MODELING PPT ON REHABILITATION ENGINEERING

Open Elective PPT for Rehabilitation Engineering

1. DIFERENCE BETWEEN PHILOSOPHY AND ENGINEERING IS THAT PHILOSOPHY DEALS WITH QUALITATIVE AND CONCEPTUAL WAYS of study where as ENGINEERING DEALS WITH QUANTITATIVE AND MEASURABLE WAYS of study MODELING AN INTRODUCTION 1

2. MODELS HELP TO CONVERT THE QUALITATIVE CONCEPTS INTO NUMERICAL VALUES THROUGH WELL DEFINED EQUATIONS OR INEQUALITIES THEREBY ENABLING A PRECISE MATHEMATICAL ANALYSIS and analytical studies. USE OF MODELS 2

3. THE PLACE OF MODELING IN TECHNOLGY IS IN BETWEEN QUALITATIVE CONCEPTS AND QUANTITATIVE CONCEPTS AS AN INTERFACING TOOL BETWEEN THEM. PLACE OF MODELING 3

4. MODEL OF A PHENOMENON HELPS TO STUDY THAT PHENOMENON INDIRECTELY . 4

5. MODEL HELPS TO STUDY ENGINEERING PROBLEMS IN A SIMPLE AND EASY WAY. UTILITY OF MODELS 5

6. MODEL IS A REPRESENTATION OF WHAT ARE FELT TO BE THE IMPORTANT FEATURES OF THE OBJECT OR THE SYSTEM UNDER STUDY. DEFINITION 6

7. BY THE MATHEMATICAL MANUPULATION OF THE REPRESENTATION, IT IS HOPED THAT NEW KNOWLEDGE ABOUT THE MODELLED PHENOMENON CAN BE OBTAINED WITHOUT THE RISK,COST OR INCONVENIENCE OF MANUPULATING THE REAL PHENOMENON ITSELF. ADVANTEGES OF MODELING 7

8. 1 USE OF GEOGRAPHICAL MAPS IN TOWN PLANING, MODIFICATION, URBAN DEVELOPMENT ETC. 2 USE OF ECG,X RAY OR SCAN PHOTOGRAPHS IN MEDICAL FIELD 3 IN ASTRONOMY, models of birth, death, and MODELS OF interaction of stars ALLOW EVALUATION OF HYPOTHESES WHICH WOULD TAKE LONG TIME AND MASSIVE AMOUNT OF FINANCIAL AND TECHNICAL RESOURCES IF DONE IN REAL TIME. EXAMPLES OF THE USE OF MODELING 8

9. MODELS help the studies in NUCLEAR PHYSICS SIGNIFICANTLY,WHERE THE RADIOACTIVE ATOMIC AND SUB ATTOMIC PARTICLES UNDER STUDY EXIST ONLY FOR A VERY SHORT PERIODE OF TIME. models help studies IN sociology and biology in a similar way. 9

10. IMPORTANT FEATURES of MANY PHYSICAL PHENOMENA CAN BE DESCRIBED NUMERICALLY with the help OF MATHEMATICAL MODELS. EXAMPLE:- EQUATION TO A STRIGHT LINE, CIRCLE. USE OF MATHEMATICS IN MODELING 10

11. MATHEMATICAL EXPRESSIONS OF THE PROPERTIES SUCH AS MASS,POSITION,MOMENTUM,ACCELARATION FORCE ,ETC. IMPORTANT FEATURES / RELATIONSHIPS EXISTING IN PHYSICAL PHENOMENA CAN BE DESCRIBED BY INEQUALITIES/ EXPRESSIONS/EQUATIONS. POPULAR MODELS---TO BE CITED AS EXAMPLES 11

12. HOWEVER, TO SUCCESSFULLY UTILIZE THE MODELLING APPROACH REQUIRES A KNOWLEDGE OF BOTH THE MODELED PHENOFEINA AND THE PROPERTIES OF THE MODELING TECHNIQUES. PREREQUSITE FOR DEVELOPING A SUCCESSFUL MODEL 12

13. MATHEMATICS HAS DEVELOPED AS A SCIENCE IN PART BECAUSE OF ITS USEFULNESS IN MODELLING THE PHENOMENA OF OTHER SCIENCES. FOR EXAMPLE:- DIFFERENTIAL CALCULUS WAS DEVELOPED IN DIRECT RESPONSE TO THE NEED FOR A MEANS OF MODELING CONTINUOUSLY CHANGING PROPERTIES SUCH AS POSITION,VELOCITY AND ACCELARATION IN PHYSICS. IMPORTANCE OF MATHEMATICS IN MODELING 13

