2014
46
2
2
0
A Sub-Optimal Look-Up Table Based on Fuzzy System to Enhance the Reliability of Coriolis Mass Flow Meter
A Sub-Optimal Look-Up Table Based on Fuzzy System to Enhance the Reliability of Coriolis Mass Flow Meter
2
2
Coriolis mass flow meters are one of the most accurate tools to measure the mass flow in the industry. However, two-phase mode (gas-liquid) may cause severe operating difficulties as well as decreasing certitude in measurement. This paper presents a method based on fuzzy systems to correct the error and improve the reliability of these sensors in the presence of two-phase model fluid. Definite available flow meter parameters are given to designed fuzzy system as inputs, and error is estimated as its output. In the proposed method, to decrease the number of rules, data are clustered using K-means clustering algorithm. The ability of this method in error correction is shown by testing it on real experimental data and compared with the least square method.
1
Coriolis mass flow meters are one of the most accurate tools to measure the mass flow in the industry. However, two-phase mode (gas-liquid) may cause severe operating difficulties as well as decreasing certitude in measurement. This paper presents a method based on fuzzy systems to correct the error and improve the reliability of these sensors in the presence of two-phase model fluid. Definite available flow meter parameters are given to designed fuzzy system as inputs, and error is estimated as its output. In the proposed method, to decrease the number of rules, data are clustered using K-means clustering algorithm. The ability of this method in error correction is shown by testing it on real experimental data and compared with the least square method.
1
10
Mohammad Amin
Tajeddini
Mohammad Amin
Tajeddini
PHD student of Electrical Engineering, Tehran University, Tehran, Iran.
PHD student of Electrical Engineering, Tehran
Iran
amintajeddini228@gmail.com
Ali
Kamali
Ali
Kamali
Assistant Professor of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
Assistant Professor of Mechanical Engineering,
Iran
alikamalie@aut.ac.ir
Coriolis mass flow meter
Reliability
Two-phase mode
clustering
Fuzzy systems
[[1] R. C. Baker, "Coriolis flowmeters: industrial practice and published information," Flow Measurement and Instrumentation, vol. 5, pp. 229-246, 1994.##[2] G. Oddie and J. R. A. Pearson, "Flow-rate measurement in two-phase flow," Annu. Rev. Fluid Mech., vol. 36, pp. 149-172, 2004.##[3] R. P. Evans, J. G. Keller, A. Stephens, and J. Blotter, "Two-phase mass flow measurement using noise analysis," Idaho National Laboratory (INL)1999.##[4] Y. Mi, M. Ishii, and L. Tsoukalas, "Flow regime identification methodology with neural networks and two-phase flow models," Nuclear Engineering and Design, vol. 204, pp. 87-100, 2001.##[5] J. Reimann, H. John, and U. Müller, "Measurements of two-phase mass flow rate: a comparison of different techniques," International Journal of Multiphase Flow, vol. 8, pp. 33-46, 1982.##[6] M. Meribout, N. Z. Al-Rawahi, A. M. Al-Naamany, A. Al-Bimani, K. Al Busaidi, and A. Meribout, "An Accurate Machine for Real-Time Two-Phase Flowmetering in a Laboratory-Scale Flow Loop," Instrumentation and Measurement, IEEE Transactions on, vol. 58, pp. 2686-2696, 2009.##[7] R. Liu, M. Fuent, M. Henry, and M. Duta, "A neural network to correct mass flow errors caused by two-phase flow in a digital coriolis mass flowmeter," Flow Measurement and Instrumentation, vol. 12, pp. 53-63, 2001.##[8] A. Skea and A. Hall, "Effects of gas leaks in oil flow on single-phase flowmeters," Flow Measurement and Instrumentation, vol. 10, pp. 145-150, 1999.##[9] V. A. Lari and F. Shabaninia, "Error correction of a coriolis mass flow meter in two-phase flow measurment using Neuro-Fuzzy," in Artificial Intelligence and Signal Processing (AISP), 2012 16th CSI International Symposium on, 2012, pp. 611-616.##[10] M. Henry, D. Clarke, N. Archer, J. Bowles, M. Leahy, R. Liu, et al., "A self-validating digital Coriolis mass-flow meter: an overview," Control engineering practice, vol. 8, pp. 487-506, 2000.##[11] Z. Feng, Q. Wang, and K. Shida, "A review of self-validating sensor technology," Sensor Review, vol. 27, pp. 48-56, 2007.##[12] M. N. Al-Khamis, A. A. Al-Nojaim, and M. A. Al-Marhoun, "Performance evaluation of coriolis mass flowmeters," Journal of energy resources technology, vol. 124, pp. 90-94, 2002.##[13] M. N. Al-Khamis, A. A. Al-Nojaim, and M. A. Al-Marhoun, "Performance evaluation of coriolis mass flowmeters," Journal of energy resources technology, vol. 124, p. 90, 2002.##[14] B. Safarinejadian, M. A. Tajeddini, and L. Mahmoodi, "A New Fuzzy Based Method for Error Correction of Coriolis Mass Flow Meter in Presence of Two-phase Fluid."##[15] J. Zarei, M. A. Tajeddini, and H. R. Karimi, "Vibration analysis for bearing fault detection and classification using an intelligent filter," Mechatronics, vol. 24, pp. 151-157, 2014.##[16] M. Anklin, W. Drahm, and A. Rieder, "Coriolis mass flowmeters: Overview of the current state of the art and latest research," Flow Measurement and Instrumentation, vol. 17, pp. 317-323, 2006. ##[17] L. A. Zadeh, "Fuzzy sets," Information and control, vol. 8, pp. 338-353, 1965.##[18] L.-X. Wang, A Course in Fuzzy Systems: Prentice-Hall press, USA, 1999.##[19] M. Tang, H. W. Yang, W. D. Hu, and W. X. Yu, "Construction of Mamdani type probabilistic fuzzy system," Systems Engineering and Electronics, vol. 34, pp. 323-327, 2012.##[20] L. X. Wang and J. M. Mendel, "Generating fuzzy rules by learning from examples," Systems, Man and Cybernetics, IEEE Transactions on, vol. 22, pp. 1414-1427, 1992.##[21] L. X. Wang and J. M. Mendel, "Fuzzy basis functions, universal approximation, and orthogonal least-squares learning," Neural Networks, IEEE Transactions on, vol. 3, pp. 807-814, 1992.##[22] A. K. Jain, "Data clustering: 50 years beyond K-means," Pattern Recognition Letters, vol. 31, pp. 651-666, 2010.##[23] V. Patel and R. Mehta, "Data Clustering: Integrating Different Distance Measures with Modified k-Means Algorithm," 2012, pp. 691-700.