Flood Susceptibility Modeling Using an Advanced Deep Learning-Based Iterative Classifier Optimizer

Abstract

We developed a novel iterative classifier optimizer (ICO) with alternating decision tree (ADT), naïve Bayes (NB), artificial neural network (ANN), and deep learning neural network (DLNN) ensemble algorithms to build novel ensemble computational models (ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO) for flood susceptibility (FS) mapping in the Padma River basin, Bangladesh. The models consist of environmental, topographical, hydrological, and tectonic circumstances, and the final result was chosen based on the causative attributes using multicollinearity analysis. Statistical techniques were utilized to assess the model’s performance. The results revealed that rainfall, elevation, and distance from the river are the most influencing variables for the occurrence of floods in the basin. The ensemble model of DLNN-ICO has optimal predictive performance (AUC = 0.93, and 0.91, sensitivity = 0.93 and 0.92, specificity = 0.90 and 0.80, F score = 0.91 and 0086 in the training and validation stages, respectively) followed by ADT-ICO, NB-ICO, and ANN-ICO, and might be a viable technique for precisely predicting and visualizing flood events.

1. Introduction

Owing to climatic variability, such as a warmer climate and excessive rainfall, flooding occurs regularly in various locations globally [1,2,3,4]. Flood risks increase as the world’s population, industrialization, and agricultural intensification accelerate [5,6]. For example, river flooding poses a substantial risk to human life and is often a direct result of catastrophic events that cause significant fatalities and economic disruption [7]. Flood events have caused more life and property losses in the 21st century than any other natural disaster, according to the Centre for Research on the Epidemiology of Disasters (CRED) [8]. Therefore, flood hazards, susceptibility, and risk evaluation are crucial to minimizing the forthcoming threat [9,10].

Many studies show floods harm over 200 million people annually [11]. Furthermore, under global warming scenarios, changes in land use patterns, and population growth, it is expected that flood occurrence rates and intensity will be worsened by 2050, potentially causing substantial damage (USD 1 trillion) [12,13,14,15,16,17,18]. As a result, research on flood modeling in affected vulnerable regions is urgently required to adopt mitigation and adaptation practices against disastrous floods [19,20,21]. Floods are divided into four categories depending on their incidence: flash flooding, riverine flooding, coastal flooding, and urbanized flooding [21,22]. Among those types of floods, flash floods are the most catastrophic events, causing massive loss of life and property [23]. With complex landscapes and low-lying areas, the flood-affected areas are stimulated for erosion by intense runoff from streams and rivers. Research scholars have focused on devastating flash floods to reduce the effect of such extreme events [24,25,26,27]. There has also been widespread destruction caused by flash floods in both developing and developed nations [28,29,30,31]. In contrast, developing countries are more affected by flash floods than developed nations due to insufficient infrastructure, vital financial resources, and technological innovation to anticipate flood events or reduce flood repercussions. It is, therefore, essential to develop an accurate model for flood susceptibility in a region.

Flood events have been expected and frequent in Bangladesh during the past two decades, due to irregular rainfall patterns and climatic variabilities [32,33]. The western region of Bangladesh is particularly vulnerable to irregular rainfall or flooding caused by thunderstorm bursting, especially in the rainy season (June–September), causing major socioeconomic and human casualties [34,35,36]. Flood susceptibility (FS) refers to regions’ vulnerability to flooding due to regional geology, geography, and hydrometeorological variables. Using flood susceptibility models (FSMs), it is possible to divide an area into flood-prone zones and develop ways to protect against flooding. The FSM can be performed considering diverse tools, including a geospatial model, data mining techniques, deep and machine learning modeling, hydrologic and hydrodynamic modeling, and so on [37,38]. Among these tools, the uses of deep and machine learning models are frequently described in the existing literature for developing flood susceptibility analysis owing to their popularity and worldwide acceptance [39,40,41,42,43,44,45].

On the other hand, many researchers have used various approaches to construct FSMs such as (1) the hierarchical analytic procedure (expert-based model) [46,47,48]; (2) quantitative and multivariate analysis modeling, such as (FR) frequency ratio [2,39,49,50], information value (IV model) [51,52], certainty factors, logistic regressions (LR), [11,53,54,55], weights-of-evidences (WoE model) [56,57], fuzzy logic (FL) [58,59], neurofuzzy logic (ANFIS) [44,60]; (3) machine learning algorithms (MLAs) [41,61,62,63]; (4) hydrological algorithms such as the Soil–Water Assessment Tools (SWAT) [64] and, among others, the River Analysis System–Hydraulic Engineering Center (HEC-RAS) [65]. The popular machine learning algorithms include alternating decision tree (ADT) [66,67]; naïve Bayes (NB) [54,68]; artificial neural networks (ANN) [29,50,69,70], and deep learning neural network (DLNN) [23,71], which can predict flood inundation areas in susceptible regions. Deep learning models were chosen for the FSMs because they can slowly build high-level features from raw datasets. The deep learning algorithms have high learning and generalization flexibility, detecting complex features hidden in the developed information. Thus, deep learning outperforms other machine learning models in FSM analysis [6,72,73,74]. Despite the advantage of the deep learning model for FSMs, it is yet challenging to generate accurate flood susceptibility mapping [71], this because deep learning models are still inadequate to understand the complicated processes and interrelations that control natural hazards, e.g., floods and landslides.

