# Hybrid Genetic Algorithm-Based Approach for Estimating Flood Losses on Structures of Buildings

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) [35]. This results from the varying magnitude of damage on horizontal and vertical surfaces in relation to the variable of flooding depth. In this respect, a model has been developed that takes building internal layout (i.e., shape and size) into account when estimating flood damage. The model proposed by Tuscher, Hanák, and Přibyl [36] predicts potential future flood damage using genetic algorithm tools; however, its 2018 version focuses solely on horizontal structures in the form of floor structures and vertical structures in the form of wall finishes without the choice of material variants. This basic model also ignores the economic impact of the flood on the openings in the building (doors, windows, etc.).

## 2. Data and Methods

^{2}] and size ratio (i.e., width-to-length ratio). These two variables, together with the depth of flooding [m], are modeled in order to infer a mathematical solution for a user-friendly, quick, and accurate unit loss estimation per 1 m

^{2}.

#### 2.1. Data

^{2}]. Furthermore, the combination of these two factors may even have a fundamental impact, especially if small-sized rooms (e.g., RSG1) and a low SR ratio are comparable to large rooms (e.g., RSG14) with a shape approaching a square [35] (see Figure 1 and Figure 2). The influence of the side ratio and size of the room on the unit amount of loss with depth of flooding is shown in Figure 1. In addition, Figure 2 clearly shows that the RSG and shape of the room have an impact on the amount of unit loss.

^{2}, while 43 SR variants were available for the largest model area of 30 m

^{2}. This irregular distribution caused great inaccuracies in the resulting algorithm, therefore, a regular distribution between RSGs was carried out for a total of 280 variants, while for each model RSG area, the size ratios of SR were defined in 20 variants with a 0.05 to 1.00 value range. With regular distribution, the resulting algorithm was already sufficiently accurate to be accepted. Basic characteristics of model rooms are given in Table 1.

#### 2.2. Methods

^{2}) and room area X, room side ratio Y, and the depth of room flooding Z.

_{PM}represents the percent error of the primary model, EL

_{PM}represents the loss estimated by the primary model, and EL

_{BoC}represents loss estimated by traditional calculation by means of bill of costs (see Section 3.1).

_{EM}represents the percent error of the entire extended model, EL

_{EM}represents the loss estimated by the entire extended model, and EL

_{BoC}represents loss estimated by traditional calculation by means of bill of costs (see Section 3.2).

## 3. Results and Discussion

#### 3.1. Verification of the Accuracy of the Primary Model Combining the Least Squares Method and the Genetic Algorithm

_{PM}items were processed for 6 combinations of variant solutions of used materials on the level of room with different RSG and SR. Statistical data on the frequency of PE

_{PM}are shown in Table 2.

_{PM}items, i.e., 92.7% of the total number of combinations performed.

_{PM}values reach acceptable values for all material variants and RSGs. For example, for the FV1-PV1 variant, the median PE

_{PM}for the whole set (i.e., 3360 items) is 0.3836%, where the maximum value was found in RSG4 (PE

_{PM}= 0.5355%) and the minimum value in RSG30 (PE

_{PM}= 0.3069%). When evaluating the median PE

_{PM}for other material variants according to RSG, the tendency to achieve lower primary model accuracy was found in RSGs with a smaller floor area compared to RSGs with a larger floor area.

_{PM}value was achieved for the FV3-PV1 combination at 2.03% (see Table 3). This maximum value still represents a very accurate result for flood damage estimation for insurance purposes. Regarding descriptive statistics of the percent error, the mean value is 0.004855% and median is 0.004390%. It can be concluded based on the results that the change of the materials used in the calculation of the algorithm does not have a significant effect on the results. The error rate is similar to the composition for various combinations of material variants used in vertical and horizontal structures. This means that the primary model and methodology of the genetic algorithm is sound and can be used for various materials and compositions, given correct inclusion of an itemized budget in the data set.

#### 3.2. Verification of Accuracy of the Entire Hybrid Computational Model on a Case Study

_{EM}values for modeled flood depths for buildings A, B, and C are 1.10%, 0.33%, and 1.03% respectively. It should be emphasized that the buildings differ significantly from each other. In the case of building A at flooding depth of 1.25 m, the windows were flooded; additionally, there are two L-shaped rooms and one very small room (room 5 with an area of 0.89 m

^{2}) with an area smaller than RSG1 (4 m

^{2}). Building B is distinct in that there are rooms with very different areas. These include, for example, room 3 with an area of 4.3 m

^{2}(area approaching RSG1) and room 4 with an area of 36.46 m

^{2}, which exceeds the area of RSG14. The room 4 is also unique in that it is L-shaped. Additionally, only a few French windows are flooded at the depth of 0.75 m. Finally, building C contains distinct room 1, which forms a long corridor with a small SR value of 0.16, while featuring a large number of doors (7 doors).

#### 3.3. Potential Interconnection of the Model with Information Systems of Insurance Companies

## 4. Conclusions

^{2}) as an additional variable in the model. Authors would also like to explore the possible use of BIM technologies for flood loss estimation purposes and their connection with the model presented herein.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Surface plot showing the dependence of the amount of loss on the side ratio and size of the room (depth of flooding 2.5 m).

