1 Fuzzy Sets and Fuzzy Logic Theory and Applications G. J. Klir, B. Yuan.
A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir...
Transcript of A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir...
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A
UDP PROJECT ENTITLED
Supervisor/Guide
UTKARSH NIGAM
Asst. Prof. SRPEC-Unjha
* “FUZZY LOGIC BASED OPERATION OF SPILLWAY
GATES: A CASE STUDY OF UKAI DAM”
Patel Gaurang K. (Enrollment No.100780106023)
Patel Ashish A. (Enrollment No.100780106047)
Patel Nilesh V. (Enrollment No.090780106012)
Patel Dhruv H. (Enrollment No.090780106041)
Co-Guide
BHAVIK G. PATEL
Asst. Prof. SRPEC-Unjha
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*1. INTRODUCTION
2. LITERATURE REVIEW
3. STUDY AREA AND DATA COLLECTION
4. METHODOLOGY
5. DATA ANALYSIS AND RESULTS
6. CONCLUSIONS
7. REFERENCES
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*FLOODING AT DOWNSTREAM OF UKAI
DAM
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*Releases more than 3,00,000 cusecs (8490 cumecs).
*High Inflows released from upstream dams.
*Low carrying capacity of Tapi river.
*Allied towards Rule level maintenance.
FLOODING
Revised demands and
water requirements
every year.
Seasonal variation and
demand variation.
Increasing minimum
water requirement
constraint.
PROBLEM DESCRIPTION
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*
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*
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*
*Spillways are the hydraulic structures constructed to surpass the
surplus water in the dam over it.
*Spillways may be Gated or ungated. Gates serves the purpose of
storing water up to a desired.
*Reservoir operation is the art of storing and releasing the water
through the reservoir to serve the various needs and objectives
throughout the year.
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**Spillway gates allow the dam owner some flexibility in the
operation of a dam both in terms of flood operations and for
environmental releases.
*Spillway gates are designed to maximise the storage capacity of a
dam while increasing the spillway capacity for a given headwater
level.
*The crest of the spillway is usually provided at F.R.L (Full
Reservoir Level). However, in order to control floods the gates
could be provided at the top and the water level could be
increased up to maximum water level.
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*In the present study for efficient and effective control of a gated
spillway and reservoir operation using fuzzy logic is discussed.
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**Fuzzy logic is inherently robust since it does not require precise,
noise-free inputs. The output control is a smooth control function
despite a wide range of input variations.
*Spillway gates and reservoirs can be operated efficiently and
effectively.
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*
*To develop method for controlled operation of gates using fuzzy
logic and to compare the results of the proposed method with
Actual (observed) data of operating spillway gates.
*To understand the downstream flooding causes and factors
influencing the flood.
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**To understand basics of fuzzy logic and its application in gated
spillways and reservoir operation.
*To develop inflow hydrograph, reservoir routing through
spillways.
*To analyse collected real time data of Ukai for gated operation in
flood and reservoir operation.
*To develop operating rules (Model) for the operation of spillway
gates using real time data of Ukai dam.
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*
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*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum
opus. An enlargement of Fuzzy Sets, Uncertainty, and Information—an
earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy
Logic addresses practically every significant topic in the broad expanse
of the union of fuzzy set theory and fuzzy logic.
*Chen G. and Pham T. T. (2000) fuzzy systems and fuzzy control
theories were the most new and an emerging technology targeting
industrial applications have added a promising new dimension to the
existing domain of conventional control system engineering.
*Ross T. J. (2004) Ross introduces the basic concept of fuzziness and
distinguishes fuzzy uncertainty from other forms of uncertainty. He also
introduces the fundamental idea of set membership, thereby laying the
foundation for all material that follows, and presents membership
functions as the format used for expressing set membership.
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*Zimmermann H.J. (2005) basic mathematical framework of fuzzy set
theory will be described, as well as the most important applications of
this theory to other theories and techniques. Since 1992 fuzzy set theory,
the theory of neural nets and the area of evolutionary programming have
become known under the name of ‘computational intelligence’ or ‘soft
computing’.
*Sivanandnam et al (2009) explains the principles of fuzzy systems in
depth with the information and the useful knowledge available for
computing processes. The various algorithms and the solutions to the
problems are well balanced pertinent to the fuzzy systems’ research
projects.
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*Beard L. R. (1963) presented a method of manual operation of
spillway gates and also this was similar to the methods
developed by U.S. Corps engineers.
*Windser J. S. (1973) gave methodology employing recursive
linear programing as the optimization tool presented for the
analysis of multi reservoir flood control systems.
*Can E. K. and Houck M. H. (1984): The goal programming
model was applied to the Green River Basin (GRB) system
comprising four multipurpose reservoirs
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*Vedula S. and Mohan S. (1990) A real-time operational
methodology was developed by S. Vedula and S. Mohan for
multipurpose reservoir operation for irrigation and hydropower
generation with application to the Bhadra reservoir system in the
state of Karnataka, India.
*Wurbs Ralph. A. developes computer models for evaluating
reservoir operations. Selecting a modeling and analysis approach
for a particular application depends upon the characteristics of
the application, the analysis capabilities provided by alternative
models
*Russell Samuel O., Campbell Paul F. (1996) they offered a
model of Fuzzy logic for the single purpose hydroelectric
project. Compared results of both Fuzzy logic and fixed rules.
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*Ozelkan E. C. Galanbosia, A. Gaucheranda E. F. and Duckstein L
(1997): Solved a stochastic reservoir control problem by means of a
linear system model and quadratic cost (LQ) framework.
*Acanal Nese, Haktanir Tefaruk (1999), A six-stage operation policy
for the routing of flood hydrographs with return periods from 1.01
years up to the Probable Maximum Flood (PMF) is proposed for any
dam having a gated spillway. The gate opening rules are determined,
based on the recent pool level. When the PMF is routed, the rising and
falling limbs of the outflow hydrograph have the appearance of a six-
step staircase with sudden jumps and sudden drops at definite times
and smooth variations between steps.
*Acanal Nese, Yurtal Recep and Haktanir Tefaruk (2000), First 6
stage operation policy was determined to route the flood and then
Dynamic Programming programme was developed to optimize both
the firm and secondary energies of hydroelectric generation at
monthly periods.
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*Panigrahi D. P. and P. P. Mujumdar P. P. (2000) They developed a fuzzy
rule based model for the operation of a single purpose reservoir. The model
was operated on an ‘if – then’ principle, where the ‘if’ is a vector of fuzzy
premises and the ‘then’ is a vector of fuzzy consequences.
*Chang L. and Chang F. (2001) combines two major procedures: the genetic
algorithm (GA) and the adaptive network-based fuzzy inference system
(ANFIS). The GA was used to search the optimal reservoir operating
histogram based on a given inflow series, which can be recognized as the
base of input-output training patterns in the next step. The ANFIS was then
built to create the fuzzy inference system, to construct the suitable structure
and parameters, and to estimate the optimal water release according to
the reservoir depth and inflow situation.