On the other hand, FSMs face various challenges, such as selecting the optimal modeling approaches, and a diverse method produces various results [75]. Furthermore, modeling or predicting FSMs using any tool has potential drawbacks. Consequently, hybrid ensemble machine learning can overcome these limitations, outperforming conventional and individual methods [76]. Recently, scholars have frequently used hybrid ensemble machine learning methods and information retrieval approaches, such as reptree [40,77] and naïve Bayes [55,78,79] for robust FSMs. Researchers use and create hybrid machine learning algorithms for FSMs [40,79] because of how well they work with hybrid machine learning techniques. In recent times, the developed hybrid ensemble learning tools have substantially enhanced the performance of FSMs. However, there is still no consensus concerning the optimal model for FSMs [56]. In general, iterative classifier optimization (ICO) is used to reduce the number of repetitions for cross-validation purpose in FSMs. The optimization tool is a function of optimized models employed to enhance the prediction accuracy of the model [70,71,72,73,74,75,76,77,78].

Based on the aforementioned discussion, the DLNN and ADT models were seldom applied in FSMs; their hybridization coupled with an optimization system is still rare in the past literature. Additionally, the ICO algorithm is used to optimize the training methods for the four machine learning algorithms.

However, the DLNN model has only been used in environmental studies and catastrophe prevention in a few cases. To the authors’ knowledge, there is no documented cited works for the DLNN and ADT models coupled with ICO for FS mapping. To fill the gap in earlier literature, we applied the proposed model in the Padma River basin in Bangladesh as a case study. The primary goals of the current study are (i) to examine and evaluate the FS map prediction abilities of the hybrid ensemble deep learning ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO models, and (ii) to evaluate flood-affecting variables in the Padma River basin, Bangladesh, to generate FS mapping. The Padma River basin, which is very prone to frequent floods, was chosen as a research case within that study to generate FS mapping. The originality of this work is that novel ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO hybrid ensemble models were developed to map FS. The findings of the study will encourage regional and municipal authorities and legislators to adopt suitable mitigation measures that will lower flood risks and avert possible harm.

2. Materials and Methods

2.1. Study Area

One of Bangladesh’s most important rivers, the Padma, occupies a total area of more than 2562 km² (Figure 1). The Ganges River begins at the Gangotri Glacier in the Himalayas and has its most crucial downstream stretch here [80]. In Bangladesh, the Ganges’ lowermost reach (known as the Padma) flows southeasterly for approximately 108 km before joining the Meghna near Chandpur [81]. This research was carried out in the Padma River system. Most of the study is focused on the Kushtia, Pabna, and Rajbari tributaries, and a few others: Manikganj, Faridpur, Rajshahi, and Natore. The research region is centered between latitudes 23°48′ and 25°18′ north and longitude 88°27′ and 89°48′ east. The river has a full bank discharge of around 75,000 m³s⁻¹, while the yearly average discharge of the river is 30,000 m³s⁻¹ (Hydraulics D, DHI (FAP 24) 1996) [82]. More than four hundred and seventy million people in China, India, Nepal, Bhutan, and Bangladesh profit from the Ganges River in many ways. The river profoundly affects the social and ecological settings of these countries [80].

Northwestern Bangladeshi riverine fish species are thought to use the Padma River for critical breeding and feeding habitat. It is also a significant commercial fishing area for many people [83]. People’s way of life depends on how well the Padma River basin can support agriculture and other businesses and provide food and aquaculture space. This freshwater delivery system is essential to the sustainability of the riverine ecology in the southwestern part of Bangladesh, by preserving salinity on the upstream side of the Bay of Bengal (BOB) and avoiding its degradation, which is largely made up of the Sundarbans. Bangladesh regularly faces massive floods of unprecedented magnitude due to this basin’s extreme flow regime fluctuations (water and sediment), which are caused by monsoonal rains. Additionally, this basin frequently experiences river bank erosion and channel shifting, which have caused both human displacement and environmental degradation. Climate change is anticipated to worsen this situation by increasing the quantity of water that flows into the basins of the Ganges, Brahmaputra, and Meghna rivers [80].

2.2. Preparation of the Data

Figure 2 displays an overview of the methodological framework followed in the current research and can be presented in the following three steps:

(1)

Flood causal variables were prepared for this study.

(2)

Datasets were demarcated into two components: training and testing, where the training data were then integrated into the deep learning models, and the hyperparameters for each method were tuned properly.

(3)

Deep learning methods were applied to detect how each important conditioning variable is in flood incidence.

Figure 2. Methodology flow chart.

Figure 2. Methodology flow chart.

2.2.1. Preparing of Causal Variables

Compiling flood inventory mapping for the area of research is the first step in developing flood vulnerability mapping [23,80,84]. Flooding inventories establish the connection between the flood and the component that generates flooding. To use the datasets described below, we created a flood inventory for the years 1988 through 2021: (i) past flood data from both public and private sources [5,35,85]; (ii) literature review; and (iii) imagery from Landsat 5 and 8, Sentinel-1, and the Moderate Resolution Imaging Spectroradiometer (MODIS) satellites. The flood inventory was prepared to utilize binary classification, with (30 m × 30 m) grid cells having flood assigned 1 and nonflood assigned 0 [35].

