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Fractional Order Mechanics: Motivations

Fractional Order Mechanics: Motivations. YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation) Lab MEAM/EECS, School of Engineering, University of California, Merced E : yqchen@ieee.org ; or , yangquan.chen@ucmerced.edu

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Fractional Order Mechanics: Motivations

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  1. Fractional Order Mechanics: Motivations YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)Lab MEAM/EECS, School of Engineering, University of California, Merced E: yqchen@ieee.org; or, yangquan.chen@ucmerced.edu T: (209)228-4672; O: SE1-254; Lab: Castle #22 (T: 228-4398) 8/29/2013. Thursday 09:00-11:15, KL217

  2. MESA Labhttp://mechatronics.ucmerced.edu • Mechatronics, Embedded Systems and Automation • Backup name: Mechatronics, Energy Systems and Autonomy • ASME DED, MESA TC. http://iel.ucdavis.edu/mesa/ • 2013 MESA conference: Portland, OR http://www.asmeconferences.org/IDETC2013/ ME280 "Fractional Order Mechanics" @ UC Merced

  3. MESA Lab Philosophy and Ambition • "We make real systems that work and others want them." • MESA Lab: Staying on top and for sustainability. • Nationally and internationally visible and prominent! ME280 "Fractional Order Mechanics" @ UC Merced

  4. MESA Research Areas/Strengths • Unmanned Aerial Systems and UAV-based Personal Remote Sensing (PRS) • Cyber-Physical Systems (CPS) • Modeling and Control of Renewable Energy Systems • Mechatronics • Applied Fractional Calculus (AFC) ME280 "Fractional Order Mechanics" @ UC Merced

  5. FOMech: WHY? 2001-2010 2005-2011 ME280 "Fractional Order Mechanics" @ UC Merced

  6. FOMech: WHY? ME280 "Fractional Order Mechanics" @ UC Merced

  7. Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  8. Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  9. Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  10. “Fractional Order Thinking” or, “In Between Thinking” • For example • Between integers there are non-integers; • Between logic 0 and logic 1, there is the “fuzzy logic”; • Between integer order splines, there are “fractional order splines” • Between integer high order moments, there are noninteger order moments (e.g. FLOS) • Between “integer dimensions”, there are fractal dimensions • Fractional Fourier transform (FrFT) – in-between time-n-freq. • Non-Integer order calculus (fractional order calculus – abuse of terminology.) (FOC) ME280 "Fractional Order Mechanics" @ UC Merced

  11. Conclusion of Talk Fractional-Order Calculus Integer-Order Calculus Slide credit: Richard L. Magin, ICCC12 ME280 "Fractional Order Mechanics" @ UC Merced

  12. Earth/moon • Fractional-Order Calculus • Integer-Order Calculus Discrete gears vs. constantly-variable transmission http://spectrum.ieee.org/energywise/energy/renewables/could-mechanics-best-power-electronics-in-evs Slide credit: Calvin Coopmans, 2/28/2013 email comment ME280 "Fractional Order Mechanics" @ UC Merced

  13. Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  14. We are here Fractional Calculus: a response to more advanced characterization of our more complex world at smaller scale Slide credit: Igor Podlubny MTS Seminar Series @ UCMerced