*Haktanir T. and Kisi O. (2001):Ten-stage operation policies for routing of
flood hydrographs from very small magnitudes up to the probable maximum
flood (PMF) for any dam having a gated spillway were suggested. The gate
opening rules were determined based on the recent pool level.
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*Kumar D. N, Prasad D. S. V., and Raju K. S. (2001) developed Optimal
reservoir operation model using Multi Objective Fuzzy Linear Programming
(MOFLP) which is computationally simple and easy to implement to the real
world situation of reservoir operation.
*Karaboga Dervis, Bagis Aytekin and Haktanir Tefaruk (2004) developed
a efficient control method based on fuzzy logic was proposed for the real-
time operation of spillway gates of a reservoir during any flood of any
magnitude up to the probable maximum flood. To demonstrate the
performance of the proposed method, they simulate the control system using
different probable overflow hydrographs. The results of the proposed control
method have been compared with the results of the conventional control
methods
*Afshar A. and Salehi A. (2011) : A multi-stage operating policy for routing
flood hydrographs through reservoir with two different operation policies for
gated spillways was presented. The first approach presents releases the flood
only based on observed reservoir water surface level. In the second
approach, both observed reservoir water surface level and flood peak in
upstream gagging station forms the release policy
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*Salehi A. (2011) Compared two Operating Rules for Gated Spillways and
its application for Karkher dam has given two different operation policies for
routing flood hydrographs through reservoirs was presented and their
performances were compared
*Haktanir Tefaruk, Citakoglu Hatice and Acanal Nese (2013) gave 15
stage flood routing method for the operation of Reservoir.
*U.S. Army Corps of Engineers method:The U.S. Army Corps of
Engineers utilized their own method of operating the gated spillways based
on the so-called ‘‘water control diagrams’’ derived considering long-
anhydrologic forecast (Hydrological 1987).
*Kensin Erol M., Taylan Emine Dilek and Yilmaz Gokhan A. Kensin,
Taylan and Yilmaz’s research on “Flow Prediction Model With Fuzzy Logic
Approaches: Dim Stream” and predicted that flow prediction methods are
countable as rainfall-runoff models or flood routing models for short
periods.
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*Yeh (1985) reviewed the state-of-the-art of mathematical models
developed for reservoir operation, including simulation. The choice of
methods depends on the characteristics of the reservoir system being
considered, on the availability of data and on the objectives and
constraints specified.
*Shreshta et. al. (1996)[34] made a fuzzy rule based model. The case
study of the Tenkiller Lake in Oklahoma was studied and illustrated
with complete methodology. Operating rules were generated taking
care of each criterion such as hydropower, municipal, industrial and
irrigation demands, flood control and navigation and environmental
criteria.
*Dubrovin T. et al (2001)[9] developed multipurpose real-time reservoir
operation by construction of a fuzzy rule-based control model.
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*
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*
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**Ukai Dam, Tapi river has been taken as the study area. The data
used in the analysis are real-time data of Ukai Dam.
*Approved by the planning commission of government of India in
1969 and the construction of the dam was completed in 1973
(Figure 3.1).
*The reservoir is expected to attain Maximum Water Level (MWL)
of 106.99 m (351ft.) while passing the Probable Maximum Flood
(PMF) of 59747 cumecs (21.16 lakh cusecs).
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*
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*Irrigation
*Water Supply
*Power Generation
*Recreation
*Flood protection (Secondary)
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*1. State Gujarat
2. District Tapi (Vyara)
3. Taluka Fort Songadh
4. Village Ukai
5. River Tapi
6. Latitude 21’15’’ N
7. Longitude 73’35’’ E
LOCATION OF DAM
HYDROLOGY
1. Catchment Area (a) At Ukai – 62225 km2 (24025 sq. miles)
(b) At kakrapar – 62308 km2 (24057 sq. miles)
(c) At Kathore bridge – 63823 km2 (24642 sq. miles)
(d) At Surat – 64100 km2 (sq. 24749 sq. miles)
2. Mean annual rainfall in the water shed 785 mm
3. Maximum annual rainfall in the watershed 1191 mm
4. Minimum annual rainfall 270 mm
5. Mean annual rainfall at the dam site 1720 Mm3 (14 Maft)
6. Observed maximum flood at the dam (Aug.
1968)
42470 m3/s (15 lakh cusec)
7. Observed maximum dry weather flow 0.03813 X 16 6 Ha.m
8. (a) Design flood
(b) Probable flood
49490 m3/s (17.48 Lakh cusecs)
59920 m3/s (21.16 Lakh cusecs)
9. Max. Regulated outflow from the reservoir 24100 m3/s (8.50 Lakh cusecs)
10. Mean annual rainfall in the command
North of Tapi river
South of Tapi river
889mm to 1145 mm
1524mm to 2032 mm
11. 75% Dependable Annual Yield 12750 MCM (9.08 Maft)
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RESERVOIR AND DAM
1. Gross storage capacity at FRL 7414.29 MCM
2. Dead storage below R.L.82.296 m 684.39 MCM
3. Live storage 6729.9 MCM
4. Full Reservoir Level 105.15 m (345 Ft.)
5. Water spread at R.L. 105.15 mt. 60095 ha.
6. (a) Cultivated land submerged
(b) Other land submerged
(c) Forest land submerged
30350 Ha.
7485 Ha.
22260 Ha.
7. Village affected by submergence 170 No
8. High Flood Level (HFL) 106.99 (351 Ft.)
9. Length of reservoir 112 km. (70 miles) 1. Length of dam –
(a) Length of Masonry section including
spillway
(b) Length of Earth dam section
Total Length –
868.83 mt.
4057.96 mt.
4926.79 mt.
2. Max height of main dam
(a) Earth dam above river bed
(b) Masonry dam above deepest foundation
68.58 mt.
80.772 mt.
3. Total earth work 23240 x 103 m3
4. Total quantity of stripping 4950 x 103 m3
5. Total quantity of Masonry concrete 1484 x 103 m3
6. Top of Dam 111.252 mt.
7. Road width on spillway 6.706 mt.
8.
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SPILLWAY
1. Crest level of spillway 91.135 mt. (299 ft.)
2. Length of spillway 425.195 mt.
3. Top of crest level 105.461 mt
4. Type of gates Radial
5. Size of Gates 15.545mt. x 14.783mt.
6. No. of Gates 22 Gates
7. Discharging capacity from all
345 gates
(1) At FRL – 345 Ft.
(2) At HFL – 351 Ft.
13.37 Lakh cusecs
16.34 Lakh cusecs
8.
