Computing fuzzy trajectories for nonlinear dynamic systems

Computers and Chemical Engineering - Tập 52 - Trang 10-25 - 2013
D. Andrei Măceş1, Mark A. Stadtherr1
1Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

Tài liệu tham khảo

Andujar, 2005, Multivariable fuzzy control applied to the physical–chemical treatment facility of a cellulose factory, Fuzzy Sets and Systems, 150, 475, 10.1016/j.fss.2004.03.023 Anile, 1995, Implementing fuzzy arithmetic, Fuzzy Sets and Systems, 72, 239, 10.1016/0165-0114(94)00355-B Arva, 1987, Fuzzy valued relational algebrae in chemical-engineering, Hungarian Journal of Industrial Chemistry, 15, 1 Berz, 1998, Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models, Reliable Computing, 4, 361, 10.1023/A:1024467732637 Chang, 2006, α-Cut fuzzy arithmetic: Simplifying rules and a fuzzy function optimization with a decision variable, IEEE Transactions on Fuzzy Systems, 14, 496, 10.1109/TFUZZ.2006.876743 Chen, 2006, Fuzzy diagnosis method for control systems with coupled feed forward and feedback loops, Chemical Engineering Science, 61, 3105, 10.1016/j.ces.2005.11.062 Chen, 2001, Advanced hybrid fuzzy-neural controller for industrial wastewater treatment, Journal of Environmental Engineering, 127, 1048, 10.1061/(ASCE)0733-9372(2001)127:11(1048) Claudel, 2003, Application of the possibility theory to the compartment modelling of flow pattern in industrial processes, Chemical Engineering Science, 58, 4005, 10.1016/S0009-2509(03)00269-0 Dohnal, 1994, A revitalization of chemical-engineering knowledge with fuzzy calculus, The Chemical Engineering Journal, 54, 155 Dong, 1987, Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, 24, 65, 10.1016/0165-0114(87)90114-X Dubois, 2004, Probability–possibility transformations, triangular fuzzy sets, and probabilistic inequalities, Reliable Computing, 10, 273, 10.1023/B:REOM.0000032115.22510.b5 Dubois, 1978, Operations on fuzzy numbers, International Journal of Systems Science, 9, 613, 10.1080/00207727808941724 Dubois, 1979, Fuzzy real algebra: Some results, Fuzzy Sets and Systems, 2, 327, 10.1016/0165-0114(79)90005-8 Dubois, 1980 Dubois, 1982, On several representations of an uncertain body of evidence, 167 Ferson, 2002 Ferson, S., Ginzburg, L., & Akçakaya, R. (1996). Whereof one cannot speak: When input distributions are unknown. Technical report. Setauket, NY: Applied Biomathematics. Available at www.ramas.com/whereof.pdf. Gromov, 1995, Theory of fuzzy sets in control of chemical engineering processes, Theoretical Foundations of Chemical Engineering, 29, 503 Gromov, 1996, Mathematical modeling of chemical-engineering units under uncertainty, Theoretical Foundations of Chemical Engineering, 30, 75 Guimarães, 2004, Fuzzy FMEA applied to PWR chemical and volume control system, Progress in Nuclear Energy, 44, 191, 10.1016/S0149-1970(04)90010-8 Gupta, 1993, A note on the transformation of possibilistic information into probabilistic information for investment decisions, Fuzzy Sets and Systems, 56, 175, 10.1016/0165-0114(93)90142-5 Hanratty, 1992, Decision making in chemical engineering and expert systems – Application of the analytic hierarchy process to reactor selection, Computers and Chemical Engineering, 16, 849, 10.1016/0098-1354(92)80037-A Hanratty, 1992, Knowledge representation and reasoning in the presence of uncertainty in an expert system for laboratory reactor selection, Industrial and Engineering Chemistry Research, 31, 228, 10.1021/ie00001a033 Hansen, 2004 Hanss, 2002, The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets and Systems, 130, 277, 10.1016/S0165-0114(02)00045-3 Hanss, 2005 Hassana, 2009, Inclusion of human errors assessment in failure frequency analysis – A case study for the transportation of ammonia by rail in Malaysia, Process Safety Progress, 28, 60, 10.1002/prs.10268 Henson, 1997, Feedback linearizing control, 149 Jaulin, 2001 Johansen, 1997, Operating regime based process modeling and identification, Computers and Chemical Engineering, 21, 159, 10.1016/0098-1354(95)00260-X Kaucsár, 2007, Fuzzy logic used to control a n-15 isotope separation plant, Revista de Chimie, 58, 809 Kaufmann, 1985 Kearfott, 1996 Klir, 1992, Probability-possibility transformations: A comparison, International Journal of General Systems, 21, 291, 10.1080/03081079208945083 Kosheleva, 1997, Fast implementations of fuzzy arithmetic operations using fast fourier transform (FFT), Fuzzy Sets and Systems, 91, 269, 10.1016/S0165-0114(97)00147-4 Li, 2004, Computer arithmetic for probability distribution variables, Reliability Engineering and System Safety, 85, 191, 10.1016/j.ress.2004.03.012 Lin, 2007, Validated solutions of initial value problems for parametric ODEs, Applied Numerical Mathematics, 57, 1145, 10.1016/j.apnum.2006.10.006 Makino, 1996, Remainder differential algebras and their applications, 63 Makino, 1999, Efficient control of the dependency problem based on Taylor model methods, Reliable Computing, 5, 3, 10.1023/A:1026485406803 Makino, 2003, Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, 4, 379 Makino, K., & Berz, M. (2004). Taylor model range bounding schemes. Presented at third international workshop on Taylor methods. Miami Beach, FL, USA. http://bt.pa.msu.edu/TM/Miami2004/TM-Slides/Miami-GO04.pdf. Makino, 2005, Verified global optimization with Taylor model-based range bounders, Transactions on Computers, 11, 1611 Meel, 2006, Plant-specific dynamic failure assessment using Bayesian theory, Chemical Engineering Science, 61, 7036, 10.1016/j.ces.2006.07.007 Moore, 2009 Nahmias, 1977, Fuzzy variables, Fuzzy Sets and Systems, 1, 97, 10.1016/0165-0114(78)90011-8 Nedialkov, N. S. (1999). Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. PhD thesis. University of Toronto. Nedialkov, 2001, An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE, Reliable Computing, 7, 449, 10.1023/A:1014798618404 Neher, 2007, On Taylor model based integration of ODEs, SIAM Journal on Numerical Analysis, 45, 236, 10.1137/050638448 Neumaier, 1990 Neumaier, 2003, Taylor forms – Use and limits, Reliable Computing, 9, 43, 10.1023/A:1023061927787 Otto, 1993, Approximating α-cuts with the vertex method, Fuzzy Sets and Systems, 55, 43, 10.1016/0165-0114(93)90300-7 Rauh, 2009, A novel interval arithmetic approach for solving differential-algebraic equations with ValEncIA-IVP, International Journal of Applied Mathematics and Computer Science, 19, 381, 10.2478/v10006-009-0032-4 Sahlodin, 2011, Convex/concave relaxations of parametric ODEs using Taylor models, Computers and Chemical Engineering, 35, 844, 10.1016/j.compchemeng.2011.01.031 Sahlodin, 2011, Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs, Applied Numerical Mathematics, 61, 803, 10.1016/j.apnum.2011.01.009 Sanjuan, 2006, Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module, Engineering Applications of Artificial Intelligence, 19, 323, 10.1016/j.engappai.2005.09.003 Schmitz, 1998, Neurofuzzy modeling of chemical process systems with ellipsoidal radial basis function neural networks and genetic algorithms, Computers and Chemical Engineering, 22, S1001, 10.1016/S0098-1354(98)00200-2 Seng, 2007, Simulating pharmacokinetic and pharmacodynamic fuzzy-parameterized models: A comparison of numerical methods, Journal of Pharmacokinetics and Pharmacodynamics, 34, 595, 10.1007/s10928-007-9061-5 Stephane, 2008, Case-based reasoning for chemical engineering design, Chemical Engineering Research and Design, 86, 648, 10.1016/j.cherd.2008.02.011 Takeda, 1994, Robust fault diagnosis for the chemical plant based on the qualitative model, Kagaku Kogaku Ronbunshu, 20, 373, 10.1252/kakoronbunshu.20.373 Tsekouras, 2002, A fuzzy logic approach for the classification of product qualitative characteristics, Computers and Chemical Engineering, 26, 429, 10.1016/S0098-1354(01)00762-1 Vrba, 1991, FUSIM – A program for fuzzy linguistic modeling and simulation of technological processes, Systems Analysis Modelling Simulation, 8, 115 Williamson, 1990, Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds, International Journal of Approximate Reasoning, 4, 89, 10.1016/0888-613X(90)90022-T Wood, 1992, Engineering design calculations with fuzzy parameters, Fuzzy Sets and Systems, 52, 1, 10.1016/0165-0114(92)90031-X Yang, 1993, Calculating functions of fuzzy numbers, Fuzzy Sets and Systems, 55, 273, 10.1016/0165-0114(93)90253-E Yong, 2007, Fault diagnosis based on fuzzy support vector machine with parameter tuning and feature selection, Chinese Journal of Chemical Engineering, 15, 233, 10.1016/S1004-9541(07)60064-0 Yu, 1991, Fault diagnosis based on qualitative quantitative process knowledge, AIChE Journal, 37, 617, 10.1002/aic.690370415 Zadeh, 1965, Fuzzy sets, Information and Control, 8, 338, 10.1016/S0019-9958(65)90241-X Zadeh, 1975, The concept of a linguistic variable and its application to approximate reasoning – Part I, Information Sciences, 8, 199, 10.1016/0020-0255(75)90036-5 Zadeh, 1975, The concept of a linguistic variable and its application to approximate reasoning – Part II, Information Sciences, 8, 301, 10.1016/0020-0255(75)90046-8 Zadeh, 1975, The concept of a linguistic variable and its application to approximate reasoning – Part III, Information Sciences, 9, 43, 10.1016/0020-0255(75)90017-1 Zadeh, 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3, 10.1016/0165-0114(78)90029-5 Zhang, 2006, From multi-scale methodology to systems biology: To integrate strain improvement and fermentation optimization, Journal of Chemical Technology and Biotechnology, 81, 734, 10.1002/jctb.1440