2.2.2. Dividing a Database

The resulting flood assessment was sequentially partitioned into two separate sets of data: 70% of the dataset from 350 flood areas was employed to train the algorithms. In contrast, 30% of the dataset from 150 flood-prone areas was utilized to validate the algorithms [86]. We expected to collect sampling points in nonfloodprone areas close to flood zones. Several studies suggested that selecting the same number of nonflood data sets as positive or inundate values [79] depended on topographic mapping, past flooding information, and a field investigation [85]. Moreover, a similar number of nonflood sites inside the research zone (70%) and validation sites (30%) were selected [35].

2.2.3. Flood Conditional Variable Preparation

The 18 relevant attributes were assessed based on previous research [39,85,87,88] and the watershed features of the research location: aspect, elevation (m), slope angle (degree), curvature, plan curvature, profile curvature, flow direction, flow accumulation, land use and land cover (LULC), normalized difference vegetation index (NDVI), distance to the rivers (m), soil types, mean annual rainfall (mm), river density (RD), stream power index (SPI), topographic wetness index (TWI), sediment transport index (STI), and geology. Aspect usually defines the horizontal direction that an elevation’s slope is facing. Figure 3 shows details on the flood-causing agents. Elevation, slope angle, aspect, profile curvature, plan curvature, SPI, TWI, STI, river density, distance to the river, flow accumulation, and flow direction datasets were retrieved from an advanced land-observing satellite (ALOS)-based digital elevation model (DEM) with a resolution of 30 m. Based on past literature, the ALOS-based DEM was the most accurate way to develop the raster layers of these flood conditioning variables [4]. Based on data from [89] and [90], a map illustrating mean annual rainfall from 2000 to 2021 was created in a GIS environment by using kriging spatial interpolation tools (https://chrsdata.eng.uci.edu/) [89]. When the geospatial coverage of the sampling areas was inadequate, kriging interpolation was used for this purpose [91]. A map of LULC and NDVI was acquired from https://earthexplorer.usgs.gov/ [92]. Geological data (scale 1:100,000) was obtained from the United States Geological Survey (USGS) website [93]. The soil-texture-types map (scale of 1:5,000,000) was acquired from the Food and Agriculture Organization (FAO) of the United Nations (UN) [94]. It is worth mentioning that decreasing the uncertainties associated with different spatial resolutions is difficult. A constant grid size of 30 m was adopted to provide meaningful findings, so all causal factors were examined within this approach [95].

2.3. Flood Susceptibility Assessment

Numerous scholars have employed a variety of methodologies to obtain accurate results in FS area assessment. At present, deep learning models have become vital for producing improved results. In this study, four important deep learning models, DLNN, ANN, ADT, and NB, were used to determine the specific flood-prone location with the help of the R package console platform (R-4.2.2).

2.3.1. Alternating Decision Tree (ADT)

Freund and Mason (1999) introduced the alternating decision tree (ADT) as a reliable machine learning classification approach based on boosting [49,66]. It integrates decision trees and boosting algorithms and is frequently used to solve classification and prediction issues [67,96]. ADT structure is more straightforward than decision tree models such as random forest, rotation forest, and classification and regression tree [97]. The decision and prediction nodes are two types of nodes included in ADT algorithms [66]. Prediction nodes represent a single value, while decision nodes define a specific circumstance [98]. ADT was created using a boosting strategy for numerical forecasting, in which a decision node and its two prediction nodes are formed at each iteration of the boosting process. Each prediction network node is given a weight corresponding to how much the node contributed to the overall prediction score. The ultimate prediction probability is obtained by adding all of the contributing weights [67].

If C₁ means a precondition, C₂ represents a base condition, and a and b represent two real numbers, then a and b are calculated with Equation (1):

$$a=0.5*ln\frac{W_{+}\left(C_1{\displaystyle \cap }{C}_2\right)}{W_{-}\left(C_1{\displaystyle \cap }{C}_2\right)}, b=0.5*ln\frac{W_{+}\left(C_1\cap {\overline{C}}_2\right)}{W_{-}\left(C_1{\displaystyle \cap }{\overline{C}}_2\right)}$$

(1)

where W is equal to the sum of the values provided by the prediction node, and the optimal $C_1$ and $C_2$ are calculated by minimizing Z_t ($C_1$, $C_2$), obtained with Equation (2):

$$\mathit{Z}\mathit{t}\left({\mathit{C}}_{\mathit{1}}, {\mathit{C}}_{\mathit{2}}\right)=\mathit{2}\sqrt{{\mathit{W}}_{+}\left({\mathit{C}}_{\mathit{1}}{\displaystyle \cap }{\mathit{C}}_{\mathit{2}}\right)*{\mathit{W}}_{-}\left({\mathit{C}}_{\mathit{1}}{\displaystyle \cap }{\mathit{C}}_{\mathit{2}}\right)}+\sqrt{{\mathit{W}}_{+}\left({\mathit{C}}_{\mathit{1}}{\displaystyle \cap }{\overline{\mathit{C}}}_{\mathit{2}}\right)*{\mathit{W}}_{-}\left({\mathit{C}}_{\mathit{1}}{\displaystyle \cap }{\overline{\mathit{C}}}_{\mathit{2}}\right)}$$

(2)

The flood-class labels are those that have the best constant prediction and consequently cross-validation [96,99].