  15. Rapid development and numerous applications Slide credit: Igor Podlubny MTS Seminar Series @ UCMerced

  16. ACOUSTICS AGRICULTURAL ECONOMICS & POLICY AGRICULTURAL ENGINEERING AGRONOMY ANESTHESIOLOGY ASTRONOMY & ASTROPHYSICS AUTOMATION & CONTROL SYSTEMS BIOCHEMICAL RESEARCH METHODS BIOCHEMISTRY & MOLECULAR BIOLOGY BIOLOGY BIOPHYSICS BIOTECHNOLOGY & APPLIED MICROBIOLOGY BUSINESS BUSINESS, FINANCE CARDIAC & CARDIOVASCULAR SYSTEMS CELL BIOLOGY CHEMISTRY, ANALYTICAL CHEMISTRY, APPLIED CHEMISTRY, INORGANIC & NUCLEAR CHEMISTRY, MULTIDISCIPLINARY CHEMISTRY, ORGANIC CHEMISTRY, PHYSICAL COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE COMPUTER SCIENCE, CYBERNETICS COMPUTER SCIENCE, HARDWARE & ARCHITECTURE COMPUTER SCIENCE, INFORMATION SYSTEMS COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS COMPUTER SCIENCE, SOFTWARE ENGINEERING COMPUTER SCIENCE, THEORY & METHODS CONSTRUCTION & BUILDING TECHNOLOGY CRIMINOLOGY & PENOLOGY CRYSTALLOGRAPHY DENTISTRY, ORAL SURGERY & MEDICINE ECOLOGY ECONOMICS EDUCATION & EDUCATIONAL RESEARCH EDUCATION, SCIENTIFIC DISCIPLINES ELECTROCHEMISTRY ENERGY & FUELS ENGINEERING, AEROSPACE ENGINEERING, BIOMEDICAL ENGINEERING, CHEMICAL ENGINEERING, CIVIL ENGINEERING, ELECTRICAL & ELECTRONIC ENGINEERING, ENVIRONMENTAL ENGINEERING, GEOLOGICAL ENGINEERING, INDUSTRIAL ENGINEERING, MANUFACTURING ENGINEERING, MECHANICAL ENGINEERING, MULTIDISCIPLINARY ENGINEERING, OCEAN ENGINEERING, PETROLEUM ENVIRONMENTAL SCIENCES ENVIRONMENTAL STUDIES EVOLUTIONARY BIOLOGY FOOD SCIENCE & TECHNOLOGY GASTROENTEROLOGY & HEPATOLOGY GENETICS & HEREDITY GEOCHEMISTRY & GEOPHYSICS GEOLOGY GEOSCIENCES, MULTIDISCIPLINARY HEMATOLOGY HISTORY & PHILOSOPHY OF SCIENCE HOSPITALITY, LEISURE, SPORT & TOURISM IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY INSTRUMENTS & INSTRUMENTATION INTERNATIONAL RELATIONS LIMNOLOGY MANAGEMENT MATERIALS SCIENCE, BIOMATERIALS MATERIALS SCIENCE, CERAMICS MATERIALS SCIENCE, CHARACTERIZATION & TESTING MATERIALS SCIENCE, COATINGS & FILMS MATERIALS SCIENCE, COMPOSITES MATERIALS SCIENCE, MULTIDISCIPLINARY MATERIALS SCIENCE, TEXTILES MATHEMATICAL & COMPUTATIONAL BIOLOGY MATHEMATICS MATHEMATICS, APPLIED MATHEMATICS, INTERDISCIPLINARY APPLICATIONS MECHANICS MEDICAL INFORMATICS MEDICINE, RESEARCH & EXPERIMENTAL METALLURGY & METALLURGICAL ENGINEERING METEOROLOGY & ATMOSPHERIC SCIENCES MINERALOGY MINING & MINERAL PROCESSING MULTIDISCIPLINARY SCIENCES MYCOLOGY NANOSCIENCE & NANOTECHNOLOGY NEUROSCIENCES NUCLEAR SCIENCE & TECHNOLOGY OCEANOGRAPHY ONCOLOGY OPERATIONS RESEARCH & MANAGEMENT SCIENCE OPHTHALMOLOGY OPTICS ORNITHOLOGY PERIPHERAL VASCULAR DISEASE PHARMACOLOGY & PHARMACY PHYSICS, APPLIED PHYSICS, ATOMIC, MOLECULAR & CHEMICAL PHYSICS, CONDENSED MATTER PHYSICS, FLUIDS & PLASMAS PHYSICS, MATHEMATICAL PHYSICS, MULTIDISCIPLINARY PHYSICS, NUCLEAR PHYSICS, PARTICLES & FIELDS PHYSIOLOGY PLANNING & DEVELOPMENT PLANT SCIENCES POLITICAL SCIENCE POLYMER SCIENCE PSYCHOLOGY, EXPERIMENTAL PSYCHOLOGY, MATHEMATICAL PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING REMOTE SENSING RESPIRATORY SYSTEM ROBOTICS SOCIAL SCIENCES, INTERDISCIPLINARY SOCIAL SCIENCES, MATHEMATICAL METHODS SOCIOLOGY SOIL SCIENCE SPECTROSCOPY SPORT SCIENCES STATISTICS & PROBABILITY SURGERY TELECOMMUNICATIONS THERMODYNAMICS TRANSPORTATION SCIENCE & TECHNOLOGY URBAN STUDIES WATER RESOURCES Fractional Calculus in WoK: 136 subject areas (applications) Slide credit: Igor Podlubny MTS Seminar Series @ UCMerced

  17. The current map of the fractional calculus ALGERIA ARGENTINA AUSTRALIA AUSTRIA BELGIUM BRAZIL BULGARIA BYELARUS CANADA CHILE CROATIA CUBA CZECH REP DENMARK EGYPT ENGLAND ESTONIA FINLAND FRANCE GERMANY GREECE GUADELOUPE HUNGARY INDIA IRAN IRELAND ISRAEL ITALY JAPAN JORDAN KUWAIT LEBANON LITHUANIA MACEDONIA MALAYSIA MEXICO MOROCCO NETHERLANDS NEW ZEALAND NIGERIA NORTH IRELAND NORWAY PAKISTAN P.R. CHINA POLAND PORTUGAL QATAR ROMANIA RUSSIA SAUDI ARABIA SCOTLAND SERBIA MONTENEG SINGAPORE SLOVAKIA SLOVENIA SOUTH AFRICA SOUTH KOREA SPAIN SWEDEN SWITZERLAND TAIWAN THAILAND TUNISIA TURKEY TURKMENISTAN U ARAB EMIRATES UKRAINE USA UZBEKISTAN VENEZUELA VIETNAM WALES YUGOSLAVIA Slide credit: Igor Podlubny MTS Seminar Series @ UCMerced Data Source: Web of Knowledge

