Availability Optimization for Coal Handling System using Genetic Algorithm

International Journal of Performability Engineering Vol. 9, o. 1, January 21, pp. 19-1. RAMS Consultants Printed in India Availability Optimization for Coal Handling System using Genetic Algorithm SAJAY AJAL 1, P. C. EWARI 2,and PARVEE SAII 1, Research Scholar,.I.., urukshetra-1119, (Haryana), India 2 Dept. of Mechanical Engineering,.I.., urukshetra-1119, India (Received on January 12, 212, revised on August 2, 212 and September 22, 212) Abstract: he paper deals with the availability optimization for Coal Handling System of a ational hermal Power Corporation (..P.C.) Plant, using Genetic Algorithm (G.A.). Mathematical formulation is carried out using probabilistic approach and Markov birth death process is used to develop the Chapman-olmogorov difference differential equations. hese equations are further solved recursively in order to derive the Steady State Availability expression. he optimal values of availability of coal handling system have been evaluated using Matlab G.A. tool. he steady state availability obtained from Markov analysis is also compared with the optimal availability calculated through G.A. eywords: Availability optimization, Genetic Algorithm, Coal handling system, Markov process, Chapman- olmogorov differential equations 1. Introduction Availability is one of the measures of system performance besides reliability under the specified conditions of use. A complex plant may have systems and the subsystems connected functionally in series, parallel or a combination of these. In the literature, some researchers [1-9] have carried out system reliability optimization and cost analysis. A stochastic model has been developed in [1] to analyze performance of a cell operating with multistate including degraded states. he applications of model to determine reliability and productivity of the cell, as well as the utilization of its components under various operational conditions have been discussed. he availability and MF expressions of washing system of a paper industry have been derived in [2] using simple probability considerations. A mathematical model of a complex bubble gum production system has been developed in [] using Markov modeling. he reliability characteristics have been evaluated and analyzed in the paper. An optimization model [] for the grid service allocation has been developed using Genetic Algorithm. A reliability model of a block-board manufacturing system in the plywood industry has been developed in [5] using time dependent and steady state availability under idealized and faulty preventive maintenance conditions. A Genetic Algorithm based optimization model [] has been proposed to optimize availability for a series parallel system. A maintenance optimization model of an engineering system assembled in a series configuration has been proposed in paper [7]. he various optimization techniques and their implementation have been discussed in [8] for some engineering problems. A systematic study for G.A. mechanism and identification of three basic operators: reproduction, crossover and mutation for obtaining near optimal solutions has been carried out in [9]. After going through comprehensive literature review, it has been felt that G.A., which has been successfully applied in various complex industries comprising series, parallel and hybrid systems, however has not been considered for availability optimization *Corresponding author s email: sanjay_kajal@rediffmail.com 19

11 Sanjay ajal, P. C. ewari, and Parveen Saini of a thermal plant so far. In addition, as the plant management is always interested in maintaining maximum availability with optimal parameters, hence, the author has made an attempt to optimize the availability of the system concerned using G.A. 2. System Description he plant is divided into many sections like Ash handling system, Water treatment system, Coal handling system, Condensate and feed water system and Air distribution system. he coal handling system comprises of various subsystems working in series and parallel configuration. he schematic diagram of Coal handling system as shown in figure 1 is as follows: Coal from railway track hopper Wagon tipplers Crusher house ransfer point Wagon tipplers wo conveyor belts in parallel wo conveyor belts in parallel wo conveyor belts in parallel Raw coal bunker 1 Raw coal bunker 2 Coal pulverizing mill 1 Coal pulverizing mill 2 Pulverizing coal bunker 1 Pulverizing coal bunker 2 Furnace Figure 1: Schematic Diagram of Coal Handling System he Coal handling system consists of the following four critical subsystems: i. Wagon ippler (C 1 ): hese are the motorized operated machines. his subsystem consists of two units of wagon tipplers. Failure of any one forces to start with standby unit. Complete failure of the system occurs when standby unit of the wagon tippler also fails. ii. Conveyor Belts (C 2 ): hese are the synthetic rubber belts, which move on metallic rollers and idlers, which are used for shifting of coal from one place to other place. here are two units of conveyors working in parallel. Failure of any one reduces the capacity of belt to transport the coal from one location to other. Complete failure of the system occurs when both the units fail. iii. Crusher House (C ): he coal is received in the form of odd shaped lumps. hese lumps are to be crushed to required size. hese lumps are crushed by coal crushers whose failure causes complete failure of the system.