POWER SECTION 1. Size of penstock 4 nos. 7.01 dia
2. Installation of 4 units of 75 MW each 300 MW
3. Generation at 35 Load factor 153 MW
4. Annual energy (Units) 670 x 106 KWH
Details
(A) Hydro
Unit No Date of Installation Capacity
I 08/07/74 75 MW
II 13/12/74 75 MW
III 22/04/75 75 MW
IV 04/03/76 75 MW
TOTAL 300 MW
(B) Mini Hydro Unit No Date of Installation Capacity
I 08/12/87 2.5 MW
II 29/1/88 2.5 MW
TOTAL 5.0 MW
(C) Thermal Unit No Date of Installation Capacity
I 19/3/76 120 MW
II 23/6/76 120 MW
III 21/1/79 200 MW
IV 11/09/79 200 MW
V 30/1/95 210 MW
TOTAL 850 MW
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CANAL BED POWER HOUSE
1. Size of Penstock 3.96 mt. X 2.05 mt.
2. Type of Hoist Hydraulic Hoist
3. Discharge through each unit 550 cumecs
IRRIGATION REQUIREMENT
1. Direct Ukai Left Bank Main
Canal (ULBMC)
727.47 MCM (0.59 MAFT)
2. Kakrapar Left and Right Bank
Main Canal (KLBMC & KRBMC)
3230.46 MCM (2.62 MAFT)
TOTAL 3957.93 MCM (3.21 MAFT)
RULE LEVEL OF UKAI DAM
1. 1ST July 97.840 m (321 ft.)
2. 1ST August 101.498 m (333 ft.)
3. 1ST September 102.108 m (335 ft.)
4. 15TH September 103.632 m (340 ft.)
5. 1ST October 105.156 m (345 ft.)
![Page 32: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/32.jpg)
**Data of flood events have been taken (2002, 2012, 2013)
*Daily Inflow-Outflow data.
*Storage capacity and Elevation details of the Ukai reservoir to get a
standard form of Stage-Storage relationship.
*Rule level and rule curve details of Ukai dam, Tapi River.
*Data regarding operation of gates including no. of gate open,
discharge released, gate height, gate opening, duration etc.
![Page 33: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/33.jpg)
*
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*The aim of fuzzy logic based control system is to adjust the dam
elevation as per rule level.
*Various factors that affect reservoir operation are inflow,
unexpected and sudden changes in reservoir water level,
amount of water discharge per unit of time, maximum possible
outflow etc. (Aprrox 3,00,000 cusec).
*Algorithms of fuzzy rules are used to obtain optimized membership
function representing fuzzy values. These rules are derived based
on the intuition and decision management depending upon the
availability of occurrence of particular flow
![Page 35: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/35.jpg)
*Elevation in
ft.
Elevation in
m
Storage
in MCM
Elevation
in ft.
Elevation
in m
Storage in
MCM
299 91.135 1960.00 330 100.584 4979.39
300 91.440 2018.36 335 102.108 5714.86
305 92.964 2348.16 340 103.632 6524.02
310 94.488 2630.21 345 105.156 7414.28
315 96.012 3149.90 346 105.461 7553.19
320 97.536 3704.00 350 106.680 8235.19
325 99.060 4311.05 351 106.985 8480.18
![Page 36: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/36.jpg)
*Elevation-Storage and Elevation-Discharge curves are developed
to find out the outflow hydrograph.
*To avoid the flooding situations in downstream of a dam and to
effectively manage the flood, state authority has revised the rule
level during year 2000 after flood of 1998.
*The Ukai reservoir was operated using this rule level till year
2006. In the year 2006, due to flash floods in the catchment area,
heavy inflow incurred in the reservoir during short duration (less
than 24 hours).
![Page 37: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/37.jpg)
*After this high flood events rule level of Ukai reservoir revised in 2006. Table
4.2 presents rule levels after 2000 and 2008. Figure 4.2 represents the rule
level for the period 2000 to 2007 and after 2008.
Rule Level 2000 Rule Level 2008
Date R.L. in
ft.
R.L. in
m Date R.L. in
ft.
R.L. in
m
01-Jul 321 97.84 01-Jul 321 97.84
01-Aug 333 101.50 01-Aug 333 101.50
01-Sep 343 104.55 01-Sep 335 102.11
16-Sep 344 104.85 16-Sep 340 103.63
01-Oct 345 105.16 01-Oct 345 105.16
Table: Rule Level in 2000 and Rule Level in 2008
![Page 38: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/38.jpg)
97
98
99
100
101
102
103
104
105
106
30-Jun 01-Aug 02-Sep 04-Oct
Res
erv
oir
Lev
el in
m
Time in days
Rule Level in 2000
(a) Rule Level 2000
97
98
99
100
101
102
103
104
105
106
30-Jun 01-Aug 02-Sep 04-Oct
Res
erv
oir
Lev
el in
m
Time in days
Rule Level in 2008
(b) Rule Level 2008
Figure : Rule Levels for period 2000-2008 and after 2008 for Ukai reservoir
![Page 39: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/39.jpg)
The basic components and levels are shown in Figure.
![Page 40: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/40.jpg)
*
*The two inputs are elevation (H) and change in elevation (dH).
Rule level is a pre-defined level that has to be maintained in
order to fill the reservoir in steps. The gate opening (d) is the
output.
![Page 41: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/41.jpg)
*
S. No. Parameters
1. Input parameter: H (Elevation),
dH (change in elevation)
2. Output parameters d (Gate opening)
3. Membership function for each
parameter H
dH
d
5
5
5
4. Total number of rules derived for
program, in fuzzy logic tool:
25
5. Membership function used: Triangular / Trapezoidal
membership function
6. Inference mechanism Mamdami type Inference
mechanism
7. Spillway Crest 91.135m (299 ft.)
8. Highest Flood Level 106.990m (351 ft.)
9. Full Reservoir Level 105.156m (345 ft.)
![Page 42: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/42.jpg)
**Crest level of Reservoir is 91.135m (299ft.), Full Reservoir Level,
FRL is 105.148m (345ft.) and Maximum Flood Level, MFL is
106.99m (351 ft.)
*For single purpose reservoir only one model is required but here
the Reservoir is multipurpose and a pre-fixed Elevation known as
“Rule Level” is required to be maintained. So, three strategies are
planned for the operation of reservoir.
*The Indian monsoon have fixed periods of four months from June
to September. The highest inflow in the reservoir likely to occur
during July to September.
![Page 43: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/43.jpg)
*For Monsoon months operating strategies for reservoir operation
are proposed through fuzzy logic technique. For each month
operating strategies for Reservoir operation using ranges of
elevation in accordance to Rule Level are planned.
*The inflow, releases and storage were collected for 15 years
period and gate openings data were collected for 7 years period
(2006 to 2012) due to lack of data. After analysing the data the
range of elevation/lake levels for monsoon months are tabulated
in Table.
Table : Range of Elevation/Lake Level
Month
Elevation/Lake Level (in ft. and m)
Maximum Minimum
in ft. in m in ft. in m
July 351 106.985 321 97.841
August 351 106.985 331 100.889
September 351 106.985 335 102.108
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*
*It varies from -1 to +1 depending upon the change in Elevation.
Change in elevation plays a vital role in flood management and
reservoir operation too. Change in elevation, dH varies from -1 to
+1 depending upon the time rate of change in Infow. Change in
Elevation (Lake Level) dH is given by equation.
