# New Hybrids of ANFIS with Several Optimization Algorithms for Flood Susceptibility Modeling

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The altitude varies from 300 to 5595 m. The climate of the study area based on De Martonne climatic classification system is very humid and its average annual rainfall is 430 mm. The entire study region is high land and mountainous area, for which slopes of 0–6° cover only 5% and ground slope varies from 0–66°. Rangelands cover 92% of the study area, and—geologically—the area is predominantly occupied by Jurassic formations.

## 3. Data Preparation and Analysis

#### 3.1. Flash Flood Inventory

#### 3.2. Dataset Collection for Spatial Modeling

^{2}) [48] and grouped into six categories, including (Figure 3e): 0–0.401, 0.401–1.17, 1.92–2.67, 2.67–3.66, and 3.66–7.3 km/km

^{2}. Field survey revealed that there are many flood occurrences adjacent to rivers, and the more the distance to river, the lower the probability of flood occurrence. The distance to river map was constructed using river and multiple ring buffer command in ArcGIS 10.2 and divided into eight classes (Figure 3h): 0–50, 50–100, 100–150, 150–200, 200–400, 400–700, 700–1000, and > 1000 m. A lithology map of the study area with 1:100,000 scale showed six groups of formations including: Teryas, Quaternary, Permain, Cretaceous, Jurassic, and Tertiary (Figure 3i). Land-use type is considered as a conditioning factor that has a significant role in flooding [9]. The areas with higher vegetation density, such as forest regions, can control surface runoff and infiltrate the water; therefore, there is negative spatial relationship between vegetation density and flood occurrence [11]. Land-use map was generated from Landsat 8 Operational Land Imager (OLI) imagery for 2013 in Environment for Visualizing Images (ENVI) 5.1 software (The Board of Trustees of the University of Illinois, Illinois, IL, USA) and classified into seven classes—namely grassland (rangeland), bare land, forest, garden, farming land, residential, and water body—using neural network algorithm and supervised classification (Figure 3j). Rainfall is the most prominent conditioning factor for flood occurrence. About 20 years, from 1991 to 2011, meteorological data was used in order to prepare rainfall maps and then classified into six classes (Figure 3g): 183–333, 334–379, 380–409, 410–448, 449–535, and 536–741 mm using a simple kriging method.

#### 3.3. Preparation of Training and Testing Dataset

#### 3.4. Analysis of Spatial Correlation

_{j}was determined by

#### 3.5. Flood Spatial Prediction Modeling

#### 3.5.1. Adaptive Neuro-Fuzzy Inference System

_{i}or B

_{i−2}as the linguistic label related to the input node i. Therefore, in Layer 2, fuzzy membership function, is computed which determines ‘full’, ‘partial’, or ‘none’ membership levels. The output function is calculated according to the equations

_{i}, b

_{i}, and c

_{i}are the parameters of the Bell function that are so-called premise parameters [65,68].

_{i}, q

_{i}, and r

_{i}are the consequent parameters of function fuzzy inference system (f

_{i}).

_{out}is final output. It can be described as

#### 3.5.2. Cultural Algorithm

#### 3.5.3. Bees Algorithm

#### 3.5.4. Invasive Weed Optimization Algorithm

_{min}starts from worth fitness and increases to reach S

_{max}for the weeds with the best fitness, as shown in Figure 8.

_{min}to σ

_{max}and is calculated with via non-linear equation which is

_{max}is the number of last iteration, σ

_{iter}is the corresponding iteration’s SD, n is the nonlinear modulation index between 2 and 3, σ

_{max}is maximum value’s SD and σ

_{min}is minimum value’s SD [81].

#### 3.5.5. Performance Assessment

_{i}and E

_{i}are observation and prediction of flood probability values, respectively, in training and testing datasets, and N is all samples.

#### 3.6. Model Validation and Comparisons

#### 3.7. Inferential Statistics

#### 3.7.1. Freidman Test

_{0}) for the current research shows that there is no difference between prediction capabilities of flood models. If the amount of the p-value (significance) is smaller than the significance level (α = 0.05), then the null hypothesis is rejected. The biggest weakness of this technique is that it only shows whether there is difference among the models performance or not, and it does not have any capability to display pairwise comparisons among the models.