##[24] S. Chiu, "Method and software for extracting fuzzy classification rules by subtractive clustering," in Fuzzy Information Processing Society, 1996. NAFIPS., 1996 Biennial Conference of the North American, 1996, pp. 461-465.##[25] N. R. Pal and D. Chakraborty, "Mountain and subtractive clustering method: improvements and generalizations," International Journal of Intelligent Systems, vol. 15, pp. 329-341, 2000.##[26] D.-W. Kim, K. Lee, D. Lee, and K. H. Lee, "A kernel-based subtractive clustering method," Pattern Recognition Letters, vol. 26, pp. 879-891, 2005.##[27] J. A. Hartigan, Clustering algorithms: John Wiley & Sons, Inc., 1975.##[28] A. K. Jain, M. N. Murty, and P. J. Flynn, "Data clustering: a review," ACM computing surveys (CSUR), vol. 31, pp. 264-323, 1999.##[29] K. Mao, "Fast orthogonal forward selection algorithm for feature subset selection," Neural Networks, IEEE Transactions on, vol. 13, pp. 1218-1224, 2002.##[30] O. Nelles, Nonlinear system identification: from classical approaches to neural networks and fuzzy models: Springer, 2001.##[31] L. X. Wang, A Course on Fuzzy Systems: Prentice-Hall press, USA, 1999.##]
Adaptive Neural Network Method for Consensus Tracking of High-Order Mimo Nonlinear Multi-Agent Systems
Adaptive Neural Network Method for Consensus Tracking of High-Order Mimo Nonlinear Multi-Agent Systems
2
2
This paper is concerned with the consensus tracking problem of high order MIMO nonlinear multi-agent systems. The agents must follow a leader node in presence of unknown dynamics and uncertain external disturbances. The communication network topology of agents is assumed to be a fixed undirected graph. A distributed adaptive control method is proposed to solve the consensus problem utilizing relative information of neighbors of each agent and characteristics of the communication topology. A radial basis function neural network is used to represent the controller’s structure. The proposed method includes a robust term with adaptive gain to counter the approximation error of the designed neural network as well as the effect of external disturbances. The stability of the overall system is guaranteed through Lyapunov stability analysis. Simulations are performed for two examples: a benchmark nonlinear systems and multiple of autonomous surface vehicles (ASVs). The simulation results verify the merits of the proposed method against uncertainty and disturbances.
1
This paper is concerned with the consensus tracking problem of high order MIMO nonlinear multi-agent systems. The agents must follow a leader node in presence of unknown dynamics and uncertain external disturbances. The communication network topology of agents is assumed to be a fixed undirected graph. A distributed adaptive control method is proposed to solve the consensus problem utilizing relative information of neighbors of each agent and characteristics of the communication topology. A radial basis function neural network is used to represent the controller’s structure. The proposed method includes a robust term with adaptive gain to counter the approximation error of the designed neural network as well as the effect of external disturbances. The stability of the overall system is guaranteed through Lyapunov stability analysis. Simulations are performed for two examples: a benchmark nonlinear systems and multiple of autonomous surface vehicles (ASVs). The simulation results verify the merits of the proposed method against uncertainty and disturbances.
11
21
B.
Karimi
B.
Karimi
Department of Electrical Engineering, Malek Ashtar University of Technology, Shahin Shar, Iran
Department of Electrical Engineering, Malek
Iran
H.
Ghiti Sarand
H.
Ghiti Sarand
Department of Electrical Engineering, Malek Ashtar University of Technology, Shahin Shar, Iran
Department of Electrical Engineering, Malek
Iran
Nonlinear Multi Input- Multi Output (MIMO) Systems
multi-agent systems
Neural Network
Adaptive control
Consensus Tracking
[[1] W. Ren, R. Beard and E. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Mag., vol. 27, pp. 71-82, March 2007.##[2] R. Olfati-Saber, J. Fax, and R. Murray, “Consensus and cooperation in networked multi-agent systems,” Proc. IEEE 95, pp 215-233, 2007.##[3] W. Ren and R. Beard, Distributed consensus in multi-vehicle cooperative control: Theory and applications, Springer-Verlag, London, 2008.##[4] W. Ren, R. Beard and E. Atkins, “A survey of consensus problems in multi-agent coordination,” Proc. American Control Conf., pp. 1859-1864, 2005.##[5] W. Ren, K. Moore and Y. Chen, “High-order and model reference consensus algorithms in cooperative control of multivehicle systems,” Proc. IEEE Int. Conf. Networking, Sensing and Control, Ft. Lauderdale, FL, pp 457-462. 2006.##[6] Z. Li, Z. Duan, G. Chen and L. Huang, “Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint,” IEEE Trans. Circuits and Systems, vol. 57, pp. 213-224, April 2010.##[7] Z. Li, Z. Duan and G. Chen, “Dynamic consensus of linear multi-agent systems,” IET Control Theory Appl., vol. 5, pp. 19-28, January 2011.##[8] D. Meng, Y. Jia and J. Du, “Robust iterative learning protocols for finite time consensus of multi-agent systems with interval uncertain topologies,” Int. J. Syst. Sci., vol. 46, pp. 857-871, May.##[9] W. Yu, G. Chen and M. Cao, “Consensus in directed networks of agents with nonlinear dynamics”, IEEE Trans. Automaic Control, vol. 56, pp. 1436-1441, June 2011.##[10] G. Wen, A. Rahmani and Y. Yu, “Consensus tracking for multi-agent systems with nonlinear dynamics under fixed communication topologies,” Proc. World Congress on Engineering and Computer Science, San Francisco, USA, 2011.##[11] Z. Li, X. Liu, M. Fu and L. Xi, “Global H∞ consensus of multi-agent systems with Lipschitz nonlinear dynamics”, IET Control Theory Appl., vol. 6, pp. 2041-2048, September 2012.##[12] W. Yu, G. Chen, M. Cao and J. Kurths, “Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics,” IEEE Trans. Syst. Man Cybern. Part B, vol. 40, pp. 881-891, June 2010.##[13] G. Wen, Z. Peng, A. Rahmani, and Y. Yu, “Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics,” Int. J. Syst. Sci., vol. 45, pp. 1892-1901, January 2014.##[14] Z. G. Wu, P. Shi, H. Su and J. Chu, “Sampled-data synchronization of chaotic Lur’e systems with time delays,” IEEE Trans. Neural Netw., vol. 24, pp. 410-421, March 2013.##[15] Z.G. Wu, P. Shi, H. Su and J. Chu, “Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay,” IEEE Trans. Neural Netw., vol. 24, pp. 1177- 1187, August2013.##[16] E. Nuño, R. Ortega, L. Basañez and D. Hill, “Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays,” IEEE Trans. Autom. Control, vol. 56, pp. 935-941, April 2011.##[17] W. Ren, “Distributed leaderless consensus algorithms for networked Euler–Lagrange systems,”##Int. J. Control, vol. 82, pp. 2137-2149, November 2009.##[18] B. Karimi and M.B. Menhaj, “Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks,” Inf. Sci., vol. 180, pp. 3335-3347, September 2010.##[19] B. Karimi, M.B. Menhaj, M. Karimi-Ghartemani and I. Saboori, “Decentralized adaptive control of large-scale affine and nonaffine nonlinear systems” IEEE Trans. Instrum. Meas., vol. 58, pp. 2239-2247, August 2007.##[20] G.P. Liu, V. Kadirkamanathan and S.A. Billings, “Variable neural networks for adaptive control of nonlinear systems,” IEEE Trans. Syst. Man Cybern. Part C, vol. 29, pp. 34-43, February 1999.##[21] C.Y. Lee and J.J. Lee, “Adaptive control for uncertain nonlinear systems based on multiple neural networks,” IEEE Trans. Syst. Man Cybern. Part B, vol. 34, pp. 325-333, February 1999.##[22] I. Kar, and L. Behera, “Direct adaptive neural control for affine nonlinear systems,” Appl. Soft Comput., vol. 9, pp. 756–764, March 2009.##[23] L.X. Wang and J.M. Mendel, “Fuzzy basis function, universal approximation, and orthogonal least-squares learning,” IEEE Trans. Neural Netw., vol. 3, pp. 807-814, September 1992.##[24] Z. Hou, L. Cheng and M. Tan, “Decentralized robust adaptive control for the multiagent system consensus problem using neural networks,” IEEE Trans. Syst. Man Cybern. Part B, vol. 39, pp. 636-647, June 2009.##[25] L. Cheng, Z. Hou, M. Tan, Y. Lin and Zhang, W. “Neural-network-based adaptive leader-following control for multiagent systems with uncertainties,” IEEE Trans. Neural Netw., vol. 21, pp. 1351-1358, August 2010.##[26] A. Das and F.L. Lewis, “Distributed adaptive control for synchronization of unknown nonlinear networked systems,” Automatica, vol. 46, pp. 2014-2021, August 2010.##[27] H. Zhang and F.L. Lewis, “Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics,” Automatica, vol. 48, pp. 1432-1439, December 2012.##[28] R. Cui, B., Ren and S.S. Ge, “Synchronized tracking control of multi-agent system with high-order dynamics,” IET Control Theory Appl., vol. 6, pp. 603-614, July 2012.##[29] Y. Liu and Y. Jia, “Adaptive consensus protocol for networks of multiple agents with nonlinear dynamics using neural networks,” Asian J. Control, vol. 14, pp. 1328-1339, September 2012. ##[30] A.M. Zou, K.D. Kumar and Z.G. Hou, “Distributed consensus control for multi-agent systems using terminal sliding mode and Chebyshev neural networks,” Int. J. Robust Nonlinear, vol. 23, pp. 334-357, February 2013.##[31] A. Das and F.L. Lewis, “Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities,” Int. J. Robust Nonlinear Control, vol. 21, pp. 1509-1524, September 2011.##[32] G.X. Wen, C.L.P. Chen, Y.J. Liu and Z. Liu, “Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems,” IET Control Theory Appl., vol. 9, pp. 1927–1934, August.##[33] H. Xu, and P.A. Ioannou, “Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds,” IEEE Trans. Automat. Control, vol. 48, pp. 728-742, May 2003.##[34] W. Yu, G. Chen and J. Lu, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, pp. 429-435, February 2009.##[35] H. Khalil, Nonlinear Systems, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ 2002.##[36] M. Fu, J. Jiao and S. Yin, “Robust coordinated formation for multiple surface vessels based on backstepping sliding mode control,” J Abstr. App. Anal., vol. 2013,July 2013.##[37] J. Almeida, C. Silvestre and A.M. Pascoal, “Cooperative control of multiple surface vessels with discrete-time periodic communications,” Int. J. Robust Nonlinear Control, vol. 22, pp. 398-419, March 2012. ##]
A New Recurrent Fuzzy Neural Network Controller Design for Speed and Exhaust Temperature of a Gas Turbine Power Plant
A New Recurrent Fuzzy Neural Network Controller Design for Speed and Exhaust Temperature of a Gas Turbine Power Plant
2
2
In this paper, a recurrent fuzzy-neural network (RFNN) controller with neural network identifier in direct control model is designed to control the speed and exhaust temperature of the gas turbine in a combined cycle power plant. Since the turbine operation in combined cycle unit is considered, speed and exhaust temperature of the gas turbine should be simultaneously controlled by fuel command signal and inlet guide vane position. Also practical limitations are applied to system inputs. In addition, demand power and ambient temperature are considered as disturbance. Simulation results show the effectiveness of proposed controller in comparison with other conventional methods such as Model Predictive Control (MPC) and H∞ control in a same operating condition
1
In this paper, a recurrent fuzzy-neural network (RFNN) controller with neural network identifier in direct control model is designed to control the speed and exhaust temperature of the gas turbine in a combined cycle power plant. Since the turbine operation in combined cycle unit is considered, speed and exhaust temperature of the gas turbine should be simultaneously controlled by fuel command signal and inlet guide vane position. Also practical limitations are applied to system inputs. In addition, demand power and ambient temperature are considered as disturbance. Simulation results show the effectiveness of proposed controller in comparison with other conventional methods such as Model Predictive Control (MPC) and H∞ control in a same operating condition
23
30
A.
Fakharian
A.
Fakharian
Assistant Professor, Department of Electrical, Biomedical and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Assistant Professor, Department of Electrical,
Iran
R.
Mosaferin
R.
