0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

Caha, J: Comparison of Fuzzy Arithmetic and Stochastic Simulation for Uncertainty Propagation in Slope Analysis

204

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
204
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
5
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript

• 1. Comparison of Fuzzy Arithmetic and Stochastic Simulation for Uncertainty Propagation in Slope Analysis Jan CAHAThis presentation is co-financed by theEuropean Social Fund and the statebudget of the Czech Republic
• 2. Introduction  uncertainty is element of data and processes associated with them  propagation of uncertainty  amount and character of uncertainty is substantial for decision making  theories for modeling and propagation of uncertainty - probability theory, Dempster–Shafer theory, fuzzy sets theory, interval mathematics … First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 3. Introduction  Stochastic Simulation (represented by the method Monte Carlo) is often used for uncertainty propagation  Monte Carlo has some undesirable properties that complicate further use of the results  possible solution is utilization of Fuzzy Arithmetic  fuzzy arithmetic is extension of standard arithmetic operations to fuzzy numbers First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 4. Comparisonof Fuzzy Arithmetic and Stochastic Simulation  three aspects of uncertainty that need to be considered while choosing method for modeling  definitions and axiomatics  semantics  should define which uncertainty theory should be used  there is no general agreement on the process  at least two approaches – statistics, fuzzy methods  different approach to the results  numeric  Stochastic simulation - what are the most probable outputs, it is possible that the result did not cover all the possible outcomes  Fuzzy arithmetic covers all the possible outcomes including the extreme solutions First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 5. Comparisonof Fuzzy Arithmetic and Stochastic Simulation  Stochastic simulations are extremely time and computational performance demanding  generation of random numbers  storage of large amount of data while performing iterations  Fuzzy arithmetic is less demanding  smaller amount of iterations  smaller demand for storage space First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 6. Slope analysis  one the basic GIS analysis of surface  uncertain surface modelled by the field model  Neighbourhood method 2 2 S (S E W SN S ) ( z1 2 z2 z3 ) ( z7 2 z6 z5 )SN S 2 4 d ( z3 2 z4 z5 ) ( z1 2 z8 z7 )SE W 2 4 d First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 7. Slope analysis First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 8. Case studies  2 case studies  uncertainty of slope in one cell  calculation of uncertainty for area of interest  slope values are presented in percentages  triangular distribution will be used for stochastic simulation  Piecewiselinear Fuzzy Numbers with 10 α-cuts  the presented solutions were programmed in Java First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 9. Comparisonof Fuzzy Arithmetic and Stochastic Simulation First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 10. Slope of the cell  3×3 cell  cell size 10 meters  z1–z8 have value 0 meters ±1 meter  case study proves how the two methods approach uncertainty differently  what is possible range of values of z9 ? First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 11. Slope of the cell  Monte Carlo Number of iterations Minimal value Maximal value Time of calculation (s-9) 100 0.18% 6.79% 9 686 759 600 0.10% 5.24% 22 836 671 1 000 0.02% 6.41% 30 969 981 100 000 000 1.18% 9.05% 134 521 347 647  Fuzzy Arithmetic – time of calculation 7 530 022 s-9  limit values - 0.0 ̶ 14.14% First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 12. Slope of the cell First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 13. Slope analysis of the area  area of interest 4×4 km  grid of size 400×400 cells  cell size 10×10 meters  time and storage demands of both methods First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 14. Slope analysis of the area (m) First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 15. Slope analysis of the area Uncertainty (m) First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 16. Slope analysis of the area First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 17. Slope analysis of the area - Time demands  Monte Carlo Number of iterations Time of calculation (s-9) 100 4 975 466 099 600 56 907 980 483 1000 91 937 539 092  Fuzzy Arithmetic 76 523 690 406 s-9 First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 18. Slope analysis of the area - Memory demands  Monte Carlo - 1 288 512 bytes per realization  100 iterations – 128 851 200 bytes  600 iterations – 773 107 200 bytes  1000 iterations – 1 288 512 000 bytes  Fuzzy Arithmetic – 28 574 944 bytes First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 19. Conclusion  methods for uncertainty propagation were compared by 3 aspects  ability to provide all possible solutions  time demands  memory demands  comparison of time demands highly depends on number of iterations and on number of alpha cuts  Fuzzy arithmetic can be further optimized by different algorithms for calculation  results of Fuzzy arithmetic offer much better foundation for use of the results in uncertainty analysis  by containinig all possible solution results of Fuzzy Arithmetic support more appropriately decision making First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
• 20. Thank you for your attention First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc