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ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) – Part

ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) – Part-3. YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation) Lab ME/EECS/SNRI/ UCSolar , School of Engineering, University of California, Merced

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ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) – Part

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  1. ME280: Fractional Order Mechanics General Motivations on Fractional Calculus and Fractional Order Thinking (FOT) –Part-3 YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)Lab ME/EECS/SNRI/UCSolar, 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) 09/10/2013. Tuesday 09:00-10:15, KL217

  2. Fractional calculus is around us? • Example-1: Heat equation (Irrational TF) • Example-2: Isodamping in motion control • Example-3: Nanoparticle manufacturing • Example-4: Biomechatronics • Example-5: Biocorrosion/Bioimagingchemotaxis • Example-6: Energy informatics • … ME280 "Fractional Order Mechanics" @ UC Merced

  3. USU Material Research Laboratory • Materials Processing, Heat Treating, Materials Joining, and Powder Metallurgy Studies using the Gleeble 1500D System Source: http://www.mae.usu.edu/faculty/leijun/gleeble.html NSF NER: Solid-state synthesis of nano-scale hydrogen storage materials by bulk mechanical alloying http://www.mae.usu.edu/faculty/leijun/ ME280 "Fractional Order Mechanics" @ UC Merced

  4. Fractional order calculus? • Dynamic force measurements vs. strokes Data credit: Leijun Li ME280 "Fractional Order Mechanics" @ UC Merced

  5. Fractional order vs. strokes ME280 "Fractional Order Mechanics" @ UC Merced

  6. Big picture of nanoparticle manufacturing • Now: given cycles, given stroke profile, see how particulate process evolves. • Future: Production process development – given final particle grain size distribution, how to achieve this by using minimum number of cycles with possible cycle-to-cycle, or run-to-run (per several cycles) adaptive learning control with variable stroke profiles. ME280 "Fractional Order Mechanics" @ UC Merced

  7. Fractional order ILC (iterative learning control)? • D-alpha type ILC with a (really good) reason?! • YangQuan Chen and Kevin L. Moore. ``On Dα-type Iterative Learning Control''. Presented at the IEEE Conference on Decision and Control (CDC'01), Dec. 3-7, 2001, Orlando, FL, USA. pp.4451-4456. http://www.csois.usu.edu/publications/pdf/pub054.pdf ME280 "Fractional Order Mechanics" @ UC Merced

  8. Fractional calculus is around us? • Example-1: Heat equation (Irrational TF) • Example-2: Isodamping in motion control • Example-3: Nanoparticle manufacturing • Example-4: Biomechatronics • Example-5: Biocorrosion/Bioimagingchemotaxis • Example-6: Energy informatics • … ME280 "Fractional Order Mechanics" @ UC Merced

  9. Biomechatronics Electronically controlled leg and hand prosthesis, neural prosthesis, retinal implants, assistive and rehabilitative robots … -- “Emerging Trends and Innovations in Biomechatronics” by Frost & Sullivan Source: http://www-personal.umich.edu/~ferrisdp/NSF/research.htm ME280 "Fractional Order Mechanics" @ UC Merced

  10. Biomechatronics • Biomechatronics is the interdisciplinary study of biology, mechanics, and electronics. Biomechatronics focuses on the interactivity of biological organs (including the brain) with electromechanical devices and systems. • Universities and research centers worldwide have taken notice of biomechatronics in light of its potential for development of advanced medical devices and life-support systems. ME280 "Fractional Order Mechanics" @ UC Merced

  11. Fractional Order Identification of Human Arm Dynamics Inés Tejado ♦ Duarte Valério Košice, April 4, 2013

  12. How (1) • Subjects (two people by the way) are required to keep the laser point steady during 40 s • The motor exerts a random force in the [0.12,15] Hz bandwidth • This random force precludes predicting what the perturbation will be • The force applied by the robot and the angle of the arm are measured with a 2 kHz sampling frequency

  13. How (2) The motor is controlled to eliminate its dynamics from the loop, because it is the arm we want to identify, not the motor or the friction.

  14. How (3)

  15. Levy’s method (1) Firstly, a frequency response is found from each time response. • Welch’s method

  16. Levy’s method (2) Then the model is found minimising Including order  among parameters would lead to a nonlinear minimisation. So different models are tried (up to 3rd order models) and the best result chosen.

  17. Conclusion Fractional models obtain equally good fits, with less parameters. There are theoretical reasons to suppose fractional models make sense.

  18. ISBN 1-56700-215-3 ; 978-1-56700-215-7 ME280 "Fractional Order Mechanics" @ UC Merced

  19. I really like this paper by Richard Magin: Fractional calculus in bioengineering: A tool to model complex dynamics Magin, Richard L.Carpathian Control Conference (ICCC), 2012 13th International Digital Object Identifier: 10.1109/CarpathianCC.2012.6228688 Publication Year: 2012 , Page(s): 464 - 469 ME280 "Fractional Order Mechanics" @ UC Merced

  20. Books by Bruce J. West • 2006. Where Medicine Went Wrong: Rediscovering the Path to Complexity (Studies of Nonlinear Phenomena in Life Science) • 2003. Biodynamics: Why the Wirewalker Doesn't Fall • 1995. The Lure of Modern Science: Fractal Thinking (Studies of Nonlinear Phenomena in Life Sciences, Vol 3) • 1994. Fractal Physiology • 1991. Fractal Physiology & Chaos in Medicine (Studies of Nonlinear Phenomena in Life Science, vol. 1) • 1986. An Essay on the Importance of Being Nonlinear (Lecture Notes in Biomathematics) ME280 "Fractional Order Mechanics" @ UC Merced