Mosaferin
Department of Mechatronics Engineering, South Branch, Islamic Azad University, Tehran, Iran
Department of Mechatronics Engineering, South
Iran
M. B.
Menhaj
M. B.
Menhaj
Professor, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran
Professor, Department of Electrical Engineering,
Iran
Recurrent fuzzy-neural network (RFNN)
Gas Turbine
Neural Network
Direct Control Model
[[1] A. Kostyuk and V. Frolov, steam and gas turbines 2ndedition, Mire publisher, Moscow,1988, Transl. D. Tavakoli, and S.R. Shamshirgaran, Iran.##[2] W. I. Rowen, “Simplified mathematical representation of heavy-duty gas turbine,” ASME, Journal of eng. Gas Turbines and Power, vol. 105, pp. 865-869, 1983.##[3] M. R. Bank Tavakoli, B. Vahidi, and W. Gawlik, “An Educational Guide to Extract the Parameters of Heavy Duty Gas Turbines Model in Dynamic Studies Based on Operational Data,” IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1366–1374, Aug. 2009.##[4] Working Group, on Prime Mover and Energy Supply Models, “Dynamic models for fossil fueled steam units in power system studies,” IEEE Trans. Power Syst., vol. 6, no. 2, pp. 753–761, May 1991.##[5] Working Group, on Prime Mover and Energy Supply Models, “Hydraulic turbine and turbine control models for system dynamic studies,” IEEE Trans. Power Syst., vol. 7, no. 1, pp. 167–179, Feb. 1992.##[6] IEEE Working Group Report, “Dynamic models for combined cycle plants in power system studies,” IEEE Trans. Power Syst., vol. 9, no. 3, pp. 1698–1707, Aug. 1994.##[7] A. R. Martinez, R. G. Ramirez and L. G. Vela-Valdes, “PI Fuzzy Gain Scheduling Speed Control at Startup of a Gas-Turbine Power Plant,” IEEE Trans. Energy Conversion, vol. 26, no. 1, March 2011.##[8] D. H. Kim, “Neuro-fuzzy tuning of PID controller for control of actual gas turbine power,” IEEE inter. conf. computational intelligence for measurements and applications, pp. 192–197, July 2004.##[9] S. Balamurugan, R. J. Xavier, and A. E. Jeyakumar, “Control of Heavy-duty Gas Turbine Plants for Parallel Operation Using Soft Computing Techniques,” Taylor and Francis, Electric Power Components and Systems, vol. 37, no. 11, pp. 1275-87, Oct. 2009.##[10] S. M. Camporeale, B. Fortunato and A. Dumas, “Non-linear simulation model and multivariable control of a regenerative single shaft gas turbine,” IEEE Inter. Conf., pp. 721-723, Oct. 1997.##[11] A. Marzoughi, H. Selamat, M. F. Rahmat and H. A. Rahim, “Optimized proportional integral derivative (PID) controller for the exhaust temperature control of a gas turbine system using particle swarm optimization,” Inter. Journal of the Physical Sciences, vol. 7, no. 5, pp. 720-729, Jan. 2012.##[12] J. W. Kim and S. W. Kim, “Design of Incremental Fuzzy PI Controllers for A Gas-Turbine Plant,” IEEE/ASME Trans. Mechatronics, vol. 8, no. 3, pp. 410-414, September 2003.##[13] H. Ghorbani, A. Ghaffari, and M. Rahnama, “Constrained Model Predictive Control Implementation for a Heavy-Duty Gas Turbine Power Plant,” WSEAS Trans. system and control, vol. 3, no. 6, pp. 507-516, June 2008.##[14] E. Najimi, and M. H. Ramezani, “Robust control of speed and temperature in a power plant gas turbine,” Elsevier, ISA Trans., vol. 51, no. 2, March 2012.##[15] W. Gua, Z. Wub, R. Boc, W. Liua, G. Zhoua, W. Chena and Z. Wua, “Modeling, planning and optimal energy management of combined cooling, heating and power microgrid: A review,” International Journal of Electrical Power and Energy Systems, vol. 54, pp. 26-37, 2014. [16] Shuvom, M. and Haq, M., "Development and Analysis of Adaptive Neural Network Control for a Cybernetic Intelligent ‘iGDI’ Engine," SAE Technical Paper 2015-01-0157, 2015.##[17] C. H. Lee and C. C. Teng, “Identification and control of dynamic systems using recurrent fuzzy neural networks,” IEEE Trans. Fuzzy Syst., vol. 8, no. 4, pp. 349 -366, August 2000.##[18] F. J. Lin, R. J. Wai, K. K. Shyu, and T. M. Liu, “Recurrent fuzzy neural network control for piezoelectric ceramic linear ultrasonic motor drive,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 48, pp. 900 -913, July 2001.##[19] A. R. Martinez, R. G. Ramirez and L. G. Vela-Valdes, “PI Fuzzy Gain Scheduling Speed Control at Startup of a Gas-Turbine Power Plant,” IEEE Trans. Energy Conversion, vol. 26, no. 1, March 2011.##[20] K. P. Venugopal, R. Sudhakar and A. S. Pandya, “An improved scheme for direct adaptive control of dynamical systems using back propagation neural networks,” J. Circuits, Syst. Signal Processing, vol. 14, no. 2, pp. 213 -236, 1995.##]
A Novel Intelligent Energy Management Strategy Based on Combination of Multi Methods for a Hybrid Electric Vehicle
A Novel Intelligent Energy Management Strategy Based on Combination of Multi Methods for a Hybrid Electric Vehicle
2
2
Based on the problems caused by today conventional vehicles, much attention has been put on the fuel cell vehicles researches. However, using a fuel cell system is not adequate alone in transportation applications, because the load power profile includes transient that is not compatible with the fuel cell dynamic. To resolve this problem, hybridization of the fuel cell and energy storage devices such as batteries and ultra-capacitors are usually applied. This article has studied a hybrid electric vehicle comprising a fuel cell system and battery pack. Energy management strategy is one of the essential issues in hybrid electric vehicles designing, for power optimal distribution as well as, improving both the fuel economy and the performance of vehicle's components. In this paper, an optimal hierarchical strategy has been proposed based on the load power prediction and intelligent controlling to achieve an optimal distribution of energy between the vehicle's power sources; and, to ensure reasonable performance of the vehicle's components. For load power prediction, a new method is presented that is based on Takagi – Sugeno fuzzy model trained by an improved differential evolutionary algorithm with an objective function formulated by support vector machine. A combination of empirical mode decomposition (EMD) algorithm capabilities, fuzzy logic controller, supervisory switching technique and improved differential evolution algorithm is used to design the proposed energy management strategy. The proposed strategy is assessed in the UDDS Standard drive cycle. Simulation results show that the proposed control strategy can fulfill all the requirements of an optimal energy management.