Availability Optimization for Coal Handling System using Genetic Algorithm 111 iv. Coal Pulverizing Mills (C ): he function of these mills is the make the fine powder of the coal for effective burning in the boiler. here are two units of Mills working in parallel. Failure of anyone reduces the capacity of the system and hence loss in production. Complete failure of the system occurs when both the mills fail. 2.1 Assumptions and otation i. Repair rates and failure rates are negative exponential and independent of each other. ii. Simultaneous failures are not allowed among the subsystems. iii. A repaired unit is, performance wise, as good as new. iv. he Switch-over devices are perfect and repair facilities are always available. v. he failure rates of other subsystems like coal bunkers and transfer point in coal handling system are almost insignificant Full Capacity State (without standby) C 1, C 2, C, C One unit of sub-system C 1 is in failed state and the system is # working with standby unit Failed State c 1, c 2, c, c Reduced capacity and Failure rates λ i ;i to Repair rates i ;i to Probability of full capacity working State and Probability of reduced capacity working state,,,, and Probability of failed state to 2.2 Mathematical Modeling and Steady State Availability for Coal Handling System he mathematical modeling for Coal handling Systemstarts with the development Chapman-olmogorov difference differential using transition diagram. he Coal handling system is required to be available for long duration of time. So, the long run or steady state availability of the Coal handling system is obtained by putting as t into differential eqns. (1) to (12) (Appendix) and solving these equations recursively, we get: 1 P1 P M1P P 2 P + P M2P 12 12 P P + P + P P P P M P 9 1 11 9 1 11 1 2 1 2 P P + P + P + P P + M P + M P + M P M P 5 7 1 8 2 5 7 1 8 2 λ λ λ λ λ λ λ λ P P + P + P + P + P M P P P + 1 1 5 1 2 1 1 5 5 5 5 5 5 5 5 λ λ M2P 1P M5P 5 5 P P + P + P + P M P + M P + M P + M P M P 1 2 5 2 1 1 2 5 2 1 λ M P +λ M P 2 1 7 1 2 5 2 1P M7P 7 P M P + M P + M P + M

112 Sanjay ajal, P. C. ewari, and Parveen Saini where 1 + 2 +λ +λ + + + +λ + 5 λ + + + + 7 λ + + λ 1 2 λ λλ λλ λ 1 5 1+ 5 λ 9 5 + 2 5 5 λ 11 +λ 8 + + + 7 λ 7 + 5 5 7 8 λ λ 1 7 + + + + 2 8 2 5 5 λ 9 1 1 + + + 7 λ 5 2 7 2 2 5 5 5 λ 12 2 - - 11 7 λ λ 1 - - λ 7 12 7 1 2 1 2 1 + -λ - 1 - - 7 12 5 5 λ - 5 5-2 5 ow using normalizing conditions i.e., sum of all the probabilities is equal to one, we get: 27 i P 1 i λ λ λ λ λ λ λ λ 1 + M + 1 2 5 7 1 2 1 1 + 5 5 P λ λ λ λ λ λ λ λ λ λ λ λ M 5 7 7 7 Steady state availability of Coal handling system ( ) may be obtained as summation of probabilities of all working and reduced capacity states, i.e., 9.2% (1) aking λ.5,.1, λ.2,., λ.5,., λ.1,.8 (Data taken from Maintenance History sheets) he availability (A ) as given by eqn. (1) includes all possible states of nature, that is, failure events ( ) and the identification of all the courses of action i.e., repair priorities (μ ). he various availability levels may be computed for different combinations of failure and repair rates. his model can be used to make strategic maintenance policies for Coal handling system.. Availability Optimization for Coal Handling System Using Genetic Algorithm In the present work, an attempt has been made to optimize the system availability using G.A. approach. G.A. is a powerful probabilistic approach for search and optimization. It uses different representations, mutations, crossovers and selection mechanisms. able 1 shows the G.A. parameters taken for performance optimization. -1