2.3.2. Naïve Bayes (NB)

Of the classical machine learning algorithms, one of the few that is based on probability theory is naïve Bayes. Its performance comparable to that of neural networks and learning based on decision trees in some domains [100]. It is a special instance of Bayesian networks in which one node is an attribute node, and the others are feature nodes that are assumed to be independent of one another. NB is a popular classification algorithm based on a basic probability theorem known as Bayes’ theorem, Bayes’ rule, or Bayes’ formula [101].

In the context of evaluating flood susceptibility, the posterior probability of flood occurrence for each cell (x, y) is the conditional probability of variables (Equation (3)):

$$\mathit{P}\left(\mathit{D}={\mathit{d}}_{\mathit{j}}|{\mathit{C}}_{\mathit{i}}\left(\mathit{x},\mathit{y}\right)\right)=\mathit{P}\left(\mathit{D}={\mathit{D}}_{\mathit{j}}\right){\prod }_{\mathit{i}=\mathit{1}}^{\mathit{v}}\mathit{P}({\mathit{C}}_{\mathit{i}}\left(\mathit{x},\mathit{y}\right)|{\mathit{d}}_{\mathit{j}})$$

(3)

where P is the posterior probability; D = {d₁ = flooding event, d₂ = not flooding event}; j = {1, 2}; v is the number of factors, and C_i is the conditional probability of the ith factor, 1 ≤ i ≤ 18. After determining the posterior probability, the probability of a flood occurring in each cell (x, y) is calculated using Equation (4):

$$\mathit{S}\mathit{u}\mathit{s}\mathit{c}\mathit{e}\mathit{p}\mathit{t}\mathit{i}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}=\frac{\mathit{P}\left(\mathit{D}={\mathit{d}}_{\mathit{1}}|{\mathit{E}}_{\mathit{i}}\left(\mathit{x},\mathit{y}\right)\right)}{\mathit{P}\left(\mathit{D}={\mathit{d}}_{\mathit{1}}|{\mathit{E}}_{\mathit{i}}\left(\mathit{x},\mathit{y}\right)\right)+\mathit{P}\left(\mathit{D}={\mathit{d}}_{\mathit{2}}|{\mathit{E}}_{\mathit{i}}\left(\mathit{x},\mathit{y}\right)\right)}$$

(4)

where susceptibility denotes a cell’s likelihood of flooding, and P (D = d₁|E_i(x, y)) and P(D = d₂|E_i(x, y)) denote the cell’s posterior probabilities of flooding and nonflooding events, respectively [79].

2.3.3. Artificial Neural Network (ANN)

An artificial neural network (ANN) is a mathematical model of human perception that may be taught to do a specific task using a dataset, particularly to investigate the link between inputs and outputs [87]. Situations in which the unknown relationships between the data can serve as an effective modeling tool [102]. The model identification and classification fields have made substantial use of ANN [37]. ANN generally consists of three interconnected layers: the input, the hidden, and the output layers. The input layer receives data from various sources. Trial and error determine the number of hidden layers and their neurons. The application determines the number of neurons in the output layers, represented by the processed class [87].

The first step in ANN computation is to add a set of numbers, called xi, to the processing node’s input layer. Through connection-specific weights, wt, these signals can be amplified as they travel along connections to each of the nodes in the adjacent layer. The layer nodes next to them serve as summing elements for the incoming signals. The processing units then apply a threshold function to the input signal to convert it into an output signal (Qj), Equation (5):

$$\mathit{f}\left(\mathit{x}\right)=\frac{\mathit{1}}{\mathit{1}+{\mathit{e}}^{-\mathit{x}}}$$

(5)

In Equation (5), the output, f(x), ranges from 0 to 1. The processing unit’s output is then determined as follows:

$${\mathit{Q}}_{\mathit{j}}=\frac{\mathit{1}}{\mathit{1}+{\mathit{e}}^{-{\displaystyle \sum }{\mathit{x}}_{\mathit{i}}{\mathit{w}}_{\mathit{i}}}}$$

(6)

The output signal Q_j is transmitted across the weighted connections to the subsequent set of nodes. To ensure the signal reaches the final output layer, the process is repeated. The output signal is then interpreted as the ANN’s response to the given input stimulus [69].