1
Based on the problems caused by today conventional vehicles, much attention has been put on the fuel cell vehicles researches. However, using a fuel cell system is not adequate alone in transportation applications, because the load power profile includes transient that is not compatible with the fuel cell dynamic. To resolve this problem, hybridization of the fuel cell and energy storage devices such as batteries and ultra-capacitors are usually applied. This article has studied a hybrid electric vehicle comprising a fuel cell system and battery pack. Energy management strategy is one of the essential issues in hybrid electric vehicles designing, for power optimal distribution as well as, improving both the fuel economy and the performance of vehicle's components. In this paper, an optimal hierarchical strategy has been proposed based on the load power prediction and intelligent controlling to achieve an optimal distribution of energy between the vehicle's power sources; and, to ensure reasonable performance of the vehicle's components. For load power prediction, a new method is presented that is based on Takagi – Sugeno fuzzy model trained by an improved differential evolutionary algorithm with an objective function formulated by support vector machine. A combination of empirical mode decomposition (EMD) algorithm capabilities, fuzzy logic controller, supervisory switching technique and improved differential evolution algorithm is used to design the proposed energy management strategy. The proposed strategy is assessed in the UDDS Standard drive cycle. Simulation results show that the proposed control strategy can fulfill all the requirements of an optimal energy management.
31
46
M.H.
Ranjbar jaferi
M.H.
Ranjbar jaferi
Department of Electrical Engineering, Shahid Bahonar University, Kerman, Iran
Department of Electrical Engineering, Shahid
Iran
S.M.A.
Mohammadi
S.M.A.
Mohammadi
Department of Electrical Engineering, Shahid Bahonar University, Kerman, Iran
Department of Electrical Engineering, Shahid
Iran
M.
Mohammadian
M.
Mohammadian
Department of Electrical Engineering, Shahid Bahonar University, Kerman, Iran
Department of Electrical Engineering, Shahid
Iran
Hybrid Electric Vehicle
Fuzzy Logic Controller
Support Vector Machine
Empirical Mode Decomposition
supervisory Switching Control
Improved Differential Evolution Algorithm
[[1] Y. Eren, O. Erdinc, H. Gorgun, M. Uzunoglu, and B. Vural, "A fuzzy logic based supervisory##controller for an FC/UC hybrid vehicular power system," international journal of hydrogen energy,##vol. 34, pp. 8681 – 8694, 2009.##[2] Amin. Hajizadeh, and Masoud. Aliakbar Golkar,"Intelligent power management strategy of hybrid##distributed generation system," Electrical Power and Energy Systems, vol. 29, pp. 783 – 795, 2007.##[3] O. Erdinc, B. Vural, and M. Uzunoglu, "A wavelet-fuzzy logic based energy management##strategy for a fuel cell/battery/ultra-capacitor hybrid vehicular power system," Journal of Power##Sources, vol. 194, pp. 369-380, 2009.##[4] Chun.Yan. Li, and Guo.Ping. Liu, "Optimal fuzzy power control and management of fuel cell/battery##hybrid vehicles," Journal of Power Sources, vol. 192, pp. 525 - 533, 2009.##[5] Junghwan. Ryu, Yeongseop. Park, and Myoungho. Sunwoo, " Electric powertrain modeling of a fuel##cell hybrid electric vehicle and development of a power distribution algorithm based on driving##mode recognition," Journal of Power Sources, vol.195, pp. 5735 - 5748, 2010.##[6] Min.Joong. Kim, and Huei. Peng, "Power management and design optimization of fuel##cell/battery hybrid vehicles," Journal of Power Sources, vol. 165, pp. 819 - 832, 2007.##[7] Richard. Meyer, Raymond.A. DeCarlo, Peter.H.Meckl, Chris. Doktorcik, and Steve. Pekarek,##"Hybrid Model Predictive Power Flow Control of a Fuel Cell-Battery Vehicle," 2011 American##Control Conference on O'Farrell Street, San Francisco, CA, USA, June 29 - July 01, 2011.##[8] Y. Ates, O. Erdinc, M. Uzunoglu, and B. Vural,"Energy management of an FC/UC hybrid##vehicular power system using a combined neural network-wavelet transform based strategy,"##International journal of hydrogen energy, vol. 35,pp. 774 – 783, 2010.##[9] O. Erdinc, B. Vural, and M. Uzunoglu, "A wavelet-fuzzy logic based energy management##strategy for a fuel cell/battery/ultra-capacitor hybrid vehicular power system," Journal of Power##Sources, vol. 194, pp. 369-380, 2009.##[10] Majid Zandi, A. Payman, Jean-P. Martin, Serge Pierfederici,B. Davat, and F. Meibody-Tabar,##"Energy Management of a Fuel Cell/Supercapacitor/Battery Power Source for Electric Vehicular Applications," IEEE transactions on vehicular technology, vol. 60, pp.433 – 443, Feb. 2011.##[11] Qi. Li, Weirong. Chen, Yankun. Li, Shukui. Liu, and Jin. Huang, "Energy management strategy for##fuel cell/battery/ultracapacitor hybrid vehicle based on fuzzy logic," Electrical Power and Energy##Systems, vol. 43, pp. 514 – 525, 2012.##[12] Gao. D, Jin. Z, and Lu. Q, "Energy management strategy based on fuzzy logic for a fuel cell hybrid##bus," Journal of Power Sources, vol. 185, pp. 311-317, 2008.##[13] M. Kim, Y. Sohn, W. Lee, and C. Kim, " Fuzzy control based engine sizing optimization for a fuel##cell/ battery hybrid mini-bus," Journal power sources, vol. 178, pp. 706-710, 2008. ##[14] Niels.J. Schoutena, M.A. Salmanb, and N.A. Kheir, "Energy management strategies for parallel hybrid vehicles using fuzzy logic," Control Engineering Practice, vol. 11, pp. 171-177, 2003.##[15] Chun.Yan. Li, and Guo.Ping. Liu, "Optimal fuzzy power control and management of fuel cell/battery hybrid vehicles," Journal of Power Sources, vol. 192, pp. 525 - 533, 2009.##[16] Wang Yifeng, Zhang Yun, Wu. Jian, and Chen. Ning, "Energy management system based on fuzzy control approach for hybrid electric vehicle," Chinese Control and Decision Conference (CCDC), 2009.