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DOI: 10.22059/jwim.2022.339537.972

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Investigation of the performance of neural gas networks in hydrological clustering

Mohammadreza Mahmoudi¹, Saeid Eslamian^2*, Alireza Gohari³, moein tahanian

1. M.Sc., Department of Water Engineering, College of Agriculture, Isfahan University of Technology, Isfahan, Iran.

2. Professor, Department of Water Engineering, College of Agriculture, Isfahan University of Technology, Isfahan, Iran.

3. Assistant Professor, Department of Water Engineering, College of Agriculture, Isfahan University of Technology, Isfahan, Iran.

4. M.Sc., Department of Water Engineering, College of Agriculture, Isfahan University of Technology, Isfahan, Iran.

Received: February 22, 2022 Accepted: July 01, 2022

Abstract

The design of many infrastructures and construction projects requires the extensive studies in the area's geographical conditions and climatic characteristics. The effectiveness of this research itself depends on the information and data required. In many cases, the project area is in a situation where no climatic information such as rainfall is available. Hence, regional frequency analysis has been received much attention. In this way, having specific conditions and mechanisms, the available information in other sites can be expanded and transferred to the other areas. In this research, clustering is one of the most effective steps that divide the existing stations into the hydrologically homogeneous areas. Therefore, in this study, in addition to the common methods in clustering, two new models, neural gas network and growing neural gas network, were used to determine the homogeneous regions in Khuzestan province, Iran. One of the unique features of these algorithms is learning the topology or shape of the distributions that governs the data space. Using the variables of longitude, latitude, altitude, mean annual rainfall, and maximum 24-hour rainfall of the station, the design area was divided into two hydrologically homogeneous areas, and the clustering process was performed. The results show that the neural gas networks has a high efficiency and accuracy in view of clustering.

The Mean Percentage Difference and Coefficient of Variation of Root Mean Square Error in neural gas were estimated to be 15.56 and 24.39 percent, respectively, which showed a considerable advantages over the conventional methods.

Keywords: Clustering, Hydrological homogeneity, Khuzestan, Regional Frequency Analysis, Topology learning.

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Arabahasa

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Lal

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Paye

Abdolkha

Bagh

Idana Machi

Sade KampJarah

Dehmoll

Cluster 1 Cluster 2

Arabahas Pole Shalu

Izeh Sus Andi

La Abasspo Gotva

Ahv TangePa SadeD

Sade Chamg

Paye

Abdolkh

Bagh

Idan Mach

Sade KampJara

Dehmol

Cluster 1 Cluster 2

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Table 1. Results of heterogeneity and discordancy measures for 24hr rainfall duration

Heterogeneity situation Heterogeneity measure

Discordant stations Number of

stations Clustering

models Cluster

H3

H2

H1

Definitely homogeneous -1.04

-1.13 -1.12

- 11

NG

1

-1.91 -0.91

- 8

GNG

-2.01 -1.11

- 9

SOM

-1.79 -0.64

- 9

FCM

-2.01 -1.11

- 9

Kmeans

-2.01 -1.11

- 9

Ward

-1.28 0.17

- 10

NG

2

-0.12 0.23

- 13

GNG

-0.04 0.39

- 12

SOM

-0.01 0.12

- 12

FCM

-0.04 0.39

- 12

Kmeans

-0.04 0.39

- 12

Ward

Table 2. Average values of goodness-of-fit indices of the difference between IDF curves based on regional and at-site probability distributions for used clustering models

Values of goodness-of-fit indices Model

∆ MBE CV^_`a

-0.04 15.56

24.39 NG

0.23 16.03

24.41 GNG

0.32 16.35

25.19 FCM

0.31 15.91

24.67 SOM, K-Means, Ward

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Table 3. Values for goodness-of-fit indices of the difference between IDF curves based on regional and at-site probability distributions at 21 rainfall stations for NG clustering model

Values of goodness-of-fit indices

Stations CV_vwxy MBE ∆

10.75 -2.11

29.46 1

24.84 -6.61

42.46 2

11.67 -2.89

26.38 3

10.04 -1.42

14.68 4

9.14 -1.77

15.61 5

8.51 -2.05

23.07 6

14.29 0.28

17.49 7

10.32 -0.11

23.38 8

5.91 1.43

13.59 9

28.14 6.85

21.3 10

8.33 1.58

18.67 11

13.06 0.80

16.27 12

20.99 -1.38

23.36 13

28.56 9.48

46.52 14

14.41 -2.34

27.05 15

18.87 -3.71

26.02 16

19.62 0.27

29.19 17

22.00 2.13

15.55 18

21.42 -3.70

35.81 19

14.33 5.12

30.17 20

11.72 -0.69

16.11 21

15.56 -0.04

24.39 Mean

Figure 5. IDF curves for four rainfall stations in Khuzestan province (Note: The values on each curve is the return period T for the curve)

0 20 40 60 80 100 120

0 50 100 150 200 250 300 350

Rainfall intensity(mm/hr)

Rainfall duration(min) Ahvaz station

At-site Regional

2 5 10 20

50 100

0 20 40 60 80 100 120

0 50 100 150 200 250 300 350

Rainfall duration(min) Sade Tanzimi station

At-site Regional

100 50 20

10 2 5 20

0 20 40 60 80 100 120 140 160

0 50 100 150 200 250 300 350

Rainfall duration(min) Susan station

At-site

2 5 10 20 50 100

0 20 40 60 80 100 120 140 160

0 50 100 150 200 250 300 350

Rainfall duration(min) Lali station

At-site Regional

2 510 20 50 100

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m f @ /

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:

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1. Generalized Extreme Value Distribution 2.Neural Gas Network

3. Growing Neural Gas Network 4. Ward

5. K-Means

6. Self-Organizing Map (SOM) 7. Fuzzy C-Means

8. Sigmoid 9. Homogeneity 10. Discordancy 11. Image Segmentation 2. Aging

3. Adaptation

4. Coefficient of Variation of Root Mean Square Error 5. Mean Percentage Difference

6. Mean Bias Error

<= % >

9 . - 0 ! . ? ;+ R #? ) !

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<& %

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