords: begonia rare cultivar, direct organogenesis, explant type, regeneration, thin cell layering (TCL)

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Authors: P. Srinivas, P. V. N. Prasad

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Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. The DTC of SRM is analysed by two methods. In one of the methods, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: direct toque control, simplified torque equation, finite element analysis, torque ripple

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

Procedia PDF Downloads 128