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

*1. INTRODUCTION

2. LITERATURE REVIEW

3. STUDY AREA AND DATA COLLECTION

4. METHODOLOGY

5. DATA ANALYSIS AND RESULTS

6. CONCLUSIONS

7. REFERENCES

*FLOODING AT DOWNSTREAM OF UKAI

DAM

*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

*

*

*

*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.

**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.

*In the present study for efficient and effective control of a gated

spillway and reservoir operation using fuzzy logic is discussed.

**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.

*

*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.

**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.

*

*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.

*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.

*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

*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.

*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.

*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.

*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

*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.

*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.

*

*

**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).

*

*Irrigation

*Water Supply

*Power Generation

*Recreation

*Flood protection (Secondary)

*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)

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.

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

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.)

**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.

*

*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

*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

*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).

*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

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

The basic components and levels are shown in Figure.

*

*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.

*

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.)

**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.

*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

*

*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

**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

*

*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.

**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

*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.

*

*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).

*

*For the defuzzification process, the standard centre of area

method (Centroid method) is employed.

*

*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

*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

*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

*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.

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

*

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)

*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

*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

*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

**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)

(a): FIS editor for August (b): Input 1: Elevation (H)

(c): Input 2: Change in Elevation (dH) (d): Output: Gate Opening (d)

*

*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

(a): FIS editor for September (b): Input 1: Elevation (H)

(c): Input 2: Change in Elevation (dH) (d): Output: Gate Opening (d)

*

*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

*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.

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

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.)

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

*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.

**(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.

*

*

*

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

*

*

*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.

*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.

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)

**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).

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

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

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

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

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

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

*

*(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.

*(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

*(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

*

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

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

**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.

*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.

*THANK YOU