2.3.4. Deep Learning Neural Network (DLNN)

In general, DLNN is classified as an ANN algorithm, but with numerous (deep) hidden layers (depending on the complexity of the features) and a feed-forward network for the back-propagation training technique. Flooding is a process that may present nonlinear relationships with other hydrological variables [103]. Since it yields precise results, it quickly gained popularity in research on susceptibility assessment to natural hazards [104]. Three layers comprise the DLNN: an input layer, several hidden layers, and an output layer. The DLNN algorithm’s basic configuration is to function in such a way that the input layer integrates data from several flood causal factors. These data are saved and evaluated in numerous hidden layers, and the output model effects are ultimately displayed in the last layer, known as the output layer. There are two possible labels for the activation function: a negative (nonflood) and a positive sign (flood). The output layer displays the categorized outcomes obtained from the final hidden layer [37].

2.4. Iterative Classifier Optimizer (ICO)

An iterative classifier optimizer (ICO) determines the best number of iterations for a specific classifier using cross-validation [105]. This approach effectively manages missing, nominal, and binary classes, including nominal, numeric, binary, and empty nominal properties [97]. This algorithm’s initialization consists of two distinct steps: Firstly, following a general model execution, the results are compared with actual measured values. Secondly, the feedback is fed back to the model to continue learning and improving the outcomes [106]. The ICO algorithm builds the model by comparing the measured and observed values and then optimizes it by adding data from the measured and observed values to the model to change the output. This study used ICO algorithms to improve how the four machine learning algorithms mentioned above are trained. For example, in the ANN model, the number of hidden neurons in the hidden layer and the weights across various layers of neurons are optimized using ICO hyperparameters to obtain the lowest RMSE value. The ICO method also assists in optimizing the total number of hidden layers and the number of hidden neurons inside each hidden layer in the DLNN. Hence, the loss and accuracy numbers are modified, and the DNNN architecture is improved. The ICO method was used in the cases of the ADT and NB models to optimize the hyperparameter represented by the maximum depth of the decision tree, allowing the model to achieve the highest level of accuracy. The maximum depth hyperparameter can influence the overall tree complexity.

2.5. Multicollinearity Assessment

The tolerance (TOL) and the variance inflation factor (VIF) were used to evaluate the multicollinearity of all causal variables, since linear collinearity lowers the performance of predictive methods [4,5,6]. In fact, if the TOL or VIF is higher than 5.0 and lower than 0.1, this indicates multicollinearity in the conditioning variable [21].

Equations (7) and (8) are used to compute the VIF [107]:

$$TOL=1-R_j^2$$

(7)

$$VIF=\frac{1}{TOL}$$

(8)

where $R_j^2$ represents the regression value of j on other different variables in a dataset.

If VIF > 10 or TOL < 0.1, the respective predictors are identical and must be eliminated from the prediction models [21].

2.6. Validation Methods for the Models

The predictive performance of the aforementioned models was demonstrated in this research by utilizing five statistical performance metrics: specificity, sensitivity, positive predictive value (PPV), negative predictive value (NPV), and receiver operating characteristics curve (ROC)-AUC analysis [108]. The number of pixels required to identify floodprone and nonfloodprone areas accurately. The validation approaches were calculated using the four statistical metrics true–positive (TP), true–negative (TN), false–negative (FN), and false–positive (FP). The accuracy of the above models depends on the results of different validation methods. When the numbers were higher, the models worked better, and vice versa [109]. Equations (9)–(12) served as the basis for the statistical methods employed in this investigation.

$$\mathit{S}\mathit{p}\mathit{e}\mathit{c}\mathit{i}\mathit{f}\mathit{i}\mathit{c}\mathit{i}\mathit{t}\mathit{y}=\frac{\mathit{T}\mathit{N}}{\mathit{F}\mathit{P}+\mathit{T}\mathit{N}}$$

(9)

$$\mathit{S}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{i}\mathit{v}\mathit{i}\mathit{t}\mathit{y}=\frac{\mathit{T}\mathit{P}}{\mathit{T}\mathit{P}+\mathit{F}\mathit{N}}$$

(10)

$$\mathit{P}\mathit{P}\mathit{V}=\frac{\mathit{T}\mathit{P}}{\mathit{F}\mathit{P}+\mathit{T}\mathit{P}}$$

(11)

$$\mathit{N}\mathit{P}\mathit{V}=\frac{\mathit{T}\mathit{N}}{\mathit{T}\mathit{N}+\mathit{F}\mathit{N}}$$

(12)

In this work, ROC-AUC analysis was also performed to evaluate the model, which is a well-established approach. ROC analysis was completed by visualizing sensitivity and specificity on the X and Y axes. It assists in assessing the prediction power of models, which is a well-established approach for this sort of assessment. The AUC values represent the model’s ability to distinguish properly between positive (flooded) and negative (nonflooded) events in the validation sample. Two axes represent the true and false positive rates on the ROC graph. A higher AUC value indicates better goodness of fit for the model. The range 0.5 to 1 shows the models’ mediocre to outstanding performance.

2.7. Graphical Representation

In the current study, a Taylor diagram is also used for model assessment and comparison. The Taylor diagram illustrates a graphical model assessment that simultaneously takes into account RMSE, r, and standard deviation to measure how close the projected models are to the associated observation data.

3. Results

3.1. Multicollinearity Assessment

The multicollinearity test was carried out to identify multicollinearity issues in all causal factors whereas tolerance and VIF were taken into consideration.

Table 1. Multicollinearity assessment.