* 𝑑𝐻 = 𝐻−𝐻𝑎𝑣𝑔.
𝑀.𝐹.𝐿.−𝐻𝑚𝑖𝑛.
*Where, H=Elevation belonging to period, Havg =Average of M.F.L.
and R.L. of that month, M.F.L.=Maximum Flood Level and Hmin.=
min. elevation for particular month’s model as depicted in Table
![Page 45: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/45.jpg)
**The output parameter is given by ‘d’, gate opening. The gate
opening ranges from minimum zero to maximum 0.81 m or 81.28
cm (32 inches).
*The membership functions are decided and ranges for particular
group of membership has been done considering observed datasets
and categorised by past data records and intuition
![Page 46: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/46.jpg)
*
*The membership functions used for the fuzzy values of the fuzzy
variables are selected based on human/expert experience. The fuzzy
values are represented by triangular/trapezoidal membership
functions for the present study.
*In the present study five membership functions are used for inputs
and output. For “H” five membership functions used are: very low,
low, medium, high and very high.
*For “dH” five membership functions used are: negative big,
negative small, zero, positive small and positive big. Lastly for “d”
(gate opening) five membership functions used are very low, low,
medium, high and very high.
![Page 47: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/47.jpg)
**The rules of the fuzzy logic based model are derived based on
users experience, intuition and past records’ data sets. The rule
base of the fuzzy logic based model is shown in Table
Table : Relation developed for Fuzzy Logic program between
membership function
H dH Negative
big
Negative
small
zero Positive
small
Positive
big
Very low Very low Very low Very low Very low Very low
Low Low Low low Low Low
Medium Medium medium medium medium Medium
High High High high High High
Very high Very
high
Very
high
Very
high
Very
high
Very
high
![Page 48: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/48.jpg)
*For examples,
*1. If dam Elevation (lake level) is low and rate of change of
Elevation is small positive, then the spillway gate will open very
low.
*2. If dam Elevation (lake level) is medium and rate of change of
Elevation is zero then, the spillway gate will open very low.
*3. If dam Elevation (lake level) is high and rate of change of
Elevation is small positive, then the spillway gate will open
medium.
![Page 49: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/49.jpg)
*
*The output of each rule is determined by Mamdani’s max-min
inference method. The fuzzy logic tool box available with the
MATLAB 7.0 is used to develop the model (MATLAB, 2007).
![Page 50: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/50.jpg)
*
*For the defuzzification process, the standard centre of area
method (Centroid method) is employed.
![Page 51: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/51.jpg)
*
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*Following steps explains the entire methodology in building the
model for month of July.
*Step 1: Click on the MATLAB 7.0 icon on desktop as shown
below in Figure
Figure : 4.6
Desktop
showing
MATLAB 7.0
icon at task bar
of PC
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*Step 2: Type “fuzzy” on the command window of MATLAB 7.0, this
will lead to appear the fuzzy inference editor (FIS) as shown
below in figure. The FIS editor displays the variables (input and
output), operations and other options on the screen as shown in
figure
Figure: 4.7 FIS editor and workspace in MATLAB 7.0
![Page 54: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/54.jpg)
*Step 3: The appeared FIS editor is untitled can be named
according to the required model.
Figure 4.8: Features of file option on FIS editor
![Page 55: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/55.jpg)
*Step 4: The edit option on the FIS editor is clicked which provide
access to add or remove the variables (inputs and outputs),
selection of membership functions and rules.
*Fuzzy logic based model has been made for the month of July. In
which variables (inputs: elevation ‘H’, change in elevation ‘dH’
and output: gate opening ‘d’) have been entered with suitable
names and membership functions. The names given to the all the
membership functions and its ranges are depicted in Table 4.7.
![Page 56: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/56.jpg)
Table 4.7: Range of Membership Function for Rule level (1 July to 31 July)
H (Name of
membership
function)
Ranges of membership
functions, spillway crest
to MFL (i.e. 321 to 351)
in ft
dH, change in
elevation (Name
of membership
functions)
Negative big
to small big (-
1 TO 1)
d, gate opening
(Name of
membership
functions)
Zero to
maximum
opening (0 to 32)
in ft
Very low 321 321 328.5 Negative big -1 -1 -.5 Very low 0 0 2
Low 321 328.5 336 Negative small -1 -.5 0 Low 0 2 4
Medium 328.7 336.2 343.7 Zero -.5 0 .5 Medium 2 4 6
High 336 343.5 351 Positive small 0 .5 1 High 4 6 12
Very high 336 343.5 351 Positive big .5 1 1 Very high 8 24 32 32
Figure 4.9: Membership function editor for fuzzy logic based model of July
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*
Figure 4.10 (a) FIS editor for July Figure 4.10 (b) Input 1: Elevation (H)
Figure 4.10 (d) Output: Gate Opening (d) Figure 4.10 (d) Output: Gate Opening (d)
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*Step 5: The membership functions have been made based on the
expert’s knowledge data base and user’s intuition. The fuzzy rules
can be made in fuzzy rule editor by simply clicking on the box
between inputs and output in the FIS editor. Also the rule editor can
be open by clicking on edit option in FIS editor and then clicking to
rules as shown in figure below.
Figure 4.11: Edit option in FIS editor and Rule editor
![Page 59: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/59.jpg)
*Step 6: By clicking view option rules can be viewed as shown in
figure 4.12. The output is a fuzzified term which is defuzzified
for which centre of area (centroid) method has been employed
Figure 4.12: Rule viewer showing all rules of inputs and output
![Page 60: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/60.jpg)
*Step 7: Once the fuzzy logic based model has been formed it can
be exported or saved in MATLAB 7.0 folder and also to
workspace. It is very important to save the file in workspace.
Following commands need to be given in MATLAB 7.0 to run the
fuzzy logic based model. The command for reading the file so that
the model can be executed is,
*fis=readfis(‘gateftjul’);
*The output is given by following command,
*out=evalfis(input,gateftjul)
*In ‘input’ the input values have to be entered
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**Similar procedure is followed to develop fuzzy logic model for the
month of August. The names and ranges of membership functions
are shown in Table . The FIS editor and membership editors for
inputs and output are shown in figure.
H (Name of
membership
function)
Ranges of membership
functions, spillway
crest to MFL (i.e. 321
to 351) in ft
dH, change in
elevation (Name
of membership
functions)
Negative
big to
small big (-
1 TO 1)
d, gate
opening
(Name of
membership
functions)
Zero to
maximum
opening (0 to 32)
in ft
Very low 331 331 336 Negative big -1 -1 -.5 Very low 0 0 2
Low 331 336 341 Negative small -1 -.5 0 Low 0 2 4
Medium 336 341 346 Zero -.5 0 .5 Medium 2 4 6
High 341 346 351 Positive small 0 .5 1 High 4 6 12
Very high 346 351 351 Positive big .5 1 1 Very high 8 24 32 32
Table 4.8: Range of Membership Function for Rule level
(1 August to 31 August)
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(a): FIS editor for August (b): Input 1: Elevation (H)
(c): Input 2: Change in Elevation (dH) (d): Output: Gate Opening (d)
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*
*Similar procedure is followed to develop fuzzy logic model for the
month of September. The names and ranges of membership
functions are shown in Table . The FIS editor and membership
editors for inputs and output are shown in figure.