##[17] [Soon-il Jeon, Yeong-il Park, Jang-moo Lee, and Sung-tae Jo, "Multi- mode driving control of a parallel hybrid electric vehicle using driving pattern recognition," Journal of Dynamic system measurement and control, Vol. 124, pp. 141-149, Aug. 2002.##[18] Takagi, and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE transaction on Systems, man, and Cybernetics, Vol. 15, pp. 116-132. 1985.##[19] Chen-Chia Chuang, Zne-Jung Lee, "Hybrid robust vector machines for regression with outliers," Journal Applied Soft Computing, vol. 11, PP. 64-72, 2011.##[20] Ruxandra Stoean, "An Evolutionary Support Vector Machines Approach to regression," 6th International Conference on Artificial Intelligence and Digital Communications, vol. 1, pp. 54-61, 2006.##[21] A. Hasan Zade, S. M. Ali. Mohammadi, and A.A. Gharaveisi, "Fuzzy Logic Controlled Differential Evolution to Identification of Takagi sugeno models," International Journal of Engineering Research & Industrial Applications, Vol. 5, No. 1, pp. 367-382, 2012.##[22] M. Willjuice Iruthayarajan, and S. Baskar, "Evolutionary algorithms based design of multivariable PID controller," Expert Systems with Applications, vol. 36, pp. 9159–9167, 2009.##[23] Z. Lu, J. Sun and K. R. Butts, "Linear Programming Support Vector Regression with Wavelet Kernel: A New Approach to Nonlinear Dynamical Systems Identification, " Mathematics and Computers in Simulation, Vol. 79, pp. 2051-2063, 2009.##[24] Hassan.Zade, and S.M.A. Mohammadi, "Fuzzy logic controller differential evolution to identification of Takagi -Sugeno models," International Journal of Engineering Research& Industrial Applications, vol. 5, pp. 367-382, 2012.##[25] K.B. Wipke, M.R. Cuddy, and S.D. Burch, "A User-friendly advanced powertrain simulation using a combined backward/forward approach," IEEE transaction vehicle technology, vol. 48, pp. 1751-1761, 1999.##[26] N. E. Huang, M.L. C.Wu, S. R. Long, S.S.P. Shen, W. Qu, P. Gloersen, and K.L. Fan, "A confidence limit for the empirical mode decomposition and Hilbert spectral analysis," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 459, pp. 2317–2345, Sep. 2003.##[27] M.Md. Thameem Ansari, and S. Veusami, "Dual mode linguistic hedge fuzzy logic controller for an isolated wind-diesel hybrid power system with superconducting magnetic energy storage unit," Energy Conversion and Management, vol. 51, pp. 169-181, 2010.##[28] Junghwan. Ryu, Yeongseop. Park, and Myoungho. Sunwoo, "Electric powertrain modeling of a fuel cell hybrid electric vehicle and development of a power distribution algorithm based on##[29] driving mode recognition," Journal of Power Sources, vol. 195, pp. 5735 - 5748, 2010.##[30] Amir poursamad, and Morteza Montazeri, "Design of genetic-fuzzy control strategy for parallel hybrid electric vehicles," Control Engineering Practice, vol. 16, pp. 861-873, 2008.##[31] Wei-Song Lin, and Chen-Hong Zhang, "Energy management of a fuel cell/ Ultra-capacitor hybrid power system using an adaptive optimal-control method," Journal of power sources, vol. 196, pp. 32280-3289, 2011.##[32] R.K. Ahluwalia, X. Wang, A. Rousseau, "Fuel economy of hybrid fuel cell vehicles," Journal of Power Sources, vol. 152, pp. 233-244. 2005.##]
Fully Distributed Modeling, Analysis and Simulation of an Improved Non-Uniform Traveling Wave Structure
Fully Distributed Modeling, Analysis and Simulation of an Improved Non-Uniform Traveling Wave Structure
2
2
Modeling and simulation of communication circuits at high frequency are important challenges ahead in the design and construction of these circuits. Knowing the fact that the lumped element model is not valid at high frequency, distributed analysis is presented based on active and passive transmission lines theory. In this paper, a lossy transmission line model of traveling wave switch (TWSW) is presented and fully distributed analysis of this structure is also introduced. In the off state, the ordinary single pole single throw (SPST) switches operate as short or open circuit and return an observable part of the signal. To improve return loss in the off state, a non-uniform structure of SPST switches is proposed which is based on the artificial tapered transmission line produced by applying various controlling voltage at the gate. The analysis of ordinary and improved structure of SPST switches is performed and it is further compared with that of the semi-distributed and fully distributed methods. The results of simulation easily approve the improvement of matching in the off state.
1
Modeling and simulation of communication circuits at high frequency are important challenges ahead in the design and construction of these circuits. Knowing the fact that the lumped element model is not valid at high frequency, distributed analysis is presented based on active and passive transmission lines theory. In this paper, a lossy transmission line model of traveling wave switch (TWSW) is presented and fully distributed analysis of this structure is also introduced. In the off state, the ordinary single pole single throw (SPST) switches operate as short or open circuit and return an observable part of the signal. To improve return loss in the off state, a non-uniform structure of SPST switches is proposed which is based on the artificial tapered transmission line produced by applying various controlling voltage at the gate. The analysis of ordinary and improved structure of SPST switches is performed and it is further compared with that of the semi-distributed and fully distributed methods. The results of simulation easily approve the improvement of matching in the off state.
47
52
H.
Khoshniyat
H.
Khoshniyat
Electrical Engineering Department, Amirkabir University of Technology,Tehran, Iran
Electrical Engineering Department, Amirkabir
Iran
A.
Abdipour
A.
Abdipour
Electrical Engineering Department, Amirkabir University of Technology,Tehran, Iran
Electrical Engineering Department, Amirkabir
Iran
G.
Moradi
G.
