ORIGINAL_ARTICLE
A meshless numerical investigation based on the RBF-QR approach for elasticity problems
In the current research work, we present an improvement of meshless boundary element method (MBEM) based on the shape functions of radial basis functions-QR (RBF-QR) for solving the two-dimensional elasticity problems. The MBEM has benefits of the boundary integral equations (BIEs) to reduce the dimension of problem and the meshless attributes of moving least squares (MLS) approximations. Since the MLS shape functions don’t have the delta function property, applying boundary conditions is not simple. Here, we propose the MBEM using RBF-QR to increase the accuracy and efficiency of MBEM. To show the performance of the new technique, the two-dimensional elasticity problems have been selected. We solve the mentioned model on several irregular domains and report simulation results.
https://ajmc.aut.ac.ir/article_3379_ffbd2283d5745c4b85031e1eaf021000.pdf
2020-02-01
1
15
10.22060/ajmc.2019.15990.1019
Boundary element method
RBF-QR approach
Two-dimensional elasticity problems
Meshless Method
Mostafa
Abbaszadeh
m.abbaszadeh@aut.ac.ir
1
Department of Mathematics and Computer Science, Amirkabir University of Technology
LEAD_AUTHOR
Mehdi
Dehghan
mdehghan@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
AUTHOR
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[3] L. Chen, Y. M. Cheng, The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations, Computational Mechanics, 62 (2018) 67-80.
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[5] Y. M. Cheng, C. Liu, F. N. Bai, M. J. Peng, Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method, Chinese Physics B, 24 (2015).
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[6] M. Dehghan, M. Abbaszadeh, A local meshless method for solving multi-dimensional Vlasov-Poisson and VlasovPoisson–Fokker–Planck systems arising in plasma physics, Engineering with Computers, 33 (2017) 961-981.
6
[7] M. Dehghan, M. Abbaszadeh, Proper orthogonal decomposition variational multiscale element free Galerkin (PODVMEFG) meshless method for solving incompressible Navier–Stokes equation, Computer Methods in Applied Mechanics and Engineering, 311 (2016) 856-888.
7
[8] M. Dehghan, M. Abbaszadeh, An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation, Engineering Analysis with Boundary Elements 92 (2018) 244-256.
8
[9] M. Dehghan, H. Hosseinzadeh, Calculation of 2D singular and near singular integrals of boundary elements method based on the complex space C, Applied Mathematical Modelling, 36 (2012) 545-560.
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[19] X. Li, J. Zhu, On a Galerkin boundary node method for potential problems, Advances in Engineering Software, 42 (2011) 927-933.
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[21] X. Li, Meshless analysis of two-dimensional Stokes flows with the Galerkin boundary node method, Eng. Anal. Bound. Elem., 34 (2010) 79-91.
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[23] X. Li , A meshless interpolating Galerkin boundary node method for Stokes flows, Eng. Anal. Bound. Elem., 51 (2015) 112-122.
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[25] G. R. Liu, Y. T. Gu, An Introduction to Meshfree Methods and Their Programming, Springer Science & Business Media, 2005.
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[26] G. R. Liu, Meshfree Methods: Moving Beyond the Finite Element Method, Taylor & Francis, 2009.
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[27] G. R. Liu, G. Y. Zhang, Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM), Int. J. Numer. Meth. Eng., 74 (2008) 1128-1161.
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[30] H. P. Ren, Y. M. Cheng, W. Zhang, An interpolating boundary element-free method (IBEFM) for elasticity problems, Physics, Mechanics & Astronomy, 53 (2010) 758-766.
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[31] Z. J. Meng, H. Cheng, L. D. Ma, Y. M. Cheng, The dimension split element-free Galerkin method for three-dimensional potential problems, Acta Mechanica Sinica/Lixue Xuebao, 34(3) (2018) 462-474.
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[32] Miao Yu, W. Yuan-han, Meshless analysis for three-dimensional elasticity with singular hybrid boundary node method, Appl. Math. Mech., 27 (2006) 673–681.
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[35] M. Peng, D. Li, Y. M. Cheng, The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems, Engineering Structures, 33 (2011) 127-135.
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[43] F. Tan, Y. Zhang, Y. Li, Development of a meshless hybrid boundary node method for Stokes flows, Eng. Anal. Bound. Elem. 37 (2013) 899-908.
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[44] F. Tan, Y. Zhang, Y. Li, An improved hybrid boundary node method for 2D crack problems, Archive of Applied Mechanics, 85 (2015) 101-116.
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[45] M. Tatari, F. Ghasemi, The Galerkin boundary node method for magneto-hydrodynamic (MHD) equation, J. Comput. Phys. 258 (2014) 634-649.
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[46] S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, third ed., McGraw-Hill, New York, 1970.
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[47] J. Wang, J. Wang, F. Sun, Y. M. Cheng, An interpolating boundary element-free method with nonsingular weight function for two-dimensional potential problems, International Journal of Computational Methods, 10 (2013) 1350043.
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[48] H. Xie, T. Nogami, J. Wang, A radial boundary node method for two-dimensional elastic analysis, Eng. Anal. Bound. Elem., 27 (2003) 853-862.
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[49] F. Yan, X. T. Feng, H. Zhou, Dual reciprocity hybrid radial boundary node method for the analysis of Kirchhoff plates, Appl. Math. Model. 35 (2011) 5691-5706.
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[50] L. W. Zhang, K. M. Liew, An improved moving least-squares Ritz method for two-dimensional elasticity problems, Appl. Math. Comput., 246 (2014) 268-282.
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[51] J. Zhang, Z. Yao, H. Li, A hybrid boundary node method, Int. J. Numer. Meth. Eng., 53 (2002) 751-763.