Table 4.8: Range of Membership Function for Rule level
(1 September to 31 September)
H (Name of
membership
function)
Ranges of
membership
functions, spillway
crest to MFL (i.e.
321 to 351) in ft
dH, change in
elevation (Name of
membership
functions)
Negative
big to
small big (-
1 TO 1)
d, gate opening
(Name of
membership
functions)
Zero to maximum
opening (0 to 32)
in ft
Very low 335 335 339 Negative big -1 -1 -.5 Very low 0 0 2
Low 335 339 343 Negative small -1 -.5 0 Low 0 2 4
Medium 339 343 347 zero -.5 0 .5 Medium 2 4 6
High 343 347 351 Positive small 0 .5 1 High 4 6 12
Very high 347 351 351 Positive big .5 1 1 Very high 8 24 32 32
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(a): FIS editor for September (b): Input 1: Elevation (H)
(c): Input 2: Change in Elevation (dH) (d): Output: Gate Opening (d)
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*
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*A detailed data analysis for the present study has been
carried out for two proposed studies
*The first model is fuzzy logic based model for the
operation of spillway gates.
*The second model is fuzzy logic based operation of
Ukai reservoir
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*Stage- Storage Relationship
*Analysis of Input Data is done and presented then the discussion of
models is described.
*Inflow increase in reservoir causes the depth and resultant volume
in the storage to be increase. The increase in depth which is called
Stage or Elevation and resulting volume are used to get a Stage-
Storage relation.
*A Stage storage relationship is the relation between the Capacity or
Volume that can be stored in a reservoir to the corresponding level
or elevation.
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Table 5.1: Stage (Elevation)-Storage Relation
Elevation
in ft.
Elevation
in m
Storage in
MCM
Elevation
in ft.
Elevation
in m
Storage in
MCM
299 91.135 1960.00 330 100.584 4979.39
300 91.440 2018.36 335 102.108 5714.86
305 92.964 2348.16 340 103.632 6524.02
310 94.488 2630.21 345 105.156 7414.28
315 96.012 3149.90 346 105.461 7553.19
320 97.536 3704.00 350 106.680 8235.19
325 99.060 4311.05 351 106.985 8480.18
Figure 5.1:
Stage-Storage
curve for Ukai
Reservoir
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Stage-Discharge Relationship
*A Stage discharge curve or Rating curve is a graph plotted between stage
(elevation) and discharge. The rating curve is usually plotted as stage on x-
axis versus discharge on y-axis.
*Equation used in development of this relation which is Ogee spillway
equation for free fall,
*Q = C x L x H3/2
*Where,
* Q= Discharge in cumecs
* C= Coefficient of discharge (for Ogee spillway C=4)
* L= Width of gate (1 gate width = 14.73 m or 48.5 ft, all 22 gates total
* width = 325.22 m or1067 ft.)
* H= Elevation height above spillway crest (91.135 m or 299 ft.)
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0.00
5000.00
10000.00
15000.00
20000.00
25000.00
30000.00
35000.00
40000.00
45000.00
50000.00
91.00 95.00 99.00 103.00 107.00
Dis
charg
e in c
um
ecs
Stage (Elevation) in m
Figure 5.2: Stage- Discharge Curve
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*The formulae which is used to calculate the discharge through gate
opening is calculated using following formulae,
*Q = C 2𝑔 W Ba Hb
*Where, Q = Discharge through Spillway Gates,
* C = Co-efficient of Discharge, 0.6 to 0.8 (for this case C=0.6)
* W= Width of Spillway Gates, 14.67 m (48.5 ft.)
* B = Gate opening Height (Varies from 0 to 32)
* H = Height of Water surface Elevation above Spillway crest.
* a = Gate opening Co-efficient (here we using 0.72), usually 1
(default)
* b = Height/Water surface Elevation constant (0.62), 0.5 default.
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**(a) Free Reservoir Level (FRL): The highest reservoir level which
can be maintained without reservoir discharge or without passing
water through under sluices. This is the highest controlled water
level.
*(b.) Maximum Water Level (MWL): The level likely to attain in a
reservoir at the Dam face, while negotiating the design flood. Also
known as Highest Flood Level.
*(c.) Minimum Draw Down Level (MDDL): It is the lowest level at
which reservoir may be depleted for meeting various needs.
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*
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*
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*
year Discharge max. Discharge min.
Date Max. in MCM Max. cusecs Max. cumecs Date Min MCM Min. cusecs Min. cumecs
1992 10/01/92 27.63 11277.552 319.34418 1/8 to 20/8 1992 2.21 902.0409 25.54291
1993 08/04/93 43.9 17918.369 507.39087 07/12/93 4.93 2012.245 56.98034
1994 09/08/94 1190.25 485816.37 13756.765 12/11/94 3.43 1400 39.64352
1995 04/30/95 48.59 19832.655 561.59732 16/7 to 28/7 1995 2.94 1200 33.98016
1996 03/19/96 43.76 17861.226 505.77276 12/7 to 2/8 1996 2.94 1200 33.98016
1997 09/05/97 74.28 30318.37 858.51922 2/8, 4/8 1997 2.21 902.0409 25.54291
1998 09/16/98 1310.2 534775.56 15143.132 7/7 to 13/7, 17/7,
2/8, 12/8 to 17/8
1998
3.18 1297.959 36.75405
1999 11/02/99 56.17 22926.533 649.20604 20/6, 21/7 to 22/7
1999
3.43 1400 39.64352
2000 01/11/00 39.38 16073.471 455.14926 1/12, 4/12 to 14/12
2000
3.31 1351.021 38.25658
2001 09/08/01 23.31 9514.2865 269.41415 17/6 to 30/6, 11/7
to 15/7 2001
2.69 1097.959 31.09069
2002 09/07/02 791.59 323097.99 9149.1011 11/3, 9/6 to 12/6
2002
3.19 1302.041 36.86963
2003 09/30/03 221.95 90591.844 2565.2711 30/6, 17/7 to 20/8
2003
2.94 1200 33.98016
2004 09/27/04 102.58 41869.391 1185.6072 30/7 to 29/8 2004 2.94 1200 33.98016
2005 09/17/05 102.43 41808.167 1183.8735 4/7 to 13/7, 1/8 to
2/8 2005
3.19 1302.041 36.86963
2006 08/08/06 2151.4 878122.52 24865.62 01/05/06 3.43 1400 39.64352
2007 07/10/07 572.25 233571.45 6613.996 09/30/07 3.675 1500 42.4752
2008 06/11/08 55.83 22787.757 645.27636 3/8 to 22/8 2008 3.19 1302.041 36.86963
2009 04/08/09 30.08 12277.552 347.66099 10/10 to 25/10,
21/12 to 10/12
2009
2.7 1102.041 31.20627
2010 09/10/10 540.07 220436.75 6242.0635 14/1 to 31/1, 16/7
to 2/8, 4/8 to 22/8
2010
2.7 1102.041 31.20627
2011 08/29/11 566.86 231371.45 6551.699 1/1 to 13/1 2011 2.76 1126.531 31.89974
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*
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*
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*The high inflow event of the years 2002, 2012 and 2013 have
taken and studied for the application of fuzzy logic. The proposed
fuzzy logic based model the flood using the uncertain and
unpredicted inflow conditions.
