An experimental investigation was conducted to explore the fundamental difference among the Mamdani fuzzy inference system (FIS), Takagi–Sugeno FIS, and the proposed flood forecasting model, known as hybrid neurofuzzy inference system (HN-FIS). The study aims finding which approach gives the best performance for forecasting flood vulnerability. Due to the importance of forecasting flood event vulnerability, the Mamdani FIS, Sugeno FIS, and proposed models are compared using trapezoidal-type membership functions (MFs). The fuzzy inference systems and proposed model were used to predict the data time series from 2008 to 2012 for 31 subdistricts in Bandung, West Java Province, Indonesia. Our research results showed that the proposed model has a flood vulnerability forecasting accuracy of more than 96% with the lowest errors compared to the existing models.
Flood disaster [
In October 2016, some regions in Indonesia were affected by the flood, and the disaster management officials reported that the flash flood in the Bandung city caused death of one person and damaged thousands of homes. The National Disaster Management Authority, also known as BNPB, informed that there was 77 mm of rainfall in the town in just 1.5 hours around midday [
The answer to overcome the flood disaster by applying the fuzzy system is assisting, predicting, and deciding these events. In 1965, Lotfi, a mathematician who created the theory of fuzzy logic, derived the result of the insufficiency of Boolean algebra for many real-world problems [
Many researchers have argued on meteorological forecasting, with the purpose to help assessing the disaster impact in some regions. Forecasting is also used in other areas such as detection and prediction of diseases [
This study proposes a hybrid approach based on the neural network and fuzzy inference system for flood event vulnerability, namely, hybrid neurofuzzy inference system (HN-FIS). The HN-FIS is a model which can automatically learn and also obtain the output which can present the essence of fuzzy logic. The system was applied in 31 subdistricts in Bandung. The flood forecasting depends on several variable inputs: population density, altitude of the area, and rainfall in time series from 2008 to 2012. The main contributions of this paper are (i) presenting a hybrid forecasting for flood vulnerability based on the neural network and fuzzy inference system for accurate flood forecasting employing data variables which utilized Bandung database for flood vulnerability forecasting and (ii) developing an effective hybrid forecasting approach for flood vulnerability with higher accuracy.
This study used data collected from Bandung, West Java Province, Indonesia (Figure
Study area map of Bandung, West Java, Indonesia.
Rainfall in 31 subdistricts in Bandung.
Month | Rain precipitation (mm) | ||||
---|---|---|---|---|---|
2008 | 2009 | 2010 | 2011 | 2012 | |
January | 265 | 208.5 | 353.3 | 63 | 82.9 |
February | 166 | 200.5 | 557.1 | 76.7 | 303.7 |
March | 425 | 365.7 | 531 | 89.4 | 155.5 |
April | 342 | 165.6 | 93 | 381.5 | 290.8 |
May | 132 | 183.8 | 345 | 193.4 | 257.1 |
June | 20 | 101 | 191.9 | 117.6 | 60.5 |
July | 24.2 | 220.8 | 77.2 | 34.2 | |
August | 80 | 0.5 | 220.8 | 3.1 | 0 |
September | 45 | 24 | 424.4 | 102.8 | 27 |
October | 303 | 234.5 | 292.2 | 103.6 | 125 |
November | 455 | 318.2 | 401.4 | 321.4 | 537 |
December | 333 | 271.1 | 237.5 | 259 | 637 |
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The primary variables (Tables Population density: the population density of the subdistricts in which the people are located. The value zero means the population density is very low (less than or equal to 50 persons/km2). The value one means the population density is very high (that is, greater than 400 persons per square kilometer). Altitude of the area: the distance above sea level of the land, mountain, sea bed, or any other place. If the altitude of an area is less than 200 meters above sea level or coastal area, it is shown in fuzzy as low level (value 0), and the altitude of area greater than 350 meters above sea level or mountain area means the altitude in high level (value 1). Rainfall: according to the rate of rainfall, it is classified as low level “0,” light rain which happens when the precipitation rate is less than 20 mm per hour, and high level “1,” very heavy rain which happens when the precipitation rate is more than 100 mm per hour. Vulnerability of flood: the inability to resist a flood or to respond when the flood occurs: 0 = safe (when the area is secured from flood) and 1 = danger (when the area is under a threat of flood).