#### 3.7.2. Wilcoxon Test

## 4. Results

#### 4.1. Spatial Relationship between Flood Occurrence and Conditioning Factors

#### 4.2. Model Comparison between the Proposed New ANFIS Ensemble Models

#### 4.3. Model Configuration and Generating of FSMs Using ANFIS Ensemble Models

#### 4.4. Validation of Flood Susceptibility Maps

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Flood conditioning factor maps in the study area: slope degree (

**a**), altitude (

**b**), curvature (

**c**), SPI (

**d**), TWI (

**e**), river density (

**f**), distance to river (

**g**), lithology (

**h**), land-use (

**i**), and rainfall (

**j**).

**Figure 4.**General ANFIS architecture of first order Takagi–Sugeno fuzzy model [65]: (

**a**) Multi-layer perception fuzzy reasoning; (

**b**) equivalent ANFIS structure.

**Figure 6.**Spaces of a cultural algorithm [74].

**Figure 7.**Flowchart of the BA for flood susceptibility mapping in Haraz watershed [76].

**Figure 8.**Procedure of seed reproduction at weeds’ colony [77].

**Figure 9.**RMSE value of training of (

**a**) ANFIS-CA, (

**c**) ANFIS-BA, (

**e**) ANFIS-IWO and for testing data samples (

**b**) ANFIS-CA, (

**d**) ANFIS-BA, and (

**f**) ANFIS-IWO.

**Table 1.**Spatial relationship between flood-conditioning factors and flooding occurrences locations by SWARA method

Sub-Factor | Class | Comparative Importance of K_{j} Average Value | Coefficient K _{j} = S_{j} + 1 | w_{j} = (Qj − 1))/k_{j} | Weight w_{j}/Σw_{j} |
---|---|---|---|---|---|