*The operation of gates using fuzzy logic can be advantageous in a
manner that it considers some latitude and flexibility to precisely
operate the gates rather than operating by crisp or fixed
conditions.
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*Release of more than 8490 cumecs (3,00,000 cusecs) causes
flooding in the downstream In the present study effort is made to
prevent flooding on the downstream side of dam by precisely
operating gates using fuzzy logic.
*The basic Mass balance equation or water balance equation used in
routing is given by
*St+1 = St + It - Rt
*Where, St+1 is storage at time interval t+1,
St = Storage at time t,
It = Inflow at time interval t
Rt = Releases at time t.
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0.00
2000.00
4000.00
6000.00
8000.00
10000.00
12000.00
14000.00
16000.00
0 50 100 150 200 250 300 350 400 450 500
Infl
ow
in c
um
ecs
Time (hours)
Inflow hydrograph 2002
Inflow hydrograph 2012
Inflow Hydrograph 2013
Figure 5.4: Inflow hydrographs of three years
(2002, 2012 and 2013)
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**The high inflow in this year lasts from 2 September to 15 September in which it
was maximum between 4 September to 6 September. The flood operation
actually observed and fuzzy operated has been compared and discussed.
*The highest magnitude of the flood observed was 9446 cumecs (3,33,378 cusecs)
on 4 September and lasts for next 3 days with peak as 9184 cumecs (3,24,523
cusecs), 9316 cumecs (3,29,187 cusecs) and 9391 cumecs (3,31,838 cusecs).
*The observed outflow was 9143 cumecs (3,23,074 cusecs) on 7th September
which caused flooding to on the downstream side of the dam. The high alert was
alarmed and outflow was managed to release water without much damage on the
downstream side. The flood routing using fuzzy logic for this inflow is given in
Table. 5.6. The simulation results produced using fuzzy logic based model for
high inflow of 2002 is as shown in figure 5.5 (a) and (b).
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DateInflow in
MCM
Inflow in
cumecs
Storage in
MCM
Elevation
in m
INPUT
NO. 1:
Elevation in
ft.
INPUT
NO. 2:
Change in
Elevation,
dH (-1 to
+1)
OUTPUT:
Gate
Opening, d
in ft.
Discharge
Q=C√2g
W B(.72)
H(.62)
fuzzy
Outflow
through all
Radial gate
in cusecs
Dishcharge
through
power
House in
cusecs
Dishcarge
through
U.L.B.M.C
. in cusecs
Evaporation
in cusecs
Total Avg.
Discharge
(fuzzy
operated
Gate) in
cusecs
Total
Volume in
MCM
(fuzzy
operated
Gate)
Actual
(observed)
Discharge
Through
Radial gates
in cusecs
Total Avg.
Discharge
cumecs
(fuzzy
operated
Gate)
Actual
(observed)
Total
Discharge
cumecs
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
02-09-2002 280.72 3239.51 5003.68 99.20 325.45 - - 0.00 0.00 0.00 800.00 500.00 1300.00 3.19 36.79 36.79
03-09-2002 707.82 8168.24 5283.90 99.89 327.73 - 0.00 0.00 0.00 3272.00 800.00 500.00 4572.00 11.20 246.43 129.39 129.39
04-09-2002 818.55 9446.07 6091.25 102.82 337.32 -0.71 1.77 5790.96 127401.11 19312.00 800.00 500.00 148013.11 362.63 7977.91 4188.77 927.56
05-09-2002 795.82 9183.76 6524.44 103.63 340.00 -0.38 2.54 7550.88 166119.37 22576.00 1050.00 500.00 190245.37 466.10 10254.23 5383.94 6760.47
06-09-2002 807.28 9316.01 6865.62 104.21 341.91 -0.14 3.38 9307.77 204770.98 22908.00 1200.00 500.00 229378.98 561.98 12363.53 6491.43 8871.85
07-09-2002 813.81 9391.37 7117.45 104.65 343.33 0.04 4.94 12263.80 269803.61 22951.00 1083.00 500.00 294337.61 721.13 15864.80 8329.75 9143.70
08-09-2002 448.91 5180.42 6845.23 104.18 341.80 -0.15 3.32 9186.68 202106.91 22561.00 1000.00 500.00 226167.91 554.11 12190.45 6400.55 5774.25
09-09-2002 196.92 2272.46 6488.04 103.56 339.77 -0.40 2.42 7289.24 160363.25 22038.00 1000.00 500.00 183901.25 450.56 9912.28 5204.41 2320.03
10-09-2002 157.47 1817.20 6194.95 103.01 337.96 -0.63 0.00 0.00 0.00 21915.00 1000.00 500.00 23415.00 57.37 1262.07 662.64 2015.21
11-09-2002 104.78 1209.16 6242.36 103.10 338.25 -0.59 0.00 0.00 0.00 21526.00 1000.00 500.00 23026.00 56.41 1241.10 651.64 651.64
12-09-2002 81.02 934.97 6266.97 103.15 338.41 -0.57 0.00 0.00 0.00 21432.00 1000.00 500.00 22932.00 56.18 1236.03 648.98 648.95
13-09-2002 71.79 828.46 6282.58 103.17 338.50 -0.56 0.00 0.00 0.00 21397.00 1000.00 500.00 22897.00 56.10 1234.15 647.99 647.99
14-09-2002 52.16 601.93 6278.64 103.17 338.48 -0.57 0.00 0.00 0.00 21388.00 1000.00 500.00 22888.00 56.08 1233.66 647.73 647.73
15-09-2002 48.23 556.57 6270.79 103.15 338.43 -0.57 0.00 0.00 0.00 21390.00 1000.00 500.00 22890.00 56.08 1233.77 647.79 647.79
TABLE 5.6: ANALYSIS OF 2002 FLOOD INFLOW USING FUZZY LOGIC
BASED MODEL FOR GATED OPERATION OF SPILLWAY GATES
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0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 50 100 150 200 250 300 350
Dis
charg
e in c
um
ecs
Time (hours)
Inflow hydrograph
Actual (observed) outflow
Fuzzy outflow
98
99
100
101
102
103
104
105
106
0 50 100 150 200 250 300 350
Ele
vati
on in m
Time (hours)
Actual (observed) Elevation
Fuzzy Elevation
Rule level 2000
Rule level 2008
Figure 5.5: Performance characteristics of fuzzy logic based model for year
2002 compared with observed Elevation and rule levels
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TABLE 5.9: ANALYSIS OF 2012 FLOOD INFLOW USING FUZZY LOGIC BASED
MODEL FOR GATED OPERATION OF SPILLWAY GATES
DateInflow in
MCM
Inflow in
cumecs
Storage in
MCM
Elevation
in m
INPUT
NO. 1:
Elevation
in ft.
INPUT
NO. 2:
Change in
Elevation,
dH (-1 to
+1)
OUTPUT:
Gate
Opening,
d in ft.
Discharge
Q=C√2g
W B(.72)
H(.62)
fuzzy
Outflow
through all
Radial gate
in cusecs
Dishcharg
e through
power
House in
cusecs
Dishcarge
through
U.L.B.M.
C. in
cusecs
Evaporati
on in
cusecs
Total Avg.
Discharge
(fuzzy
operated
Gate) in
cusecs
Total
Volume in
MCM
(fuzzy
operated
Gate)
Actual
(observed)
Discharge
Through
Radial gates
in cusecs
Total Avg.
Discharge
cumecs
(fuzzy
operated
Gate)
Actual
(observed)
Total
Discharge
cumecs
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
30-08-2012 42.09 485.72 5600.12 101.87 334.22 - - 0.00 0.00 22182.00 1200.00 400.00 23782.00 58.27 - 673.03 673.03
31-08-2012 107.09 1235.82 5648.94 101.97 334.55 - 0.00 0.00 0.00 22606.00 1200.00 400.00 24206.00 59.30 48805.00 685.03 685.03
01-09-2012 182.52 2106.28 5772.16 102.21 335.35 -0.96 0.90 3556.38 78240.40 21912.00 1200.00 400.00 101752.40 249.29 27208.00 2879.59 2879.59
02-09-2012 137.10 1582.13 5659.97 101.99 334.62 -1.05 0.00 0.00 0.00 19723.00 1200.00 400.00 21323.00 52.24 27369.00 603.44 603.44
03-09-2012 95.53 1102.42 5703.25 102.08 334.92 -1.01 0.00 0.00 0.00 19066.00 1200.00 400.00 20666.00 50.63 13700.00 584.85 584.85
04-09-2012 105.33 1215.51 5757.95 102.19 335.26 -0.97 0.00 0.00 0.00 11665.00 1200.00 400.00 13265.00 32.50 0.00 375.40 375.40
05-09-2012 209.84 2421.55 5935.29 102.52 336.36 -0.83 1.46 5034.46 110758.18 22501.00 1200.00 400.00 134859.18 330.40 78064.00 3816.51 3816.51
06-09-2012 749.04 8643.92 6353.93 103.31 338.94 -0.51 2.00 6344.80 139585.66 23677.00 1200.00 400.00 164862.66 403.91 246767.00 4665.61 4665.61
07-09-2012 1150.44 13276.08 7100.46 104.62 343.23 0.03 4.00 10532.86 231722.98 23387.00 1200.00 400.00 256709.98 628.94 299923.00 7264.89 7264.89
08-09-2012 477.51 5510.47 6949.03 104.36 342.38 -0.08 3.60 9748.40 214464.82 23357.00 1200.00 400.00 239421.82 586.58 249206.00 6775.64 6775.64
09-09-2012 108.26 1249.32 6470.70 103.53 339.67 -0.42 2.37 7179.18 157941.89 22772.00 1200.00 400.00 182313.89 446.67 - 5159.48 5159.48
10-09-2012 223.59 2580.23 6247.62 103.11 338.29 -0.59 1.94 6199.79 136395.36 22529.00 1200.00 400.00 160524.36 393.28 75058.00 4542.84 4542.84
11-09-2012 210.21 2425.82 6064.55 102.77 337.16 -0.73 0.00 0.00 0.00 21912.00 1200.00 400.00 23512.00 57.60 27208.00 665.39 665.39
12-09-2012 288.60 3330.44 6295.54 103.20 338.58 -0.55 0.00 0.00 0.00 19723.00 1200.00 400.00 21323.00 52.24 27369.00 603.44 603.44
13-09-2012 208.02 2400.55 6451.32 103.49 339.55 -0.43 0.00 0.00 0.00 19066.00 1200.00 400.00 20666.00 50.63 13700.00 584.85 584.85
14-09-2012 143.04 1650.68 6543.73 103.67 340.11 -0.36 0.00 0.00 0.00 11665.00 1200.00 400.00 13265.00 32.50 0.00 375.40 375.40
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0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 300 350 400
Dis
charg
e in c
um
ecs
Time (hours)
Inflow hydrograph
Actual (observed) outflow
Fuzzy outflow
101.5
102
102.5
103
103.5
104
104.5
105
0 50 100 150 200 250 300 350 400
Ele
vati
on in m
Time (hours)
Actual (observed) Elevation
Fuzzy Elevation
Rule level 2000
Rule level 2008
Figure 5.8: Performance characteristics of fuzzy logic based model for
year 2012 compared with observed Elevation and rule levels
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TABLE 5.10: ANALYSIS OF 2013 FLOOD INFLOW USING FUZZY LOGIC BASED
MODEL FOR GATED OPERATION OF SPILLWAY GATES
DateInflow in
MCM
Inflow in
cumecs
Storage in
MCM
Elevation
in m
INPUT
NO. 1:
Elevation
in ft.
INPUT
NO. 2:
Change in
Elevation,
dH (-1 to
+1)
OUTPUT
:Gate
Opening,
d in ft.
Discharge
Q=C√2g
W B(.72)
H(.62)
fuzzy
Outflow
through all
Radial gate
in cusecs
Dishcharg
e through
power
House in
cusecs
Dishcarge
through
U.L.B.M.
C. in
cusecs
Evaporati
on in
cusecs
Total Avg.
Discharge
(fuzzy
operated
Gate) in
cusecs
Total
Volume in
MCM
(fuzzy
operated
Gate)
Actual
(observed)
Discharge
Through
Radial gates
in cusecs
Total Avg.