  18. FOMs and Fractional Order Controls • IO Controller + IO Plant • FO Controller + IO Plant • FO Controller + FO Plant • IO Controller + FO Plant Concepcin A. Monje, YangQuan Chen, Blas Vinagre, Dingyu Xue and Vicente Feliu (2010). “Fractional Order Systems and Controls - Fundamentals and Applications.” Advanced Industrial Control Series, Springer-Verlag, www.springer.com/engineering/book/978-1-84996-334-3 (2010), 415 p. 223 ill.19 in color. ME280 "Fractional Order Mechanics" @ UC Merced

  19. Rule of thumb for Fractional Order Thinking • Porous media • Particulate • Granular • Lossy • Anomaly • Disorder • Soil, tissue, electrodes, bio, nano, network, transport, diffusion, soft matters (biox) … • Self-similar • Scale-free/Scale-invariant • Power law • Long range dependence (LRD) • 1/f a noise ME280 "Fractional Order Mechanics" @ UC Merced

  20. Fractional Order Mechanics: WHY? • Softmatter / hardmatter • Softbody / Rigidbody • Lumped / distributed • Granular, particulate, porous, disordered … materials • … ME280 "Fractional Order Mechanics" @ UC Merced

  21. Soft matter？ • Soft matters, also known as complex fluids, behave unlike ideal solids and fluids. • Mesoscopic macromolecule rather than microscopic elementary particles play a more important role. ME280 "Fractional Order Mechanics" @ UC Merced

  22. Typical soft matters • Granular materials • Colloids, liquid crystals, emulsions, foams, • Polymers, textiles, rubber, glass • Rock layers, sediments, oil, soil, DNA • Multiphase fluids • Biopolymers and biological materials highly deformable, porous, thermal fluctuations play major role, highly unstable ME280 "Fractional Order Mechanics" @ UC Merced

  23. ME280 "Fractional Order Mechanics" @ UC Merced Slide credit: Wen Chen of HHU

  24. Constitutive relationships • Hookian law in ideal solids: • Ideal Newtonian fluids: • Newtonian 2nd law for rigid solids: • One model of soft matter: Slide credit: Wen Chen of HHU ME280 "Fractional Order Mechanics" @ UC Merced

  25. Fractional Order Mechanics! Going in-between: interpolation of operators: ME280 "Fractional Order Mechanics" @ UC Merced

  26. Kurt Lewin: “There is nothing so practical as good theory" (p. 169). • Lewin, K. (1951). Field theory in social science. New York: Harper & Row. ME280 "Fractional Order Mechanics" @ UC Merced

  27. Google says“Fractional Order Mechanics” ME280 "Fractional Order Mechanics" @ UC Merced

  28. G.W. Scott Blair (1950) • “We may express our concepts in Newtonian terms if we find this convenient but, if we do so, we must realize that we have made a translation into a language which is foreign to the system which we are studying.” ME280 "Fractional Order Mechanics" @ UC Merced

  29. Key reference links • CDC10 tutorial: http://mechatronics.ece.usu.edu/foc/cdc10tw/ • http://people.tuke.sk/igor.podlubny/USU/ • http://mechatronics.ece.usu.edu/foc/afc/ • http://www.wydawnictwa.pcz.pl/book/102/introduction-fractional-mechanics • FDA Express: http://em.hhu.edu.cn/fda/ • ICFDA2014 http://www.icfda14.dieei.unict.it/committee.html ME280 "Fractional Order Mechanics" @ UC Merced

  30. FOMech: What should be included in the course? • At UC Merced, ME280 “Fractional Order Mechanics” will be officially offered from Fall 2013 by Prof. YangQuan Chen. (was VOM) • We are defining this course right now with some initial thinking ME280 "Fractional Order Mechanics" @ UC Merced

  31. TOC of ME280 FOMech • FC basics; FC signals and systems • FC modeling (ML fitting) of complex relaxation processes • Bagley-Torvik mechanics • Fractional Euler-Lagrange Equation • Advanced topics (application oriented) (FISP – focused independent study and presentation) • Battery system models, biological signal processing • Fractional Order ESC, nanomaterial modeling • Salinity dynamics, complexity quantification • Hysteresis modeling and compensation • FO stochastic mechanics for evolving complex networks etc. ME280 "Fractional Order Mechanics" @ UC Merced

  32. FOMech: WHEN? • Self-similar • Scale-free/Scale-invariant • Power law • Long range dependence (LRD) • 1/f a noise • Porous media • Particulate • Granular • Lossy • Anomaly • Disorder • Soil, tissue, electrodes, bio, nano, network, transport, diffusion, soft matters (biox) … ME280 "Fractional Order Mechanics" @ UC Merced

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