Population density in 31 subdistricts in Bandung.
No. | Subdistrict | Population density (people/km2) | ||||
---|---|---|---|---|---|---|
2008 | 2009 | 2010 | 2011 | 2012 | ||
1 | Ciwidey | 1613 | 1643 | 1465 | 1490 | 1500 |
2 | Rancabali | 355 | 359 | 324 | 330 | 332 |
3 | Pasirjambu | 342 | 346 | 334 | 339 | 341 |
4 | Cimaung | 1357 | 1377 | 1328 | 1355 | 1378 |
5 | Pangalengan | 734 | 748 | 710 | 723 | 728 |
6 | Kertasari | 463 | 466 | 432 | 428 | 430 |
7 | Pacet | 1139 | 1151 | 1100 | 1120 | 1129 |
8 | Ibun | 1391 | 1406 | 1389 | 1417 | 1428 |
9 | Paseh | 2026 | 2055 | 2053 | 2098 | 2118 |
10 | Cikancung | 1936 | 1954 | 2028 | 2084 | 2123 |
11 | Cicalengka | 3030 | 3093 | 3059 | 3123 | 3152 |
12 | Nagreg | 1005 | 1022 | 985 | 1008 | 1018 |
13 | Rancaekek | 3634 | 3691 | 3675 | 3760 | 3795 |
14 | Majalaya | 6284 | 6399 | 5976 | 6079 | 6125 |
15 | Solokan Jeruk | 3353 | 3390 | 3230 | 3289 | 3324 |
16 | Ciparay | 3266 | 3306 | 3270 | 3336 | 3369 |
17 | Baleendah | 4532 | 4602 | 5364 | 5580 | 5730 |
18 | Arjasari | 1421 | 1444 | 1401 | 1429 | 1447 |
19 | Banjaran | 2618 | 2638 | 2667 | 2726 | 2755 |
20 | Cangkuang | 2456 | 2479 | 2640 | 2743 | 2812 |
21 | Pameungpeuk | 4552 | 4591 | 4757 | 4876 | 4961 |
22 | Katapang | 4109 | 4193 | 4682 | 4866 | 4997 |
23 | Soreang | 2034 | 2075 | 2068 | 2123 | 2157 |
24 | Kutawaringin | 5963 | 6102 | 6126 | 6295 | 6374 |
25 | Margaasih | 7100 | 7245 | 7482 | 7728 | 7895 |
26 | Margahayu | 11655 | 11788 | 11417 | 11607 | 11687 |
27 | Dayeuhkolot | 10905 | 10993 | 10278 | 10388 | 10396 |
28 | Bojongsoang | 3071 | 3120 | 3804 | 3983 | 4133 |
29 | Cileunyi | 4211 | 4254 | 5197 | 5482 | 5709 |
30 | Cilengkrang | 1436 | 1458 | 1559 | 1613 | 1648 |
31 | Cimenyan | 1833 | 1871 | 1971 | 2031 | 2078 |
Altitude of the areas in 31 subdistricts in Bandung.
No. | Subdistrict | Altitude of the area (masl) |
---|---|---|
1 | Ciwidey | 700–1200 |
2 | Rancabali | 1200–1550 |
3 | Pasirjambu | 1000–1200 |
4 | Cimaung | 765–1057 |
5 | Pangalengan | 984–1571 |
6 | Kertasari | 1250–1812 |
7 | Pacet | 700–1116 |
8 | Ibun | 700–1200 |
9 | Paseh | 600–800 |
10 | Cikancung | 600–1200 |
11 | Cicalengka | 667–850 |
12 | Nagreg | 715–948 |
13 | Rancaekek | 608–686 |
14 | Majalaya | 681–796 |
15 | Solokan Jeruk | 671–700 |
16 | Ciparay | 678–805 |
17 | Baleendah | 600–715 |
18 | Arjasari | 550–1000 |
19 | Banjaran | 750–800 |
20 | Cangkuang | 700–710 |
21 | Pameungpeuk | 650–675 |
22 | Katapang | 675–700 |
23 | Soreang | 700–825 |
24 | Kutawaringin | 500–1100 |
25 | Margaasih | 600 |
26 | Margahayu | 700 |
27 | Dayeuhkolot | 600 |
28 | Bojongsoang | 681–687 |
29 | Cileunyi | 600–700 |
30 | Cilengkrang | 600–1700 |
31 | Cimenyan | 750–1300 |
The flood vulnerability in 31 subdistricts in Bandung is predicted using the Mamdani system, Sugeno system, and proposed flood forecasting model (HN-FIS). It consists of three inputs for vulnerability of flood level: population density, altitude of the area, and rainfall. The population density is in the range of 350 to 9000 people/km2. The altitude of the area is in the range of 0 to more than 1000 meters above sea level (masl). The rainfall is in the range of 0 to more than 200 mm. All the fuzzy models in this research were applied in the trapezoidal type trying to find the best one for the prediction of the vulnerability of flood event. The classification of fuzzy sets employed in the flood forecasting method is presented in Table
Example of fuzzy sets in flood forecasting.