Availability Optimization for Coal Handling System using Genetic Algorithm 11 able1: Genetic Algorithm Parameters for Coal Handling System Population ype: Double Vector Reproduction (Elite Count):2 Population Size: 2 to in step size of 2 Reproduction (Crossover fraction):.8 Creation Function: Uniform Mutation Probability:. Fitness Scaling: Rank Crossover Probability: Heuristic-.85 Selection: Stochastic Migration: Direction- Forward Stopping Criteria: Generation-5 to 5 in umber of Variables:8 step size 5 he failure and repair parameters of each subsystem affect the performance optimization of Coal handling system. Genetic Algorithm is hereby proposed to synchronize the failure and repair parameters of each subsystem for getting optimal availability. o use Genetic Algorithm for solving the given problem, the chromosomes are coded in real structures. he system parameters are mapped in between the specific bound [lower, upper]. he system has four constraint parameters (four failure and four repair parameters). hese parameters are optimized keeping in view the fitness function i.e., the maximum availability. he designed ranges of failure and repair rates are taken from the maintenance history sheets of the plant. Parameter Range.5-.25.-.55. Results and Discussion.2-.1.-.55.5-.5.12-..1-..8-. Firstly, the availability optimization is carried out by varying the number of generations from 5 to 5 in step size of 5. It is observed that the optimum availability of Coal handling system of..p.c plant comes out to be 98.8 % at 25 number of generations. he corresponding values of failure and repair rates are λ.11,.751, λ.22,.528, λ.5,.5, λ.1,.892, which is the best possible combination of failure and repair rates of different subsystems. he effect of number of generations on availability of Coal handling system is shown by Figure2. Secondly, the optimization is carried out by varying the population size from 2 to in step size of 2. It is evident that the best possible combination of failure and repair parameters are λ.9, μ.719, λ.215,μ.51857, λ.5191, μ.5891, λ.15, μ.72, at which the optimum value of system availability is 98.87% with population size 12. he effect of population size on system availability is shown in Figure.

1 Sanjay ajal, P. C. ewari, and Parveen Saini.99.989.988.987.98.985.98.98.982.981.98 5 1 2 25 5 5 5.99.989.988.987.98.985.98.98.982.981.98 2 8 1 12 18 umber of Generation Figure 2: Effect of umber of Generations on the Availability of Coal Handling System Population Size Figure : Effect of Population Size on the Availability of Coal Handling System 5. Conclusions he availability optimization of the Coal handling system is discussed in this paper. he steady state availability is calculated as 9.2% by putting the values of failure and repair rates taken from maintenance history sheets. Genetic algorithm is hereby used to calculate optimal value of availability, which comes out to be 98.87% i.e., the increase of 2.7%. he comparison in steady state availability and optimized availability using genetic algorithm is shown by table. able : Comparison in Steady State Availability and Optimized Availability Using G.A. System Steady state Availability Optimized Availability Using Genetic Algorithm Coal handling system 9.2% λ.5,.1, λ.2,., λ.5,., λ.1,.8 98.87% λ.9,.719, λ.215,.51857, λ.5191,.5891, λ.15,.72 he effect of number of generation and population size on system availability is also discussed in the paper. hese optimized parameters will be useful to the plant management for the timely execution of proper maintenance decisions and hence to enhance the system performance of Coal handling system. In order to achieve the optimum availability level, the corresponding repair and failure rates of the subsystems should be maintained. he failure rates can be maintained through good design, reliable machines, proper preventive maintenance schedule and providing standby components etc. he corresponding repair rates can be achieved by employing more trained workers and utilizing better repair facilities. Acknowledgement: he authors are grateful to Dr. Sudarshan Chakrobarty, A.G.M. (Piping Division),..P.C., for providing every possible help for the project. References [1] Savsar, M. Multi-State Reliability Modeling of A Manufacturing Cell. International Journal of Performability Engineering, 211; 7(): 2-228. [2] umar, D., J. Singh, and P. C. Pandey. Availability Analysis of the Washing System in the Paper Industry. Microelectronics & Reliability, 1989; 29(5): 775-778.