Sl. No.	Variables	Collinearity
		TOL	VIF
1	Aspect	0.453	2.208
2	Elevation	0.336	2.976
3	Slope	0.499	2.004
4	Curvature	0.638	1.567
5	Plan curvature	0.913	1.095
6	Profile curvature	0.561	1.783
7	Flow direction	0.391	2.558
8	Flow accumulation	0.559	1.789
9	LULC	0.369	2.710
10	NDVI	0.779	1.284
11	Distance from River	0.652	1.534
12	Soil	0.449	2.227
13	Rainfall	0.305	3.279
14	River density	0.297	3.367
15	SPI	0.369	2.710
16	TWI	1.245	0.803
17	STI	0.951	1.052
18	Geology	0.993	1.007

depicts that TWI has the highest tolerance (1.245) and lowest VIF (0.803), while river density has the lowest TOL (0.305) and highest VIF (3.367), implying that all values fall within 0.1 to 5. Thus, all causal variables reveal no multicollinearity issue, and it is free of multicollinearity and is fit for mapping the FS [18].

3.2. Floods Susceptibility (FS) Assessments

Mapping of FS in this basin is evaluated by utilizing the four ensemble learning algorithms (ADT, ANN, NB, and DLNN) with an ICO optimizer. Figure 4 depicts the resulting FS maps from the models, divided into five classes of susceptibility, and lists the areas and percentages of each type. The deep learning neural network–iterative classifier optimizer (DLNN-ICO) highlights highly vulnerable areas, whereas an artificial neural network (ANN-ICO) highlights less susceptibility. In contrast, ANN-ICO found very low susceptibility compared to DLNN-ICO. The areal coverages of very high and very low FS areas within the alternating decision tree–iterative classifier optimizer (ADT-ICO) model were 786.38 and 881.17 km², respectively. The remainder of this watershed was connected to low, moderate, and high susceptibility zones, with the areal coverage of these zones being 389.25 (12.36%), 388.31 (12.33%), and 704.18 km² (22.36%), respectively (Figure 4a). Although the whole region shows moderate to high susceptibility, the southwestern section of the watersheds is more susceptible. Naïve Bayes with the iterative classifier optimizer (NB-ICO) estimated 842.12 and 346.11 km² as very high and high flood-prone zones, accounting for 26.74% and 10.99% of the total flood-prone area (Figure 4b). In the NB-ICO-based model, the very low class covers the highest area (987.93 km² shown in dark green). By the ANN-ICO (Figure 4c) machine learning technique, the very low flood susceptibility class occupied the largest percentage (36.01) area. About 1134.06 km² of the general areas have a very low flooding risk. Within this model, the low, moderately high, and very high classes each comprise 12.34%, 8.35%, 22.19%, and 21.31% of the area remaining. Among the four maps of susceptibility, the DLNN-ICO (Figure 4d) combination indicated a maximum area of 1142.25 km² of very high flood susceptibility and 379.49 km² of very low susceptibility. According to the DLNN-ICO map (Figure 4d), floods were more likely to be extremely severe in the southwest part of the basin. Besides that, the remaining areas are linked to low, moderate, and high flood-prone zones, with an aerial coverage of 294.77, 13.03, and 292.43 km², respectively (Figure 5).

3.3. Validation

The FS maps were evaluated using the models through training and validation data sets based on AUC-ROC curve analysis. For the training datasets (

Table 2. Validation of the models.

Models	Complete Dataset		Prediction		Total	Correct (%)	Wrong (%)	Sensitivity	Specificity	Recall	F score	PPV	NPV	AUC
			Nonflood (0)	Flood (1)
Training	DLNN-ICO	0	274	40	314	195.714	18.571	0.909	0.873	0.909	0.887	0.867	0.913	0.932
		1	26	260	286	185.714	20.000
		Total	300	300	600	190.714	19.286
	ADT-ICO	0	264	40	304	188.571	25.714	0.878	0.868	0.878	0.872	0.867	0.880	0.891
		1	36	260	296	185.714	20.000
		Total	300	300	600	187.143	22.857
	NB-ICO	0	260	44	304	185.714	28.571	0.865	0.855	0.865	0.859	0.853	0.867	0.873
		1	40	256	296	182.857	22.000
		Total	300	300	600	184.286	25.286
	ANN-ICO	0	258	52	310	184.286	30.000	0.855	0.832	0.855	0.841	0.827	0.860	0.835
		1	42	248	290	177.143	26.000
		Total	300	300	600	180.714	28.000
Validation	DLNN-ICO	0	130	18	148	92.857	14.286	0.868	0.878	0.868	0.874	0.880	0.867	0.917
		1	20	132	152	94.286	9.000
		Total	150	150	300	93.571	11.643
	ADT-ICO	0	128	20	148	91.429	15.714	0.855	0.865	0.855	0.861	0.867	0.853	0.864
		1	22	130	152	92.857	10.000
		Total	150	150	300	92.143	12.857
	NB-ICO	0	126	24	150	90.000	17.143	0.840	0.840	0.840	0.840	0.840	0.840	0.845
		1	24	126	150	90.000	12.000
		Total	150	150	300	90.000	14.571
	ANN-ICO	0	123	24	147	87.857	19.286	0.824	0.837	0.824	0.832	0.840	0.820	0.801
		1	27	126	153	90.000	12.000
		Total	150	150	300	88.929	15.643