Population density | Altitude of the area | Rainfall | Vulnerability of flood |
---|---|---|---|
Very low | Low | Low | Safe |
Low | Moderate | Moderate | Alert |
High | High | High | Danger |
Over | Extreme |
Fuzzy classification of population density.
Population density rating | Very low | Low | High | Over |
---|---|---|---|---|
Population density (people/km2) | <350 | [350, 3350] | [3500, 9000] | >9000 |
Fuzzy classification of the altitude of the area.
Altitude of area rating | Low | Moderate | High |
---|---|---|---|
Altitude of the area (masl) | <500 | [500, 1000] | >1000 |
Fuzzy classification of rainfall.
Rainfall rating | Low | Moderate | High | Extreme |
---|---|---|---|---|
Rainfall value (mm) | [0, 50] | [50, 100] | [100, 200] | >200 |
Membership function curves of flood forecasting fuzzy variable premises.
Fuzzy classification of the vulnerability of flood.
Vulnerability of flood rating | Safe | Alert | Danger |
---|---|---|---|
Vulnerability of flood | <248 | [248, 374] | >374 |
Membership function curves of flood forecasting fuzzy variable output.
According to Table
Table
In Table
Table
Based on the measurement and theoretical analysis, both Mamdani and Sugeno models required a significant number of forecasting to obtain a higher level of accuracy for the vulnerability of flood. The models considered the parameters that are in flood forecasting. We present the Mamdani model and the Sugeno model for practically distributed flood prediction.
Mamdani and Assilian proposed the first type of fuzzy inference system (FIS) in 1975 [
Mamdani fuzzy inference system architecture.
According to Figure
Takagi and Sugeno proposed the first fuzzy inference system, namely Sugeno FIS, in 1985 [
Referring to the same assumptions as for the Mamdani FIS, the architecture for the Sugeno FIS is illustrated in Figure
The architecture of the Sugeno fuzzy inference system.
In this short of fuzzy inference system, only the antecedents of the rules are fuzzy, and it means the rules act as an inference mechanism themselves [
Takagi and Sugeno [
Considering Figures
According to that fuzzy inference system, many parameters can be employed in the consequents of the rules of a Sugeno FIS which reasonably approximates a Mamdani FIS. This session described how the proposed flood forecasting model (hybrid neurofuzzy inference system (HN-FIS)) works.
The Takagi-Sugeno (Sugeno) fuzzy model and Mamdani fuzzy model are two great fuzzy rule-based inference systems. The Sugeno fuzzy inference system works well with linear techniques and guarantees continuity of the output surface [
A function needs to be assigned to specify the operation of the Mamdani fuzzy model entirely with the following steps: Operator OR or operator AND to the rule firing strength computation with OR’ed or AND’ed references Consequent membership function calculated from the implication operator based on a given firing strength Aggregate operator used to produce overall output membership function by combining the aggregated qualified consequents Defuzzification operator aims to transform an output membership function to a crisp single output value
If the first step is the AND operator, the second step is a product, the third step is the sum, and the fourth step is the centroid of the area (COA) [
Equations (
The rules of the HN-FIS model are given as follows: Rule 1( Rule 2 ( … Rule
According to the rules, the HN-FIS model can be expressed as shown in Figure
Proposed flood forecasting model (HN-FIS) architecture.