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52
ORIGINAL_ARTICLE
The bimodal standard normal density and kurtosis
In this article, first a density by the name ”The bimodal standard normal density” is introduced and denoted by bφ(z). Then, a definition for the kurtosis of bimodal densities relative to bφ(z) is presented. Finally, to illustrate the introduced kurtosis, a few examples are provided and a real data set is studied, too.
https://ajmc.aut.ac.ir/article_3040_cba0b169b1d9096e97113d867cacd623.pdf
2020-02-01
17
25
10.22060/ajmc.2018.3040
normal density
mixed normal density
bimodal standard normal density
kurtosis of a bimodal density
Javad
Behboodian
behboodian@shirazu.ac.ir
1
Department of Statistics, School of Science, Shiraz University, Shiraz
AUTHOR
Maryam
Sharafi
msharafi@shirazu.ac.ir
2
Department of Statistics, School of Science, Shiraz University, Shiraz
AUTHOR
Zahra
Sajjadnia
sajjadnia@shirazu.ac.ir
3
Department of Statistics, School of Science, Shiraz University, Shiraz
LEAD_AUTHOR
Mazyar
Zarepour
mazyar_z@hotmail.com
4
Department of Mathematics, Islamic Azad University, Shiraz Branch, Shiraz, Iran.
AUTHOR
[1] J. Arrue, H. W. Gomez, H. S. Salinas, H. Bolfarine, A new class of Skew-Normal-Cauchy distribution, SORT-Statistics and Operations Research Transactions, 39(1), (2015) 35-50.
1
[2] D. Elal-Olivero, Alpha-skew-normal distribution, Proyecciones Journal of Mathematics, 29(3) (2010), 224-240.
2
[3] K. Pearson, Das Fehlergesetz und seine Verallgemeinerungen Durch Fechner und Pearson, A Rejoinder. Biometrika, 4, (1905) 169-212.
3
[4] M. Sharafi, Z. Sajjadnia, J. Behboodian, A new generalization of alpha-skew-normal distribution, Communication in Statistics, Theory and Method, 46, (2017), 6098–6111.
4
[5] J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Spring Verlag, New York, 1991.
5
ORIGINAL_ARTICLE
(α, β)-Metrics with Killing β of Constant Length
The class of (α,β)-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study (α,β)-metrics with Killing of constant length 1-form β and find a simplified formula for their Ricci curvatures. Then, weshow that if F=α+β+b\frac{β^2}{α} is an Einstein Finsler metric, then α is an Einstein Riemann metric.
https://ajmc.aut.ac.ir/article_3038_ec3b89402c7338eacb774d68fb1a1cb0.pdf
2020-02-01
27
36
10.22060/ajmc.2018.3038
Finsler metric
(α,β)-metric
Einstein manifold
Tayebeh
Tabatabaeifar
t.tabaee@gmail.com
1
Amirkabir university
AUTHOR
Behzad
Najafi
behzad.najafi@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
LEAD_AUTHOR
[1] D. Bao, C. Robles, Z. Shen, Zermelo navigation on Riemannian manifolds, J. Diff. Geom., 66(3) (2004) 377-435.
1
[2] S. Basco, X. Cheng, Z. Shen, Curvature properties of (α, β)-metrics, In “Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto”, ed. S. Sabau and H. Shimada, Advanced Studies in Pure Mathematics 48, Mathematical Society of Japan, (2007) 73-110.
2
[3] V. N. Berestovskii , Yu. G. Nikonorov, Killing vector fields of constant length on Riemannian manifolds, (Russian) Sibirsk. Mat. Zh. 49(3) (2008) 497-514; translation in Sib. Math. J., 49(3) (2008) 395-407.
3
[4] B. Li, Z. Shen, On Randers metrics of quadratic Riemannian curvature, Internat. J. Math., 20(3) (2009) 369-376.
4
[5] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha, Japan, 1986.
5
[6] B. Rezaei, A. Razavi, N. Sadeghzadeh, On Einstein (α, β)-metrics, Iranian Journal of Science and Technology, 31 (2007) 403-412.
6
ORIGINAL_ARTICLE
On Sobolev spaces and density theorems on Finsler manifolds
Here, a natural extension of Sobolev spaces is defined for a Finsler structure F and it is shown that the set of all real C∞ functions with compact support on a forward geodesically complete Finsler manifold (M, F), is dense in the extended Sobolev space H p 1 (M). As a consequence, the weak solutions u of the Dirichlet equation ∆u = f can be approximated by C∞ functions with compact support on M. Moreover, let W ⊂ M be a regular domain with the C r boundary ∂W, then the set of all real functions in C r (W) ∩ C 0 (W) is dense in H p k (W), where k ≤ r. Finally, several examples are illustrated and sharpness of the inequality k ≤ r is shown
https://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf
2020-02-01
37
45
10.22060/ajmc.2018.3039
Density theorem
Sobolev spaces
Dirichlet problem
Finsler space
Behrooz
Bidabad
bidabad@aut.ac.ir
1
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
LEAD_AUTHOR
Alireza
Shahi
alirezashahi@aut.ac.ir
2
Faculty of Mathematics and computer science, Amirkabir University of Technology
AUTHOR
[1] R. Adams, Sobolev spaces, Academic press, New York, 1975.
1
[2] H. Akbar-Zadeh, Initiation to Global Finslerian Geometry, North- Holland Mathematical Library, 2006.
2
[3] T. Aubin, Some nonlinear problems in Riemannian geometry, Springer-Verlag, 1988.
3
[4] S. Azami, A. Razavi, Existence and uniqueness for a solution of Ricci flow on Finsler manifolds, Int. J. of Geom. Meth. in Mod. Phy., 10(3) (2013) 1-21.
4
[5] D. Bao, S. S. Chern, Z. Shen, Riemann-Finsler geometry, Springer-Verlag, 2000.
5
[6] D. Bao, B. Lackey, A Hodge decomposition theorem for Finsler spaces, C. R. Acad. Sci. Paris S´er. I Math., 323(1) (1996) 51-56.