  21. Biocorrosion /Bioimplants X.Y.Zhou, et al./ Corros. Sci. 44(2002) 841-860 Biocompatibility study needs a non-destructive method – Electrochemical noise (ECN) measurement offers unique advantages ! Slide credit: A. Zhou ME280 "Fractional Order Mechanics" @ UC Merced

  22. Chemotaxis characterization Zhou, A. (PI), Chen, Y.Q., Sims, R., Miller, C. NIH R15 Grant# ES013688-01A1 (2006-2009) Slide credit: A. Zhou ME280 "Fractional Order Mechanics" @ UC Merced

  23. For more FOSP and applications, see • http://mechatronics.ece.usu.edu/foc/fospbook/ • Hu Sheng, YangQuan Chen and TianshuangQiu“Fractional Processes and Fractional Order Signal Processing: Techniques &Applications” • Foreword by Professor Richard L. Magin • Springer-Verlag (2011) • 318 pages ME280 "Fractional Order Mechanics" @ UC Merced

  24. Now, energy informatics • Energy Informatics http://cei.usc.edu/ • “Energy+Information < Energy” • energy experts, • computer scientists, and • social and behavioral studies experts • Papers/articles (as of 3/3/2011) • ISI: 3 ; ScienceDirect: 37; ieeeXplore: 6 ; Google: 3280; GoogleScholar: 193 ME280 "Fractional Order Mechanics" @ UC Merced

  25. “data mining” @ ieeeXplore (x1000) • Control/820; network/1100; signal/1087; comm*/1182;energy/847; power/1013; system/2117; circuit/1439; education/50; • Kalman/15; Lyapunov/15; Kharitonov/0.328; Youla/0.337 • Observer/14; feedforward/15; feedback/105; optim*/325 • Adaptive/118; nonlinear/149;stability/123; linear/195; robust/83 • Fuzzy/55; neural/94; cybernetics/35; physical/82; chemical/83 • Friction/10; hyster*/19; dead*/13; vision/63; image/297;pattern/177 • PID/7; UAV/2; interval/26; anomal*/12.3; random/82; stochastic/40 • Geometrical/17; algebraic/11; math*/667; fluctuation/30; noise/202 • Forecast/21.4; demand/56.6; behavi*/143; social/18.5 ME280 "Fractional Order Mechanics" @ UC Merced

  26. Signal -> Information -> Knowledge -> Wisdom • Signals are from man-made large scale, complex systems, usually LRD (long range dependent) • Enabled by “cyberinfrastructure”, anything, anytime, anywhere • Information is the third essence of the natural world supplementing matter and energy • Extract from signals considering FOSP! • Knowledge is in particular useful in social context (behavior, policy level) • Put information in (social) context • Wisdom: ? ME280 "Fractional Order Mechanics" @ UC Merced

  27. Opportunities • Battery Management Systems • Demand/load forecast • FOSP for FLOM processes; LRD + infinite variance • Inference from variability • Hypothesis in social contexts • Social behavior modeling (energy consumption/conservation) • Culture model (energy consumption) • Policy implications, optimal trading/pricing etc. ME280 "Fractional Order Mechanics" @ UC Merced

  28. So, what’s beyond? ME280 "Fractional Order Mechanics" @ UC Merced

  29. Rule of thumb for Fractional Order Thinking – about everything • 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

  30. Concluding remarks • “Go west, young man.” – Horace Greeley • “Go Fractional.” – YangQuan Chen • Fractional Order Thinking enables exciting multidiscipline joint research that matters! Do more and do better!! ME280 "Fractional Order Mechanics" @ UC Merced

  31. To probe further Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  32. We are here Fractional Calculus: a response to more advanced characterization of our more complex world at smaller scale Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  33. Rapid development and numerous applications Slide credit: Igor Podlubny ME280 "Fractional Order Mechanics" @ UC Merced

  34. 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 ME280 "Fractional Order Mechanics" @ UC Merced

  35. 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 ME280 "Fractional Order Mechanics" @ UC Merced Data Source: Web of Knowledge

  36. Key reference links • http://mechatronics.ucmerced.edu/research/applied-fractional-calculus • CDC10 tutorial: http://mechatronics.ece.usu.edu/foc/cdc10tw/ • http://mechatronics.ece.usu.edu/foc/afc/ • FDA Express: http://em.hhu.edu.cn/fda/ • ICFDA2014: http://www.icfda14.dieei.unict.it/committee.html ME280 "Fractional Order Mechanics" @ UC Merced

  37. Igor Podlubny’s online lectures • http://people.tuke.sk/igor.podlubny/ravello2012/ • Recorded lecture with slides, MATLAB codes • Excellent lecture notes 170+ pages http://people.tuke.sk/igor.podlubny/ravello2012/podlubny-ravello2012-LN-draft-20121002.pdf • Utah State University full summer course http://people.tuke.sk/igor.podlubny/USU/ ME280 "Fractional Order Mechanics" @ UC Merced

  38. Gorenflo Master Piece LecturesBack to fundamentals! • http://web.tuke.sk/fda10/activities.html • Slides were type-set in nice PDF slides form. ME280 "Fractional Order Mechanics" @ UC Merced

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