), the AUC values for ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO are 0.891, 0.873, 0.835, and 0.932, respectively (Figure 6a). For the validation datasets (Table 2), they are 0.864, 0.845, 0.801, and 0.917, respectively (Figure 6b). The model DLNN-ICO (AUC = 0.932) performs the best on training datasets, followed by ADT-ICO (AUC = 0.891), NB-ICO (AUC = 0.873), and ANN-ICO (AUC = 0.835) (Figure 6a). Similarly, DLNN-ICO has a high prediction accuracy (AUC = 0.917) in the validation datasets.

The training dataset’s sensitivity, specificity, recall, F score, PPV, and NPV value in the ADT-ICO model is 0.88, 0.87, 0.88, 0.87, 0.87, and 0.88, respectively (Figure 7a). In addition, the sensitivity, specificity, recall, F score, PPV, and NPV values of this model’s validation datasets (Figure 7b) are 0.86, 0.87, 0.86, 0.86, 0.87, and 0.85, respectively. The NB-ICO model training and validation datasets of sensitivity, specificity, recall, F score, PPV, and NPV values are (0.87, 0.86, 0.87, 0.86, 0.85, and 0.87) and (0.84, 0.84, 0.84, 0.84, 0.84, and 0.84) (Table 2). However, the validation datasets of the six parameters are 0.87, 0.88, 0.87, 0.87, 0.88, and 0.87, respectively, for DLNN-ICO.

The Taylor diagram helps to compare the four models’ prediction abilities and identifies the most suitable one [99]. In terms of ideal capacity, DLNN-ICO performed best, followed by ADD-ICO, NB-ICO, and ANN-ICO (Figure 8). Convergence of the objective cost function in the ICO-DLNN model is shown in Figure 9. It clearly depicts the optimal nature of the predictive model in FS assessment. It determines and expresses as a single real number the difference between the projected value and expected value. The results of the optimal model (ICO-DLNN) show that costs decrease as the number of iterations increases (Figure 9).

3.4. Importance of the Variables

Table 3. Importance of the variables.

Parameters	AD-ICO	NB-ICO	ANN-ICO	DLNN-ICO
Aspect	14	9	12	15
Elevation	50	40	55	65
Slope	35	35	30	40
Curvature	20	15	25	20
Plan curvature	20	20	30	15
Profile curvature	10	20	15	20
Flow direction	15	25	20	10
Flow accumulation	30	35	20	15
LULC	20	20	35	25
NDVI	20	30	25	20
Distance from River	70	75	70	80
Soil	30	35	25	30
Rainfall	70	60	65	70
River density	40	45	50	50
SPI	30	30	35	30
TWI	15	20	20	10
STI	20	25	20	30
Geology	20	20	25	25

shows that the four variables, i.e., elevation, distance from the river, rainfall, and river density, with high correlation had the most effect on the FSMS. On the other hand, other variable combinations with moderate to low correlations had little effect on the FLMs.

4. Discussion

Our research aimed to suggest hybrid ensemble models (DLNN-ICO, ANN-ICO, NB-ICO, and ADT-ICO) for flash FSMs in the study basin. Many investigations have used spatial ensemble models [35,82,96,110,111,112] for FS mapping. Accurately estimating FS zones is a great challenge for developing realistic and efficient mitigating strategies [39]. Therefore, the FSM has become the global management basis [4,39,61]. As a result, experts are constantly looking for innovative and dependable strategies to produce detailed and accurate findings that can be used to propose flood control measures [4,23,48,61,113]. Various statistical and machine learning tools were used to model FS. However, there is a constraint and a disadvantage to the findings of the analysis of FS using a stand-alone approach [19]. Owing to inadequate datasets, stand-alone models frequently fail to identify the best-fit function in the hypothesis space or the actual probability of the subset [100]. As a result, hybrid or ensemble modeling is used to predict the FS region accurately [3].

This method’s outcomes may vary depending on input environmental variables. The approach is sensitive to this research area. To understand the model’s sensitivity, this approach may be reproduced elsewhere. Input factors may affect results. The OneR method was employed to find that land use, geology, and slope affect flood events in Vietnam [113]. Khosravi et al. [66] identified slope as being the most essential factor in flash-flood mapping in Iran. Distance from the river and rainfall are the two most important factors in flooding in this study’s four models. High-intensity rainfall over a short duration and distance create a large volume of water in the river channels, moving from greater elevations to the basin’s lower flat region. Low height increases flood incidence. Except for river distance, rainfall, elevation, river density, and slope were major flood risk determinants in the study basin. These results agree with earlier works [35,85].