6
[7] B. Bidabad, On compact Finsler spaces of positive constant curvature C. R. Acad. Sci. Paris S´er. I Math., 349 (2011) 1191-1194.
7
[8] B. Bidabad, A. Shahi, Harmonic vector fields on Finsler manifolds, C. R. Acad. Sci. Paris S´er. I Math., 354 (2016) 101-106.
8
[9] B. Bidabad, A. Shahi, M. Yar Ahmadi, Deformation of Cartan curvature on Finsler manifolds, Bull. Korean Math. Soc. 54(6) (2017) 2119-2139.
9
[10] B. Bidabad, M. Yar Ahmadi, Convergence of Finslerian metrics under Ricci flow, Sci. China Math. 59(4) (2016) 741-750.
10
[11] Y. Ge, Z. Shen, Eigenvalues, and eigenfunctions of metric measure manifolds, Proc. London Math. Soc., 82(3) (2001) 725-746.
11
[12] Q. He, Y. Shen, On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle, Proc. Amer. Math. Soc., 134(3) (2006) 871-880.
12
[13] M. Jim´enez-Sevilla, L. Sanchez-Gonzalez, On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach-Finsler manifolds, Nonlinear Anal. 74(11) (2011) 3487-3500.
13
[14] A. Krist´aly, I. Rudas, Elliptic problems on the ball endowed with Funk-type metrics, Nonlinear Anal., 119 (2015) 199-208.
14
[15] S. Lakzian, Differential Harnack estimates for positive solutions to heat equation under Finsler-Ricci flow, Pacific J. Math., 278(2) (2015) 447-462
15
[16] H. Mosel, S. Winkelmann, On weakly harmonic maps from Finsler to Riemannian manifolds, Ann. I. H. Poincar´e, 26 (2009) 39-57.
16
[17] S. B. Myers, Algebras of differentiable functions, Proc. Amer. Math. Soc., 5 (1954) 917-922.
17
[18] S. Ohta, Nonlinear geometric analysis on Finsler manifolds, European Journal of Math., 3(4) (2017) 916-952.
18
[19] Z. Shen, Lectures on Finsler geometry, World Scientific, 2001.
19
[20] N. Winter, On the distance function to the cut locus of a submanifold in Finsler geometry, Ph.D. thesis, RWTH Aachen University, (2010).
20
[21] Y. Yang, Solvability of some elliptic equations on Finsler manifolds, math.pku.edu.cn preprint, 1-12.
21
ORIGINAL_ARTICLE
A simple greedy approximation algorithm for the unit disk cover problem
Given a set P of n points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of P. We present a new 4-approximation algorithm with running time O(n log n) for this problem. Our proposed algorithm uses a simple approach and is easy to understand and implement.
https://ajmc.aut.ac.ir/article_3044_69fd7125903ed84f45ff4a2b2a419779.pdf
2020-02-01
47
55
10.22060/ajmc.2018.3044
computational geometry
approximation algorithms
unit disk cover problem
facility location
Mahdi
Imanparast
m.imanparast@aut.ac.ir
1
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
AUTHOR
Seyed Naser
Hashemi
nhashemi@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
LEAD_AUTHOR
[1] R. J. Fowler, M. S. Paterson, S. L. Tanimoto, Optimal packing and covering in the plane are NP-complete, Information Processing Letters, 12(3) (1981) 133-137.
1
[2] D. S. Hochbaum, W. Maass, Approximation schemes for covering and packing problems in image processing and VLSI, Journal of ACM, 32 (1985) 130-136.
2
[3] T. F. Gonzalez, Covering a set of points in multidimensional space, Information Processing Letters, 40(4) (1991) 181-188.
3
[4] H. Bronnimann, M. T. Goodrich, Almost optimal set covers in finite VC-dimension, Discrete and Computational Geometry, 14(4) (1995) 463-479.
4
[5] M. Franceschetti, M. Cook, J. Bruck, A geometric theorem for approximate disk covering algorithms, Technical report, (2001).
5
[6] B. Fu, Z. Chen, M. Abdelguerfi, An almost linear time 2.8334-approximation algorithm for the disc covering problem, In Proceedings of the 3rd International Conference on Algorithmic Applications in Management (AAIM’07), (2007) 317-326.
6
[7] P. Liu, D. Lu, A fast 25/6-approximation for the minimum unit disk cover problem, CoRR, abs/1406.3838, (2014).
7
[8] A. Biniaz, P. Liu, A. Maheshwari, M. Smid, Approximation algorithms for the unit disk cover problem in 2D and 3D, Computational Geometry: Theory and Applications, 60 (2017) 8-18.
8
[9] M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, Computational Geometry: Algorithms and Applications, Springer Berlin Heidelberg, (2008) 95-115.
9
ORIGINAL_ARTICLE
The Complementary Odd Weibull Power Series Distribution: Properties and Application
In this paper, a new four-parameters model called the complementary odd Weibull power series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes such as increasing, decreasing, bathtub-shaped and J-shape hazard rates. Some of its mathematical properties are obtained including moments, quantiles reliability, and moment generating functions. The maximum likelihood estimation method is used to estimate the vector of parameters. A simulation study is presented to investigate the performance of the estimators. Finally, The usefulness of the model has been demonstrated by applying it to a real-life dataset.
https://ajmc.aut.ac.ir/article_3722_1be02552deb40e99ef41e3344ca6aa8e.pdf
2020-02-01
57
67
10.22060/ajmc.2019.15207.1015
Odd Weibull distribution
Power series distribution
Compound distribution
Maximum Likelihood Estimation
Mehdi
Goldoust
mehdigoldust@yahoo.com
1
Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran
LEAD_AUTHOR
[1] M. Alizadeh, M. Emadi, M. Doostparast, G. M. Cordeiro, E. Ortega, R. Pescim, A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications, Hacet. J. Math. Stat. 44(6) (2015) 1491-1512.