14. DEVELOPMENT OF HIGH SPEED COMPUTERS HAS GREATELY INCREASED THE USE AND USEFULNESS OF MODELING. BY REPRESENTING A SYSTEM AS A MATHEMATICAL MODEL ,CONVERTING THAT MODEL INTO INSTRUCTIONS FOR A COMPUTER, AND RUNNING THE COMPUTER, IT IS POSSIBLE TO MODEL LARGER AND MORE COMPLEX SYSTEMS THAN EVER BEFORE. IMPORTANCE OF COMPUTERS IN MODELING 14

15. IN BRIEF MODELS HELP TO DEVELOP 1)NEW SYSTEMS, 2)ANLYSE THE PERFORMANCE OF EXISTING SYSTEMS, 3)IMPROVE THE SYSTEMS BY MODIFYING THE CURRENT DESIGN ETC. 4) IMPROVE THE PERFORMANCE OF THE SYSTEMS. CONCLUSION 15

16. EXAMPLES ONE :- Models helps to improve the performance of the systems. A typical example is the utilization of dynamic models for the balancing of electrical distribution system. 16 MODELS FOR IMPROVEMENTS OF THE SYSTEM

17. The description given here is purely the research findings of the department of electrical engineering ,n I t Calicut, Kerala. 17 RESEARCH RESULT

18. Model selected for the purpose is the Nth order linear differential equation with constant coefficients. 18 MODEL SELECTED

19. MOST POPULAR MATHEMATICAL MODEL WIDELY USED FOR THE STUDY OF MEASUREMENT SYSTEM DYNAMIC RESPONSE IS THE ORDINARY LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS. 19 POPULAR MATHEMATICAL MODEL

20. THE MODEL IS EXTENDED TO THE STUDY OF OUTPUT DYNAMICS OF A DISTRIBUTION SYSTEM 20 EXTENDED TO THE STUDY OF OUTPUT RESPONSE

21. It is assumed that the relation between any particular input and the out put can, by application of suitable simplifying assumption be put in the form of a :- (…………………………………………………………………..) (Write linear diferential equation here) 21 ASSUMPTION

22. The philosophy mentioned above is extended as the dynamic study of the output to any input of any system can be studied by representing the out put by a linear differential equation with suitable assumption. OR The system out put dynamics can be modeled approximately as a linear differential equation OR The linear differential equation can be considered as a model ( apprximate ) for the dynamic out put response of a system. 22

23. The differential equation is interpreted as an infinite series consisting of Base term having no differential term A term containing a variational term(first differential) A term containing second differential term Terms containing infinite differential term` The coefficients(which are constants) represents the combination of system physical parameters 23 ANALYSIS

24. It is interpreted as follows The dynamic output response is the summation of an infinite number of components involving a base term subsequently followed by infinite number of variational terms. 24 INTERPRATION

25. This is utilized for the balancing purpose 25

26. T he model is modified as follows. The continuous differential terms are suitably modified as digital variational terms 26 Appropriate modifications

27. H ere in this slide write the modified equation model in digital forms (………………………………………………………………………) Write the modified differential equation in digital form 27 Modified diferential equation in digital forms

28. Hence the model will become as an infinite series consists of an infinite summation of a base term plus first variational term plus second variational term etc. Etc……. 28 Modified model

29. Measure the out put for definite time period 29

30. Divide them into different sectors As sector1, sector2, sector3, etc. 30

31. Find the average of the readings of sector 1 as a1 Similarly of Sector2 as a2 And so on. 31

32. Determine the average a1,a2 etc as a And this a is taken as the base term 32 AVERAGE VALUE

33. These values A1 , A2 etc. are used to find the first term 33 Formation of first term

34. From the readings identify the secondary sectors From the secondary sectors find the first variational term A11,A22 etc, i.e second term of the model 34 FIRST VARIATIONAL TERM

35. U sing the tertiary sector find third variational term A111,A222 , etc 35 Formation of tertiary sector

36. Using these sets of values form three equations and solving them will provide the constant coefficients. 36 DETERMINATION OF COEFICIENTS

37. The number of variational terms are decided by the accuracy demanded by the system. Here it is selected as three 37 Number of variational term

38. DISTRIBUTION NET WORK OF KERALA STATE ELECTRICITY BOARD 38 SYSTEM

39. On constant observation for a definite period of time On the real system collect the RMS values of three phases of a feeder. Using these values select the time sectors as first Time sector, secondary sector, tertiary sector etc. Determine the term,first difertial term, second deffertial term etc. Sum up allvalues , and this sum is used as the reference 39 Utilisation

40. N ow on real time measure the RMS values in all the three phases of the feeder for a comparatively short Period of time ,find the average in all the three feeders Compare this average with the above reference Nullify the diference by adjusting the load through proper switching so that the difernce is minimum That is the load is balenced in real time Repeate the procedure periodically in real time Thus utility of the model is justified 40

41. Periodically up date the model by utilizing the readings obtained from the running system and set the reference For the future 41 PRRIODIC UPDATING OF THE MODELS