Moradi
Electrical Engineering Department, Amirkabir University of Technology,Tehran, Iran
Electrical Engineering Department, Amirkabir
Iran
Fully-distributed model
single pole single throw switch (SPST)
traveling wave switch (TWSW)
non-uniform structure
lossy transmission line model
[[1] H. Mizutani, and Y. Takayama, ”DC-110-GHz MMIC traveling waveswitch," IEEE Trans.##Microwave Theory Tech., vol. 48, No. 5, pp. 840-845, May, 2000.##[2] H. Mizutani, N. Iwata, Y. Takayama, and K. Honjo, “Design Considerations for Traveling-##Wave Single-Pole Multithrow MMIC Switch Using Fully Distributed FET," IEEE Trans. Microwave Theory Tech., vol. 55, No. 4, pp. 664-671, April 2007.##[3] H. Khoshniyat, G. Moradi, A. Abdipour, and K. Afrooz, “Optimization and Fully Distributed Analysis of Traveling Wave Switches at Millimeter Wave Frequency Band," 1st MMWATT Conf., pp. 45-49, Dec, 2009.##[4] G. L. Lan, D. L. Dunn, J. C. Chen, C. K. Pao, and D. C. Wang, “A high performance V-band##monolithic FET transmit-receive switch," IEEE Microwave Millimeter-Wave Monolithic Circuits##Symp. Dig., pp. 99-101, May, 1988.##[5] H. Takasu, F. Sasaki, H. Kawasaki, H. Tokuda, and S. Kamihashi, “W-band SPST transistor##switches," IEEE Microwave Guided Wave Lett.,vol. 6, pp. 315-316, Sept, 1996.##[6] H. Mizutani, M. Funabashi, M. Kuzuharad, and Y.Takayama, “Compact DC-60 GHz HJFET MMIC##switches using ohmic electrode- sharing technology," IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1597-1603, Nov. 1998.##[7] H. Khoshniyat, G. Moradi, A. Abdipour, K. Afrooz, "Optimization and Fully-Distributed##Analysis of Single-Pole Single-Throw Traveling Wave Switches at Millimeter Wave Frequency##Band,” International Journal of Information and Communication Technology (IJICT), vol.3, no.2,##pp.19-25, March 2011.##[8] H. Khoshniyat, G. Moradi, A. Abdipour, K. Afrooz, "Fully distributed analysis of an improved##single pole single throw traveling wave switches,"21st Iranian Conference on Electrical Engineering##(ICEE 2013), pp.1-4, May, 2013. ##]
Failure Process Modeling with Censored Data in Accelerated Life Tests
Failure Process Modeling with Censored Data in Accelerated Life Tests
2
2
Manufacturers need to evaluate the reliability of their products in order to increase the customer satisfaction. Proper analysis of reliability also requires an effective study of the failure process of a product, especially its failure time. So, the Failure Process Modeling (FPM) plays a key role in the reliability analysis of the system that has been less focused on. This paper introduces a framework defining an approach for the failure process modeling with censored data in Constant Stress Accelerated Life Tests (CSALTs). For the first time, various types of censoring schemes are considered in this study. Usually, in data analysis, it is impossible to get closed form of estimates of the unknown parameter due to complex and nonlinear likelihood equations. As a new approach, a mathematical programming problem is formed and the Maximum Likelihood Estimation (MLE) of parameters is obtained to maximize the likelihood function. A case study in red Light- Emitting Diode (LED) lamps is also presented. The MLE of parameters is obtained using genetic algorithm (GA). Furthermore, the Fisher information matrix is obtained for constructing the asymptotic variances and the approximate confidence intervals of estimates of the parameters.
1
Manufacturers need to evaluate the reliability of their products in order to increase the customer satisfaction. Proper analysis of reliability also requires an effective study of the failure process of a product, especially its failure time. So, the Failure Process Modeling (FPM) plays a key role in the reliability analysis of the system that has been less focused on. This paper introduces a framework defining an approach for the failure process modeling with censored data in Constant Stress Accelerated Life Tests (CSALTs). For the first time, various types of censoring schemes are considered in this study. Usually, in data analysis, it is impossible to get closed form of estimates of the unknown parameter due to complex and nonlinear likelihood equations. As a new approach, a mathematical programming problem is formed and the Maximum Likelihood Estimation (MLE) of parameters is obtained to maximize the likelihood function. A case study in red Light- Emitting Diode (LED) lamps is also presented. The MLE of parameters is obtained using genetic algorithm (GA). Furthermore, the Fisher information matrix is obtained for constructing the asymptotic variances and the approximate confidence intervals of estimates of the parameters.
53
65
N.
Ramezanianpour
N.
Ramezanianpour
Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
Department of Industrial Engineering, Amirkabir
Iran
M.
Seyyed-Esfahani
M.
Seyyed-Esfahani
Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
Department of Industrial Engineering, Amirkabir
Iran
T.H.
Hejazi
T.H.
Hejazi
Department of Industrial & Material Engineering, Sadjad University of Technology, Mashhad, Iran
Department of Industrial & Material Engineerin
Iran
Reliability
Failure process modeling
Accelerated life test
Censored data
[[1] Ascher, H. and Feingold, H. “Repairable systems reliability: Modeling, inference, misconceptions and their causes,” 1th ed., Marcel Dekker, New York, 1984.##[2] Vaurio, J.K. “Identification of process and distribution characteristics by testing monotonic and non-monotonic trends in failure intensities and hazard rates,” Reliability Engineering and System Safety, vol. 64, no.3, pp. 345–357, 1999.##[3] Louit, D.M.,Pascual, R. and Jardine, A.K.S. “A practical procedure for the selection of time-to-failure models based on the assessment of trends in maintenance data,” Reliability Engineering and System Safety, vol. 94, no. 10, pp.1618-1628, 2009.##[4] Regattieri, A.,Manzini, R. and Battini, D. “Estimating reliability characteristics in the presence of censored data: A case study in a light commercial vehicle manufacturing system,” Reliability Engineering and System Safety, vol. 95, pp.1093–1102, 2010.##[5] Nelson WB. Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, John Wiley & Sons, New York, 1990.##[6] Chernoff, H. “Optimal accelerated life designs for estimation,” Technometrics, vol. 4, no. 3, pp. 381–408, 1962.##[7] Bessler, S.,Chernoff, H. and Marshall, A.W. “An optimal sequential accelerated life test,” Technometrics, vol. 4, no. 3, pp. 367–379, 1962.##[8] Chenhua L. “Optimal step-stress plans for accelerated life testing considering reliability/life prediction,” PhD Thesis, Department of Mechanical and Industrial Engineering, Northeastern University, USA, 2009.##[9] Bai, D. and Chung, S. “An accelerated life test model with the inverse power law,” Reliability##Engineering and System Safety, vol. 24, no. 3, pp. 223-230, 1989.##[10] Teng, N.H. and Kolarik, W.J. “On/off cycling under multiple stresses,” IEEE Trans. Reliability, vol. 38, no. 4, pp. 494–498, 1989.##[11] Fan, T.H. and Yu, C.H.