1
[2] M. Alizadeh, H. M. Yousof, M. Rasekhi, E. Altun, The odd Log-Logistic Poisson-G family of distributions, J. Math. Exten., 12(3) (2018) 81-104.
2
[3] W. Barreto-Souza, A. H. S. Santos, G. M. Cordeiro, The beta generalized exponential distribution, J. Stat. Comput. Simul. 80(1-2) (2010) 159-172.
3
[4] V. G. Canchoa, F. Louzada-Neto, G. D.C. Barriga, The Poisson-exponential lifetime distribution, Computational Statistics and Data Analysis, 55 (2011) 677-686.
4
[5] K. Cooray, Generalization of the Weibull distribution: the odd Weibull family, Statistical Modelling, 6 (2006) 265-277.
5
[6] G. M. Cordeiro, M. Alizadeh, E. M. M. Ortega, L. H. Valdivieso Serrano, The Zografos-Balakrishnan odd log-logistic family of distributions: properties and applications, Hacet. J. Math. Stat, 45(6) (2016) 1781-1803.
6
[7] G. M. Cordeiro, M. Alizadeh, M. H. Tahir, M. Mansoor, M. Bourguignon, G. G. Hamedani, The beta odd log-logistic generalized family of distributions, Hacet. J. Math. Stat, 45 (2016) 1175-1202.
7
[8] G. M. Cordeiro, R. B. Silva, The complementary extended Weibull power series class of distributions, Ciˆencia e Natura, 36 (2014) 1-13.
8
[9] D. Cox, D. Hinkley, Theoretical Statistics, Chapman and Hall, New York, first edition, 1979.
9
[10] I. Elbatal, A. Asgharzadeh, F. Sharafi, A new class of generalized power Lindley distributions, Journal of Applied Probability and Statistics, 10 (2015) 89-116.
10
[11] F. Famoye, C. Lee, O. Olumolade, The beta-Weibull distribution, J. Stat. Theory Appl., 4(2) (2005) 121-136.
11
[12] J. Flores, P. Borges, V. G. Cancho, F. Louzada, The complementary exponential power series distribution, Brazilian Journal of Probability and Statistics, 27 (2013) 565-584.
12
[13] M. Goldoust, S. Rezaei, Y. Si, S. Nadarajah, Lifetime distributions motivated by series and parallel structures, Comm. Statist. Simulation Comput. 48(2) (2019) 556-579.
13
[14] A. W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84(3) (1997) 641-652.
14
[15] B. G. Munteanu, A. Leahu, I. Pˆartachi, The max-Weibull power series distribution, An. Univ. Oradea Fasc. Mat., 21(2) (2014) 133-139.
15
[16] A. Noack, A class of random variables with discrete distributions, Ann. Math. Statistics, 21 (1950) 127-132.
16
ORIGINAL_ARTICLE
A generalization of Marshall-Olkin bivariate Pareto model and its applications in shock and competing risk models
Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by compounding the Pareto Type II and geometric distributions. This new bivariate distribution has natural interpretations and can be applied in fatal shock models or in competing risks models. We call the new proposed model Marshall-Olkin bivariate Pareto-geometric (MOBPG) distribution, and then investigate various properties of the new distribution. This model has five unknown parameters and the maximum likelihood estimators cannot be afforded in explicit structure. We suggest to use the EM algorithm to calculate the maximum likelihood estimators of the unknown parameters, and this structure is quite flexible. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes.
https://ajmc.aut.ac.ir/article_3125_8385d20bf3dcd48513f53a4a97c11981.pdf
2020-02-01
69
87
10.22060/ajmc.2018.14869.1012
Bivariate model
Competing risk model
Expectation-Maximization algorithm
Pareto Type II distribution
Shock model
Shirin
Shoaee
shirin_shoaee@aut.ac.ir
1
Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.
LEAD_AUTHOR
Esmaeil
Khorram
eskhor@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
AUTHOR
[1] M.V. Aarset, How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36 (1987) 106-108.
1
[2] A. Al-Khedhairi, A. El-Gohary, A new class of bivariate Gompertz distributions and its mixture, International Journal of Mathematical Analysis, 2 (2008) 235-253.
2
[3] A.V. Asimit, E. Furman, R. Vernic, On a multivariate Pareto distribution, Insurance: Mathematics and Economics, 2 (2010) 308–316.
3
[4] A.V. Asimit, E. Furman, R. Vernic, Statistical inference for a new class of multivariate Pareto distributions, Communications in Statistics-Simulation and Computation, 2, (2016) 456-471.
4
[5] S.F. Bagheri, E. Bahrami Samani, M. Ganjali, The generalized modified Weibull power series distribution: Theory and applications, Computational Statistics and Data Analysis, 94 (2016) 136-160.
5
[6] N. Balakrishnan, C.D. Lai, Continuous bivariate distributions, New York, Springer, 2 2009.
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[7] R.E. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, Probability Models, Maryland, Silver Spring, 1981.
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[8] W. Barreto-Souza, Bivariate gamma-geometric law and its induce Levy process, Journal of Multivariate Analysis, 109 (2012) 130-145.
8
[9] G. Dinse, Non-parametric estimation of partially incomplete time and types of failure data, Biometrics, 38 (1982) 417-431.
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[10] M. Chahkandi, M. Ganjali, On some lifetime distributions with decreasing failure rate, Computational Statistics and Data Analysis, 53 (2009) 4433-4440.
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[11] M. Ghitany, E. Al-Hussaini, R. Al-Jarallah, Marshall-Olkin extended Weibull distribution and its application to censored data, Journal of Applied Statistics, 32 (2005) 1025-1034.
11
[12] M. Ghitany, F. Al-Awadhi, L. Alkhalfan, Marshall-Olkin extended lomax distribution and its application to censored data, Communications in Statistics - Theory and Methods, 36 (2007) 1855-1866.
12
[13] N.L. Johnson, S. Kotz, A vector of multivariate hazard rate, Journal of Multivariate Analysis, 5 (1975) 53-66.