The iterative classifier optimizer (ICO) assisted the four machine learning models to improve their predictive power and accuracy. ADT, NB, ANN, and DLNN have been extensively used for landslide hazard modeling [23,78,108,114,115,116,117,118], flood hazard modeling [3,66,68,85,97,119,120,121], gully erosion [22,112,122,123,124,125,126], and wildfire models [119,127,128,129]. However, little research has used ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO to forecast potential calamities such as FS. The results revealed that the ensemble DLNN-ICO modeling outperforms the other three models (AUC for training dataset: 0.932, and AUC for validation datasets: 0.917) [37,112,121]. Thus, DLNN-ICO performed better than the other algorithms because it is a common objective cost approach that has been successfully used to predict natural disasters and other environmental factors [37]. This is supported by the fact that DLNN-ICO requires less computation time and fewer errors. Research described in [130] followed the traditional ANN paradigm in needing more memory, a larger dataset, and a longer time for calculation. Additionally, typical statistical approaches are inappropriate due to lengthy computations, vast datasets, and more input variables [108]. The DLNN-ICO method demonstrated greater accuracy than other models. It is important to note that there is no prior research on DLNN-ICO evaluating FS. It is worth mentioning that the proposed model worked effectively in Bangladesh’s Padma River basin, allowing it to make excellent predictions about the likelihood of FS. Other research scholars have used DLNN models and other methods to forecast landslides and have obtained highly accurate results [131].

These findings confirmed earlier FS studies on a cross-section of the study area. For instance, the authors of [5] studied FS for the northeast Bangladesh using ANN. They found that the Sumanganj areas are more susceptible to flooding. Mia et al. [4] identified sensitive areas in the Brahmaputra River system using an ensemble of CNN algorithms. Our research also identified such areas close to the Padma River. Even though the Padma floodplain is more at risk, no research on western regions was available. Our precise results will help local authorities develop important mitigation methods for those living on the Padma floodplain, which is threatened by floods. In past cited works, there was no discussion on an ensemble of DLNN-ICO in FS mapping. Thus, we could not make a direct comparison of our model with the past cited works. As a consequence, DLNN has higher accuracy than previous ML techniques. Using a deep learning technique has several benefits, one of which is its independence in doing feature engineering [37]. In this method, an algorithm searches the data to find traits that correlate and then combines them to encourage quicker learning without being specifically instructed to do so. In contrast, ICO’s approach has the clear benefit of allowing fewer faults in the final model since iteration allows the model to self-correct whenever there is a mistake. Another crucial factor is that the supervisor has control over the model’s modifications since the error feedback used to train the model is performed externally [99]. This has the drawback that the model does not automatically learn to remove inaccuracies. However, DLNN outperformed other machine learning algorithms, i.e., NB, ANN, ADT, etc., as a single model [4]. Because of its better performance, decision makers and water managers can apply DLNN-ICO to give a precise outcome for local communities in similar environments.

Owing to a lack of hydrodynamic data on floods, this study has some limitations. First, the inconsistent spatial resolution of DEM-derived causative variables may cause issues with the proposed method. Second, we solely studied fluvial flash floods. In the Padma River basin, random nonflood locations were selected, which may have some bias [66]. Future research should use field survey-based nonflood sites to improve input datasets. The study’s results will assist flood hazard managers and researchers in evaluating FSMs and mitigating flood impacts. The proposed robust tool could effectively assess FS in various basins when incorporating geoenvironmental elements and model input variables with hydrodynamic information. The proposed methodology is suggested for evaluating flash-flood risk in a similar basin. Finally, the geographical investigation of the generated factors (such as DEM, land cover, geology, soil, rain, and other indicators) was not always consistent. However, that is the typical scenario and another limitation of this research, which is related to uncertainties that are difficult to precisely quantify.

5. Conclusions

Accurate and reliable FSMs are beneficial for reducing the effects of floods. Using tolerance and VIF approaches, the result was evaluated for sensitivity, specificity, NPV, and PPV. Identifying the floodprone region of the Padma River basin, Bangladesh, we presented the coupled ensemble algorithms (ADT-ICO, NB-ICO, ANN-ICO, and DLNN-ICO). In this respect, 18 environmental and topographical flood conditioning variables were determined, and the models were run employing a realistic and empirical technique. The ICO-based component significance analyses were used to select and rank the 18 flood conditioning variables for geospatial simulation. The DLNN-ICO model’s findings showed that river density (50), elevation (65), rainfall (70), and distance from the river (80) were the key variables affecting flood occurrence in the study basin. The DLNN-ICO model outscored the other three methods tested in this research. This model’s high and very high flash-flood vulnerable areas cover 922 km² (29.29%) and 1142 km² (36.27%) of the total area, respectively. The remaining area is covered by moderate, low, and very low floodprone zones, which were mostly located in lower coarse river basins around the northwest and northern regions. The findings of this study demonstrate that the flash-flood-sensitive zone may be identified in a similar climate region using the DLNN-ICO modeling technique. The suggested models are robust overall for analyzing FS. ICO methods and multiverse optimization could improve the single DNNN model for FSMs. However, these methods can also solve different hydrological problems, which could be considered in future research. The findings of this study can help policymakers at the regional and national levels implement a viable approach to reducing flood risk, thereby limiting financial damage and loss of life in the studied region, particularly for people who live near the river system. To improve the suggested model, more research should be performed on how ensemble models that use deep learning and hydrodynamics can take uncertainty into account.