“Statistical inference on constant stress accelerated life tests under generalized Gamma lifetime distributions,” Quality and Reliability Engineering International, vol. 29, no. 5, pp. 631-638, 2013.##[12] Zhang, J., Liu, C., Cheng, G.,Chen, X., Wu, J., Zhu, Q. and Zhang, L. “Constant-stress accelerated life test of white organic light-emitting diode based on least square method under Weibull distribution,” Journal of Information Display, vol. 15, no. 2, PP. 71-75, 2014.##[13] Guan, Q., Tang, Y., Fu, J. and Xu, A. “Optimal multiple constant-stress accelerated life tests for generalized Exponential distribution,” Communications in Statistics - Simulation and Computation, vol. 43, no. 8, PP.1852-1865, 2014.##[14] Nelson WB. Applied Life Data Analysis, John Wiley & Sons, New York (1982).##[15] Yang, G.B. “Optimum constant-stress accelerated life test plans,” IEEE Trans. Reliability, vol. 43, no. 4, PP. 575–581, 1994.##[16] Mettas, A. “Modeling and analysis for multiple stress-type accelerated life data,” in Proceedings of Annual Reliability and Maintainability Symposium, Los Angeles, CA, pp. 138–143, 2000.##[17] Zhou, K., Shi, Y. and Sun, T. “Reliability analysis for accelerated life-test with progressive hybrid censored data using geometric process,” Journal of Physical Sciences, vol. 16, PP.133-143, 2012.##[18] Bai, D. and Kim, M. “Optimum simple step-stress accelerated life tests for Weibull distribution and type-I censoring,” Naval Res. Logist, vol. 40, no. 2, PP. 193–210, 1993.##[19] Xiong, C. “Inference on a simple step-stress model with type-II censored Exponential data,” IEEE Trans. Reliability, vol. 47, no. 2, PP. 142–146, 1998.##[20] Tang, L.C., Goh, T.N., Sun, Y.S. and Ong, H.L. “Planning accelerated life tests for censored two-parameter Exponential distributions,” Nav Res Logistic, vol. 46, no. 2, PP. 169–186, 1999.##[21] Abdel-Ghaly, A., Attia, A. and Abdel-Ghani, M. “The maximum likelihood estimates in step partially accelerated life tests for the Weibull parameters in censored data,” Commun. Statist.Theory Meth, vol. 31, no. 4, PP. 551–573, 2002. ##[22] Balakrishnan, N., Kundu, D., Tony Ng, H.K. and Kannan, N.“Point and interval estimation for a simple step-stress model with type-II censoring,” J. Qual. Technol, vol. 39, no. 1, pp. 35–47, 2007.##[23] Balakrishnan, N. and Xie, Q. “Exact inference for a simple step-stress model with type-I hybrid censored data from the Exponential distribution,” J. Statist. Plann. Inference, vol. 137, no. 11, PP. 3268–3290, 2007.##[24] Li, C. and Fard, N. “Optimum bivariate step-stress accelerated life test for censored data,” IEEE Trans. Reliability, vol. 56, no. 1, PP. 77–84, 2007.##[25] Kateri, M. and Balakrishnan, N. “Inference for a simple step-stress model with type-II censoring, and Weibull distributed lifetimes,” IEEE Trans. Reliability, vol. 57, no. 4, PP. 616-626, 2008.##[26] Watkins, A. and John, A. “On constant stress accelerated life tests terminated by type II censoring at one of the stress levels,” Journal of statistical Planning and Inference, vol. 138, no. 3, PP. 768-786, 2008.##[27] Abdel-Hamid, A. and AL-Hussaini, E. “Estimation in step-stress accelerated life tests for the exponentiated Exponential distribution with type-I censoring,” Computational Statistics & Data Analysis, vol. 53, no. 4, PP. 1328-1338, 2009.##[28] Guan, v. and Tang, Y. “Optimal step-stress test under type-I censoring for multivariate Exponential distribution,” Journal of Statistical Planning and Inference, vol. 142, no. 7, PP. 1908-1923, 2012.##[29] Ling, L., Xu, W. and Li, M. “Optimal bivariate step-stress accelerated life test for type-I hybrid censored data,” Journal of Statistical Computation and Simulation, vol. 81, no. 9, PP. 1175–1186, 2010.##[30] Attia, A.F.,Aly, H.M. and Bleed, S.O. “Estimating and planning accelerated life test using constant stress for generalized Logistic distribution under type-I censoring,” ISRN Applied Mathematics; 203618, 15 pages, 2011.##[31] Lee, J. and Pan, R. “Bayesian analysis of step-stress accelerated life test with Exponential distribution,” Quality and Reliability Engineering International, vol. 28, no.3, PP. 353-361, 2012.##[32] Wang, R.,Xu, X., Pan, R. and Sha, N. “On parameter inference for step-stress accelerated life test with Geometric distribution,” Communications in Statistics - Theory and Methods, vol. 41, no. 10, pp.1796-1812, 2012.##[33] Srivastava, P.W. and Mittal, N. “Optimum multi-objective modified constant-stress accelerated life test plan for the Burr type-XII distribution with type-I censoring, ” Proceedings of the Institution of##Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 227, no. 2, PP. 132-143, 2013.##[34] Kamal, M. andZarrin, S. “Design of accelerated life testing using geometric process for Pareto distribution withtype-I censoring,” Journal of global research in mathematical archives, vol. 1, no. 8, PP. 59-66, 2013.##[35] Aly, H.M. and Bleed, S.O. “Bayesian estimation for the generalized Logistic distribution type-II censored accelerated life testing,” Int. J. Contemp. Math. Sciences, vol. 8, no. 20, PP. 969 – 986, 2013.##[36] Shi, Y.M., Jin, L., Wei, C. and Yue, H.B. “Constant-stress accelerated life test with competing risks under progressive type-II hybrid censoring,” Advanced Materials Research, vol. 712 – 715, pp. 2080-2083, 2013.##[37] Aly, H.M. and Bleed, S.O. “Estimating and planning step stress accelerated life test for generalized Logistic distribution under type-I censoring,” International Journal of Applied Mathematics & Statistical Sciences, vol. 2, no. 2, pp. 1-16, 2013.##[38] Asser, S. and Abd EL-Maseh, M.“Estimation of the parameters of the bivariate generalized Exponential distribution using accelerated life testing with censoring data,” International Journal of Advanced Statistics and Probability, vol. 2, no. 2, pp. 77-83, 2014.##[39] Amal, S.H., Assar, S.M. and Shelbaia, A. “Optimum inspection times of step stress accelerated life tests with progressively type-I interval censored,” Australian Journal of Basic and Applied Sciences, vol. 8, no. 17, pp. 282-292, 2014.##[40] Saleem, Z.A. “Effect of progressive type-I right censoring on Bayesian statistical inference of simple step-stress acceleration life testing plan under Weibull life distribution,” International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, vol. 8, no. 2, pp. 325-329 , 2014.##[41] Zhao, J., Shi, Y. and Yan, W. “Inference for constant-stress accelerated life test with type-I progressively hybrid censored data from Burr-XII distribution,” Journal of Systems Engineering and Electronics, vol. 25, no. 2, pp. 340-348, 2014.##[42] Cox, D.R. “Regression models andlife tables,” Springer-Verlag, New York, pp. 527-541, 1992.##[43] Holland, J.H. Adaptation in natural and artificial systems: An introductory analysis with Applications to Biology, Control, and Artificial Intelligence, 1th ed., MIT Press, Cambridge, 1992. ##[44] Wang, F.K., Cheng, Y.F. and Lu, W.L., ”Partially accelerated life tests for the weibull distribution under multiply censored data,” Communications in Statistics-Simulation and computation, vol. 41, no. 9, pp. 1667-1678.##]