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[14] R.A. Johnson, D.W. Wiechern, Applied Multivariate Statistical Analysis, New Jersey, Prentice Hall, 1992.
14
[15] S. Kotz, N. Balakrishnan, N.L. Johnson, Continuous multivariate distributions, New York, John Wiley and Sons, 2000.
15
[16] D. Kundu, Parameter estimation for partially complete time and type of failure data, Biometrical Journal, 46 (2004) 165–179.
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[17] D. Kundu, A. Dey, Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm, Computational Statistics and Data Analysis, 35 (2009) 956–965.
17
[18] D. Kundu, R.D. Gupta, Estimation of R = P(Y < X) for Weibull distribution, IEEE Transactions on Reliability, 55 (2006) 270–280.
18
[19] D. Kundu, R.D. Gupta, Modified Sarhan-Balakrishnan singular bivariate distribution, Journal of Statistical Planning and Inference, 140 (2010) 526–538.
19
[20] E.L. Lehmann, Some concepts of dependence, Annals of Mathematical Statistics, 37 (1966) 1137–1153.
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[21] T.A. Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society, 44 (1982) 226–233.
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[25] S.G. Meintanis, Test of fit for Marshall-Olkin distributions with applications, Journal of Statistical Planning and inference, 137 (2007) 3954–3963.
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[26] H. Pham, C.D. Lai, On recent generalizations of the Weibull distribution, IEEE Transactions on Reliability, 56 (2007) 454–458.
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[27] A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, Journal of Multivariate Analysis, 98 (2007) 1508–1527.
27
[28] R.B. Silva, M. Bourguignon, C.R.B. Dias, G.M. Cordeiro, The compound class of extended Weibull power series distributions, Computational Statistics and Data Analysis, 58 (2013) 352–367.
28
[29] P. Veenus, KRM. Nair, Characterization of a bivariate Pareto distribution, Journal of Indian Statistical Association, 32 (1994) 15–20
29
ORIGINAL_ARTICLE
The Validity of a Thompson’s Problem for PSL(4, 7)
Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $.In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.
https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf
2020-02-01
89
94
10.22060/ajmc.2019.16174.1022
Thompson’s problem
Characterization
Number of elements of the same order
Projective special linear group
Hall subgroup
NSE
Sporadic groups
Python
Behrooz
Khosravi
bkhosravi@aut.ac.ir
1
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
LEAD_AUTHOR
Cyrus
Kalantarpour
siruspoly@gmail.com
2
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
AUTHOR
[1] A. K. Asboei, S. S. S. Amiri, A. Iranmanesh, A. Tehranian, A characterization of sporadic simple groups by nse and order, J. Algebra Appl, 12(2) (2013) 1250158(3 pages).
1
[2] A. K. Asboei, S. S. S. Amiri, A. Iranmanesh, A new characterization of PSL(2, q) for some q, Ukrainian Mathematical Journal, 67 (9) (2016) 1297–1305.
2
[3] Chen .Deqin, A characterization of PSU(3, 4) by nse, International Journal of Algebra and Statistics, 2(1) (2013) 51–56.
3
[4] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Maximal subgroups and ordinary characters for simple groups, Clarendon Press New York, 1985.
4
[5] J. D. Frobenius, Verallgemeinerung des Sylowschen Satse, Berliner Sitz, (1895) 981–993.
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[6] M. Hall, The Theory of Groups, Macmillan, New York 1959.
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[7] A. Jafarzadeh, A. Iranmanesh, On simple Kn-groups for n = 5, 6, London Mathematical Society Lecture Note Series, 340(2) (2005) 517-526.
7
[8] M. Khatami, B. Khosravi, Z. Akhlaghi, A new characterization for some linear groups, Monatsh. Math, 163 (2009) 39-50.
8
[9] S. Liu, A characterization of PSL(3, 4), Science Asia, 39 (2013) 436–439.
9
[10] Leila. Mousavi, Bijan. Taeri, A characterization of L2(81) by nse, International Journal of Group Theory, 1(5) (2016) 29-35.
10
[11] C. G. Shao, W. J. Shi, Q. H. Jiang, A new characterization of simple K3-groups, Adv. Math, 38 (2009) 327-330.
11
[12] C. G. Shao, Q. Jiang, New characterization of simple linear groups by nse, J. Algebra Appl, 13, 1350094 (2014). [13] C. Shao, W. Shi, Q. Jiang, A new characterization of simple K4-groups, Front. Math. China, 3 (2008) 355-370.
12
[14] R. Shen, C. Shao, Q. Jiang, W. Shi, V. Mazurov, A new characterization of A5, Monatsh. Math, 160 (2010) 337-341. [15] W.J. Shi, On simple K4-groups, Chine.Sci. Bull, 36 (1991) 1281-1283.
13
[16] The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.8.3 (2016) http://www.gap-system.org
14
[17] Yong. Yang, Shitian. Liu, A characterization of some linear groups by nse, An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.), vol. 2 (2016).
15
ORIGINAL_ARTICLE
A real-time decision support system for bridge management based on the rules generalized by CART decision tree and SMO algorithms
Under dynamic conditions on bridges, we need a real-time management. To this end, this paper presents a rule-based decision support system in which the necessary rules are extracted from simulation results made by Aimsun traffic micro-simulation software. Then, these rules are generalized by the aid of fuzzy rule generation algorithms. Then, they are trained by a set of supervised and the unsupervised learning algorithms to get an ability to make decision in real cases. As a pilot case study, Nasr Bridge in Tehran is simulated in Aimsun and WEKA data mining software is used to execute the learning algorithms. Based on this experiment, the accuracy of the supervised algorithms to generalize the rules is greater than 80%. In addition, CART decision tree and sequential minimal optimization (SMO) provides 100% accuracy for normal data and these algorithms are so reliable for crisis management on bridge. This means that, it is possible to use such machine learning methods to manage bridges in the real-time conditions.
https://ajmc.aut.ac.ir/article_3043_5969ea2b069b3fd8d1e298c8a6383f87.pdf
2020-02-01
95
100
10.22060/ajmc.2018.3043
Intelligent Transportation Systems
Knowledge Extraction
Learning Algorithms
Traffic Simulators
Fuzzy Rule Generation Algorithm
Shadi
Abpeykar
shadi.a@aut.ac.ir
1
Department of Computer Science
AUTHOR
Mehdi
Ghatee
ghatee@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
LEAD_AUTHOR
[1] V. Kodur and M. Naser, “Importance factor for design of bridges against fire hazard,” Engineering Structure, vol. 54, no. 1, pp. 207-220, 2013.