Slope | 0–0.5 | 1.00 | 1.00 | 0.40 | |

0.5–2 | 0.80 | 1.80 | 0.56 | 0.22 | |

2–5 | 0.20 | 1.20 | 0.46 | 0.18 | |

5–8 | 0.60 | 1.60 | 0.29 | 0.11 | |

8–13 | 1.15 | 2.15 | 0.13 | 0.05 | |

13–20 | 1.50 | 2.50 | 0.05 | 0.02 | |

20–30 | 0.55 | 1.55 | 0.01 | 0.00 | |

>30 | 2.70 | 3.70 | 0.01 | 0.01 | |

Elevation | 328–350 | 1.00 | 1.00 | 0.63 | |

350–400 | 0.35 | 1.35 | 0.16 | 0.10 | |

400–450 | 3.70 | 4.70 | 0.21 | 0.13 | |

450–500 | 0.55 | 1.55 | 0.10 | 0.06 | |

500–1000 | 0.65 | 1.65 | 0.06 | 0.04 | |

1000–2000 | 3.95 | 4.95 | 0.01 | 0.01 | |

2000–3000 | 0.00 | 1.00 | 0.01 | 0.01 | |

3000–4000 | 0.00 | 1.00 | 0.01 | 0.01 | |

>4000 | 0.00 | 1.00 | 0.01 | 0.01 | |

Curvature | Concave | 1.00 | 1.00 | 0.46 | |

Flat | 0.05 | 1.05 | 0.95 | 0.43 | |

Convex | 3.00 | 4.00 | 0.24 | 0.11 | |

SPI | 0–80 | 3.70 | 4.70 | 0.09 | 0.03 |

80–400 | 0.70 | 1.70 | 0.41 | 0.13 | |

400–800 | 0.30 | 1.30 | 0.70 | 0.22 | |

800–2000 | 0.10 | 1.10 | 0.91 | 0.29 | |

2000–3000 | 1.00 | 1.00 | 0.32 | ||

>3000 | 3.95 | 4.95 | 0.02 | 0.01 | |

TWI | 1.9–3.94 | 0.05 | 1.05 | 0.03 | 0.00 |

3.94–4.47 | 3.50 | 4.50 | 0.03 | 0.00 | |

4.47–5.03 | 2.70 | 3.70 | 0.15 | 0.01 | |

5.03–5.72 | 0.65 | 1.65 | 0.55 | 0.04 | |

5.72–6.96 | 0.10 | 1.10 | 0.91 | 0.07 | |

6.96–11.5 | 1.00 | 1.00 | 0.08 | ||

River density | 0–0.401 | 3.95 | 4.95 | 0.01 | 0.00 |

0.401–1.17 | 3.95 | 4.95 | 0.03 | 0.01 | |

1.17–1.92 | 2.50 | 3.50 | 0.15 | 0.06 | |

1.92–2.67 | 0.85 | 1.85 | 0.54 | 0.20 | |

2.67–3.66 | 1.00 | 1.00 | 0.37 | ||

3.66–7.3 | 0.00 | 1.00 | 1.00 | 0.37 | |

Distance to river | 0–50 | 1.00 | 1.00 | 0.59 | |

50–100 | 1.75 | 2.75 | 0.36 | 0.22 | |

100–150 | 0.85 | 1.85 | 0.20 | 0.12 | |

150–200 | 1.20 | 2.20 | 0.09 | 0.05 | |

200–400 | 2.70 | 3.70 | 0.02 | 0.01 | |

400–700 | 2.70 | 3.70 | 0.01 | 0.00 | |

700–1000 | 3.00 | 4.00 | 0.00 | 0.00 | |

>1000 | 0.00 | 1.00 | 0.00 | 0.00 | |

Lithology | Teryas | 1.00 | 1.00 | 0.31 | |

Quaternary | 0.50 | 1.50 | 0.67 | 0.21 | |

Permain | 0.00 | 1.00 | 0.67 | 0.21 | |

Cretaceous | 0.40 | 1.40 | 0.48 | 0.15 | |

Jurassic | 1.10 | 2.10 | 0.23 | 0.07 | |

Teratiary | 0.10 | 1.10 | 0.21 | 0.06 | |

Land use | Water bodies | 1.00 | 1.00 | 0.75 | |

Residential area | 3.90 | 4.90 | 0.20 | 0.15 | |

Garden | 1.55 | 2.55 | 0.08 | 0.06 | |

Forest land | 2.00 | 3.00 | 0.03 | 0.02 | |

Grassland | 0.70 | 1.70 | 0.02 | 0.01 | |

Farming land | 3.95 | 4.95 | 0.00 | 0.00 | |

Barren land | 0.00 | 1.00 | 0.00 | 0.00 | |

Rainfall | 188–333 | 1.00 | 1.00 | 0.40 | |

333–379 | 0.10 | 1.10 | 0.31 | 0.12 | |

379–409 | 1.20 | 2.20 | 0.45 | 0.18 | |

409–448 | 0.35 | 1.35 | 0.34 | 0.13 | |

448–535 | 0.05 | 1.05 | 0.29 | 0.12 | |

535–471 | 1.15 | 2.15 | 0.14 | 0.05 |

Number | Flood Models | Mean Ranks | Chi-Square | p-Value (Significance) |
---|---|---|---|---|

1 | ANFIS-CA | 1.68 | 16.6 | 0.00 |

2 | ANFIS-BA | 2.08 | ||

3 | ANFIS-IWO | 2.24 |

Number | Pairwise Comparison | z-Score | p-Value (Significance) | Judgment |
---|---|---|---|---|

1 | ANFIS-CA vs. ANFIS-BA | −3.225 | 0.001 | Yes |

2 | ANFIS-CA vs. ANFIS-IWO | −3.906 | 0.000 | Yes |

3 | ANFIS-BA vs. ANFIS-IWO | −1.128 | 0.259 | NO |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tien Bui, D.; Khosravi, K.; Li, S.; Shahabi, H.; Panahi, M.; Singh, V.P.; Chapi, K.; Shirzadi, A.; Panahi, S.; Chen, W.;
et al. New Hybrids of ANFIS with Several Optimization Algorithms for Flood Susceptibility Modeling. *Water* **2018**, *10*, 1210.
https://doi.org/10.3390/w10091210

**AMA Style**

Tien Bui D, Khosravi K, Li S, Shahabi H, Panahi M, Singh VP, Chapi K, Shirzadi A, Panahi S, Chen W,
et al. New Hybrids of ANFIS with Several Optimization Algorithms for Flood Susceptibility Modeling. *Water*. 2018; 10(9):1210.
https://doi.org/10.3390/w10091210

**Chicago/Turabian Style**

Tien Bui, Dieu, Khabat Khosravi, Shaojun Li, Himan Shahabi, Mahdi Panahi, Vijay P. Singh, Kamran Chapi, Ataollah Shirzadi, Somayeh Panahi, Wei Chen,
and et al. 2018. "New Hybrids of ANFIS with Several Optimization Algorithms for Flood Susceptibility Modeling" *Water* 10, no. 9: 1210.
https://doi.org/10.3390/w10091210