Availability Optimization for Coal Handling System using Genetic Algorithm 1 [] Goyal, A., and P. Gupta. Performance Evaluation of a Multi-State Repairable Production System: A Case Study. International Journal of Performability Engineering, 212; 8(): - 8. [] Dai, Y.S., and X.L. Wang. Optimal Resource Allocation on Grid Systems for Maximizing Service Reliability Using a Genetic Algorithm. Reliability Engineering and System Safety, 2; 91(9): 171-182. [5] Garg, S., J. Singh, and D.V. Singh. Availability and Maintenance Scheduling of a Repairable Block-Board Manufacturing System. International Journal of Reliability and Safety, 21; (1): 1-118. [] Juang, Y.S., S.S. Lin, and H.P. ao. A nowledge Management System for Series Parallel Availability Optimization and Design.Journal of Expert System with Application, 28; (1): 181-19. [7] Castro, H. F. and. Cavalca. Availability Optimization with Genetic Algorithm. International Journal of Quality and Reliability Management, 2; 2(7): 87-8. [8] Srinivas,. and. Deb. Multi Objective Optimization Using on Dominated Sorting in Genetic Algorithms, Evolution of Competition, 1995; 2():221-28. [9] Goldberg, D. E. Genetic Algorithm in Search Optimization and Machine Learning. Addison- Wesley Longman Publishing Co, Boston, USA, 1989. Sanjay ajal is Assistant Professor at University Institute of Engineering and echnology, urukshetra University urukshetra Haryana (India). He received his Bachelor of Engineering (B.E.) degree from D.C.R.U.S., Murthal (India) and Master of echnology from Guru anak Dev Engineering College, Jalandhar, Punjab (India). He is pursuing Ph.D. in Industrial Engineering from ational Institute of echnology, urukshetra, Haryana (India). He has 12 years of teaching and two years of Industrial experience. He has published 7 research papers in ational and International Journals. His research areas are reliability engineering, simulation modeling, stochastic behaviour of system and maintenance engineering. P. C. ewari is Professor in the Department of Mechanical Engineering at ational Institute of echnology, urukshetra, Haryana (India). He received his Bachelor of Engineering (B.E.) and M.E. from University of Roorkee (now II, Roorkee), (India) and Ph.D. from urukshetra University, urukshetra, Haryana (India). He has about 25 years of experience in teaching and research. He has published more than papers in International and ational Journals and Conferences. His fields of interests are reliability engineering, performance evaluations and optimization, decision support system, and resource allocation. Parveen Saini is presently working as Assistant Professor at Govt. Polytechnic, ilokheri. He received his Bachelor of echnology from urukshetra University, urukshetra and M.E. from SLIE, Longowal (India). He is doing Ph.D. in Industrial Engineering from ational Institute of echnology, urukshetra, Haryana (India).

1 Sanjay ajal, P. C. ewari, and Parveen Saini Appendix he difference differential equations are generated using Markov birth-death process and are as follows: i i i i i 1 1 ( ) + λ P P + P ( t ) + P P t ( ) (1) i 1 1 5 7 11 12 P ( t ) + ( λ i + ) P λ P + P + P + P + P (2) i 2 2 7 8 9 P ( t ) + ( λ i + ) P λ P + P + P + P + P () i i i 2 i i+ 1 () ( ) + λ + + P ( t ) λ P + λ P + P + P P t ( ) i 5 1 19 i 5 ( ) + λ i + + P5 λ P1 + λ P ( t ) + P + P + P ( t ) + ( λ i + ) P λ P + P + P + P + P (5) P t ( ) () ( ) + ( ) P t P t 2 i i i 5 7 i i+ 7 (7) ( ) + λ + + + P λ P + λ P + λ P + P P t ( ) ( ) ( ) + P t + P t 2 2 i 7 7 2 1 27 2 P ( t ) + ( λ i + + ) P λ P + λ P + P + P (8) P25 P ( ) ( ) λ + + i i j P t + P t P (9) For i 12, j 1; i, j 5; i 21, j ; i 27, j 7. Pi + Pi λ Pj (1) For i 9, j 2; i, j ; i 22, j ; i 2, j 7. Pi + Pi λ Pj (11) For i 8, j 1; i 1, j ; i 11, j 1; i 1, j ; i, j 5; i, j ; i 2, j ; i 25, j 7. Pi + Pi λ Pj (12) For i 18, j ; i 19, j ; i 2, j 5; i 2, j. Initial conditions at time t are 1 for i and for i