1
[2] M. Garlock, I. Paya-Zaforteza, V. Kodur and L. Gu, “Fire hazard in bridges: Review, assessment and repair strategies,” Engineering Structure, vol. 35, no. 1, pp. 89- 98, 2012.
2
[3] W. Wang, R. Liu and B. Wu, “Analysis of a bridge collapsed by an accidental blast loads,” Engineering Failure Analysis, vol. 36, no. 1, pp. 353-361, 2014.
3
[4] M. Bielli, “A DSS approach to urban traffic management,” European Journal of Operational Research, vol. 61, no. 1-2, pp. 106-113,, 1992.
4
[5] R. Asadi and M. Ghatee, “A rule-based decision support system in intelligent Hazmat transportation system,” IEEE Transactions on Intelligent Transportation Systems, vol. 16, no. 5, pp. 2756-2764, 2015.
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[6] K. Zografos, K. Androutsopoulos and G. Vasilakis, “A real-time decision support system for roadway network incident response logistics,” Transportation Research Part C: Emerging Technologies, vol. 10, no. 1, pp. 1-18, 2002.
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[7] B. Yanev, “The management of bridges in New York City,” Engineering Structure, vol. 20, no. 11, pp. 1020-1026, 1998.
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[8] R. Klashner and S. Sabet, “A DSS Design Model for complex problems: Lessons from mission critical infrastructure,” Decision Support System, vol. 43, no. 3, pp. 990-1013, 2007.
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[9] S. Yehia, O. Abudayyeh, I. Fazal and D. Randolphc, “A decision support system for concrete bridge deck maintenance,” Advance Engineering Software, vol. 39, no. 3, pp. 202-210, 2008.
9
[10] S. Abpeykar and M. Ghatee, “Supervised and unsupervised learning DSS for incident management in intelligent tunnel: A case study in Tehran Niayesh tunnel,” Tunnelling and Underground Space Technology, vol. 42, pp. 293-306, 2014.
10
[11] E. Abbasi, M. E. Shiri and M. Ghatee, “A regularized root–quartic mixture of experts for complex classification problems,” Knowledge-Based Systems, vol. 110, pp. 98-109, 2016.
11
[12] H. Eftekhari and M. Ghatee, “An inference engine for smartphones to preprocess data and detect stationary and transportation modes,” Transportation Research Part C: Emerging Technologies, vol. 69, pp. 313-327, 2016.
12
[13] M. M. Bejani and M. Ghatee, “A context aware system for driving style evaluation by an ensemble learning on smartphone sensors data,” Transportation Research Part C: Emerging Technologies, vol. 89, pp. 303-320, 2018.
13
[14] J. Lu, S. Chen, W. Wang and H. Zuylen, “A hybrid model of partial least squares and neural network for traffic incident detection,” Expert Systems with Application, vol. 39, no. 5, pp. 4775-4784, 2012.
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[15] D. Srinivasan, X. Jin and R. Cheu, “Adaptive neural network models for automatic incident detection on freeways,” Neurocomputing, vol. 64, no. 1, pp. 473-469, 2005.
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[16] S. Che and W. Wang, “Decision tree learning for freeway automatic incident detection,” Expert System with Application, vol. 36, no. 2, pp. 4101-4105, 2009.
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[17] J. Abellán, G. López and J. Oña, “Analysis of traffic accident severity using Decision Rules via Decision Trees,” Expert System with Application, vol. 40, no. 15, pp. 6047- 6054, 2013.
17
[18] W. Yeung and J. Smith, “Damage detection in bridges using neural networks for pattern recognition of vibration signatures,” Engineering Structure, vol. 27, no. 5, pp. 685-698, 2005.
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[19] P. Chen, H. Shen, C. Lei and L. Chang, “Support-vector-machine-based method for automated steel bridge rust assessment,” Automation in Construction, vol. 23, no. 1, p. 9–19, 2012.
19
[20] E. Abbasi, M. Shiri and M. Ghatee, “A regularized root–quartic mixture of experts for complex classification problems,” Knowledge-Based Systems, vol. 110, pp. 98-109, 2016.
20
[21] S. Abpeykar and M. Ghatee, “An ensemble of RBF neural networks in decision tree structure with knowledge transferring to accelerate multi-classification,” Neural Computing and Applications, vol. in press, pp. 1-21, 2018.
21
[22] S. Abpeykar and M. Ghatee, “Decent direction methods on the feasible region recognized by supervised learning metamodels to solve unstructured problems,” Journal of Information and Optimization Sciences, vol. in press, pp. 1-18, 2018.
22
[23] M. Georgiopoulos, C. Li and T. Kocak, “Learning in the feed-forward random neural network: A critical review,” Performance Evaluation, vol. 68, no. 4, pp. 361- 384, 2011.
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[24] P. Pumpuang, A. Srivihok and P. Praneetpolgrang, “Comparisons of classifier algorithms: Bayesian network, C4.5, decision forest and NB tree for course registration planning model of undergraduate students,” Singapore, 2008.
24
[25] L. Bel, D. Allard, J. Laurent, C. R. and B.-H. A., “CART algorithm for spatial data: application to environmental and ecological data,” Computational Statistics & Data Analysis, vol. 53, no. 8, p. 3082–3093, 2009.