The HN-FIS architecture is composed of five layers, and Figure
The membership function is the generalized trapezoidal function, denoted as follows:
In this layer, the product method is generated for the firing strength
The product of this layer comes from the implication operator.
The result of this layer is the sum of all implication operators in the implication layer. The following parameters are denoted by
The defuzzification (
In this paper, the trapezoidal functions generalized were used for the type of membership functions (MFs) of the inputs and had four nonlinear parameters to be adjusted ({
If
Since there are measured values and predictions for
The mean absolute error is defined by first making each error positive by taking its absolute value and then averaging the result in the square root. The RMSE is defined by the similar idea of the mean absolute error. In RMSE, the errors are made positive by squaring each one, and then the squared root errors are averaged. The MAE has the advantage of being more interpretable and easier to describe nonspecialists. The RMSE has the advantage of being easier to handle mathematical problems. Each of these statistics deals with measures of accuracy whose size depends on the scale of the data [
The discussion of the results begins with explanation of the performance of the proposed vulnerability of the flood forecasting model based on the neurofuzzy system approach, namely HN-FIS. The flood forecasting models are developed employing MATLAB 2017 software [
In our experiment, three graphics illustrated in Figure
Vulnerability values of flood: (a) proposed model (HN-FIS), (b) Mamdani model, and (c) Sugeno model in 2008, 2009, 2010, 2011, and 2012, respectively.
Comparing error of the Mamdani model, Sugeno model, and proposed model (HN-FIS) in (a) 2008, (b) 2009, (c) 2010, (d) 2011, and (e) 2012.
In order to evaluate the performance of the proposed model, other commonly used techniques such as the Mamdani model and the Sugeno model were employed for comparison purposes. The forecasting errors obtained are presented in Table
MAE and RMSE of the Mamdani model, the Sugeno Model, and the proposed flood forecasting model (HN-FIS).
Forecasting model | MAE (%) | RMSE (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
2008 | 2009 | 2010 | 2011 | 2012 | 2008 | 2009 | 2010 | 2011 | 2012 | |
Mamdani | 0.8496 | 1.5693 | 1.1420 | 4.0662 | 1.2714 | 0.0302 | 0.0628 | 0.0354 | 0.0154 | 0.0473 |
Sugeno | 0.2425 | 1.0729 | 0.8213 | 4.0499 | 0.8307 | 0.7519 | 4.2681 | 1.5261 | 0.4739 | 2.7197 |
HN-FIS | 0.3489 | 0.5825 | 0.7382 | 4.0950 | 0.5133 | 0.0126 | 0.0477 | 0.0548 | 0.0294 | 0.0410 |
Figure
(a) MAE and (b) RMSE between Mamdani vs. Sugeno vs. proposed model (HN-FIS).
Compared with the other methods presented in the literature using other databases, the proposed hybrid model provides reliable flood vulnerability forecasting, as shown in Table
Neural network adopts a linear equation in the consequent part, which cannot present human assessment reasonably. In this case, we propose the hybrid model based on neural network and fuzzy inference system (HN-FIS) which has greater advantages in the following part and intuitive part of fuzzy reasoning. The proposed model has been constructed by a hybrid technique of the Mamdani model and Sugeno model based on the neurofuzzy inference system approach. The HN-FIS model can show its readability and understandability and present the essence of fuzzy logic more clearly. The current study aimed to determine and optimize the performance of the proposed model (HN-FIS). As supported by measurement and the predicted values based on simulation, the proposed model compares favorably with the Mamdani model and the Sugeno model in the capabilities of predicting the vulnerability of flood in 31 subdistricts in Bandung, Indonesia. The most apparent finding to emerge from this study is that three model flood forecasting (Mamdani, Sugeno, and proposed model) achieved the performance of more than 96%. However, the proposed model (HN-FIS) achieved the lowest error rate in both RMSE and MAE (0.0371% and 1.2556%, respectively) and obtained the best performance in flood vulnerability forecasting compared with existing models.
The data used to support the findings of this study are available from the corresponding author upon request.
There are no conflicts of interest to declare in this paper.
The authors thank Prof. Hou Rongtao and Dr. Irfan Dwiguna Sumitra for their support in this research.