Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

Springer Science and Business Media LLC - Tập 13 - Trang 319-347 - 2011
Songlin Nie1, Jiandong Wen1, Yongping Li2, Xionghui Tang3, Guohe Huang4
1College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China
2Research Academy of Energy and Environmental Studies, North China Electric Power University, Beijing, China
3Office of Naval Represetatives in 431 Dockyard, Huludao, China
4Faculty of Engineering, University of Regina, Regina, Canada

Tóm tắt

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.

Tài liệu tham khảo

Ben-Tal A, Nemirovski A (1999) Robust solutions to uncertain linear programs. Oper Res Lett 25:1–13 Ben-Tal A, Nemirovski A (2002) Robust optimization—methodology and applications. Math Program Ser B 92:453–480 Chang NB, Wang SF (1997) A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems. J Oper Res 32:303–321 David CD (1997) Keeping hydraulic fluid clean. Plant Eng 51(3):86–88 Dubois D, Prade H (1999) Qualitative possibility theory and its applications to constraint satisfaction and decision under uncertainty. Int J Intell Syst 14(1):45–53 Frith RH, Sott W (1993) Control of solids contamination in hydraulic systems—an overview. Wear 165:69–74 Hong IT, Fitch EC (1984) Evaluation of hydraulic cylinder contaminant sensitivity. In: Proceedings of the 17th annual fluid power research conference, New York, USA, pp 380–393 Huang GH, Baetz BW, Patry GG (1995) Grey integer programming: an application to waste management planning under uncertainty. Eur J Oper Res 83:594–620 Huang GH, Chi GF, Li YP (2005a) Long-term planning of an integrated solid waste management system under uncertainty. I. Model development. Environ Eng Sci 22(6):823–834 Huang GH, Chi GF, Li YP (2005b) Long-term planning of an integrated solid waste management system under uncertainty. II. A North American case study. Environ Eng Sci 22(6):835–853 Inuiguchi M, Ichihashi H, Tanaka H (1990) Fuzzy programming: a survey of recent developments. In: Slowinski R, Teghem J (eds) Stochastic versus fuzzy approaches to multi-objective mathematical programming under uncertainty. Kluwer Academic, Dordrecht, pp 45–70 Inuiguchi M, Sakawa M (1998) Robust optimization under softness in a fuzzy linear programming problem. Int J Approx Reason 18:21–34 Jairaj PG, Vedula S (2000) Multi-reservoir system optimization using fuzzy mathematical programming. Water Resour Manage 14:457–472 Jensen JP (1996) The distribution of contaminations through a hydraulic circuit. MSc thesis, University of Science and Technology, Trondheim, Norway Kunjur A, Krishnamurty S (1997) A robust multi-criteria optimization approach. Mech Mach Theory 32(7):797–810 Leung Y (1988) Spatial analysis and planning under imprecision (studies in regional science and urban economics). Elsevier, Amsterdam Li YP, Huang GH, Veawab A (2006) Two-stage fuzzy-stochastic robust programming: a hybrid model for regional air quality management. J Air Waste Manage Assoc 56(8):1070–1082 Li YP, Huang GH, Nie SL, Mo DW (2008a) Interval-parameter robust quadratic programming for water quality management under uncertainty. Eng Optim 40(7):613–635 Li YP, Huang GH, Nie XH, Nie SL (2008b) An inexact fuzzy-robust two-stage programming model for managing sulfur dioxide abatement under uncertainty. Environ Model Assess 13:77–91 Li YP, Huang GH, Yang ZF, Nie SL (2008c) Interval-fuzzy multistage programming for water resources management under uncertainty. Resour Conserv Recycl 52(5):800–812 Li YP, Huang GH, Nie XH, Liu L, Nie SL (2008d) A two-stage fuzzy robust integer programming approach for capacity planning of environmental management systems. Eur J Oper Res 189:399–420 Liu C (1995) A system approach to monitoring and controlling of contamination/wear in hydraulic control system. PhD thesis, Monash University, Australia Liu L, Huang GH, Liu Y, Fuller GA (2003) A fuzzy-stochastic robust programming model for regional air quality management under uncertainty. Eng Optim 35(2):177–199 Luhandjula MK, Gupta MM (1996) On fuzzy stochastic optimization. Fuzzy Sets Syst 81:47–55 Matarazzo B, Munda G (2001) New approaches for the comparison of L-R fuzzy numbers: a theoretical and operational analysis. Fuzzy Sets Syst 118:407–418 Multanen P, Rinkinen J, Kangasniemi H (2000) Filtration efficiency under variable flow conditions-test series with different flow amplitudes. In: Proceedings of IFPE, Chicago, USA, pp 233–239 Negoita CV, Minoiu S, Stan E (1976) On considering imprecision in dynamic linear programming. Econ Comput Econ Cybern Stud Res 3:83–96 Nie SL, Huang GH, Zhu YQ, Li ZY, Li YP (2005) SEWHAPM: development of a water hydraulic axial piston motor for underwater tool systems. Proc Inst Mech Eng, Part C, J Mech Eng Sci 219(7):639–656 Nie SL, Huang GH, Li YP, Yang YS, Zhu YQ (2006) Research on low cavitation in water hydraulic two-stage throttle poppet valve. Proc Instn Mech Engrs, Part E, J Proc Mech Eng 220(3):167–179 Nie SL, Li YP, Shi XY, Huang GH, Hu B (2009) IPINP model for assessment of filter allocation and replacement strategies in hydraulic contamination control system under uncertainty. Proc Inst Mech Eng, Part C, J Mech Eng Sci 223(4):999–1015 Nie SL, Li YP, Xiong ZB, Huang GH, Hu B (2010a) IFQP: a hybrid optimization method for filters management in fluid power system under uncertainty. Eng Optim 42(1):45–68 Nie SL, Xiong ZB, Li YP, Huang GH (2010b) An improved fuzzy programming model with an L-R fuzzy number for filter management strategies in fluid power systems under uncertainty. Proc. Instn. Mech. Engrs., Part C. J Mech Eng Sci 224(9):2011–2026 Nirmal KM, Tapan KR (2006) A displayed inventory model with L-R fuzzy number. Fuzzy Optim Decis Mak 5:227–243 Poeth B (2005) Proactive maintenance. Fluid Power J 12(1):28–30 Rapoport EY (1995) Robust parametric optimization of dynamic systems under bounded uncertainty. Autom Remote Control 56(31/2):379–386 Saad OM (2005) An iterative goal programming approach for solving fuzzy multi-objective integer linear programming problems. Appl Math Comput 170:216–225 Tu QZ, Gong LH, Wang Q (2001) Modeling for the hydraulic contamination control system. China Mech Eng 12(6):629–631 Wu Y (1995) Equation for controlling contamination of hydraulic fluid in the hydraulic system. J China Coal Soc 20(6):647–652 Xia ZX (1992) Contamination control of hydraulic system. China Machine Press, Beijing Zhao DQ (1993) Contamination wear and control of hydraulic pump. China Coal Industry Press, Beijing (in Chinese) Yao CY, Zhao JY (2006) Application of silting principle to on-line monitoring oil contamination in hydraulic system. China Mech Eng 17(2):112–124 Zimmermann HJ (1991) Fuzzy sets theory and its application. Kluwer Academic, Dordrecht