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28
[29] S. Mahdevari, H. Haghighat and S. Torabi, “A dynamically approach based on SVM algorithm for prediction of tunnel convergence during excavation,” Tunnelling and Underground Space Technology, vol. 38, no. 1, p. 59–68, 2013.
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[33] M. Blachnik and W. Duch, “LVQ algorithm with instance weighting for generation of prototype-based rules,” Neural Networks, vol. 24, no. 8, p. 824–830, 2011.
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[34] Pallavi and S. Godara, “A comparative performance analysis of clustering algorithms,” International Journal of Engineering Research and Applications, vol. 1, no. 3, p. 441–445, 2011.
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[35] M. Kiang, D. Fisher, J. Chen, S. Fisherd and R. Chia, “The application of SOM as a decision support tool to identify AACSB peer schools,” Decision Support System, vol. 47, no. 1, p. 51–59, 2009.
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37
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40
ORIGINAL_ARTICLE
Statistical and Fuzzy Clustering Methods and their Application to Clustering Provinces of Iraq based on Agricultural Products
The important approaches to statistical and fuzzy clustering are reviewed and compared, and their applications to an agricultural problem based on a real-world data are investigated. The methods employed in this study includes some hierarchical clustering and non-hierarchical clustering methods and Fuzzy C-Means method. As a case study, these methods are then applied to cluster 15 provinces of Iraq based on some agricultural crops. Finally, a comparative and evaluation study of different statistical and fuzzy clustering methods is performed. The obtained results showed that, based on the Silhouette criterion and Xie-Beni index, fuzzy c-means method is the best one among all reviewed methods
https://ajmc.aut.ac.ir/article_3245_a255154ebe44780b879781a7e0ee6123.pdf
2020-02-01
101
112
10.22060/ajmc.2019.14873.1013
Hierarchical Clustering
Non-Hierarchical Clustering
Fuzzy C-Means Clustering
Israa
Atiyah
israa.zad@aut.ac.ir
1
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran
AUTHOR
Seyed Mahmoud
Taheri
sm_taheri@ut.ac.ir
2
School of Engineering Science, College of Engineering, University of Tehran
LEAD_AUTHOR
[1] Y. Al-Fahad and T. Abbas, GIS Center Central Bureau of Statistics (NBS), Iraq, 2011.
1
[2] N. Aguilar-Gallegos, M. Munoz-Rodriguez, H. Santoyo-Cortes, J. Aguilar-Avila, and L. Klerkx, Information Networks that Generate Economic Value: A Study on Clusters of Adopters of New or Improved Technologies and Practices among Oil Palm Growers in Mexico, Agricultural Systems, vol. 135, pp. 122-132, 2015.
2
[3] A. Ansari, P. S. Sikarwar, S. Lade, H. K. Yadav and S. A. Randade, Genetic Diversity in Germplasm of Cluster Bean, an Important Food and an Industrial Legume Crop, J. Agr. Sci. Tech., vol. 18, pp. 1393-1406, 2016.
3
[4] D. J. Bora and A. K. Gupta, A Comparative Study between Fuzzy Clustering Algorithm and Hard Clustering Algorithm, International Journal of Computer Trends and Technology, vol. 10, pp. 785-790, 2014.
4
[5] C. T. Chang, J. Z. C. Lai and M. D. Jeng, A Fuzzy K-means Clustering Algorithm Using Cluster Center Displacement, Journal of Information Science and Engineering, vol. 27, pp. 995-1009, 2011.
5
[6] S. Chattopadhyay, D. K. Pratihar, S. C. D Sarkar, A Comparative Study of Fuzzy C-Means Algorithm and Entropy Based Fuzzy Clustering Algorithms, Computing and Informatics, vol.30, pp. 701–720, 2011.
6
[7] R. Dave, Fuzzy Shell-Clustering and Applications to Circle Detection in Digital Images, lnt. J. General Systems, vol. 16,. pp. 343-355, 1989.
7
[8] J. V. De Oliveira and W. Pedrycz, Advances in Fuzzy Clustering and Its Applications, John Wiley and Sons, New York, 2007.
8
[9] M. Fajardo, A. Mc. Bratney and Whelan, Fuzzy Clustering of Vis–NIR Spectra for the Objective Recognition of Soil Morphological Horizons in Soil Profiles, Geoderma, vol. 263, pp. 244–253, 2016.
9
[10] M. B. Ferraro, and P. Giordani, A Toolbox for Fuzzy Clustering Using the R Programming Language, Fuzzy Sets and Systems, vol. 279, pp. 1–16, 2015.
10
[11] G. Gan, C. Ma and J. Wu, Data Clustering Theory, Algorithms, and Applications, SIAM, Virginia, 2007.
11
[12] C. Gomathi and K. Velusamy, Solving Fuzzy Clustering Problem Using Hybridization of Fuzzy C-Means and Fuzzy Bee Colony Optimization, International Journal of Computer Engineering and Applications, vol. 12, pp. 317–324, 2018.
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[13] N. Grover, A Study of Various Fuzzy Clustering Algorithms, International Journal of Engineering Research, vol. 3, pp. 177–181, 2014.
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[14] Z. Huang and M. Ng, A Fuzzy K-Modes Algorithm for Clustering Categorical Data. IEEE Transactions on Fuzzy Systems, vol.7, pp.446–452, 1999.
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[15] J. G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, New York, 1995.
15
[16] P. Kostov and S. Mc Erlean, Using the Mixtures- of Distributions Technique for the Classification of Farms into Representative Farms. Agricultural Systems, vol. 88, pp. 528-537, 2006.
16
[17] E. Mansour, A. B. Khaled, T. Triki, M. Abid, K. Bachar, and A. Ferchichi, Evaluation of Genetic Diversity among South Tunisian Pomegranate Accessions Using Fruit Traits and RAPD Markers. J. Agr. Sci. Tech., vol. 17, pp. 109-119, 2015.