Discharge
cumecs
(fuzzy
operated
Gate)
Actual
(observed)
Total
Discharge
cumecs
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
21-09-2013 69.32 800.00 6472.23 103.53 339.68 - - 0.00 0.00 2644.00 1800.00 900.00 5344.00 13.09 4444.00 151.24 277.00
22-09-2013 63.78 736.00 6536.01 103.63 339.99 -0.38 2.54 7550.74 166116.34 5002.00 1800.00 900.00 173818.34 425.85 6802.00 4919.06 410.46
23-09-2013 704.25 8127.00 7240.26 104.10 341.55 -0.18 5.00 12331.06 271283.34 19646.00 1800.00 900.00 293629.34 719.39 124178.00 8309.71 4146.63
24-09-2013 1247.05 14391.00 8487.31 105.01 344.52 0.19 5.00 12397.43 272743.51 21026.00 1800.00 900.00 296469.51 726.35 432813.00 8390.09 12920.05
25-09-2013 620.97 7166.00 9108.28 104.83 343.92 0.11 4.00 10545.99 232011.69 23778.00 1800.00 900.00 258489.69 633.30 294233.00 7315.26 9076.12
26-09-2013 379.98 4385.00 9488.26 104.39 342.50 -0.06 0.00 0.00 0.00 22501.00 1800.00 900.00 25201.00 61.74 187628.00 713.19 6023.06
27-09-2013 127.21 1468.00 9615.47 104.51 342.87 -0.02 0.00 0.00 0.00 21909.00 1800.00 900.00 24609.00 60.29 72930.00 696.43 2760.35
28-09-2013 130.50 1506.00 9745.98 104.63 343.26 0.03 0.00 0.00 0.00 21546.00 1800.00 900.00 24246.00 59.40 23340.00 686.16 1346.68
29-09-2013 110.66 1277.00 9856.64 104.71 343.55 0.07 0.00 0.00 0.00 21484.00 1800.00 900.00 24184.00 59.25 23284.00 684.41 1343.34
30-09-2013 87.09 1005.00 9943.72 104.76 343.71 0.09 0.00 0.00 0.00 21324.00 1800.00 900.00 24024.00 58.86 23124.00 679.88 1334.29
01-10-2013 101.39 1170.00 10045.11 104.84 343.95 0.12 0.00 0.00 0.00 21304.00 1800.00 900.00 24004.00 58.81 23104.00 679.31 1333.16
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0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
0 50 100 150 200 250
Dis
charg
e in c
um
ecs
Time (hours)
Inflow hydrograph
Actual (observed) outflow
Fuzzy outflow
103.4
103.6
103.8
104
104.2
104.4
104.6
104.8
105
105.2
105.4
0 50 100 150 200 250
Ele
vati
on in m
Time (hours)
Actual (observed) Elevation
Fuzzy Elevation
Rule level 2000
Rule level 2008
Figure 5.9: Performance characteristics of fuzzy logic based model for
year 2013 compared with observed Elevation and rule levels
![Page 88: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/88.jpg)
*
![Page 89: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/89.jpg)
*(a) Root Mean Square Error (RMSE):The root mean
square error (RMSE) is one of the most convenient
approaches for assessing simulation models. It
measures the deviation between the trend of the
predicted and measured values.
*𝑅𝑀𝑆𝐸 = ( 𝑄𝑏𝑜− 𝑄𝑏𝑝 )𝑖
2
𝑛𝑛𝑖=1
1/2
*A zero value of RMSE indicates a perfect fit between
measured and predicted values.
*The values of RMSE have shown that the errors of
predicted and actual (observed) are within expected
intervals and shows a good prediction over observed
values.
![Page 90: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/90.jpg)
*(b) Inequality Coefficient (U):The inequality coefficient
is a simulation statistics related to the RMSE, defined as
under,
* 𝑈 = 𝑅𝑚𝑠𝑒
1
𝑛 (𝑄𝑏𝑜)𝑖
2𝑛𝑖=1
1/2+
1
𝑛 (𝑄𝑏𝑝)𝑖
2𝑛𝑖=1
1/2
*The numerator is the root mean square error. If U=0 then
𝑄𝑏𝑝 =𝑄𝑏𝑜 and there is a perfect fit. If U=1, then Qbp ≠ Qbo
and the lacks predicative value
![Page 91: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/91.jpg)
*(c) Discrepancy Ratio (D.R.):The discrepancy ratio is
the measure of an equation to replicate data
accurately. Discrepancy ratio may be defined as the
ratio of fuzzy predicted elevation and actual
(observed) elevation. The discrepancy ratio for the
best model should be within value of 1.
*Discrepancy ratio j =𝑞𝑏 (𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑)
𝑞𝑏 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)
*(d) Confidence band: Confidence band or limit is the
accepted limit within which all the predicted and
observed values fall. The confidence band/limit has
been done graphically
![Page 92: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/92.jpg)
*
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Table 5.11: Statistical parameters and values for five year high inflow or
flood events
Years RMSE
Inequality
Coefficient
(U)
Discrepancy
Ratio (D.R.)
Confidence
Level (+/-
in %)
Mean
Elevation
predicted
fuzzy in m
Mean
Elevation
(observed)
in m
2002 0.36 0.0028 0.9979 1 103.1413 102.9209
2012 0.45 0.0033 1.0032 2 102.5974 102.9308
2013 0.19 0.0017 1.0019 1 104.2477 104.4494
99
100
101
102
103
104
105
106
99 100 101 102 103 104 105 106
Pre
dic
ted f
uzzy e
levati
on (
in m
)
Observed elevation (in m)
perfect line
1
-1
Elevationscatters
Figure 5.10: Predicted Fuzzy Elevation v/s Observed Elevation for high
inflow of 2002
![Page 94: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/94.jpg)
99
100
101
102
103
104
105
106
99 100 101 102 103 104 105 106
Pre
dic
ted f
uzzy E
levati
on (
in m
)
observed Elevation (in m)
perfectline
1.5
-1.5
Elevationscatters
Figure 5.11: Predicted Fuzzy Elevation v/s
Observed Elevation for high inflow of 2003
99
100
101
102
103
104
105
106
99 100 101 102 103 104 105 106
Pre
dic
ed f
uzzy E
levati
on (
in m
)
observed Elevation (in m)
perfectline
1
-1
Elevationscatters
Figure 5.12: Predicted Fuzzy Elevation v/s
Observed Elevation for high inflow of 2011
99
100
101
102
103
104
105
106
99 100 101 102 103 104 105 106
Pre
dic
ted f
uzzy E
levati
on (
in m
)
observed Elevation (in m)
perfectline
2
-2
Elevationscatters
Figure 5.13: Predicted Fuzzy Elevation v/s
Observed Elevation for high inflow of 2012
99
100
101
102
103
104
105
106
99 100 101 102 103 104 105 106
Pre
dic
ted f
uzzy E
levati
on (
in m
)
observed Elevation (in m)
perfectline1
-1
Elevationscatters
Figure 5.14: Predicted Fuzzy Elevation v/s
Observed Elevation for high inflow of 2013
![Page 95: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/95.jpg)
**The following findings can be summarised as an outcome of
present study:
*The Fuzzy Logic based model gives lower peak than observed
outflow peak.
*The actual outflow caused flooding or flood alarming situation by
releasing high inflow on the downstream side. The proposed fuzzy
logic model based outflow prevents flooding on downstream side.
![Page 96: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/96.jpg)
*The fuzzy Logic based flood hydrograph have wider base and
low peak compare to observed flood hydrograph.
*In either case flood cushion is used for the storage of water in
the reservoir. However, the fuzzy logic based model proposes
higher storages than actual storage for the same period.
*The fuzzy logic based model route the flow and bring it well
below the proposed new rule level of 2008.
![Page 97: A UDP PROJECT ENTITLED - Home | Civilcivil.srpec.org.in/files/Project/2015/12.pdf*George J. Klir (1995) Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets,](https://reader033.fdocuments.in/reader033/viewer/2022042004/5e6f0adaff26ac1d9e037fbb/html5/thumbnails/97.jpg)
*THANK YOU