17
[18] B. Panda, S. Sahoo, and S. K. Patnaik, A Comparative Study of Hard and Soft Clustering Using Swarm Optimization: International Journal of Scientific & Engineering Research, vol. 4, pp. 785- 790, 2013.
18
[19] P. J. Rousseeuw, Silhouettes A Graphical Aid to the Interpretation and Validation of Cluster Analysis, Journal of Computational and Applied Mathematics, vol. 20, pp. 53-65, 1987.
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[20] A. C. Rencher, Methods of Multivariate Analysis, John Wiley and Sons, New York, 2002.
20
[21] H. Timm, C. Borgelt, C. Doring, and R. Kruse, An Extension to Possibilistic Fuzzy Cluster Analysis, Fuzzy Sets and Systems, 147, 3–16, 2004.
21
[22] T. Volmurgan, Austria Performance Comparison Between K-means and Fuzzy C- means, Wulfenia Journal Using Arbitrary Data Points, vol. 19, pp. 1-8, 2012.
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[23] R. Suganya, and R. Shanthi, Fuzzy C- Means Algorithm - A Review, International Journal of Scientific and Research Publications, vol. 2, pp. 440-442, 2012.
23
[24] X.L. Xie, and G. Beni, A validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 8, pp. 841-847, 1991.
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25
ORIGINAL_ARTICLE
Smartphone-based System for Driver Anger Scale Estimation Using Neural Network on Continuous Wavelet Transformation
Monitoring of the driver decreases accidents by reducing the risky behaviors and causes decreases the fuel consumption by preventing aggressive behavior. But this monitoring is costly due to built-in equipment. In this study, we propose a new model to recognize driving behavior by smartphone data without any extra equipment in the vehicles which is an important added value for smartphones. This recognition process is done in this paper based on the continuous wavelet transformation on accelerometer data. Then these patterns are fed to multilayer perceptron neural network to extend the information extracted from the corresponding features. Also the magnetometer sensor is used to detect the maneuvers through the driving period. Results show the accuracy of the proposed system is near 80% for pattern recognition. Driver scale based on a standard questionnaires regarding to driver angry scale (DAS), is also estimated by the proposed multilayer perceptron neural network with 3.7% errors in the average.
https://ajmc.aut.ac.ir/article_3287_964f797962c44f02c009a4313255f902.pdf
2020-02-01
113
124
10.22060/ajmc.2019.15327.1016
Risky behavior
Driver monitoring
smartphone
Wavelet transformation
Multilayer perceptron neural network
Hamid Reza
Eftekhari
eftekhari@malayeru.ac.ir
1
Department of Computer engineering, Faculty of Engineering, Malayer University, Hamedan, Iran
LEAD_AUTHOR
[1] Wiegmann DA, Shappell SA. (2003) A Human Error Approach to Aviation Accident Analysis: The Human Factors Analysis and Classification System. 1st ed. London: Ashgate Publishing.
1
[2] Mehri, T. (2016) Interview on Police News Agency http://news.police.ir/News/fullStory.do?Id=252579.
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[3]. Hickman, Jeffrey S., and E. Scott Geller. (2005): “Self-management to increase safe driving among short-haul truck drivers.” Journal of Organizational Behavior Management 23.4 1-20.
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[4].P. I. J.Wouters and J. M. J. Bos, (2000 ) “Traffic accident reduction by monitoring driver behavior with in-car data recorders,” Accident Anal. Prev., vol. 32, no. 5, pp. 643–650,.
4
[5]. Alessandrini, A., Cattivera, A., Filippi, F., & Ortenzi, F. (2012). “Driving style influence on car CO2 emissions”. In 20th International Emission Inventory Conference - Tampa, Florida, August 13 –16.
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[6]. Seeing machines. (2016). Retrieved from http://www.seeingmachines.com/
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[7] Towergate . (2016). Retrieved from Towergate Underwriting Group Limited. Fair Pay a radical new approach to motor insurance: http://www.fairpayinsurance.co.uk
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[8] Eftekhari, Hamid Reza, and Mehdi Ghatee. (2018) “Hybrid of discrete wavelet transform and adaptive neuro fuzzy inference system for overall driving behavior recognition.” Transportation Research Part F: Traffic Psychology and Behaviour 58: 782-796.
8
[9] Zadeh, Roya Bastani, Mehdi Ghatee, and Hamid Reza Eftekhari. (2018) “Three-phases smartphone-based warning system to protect vulnerable road users under fuzzy conditions.” IEEE Transactions on Intelligent Transportation Systems 19, no. 7: 2086-2098.
9
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ORIGINAL_ARTICLE
Adopting GRASP to solve a novel model for bus timetabling problem with minimum transfer and fruitless waiting times
This paper addresses a variant of bus timetabling problem assuming that travel times changes dynamically over the planning horizon. In addition to minimizing the transfer waiting time, another objective, namely minimizing the fruitless waiting time, is introduced in this paper as a new realistic objective. First, the problem is formulated as a mixed integer linear programming model. Then, since commercial solvers become inefficient to solve moderate and large sized instances of the problem (due to the NP-hardness), a GRASP heuristic algorithm is developed. Computational experiments over a variety of random instances verify the performance of the proposed method.
https://ajmc.aut.ac.ir/article_3323_85cc256ebddca4a51b227d38698683da.pdf
2020-02-01
125
134
10.22060/ajmc.2019.15497.1018
Bus timetabling
Dynamic travel time
Transfer waiting time
Fruitless waiting time
GRASP
Javad
Zamani Kafshani
j.zamani@aut.ac.ir
1
Amirkabir University of Technology
AUTHOR
Seyyed Ali
Mirhassani
a_mirhassani@aut.ac.ir
2
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
LEAD_AUTHOR
Farnaz
Hooshmand
f.hooshmand.khaligh@aut.ac.ir
3
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
AUTHOR
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