**Figure 4.**Floor plans of buildings: (

**a**) building used in variant A, (

**b**) building used in variant B, (

**c**) building used in variant C.

**Figure 5.**Diagram of potential interconnection of the model and information system of an insurance company.

RSG (Room Size Group) | Size of the Room [m^{2}] | Initial Number of Model Rooms with Various SR | Adapted Number of Model Rooms with Various SR |
---|---|---|---|

RSG1 | 4 | 11 | 20 |

RSG2 | 6 | 15 | 20 |

RSG3 | 8 | 19 | 20 |

RSG4 | 10 | 22 | 20 |

RSG5 | 12 | 25 | 20 |

RSG6 | 14 | 28 | 20 |

RSG7 | 16 | 31 | 20 |

RSG8 | 18 | 33 | 20 |

RSG9 | 20 | 35 | 20 |

RSG10 | 22 | 37 | 20 |

RSG11 | 24 | 39 | 20 |

RSG12 | 26 | 41 | 20 |

RSG13 | 28 | 43 | 20 |

RSG14 | 30 | 45 | 20 |

TOTAL | - | 424 | 280 |

**Table 2.**Statistical data on the frequency of percent errors for individual material variants of the primary model.

PE_{PM} [%] | Frequency of Occurrence for Individual Material Variants | |||||
---|---|---|---|---|---|---|

FV1-PV1 | FV1-PV2 | FV2-PV1 | FV2-PV2 | FV3-PV1 | FV3-PV2 | |

0.00–0.10 | 519 | 456 | 383 | 353 | 337 | 303 |

0.10–0.20 | 471 | 472 | 385 | 330 | 369 | 344 |

0.20–0.30 | 380 | 422 | 373 | 359 | 283 | 337 |

0.30–0.40 | 358 | 413 | 418 | 524 | 325 | 359 |

0.40–0.50 | 313 | 356 | 398 | 294 | 272 | 340 |

0.50–0.60 | 310 | 330 | 384 | 378 | 286 | 294 |

0.60–0.70 | 231 | 263 | 375 | 360 | 294 | 299 |

0.70–0.80 | 230 | 226 | 287 | 330 | 279 | 311 |

0.80–0.90 | 177 | 214 | 107 | 185 | 242 | 292 |

0.90–1.00 | 158 | 123 | 63 | 100 | 184 | 164 |

1.00–1.10 | 102 | 42 | 74 | 47 | 151 | 93 |

1.10–1.20 | 62 | 25 | 30 | 38 | 96 | 52 |

1.20–1.30 | 26 | 13 | 26 | 36 | 71 | 47 |

1.30–1.40 | 12 | 5 | 19 | 13 | 47 | 50 |

1.40–1.50 | 8 | 0 | 15 | 8 | 34 | 29 |

1.50–1.60 | 3 | 0 | 9 | 4 | 27 | 20 |

1.60–1.70 | 0 | 0 | 6 | 1 | 27 | 14 |

1.70–1.80 | 0 | 0 | 4 | 0 | 16 | 11 |

1.80–1.90 | 0 | 0 | 3 | 0 | 10 | 1 |

1.90–2.00 | 0 | 0 | 1 | 0 | 8 | 0 |

2.00–2.10 | 0 | 0 | 0 | 0 | 2 | 0 |

Material Variant | PE_{PM} Min [%] | PE_{PM} Max [%] |
---|---|---|

FV1-PV1 | 0.0001 | 1.5393 |

FV1-PV2 | 0.0000 | 1.3310 |

FV2-PV1 | 0.0001 | 1.9500 |

FV2-PV2 | 0.0003 | 1.6018 |

FV3-PV1 | 0.0001 | 2.0316 |

FV3-PV2 | 0.0003 | 1.8198 |

Building Variant | Room No. | Length | Width | Horizontal Construction | Vertical Construction | Window | Door—Doorframe |
---|---|---|---|---|---|---|---|

A | 1 | 3.46 | 2.74 | FV2 | PV1 | - | adjustable |

2 | 2.25 | 1.67 | FV2 | PV1 | - | adjustable | |

3 | 3.48 | 3.45 | FV1 | PV1 | plastic | adjustable | |

4 | 4.12 | 3.45 | FV1 | PV1 | plastic | adjustable | |

5 | 0.95 | 0.94 | FV2 | PV1 | - | adjustable | |

6 | 2.40 | 1.49 | FV2 | PV1 | - | adjustable | |

7 | 5.87 | 3.47 | FV3 | PV1 | plastic | adjustable | |

8 | 3.46 | 3.04 | FV1 | PV1 | plastic | adjustable | |

B | 1 | 3.45 | 1.67 | FV2 | PV2 | - | adjustable |

2 | 3.45 | 3.03 | FV1 | PV2 | - | adjustable | |

3 | 2.39 | 1.80 | FV2 | PV2 | - | adjustable | |

4 | 7.70 | 7.09 | FV1 | PV2 | wooden | adjustable | |

5 | 3.82 | 3.45 | FV3 | PV2 | wooden | adjustable | |

6 | 3.77 | 3.45 | FV3 | PV2 | wooden | adjustable | |

C | 1 | 7.70 | 1.20 | FV1 | PV1 | - | steel |

2 | 4.49 | 3.85 | FV1 | PV1 | plastic | steel | |

3 | 3.60 | 2.39 | FV2 | PV1 | plastic | steel | |

4 | 4.49 | 3.85 | FV3 | PV1 | plastic | steel | |

5 | 4.49 | 3.60 | FV2 | PV1 | plastic | steel | |

6 | 2.00 | 1.20 | FV2 | PV1 | - | steel | |

7 | 2.30 | 2.00 | FV2 | PV1 | plastic | steel |

**Table 5.**Comparison of the amount of damage [EUR] determined by the extended THP model and the itemized budget.

Building A | Building B | Building C | |
---|---|---|---|

Extended THP model | 8341.43 | 8585.03 | 7486.34 |

Bill of costs | 8249.71 | 8556.42 | 7408.99 |

PE_{EM} | 1.11% | 0.33% | 1.04% |

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## Share and Cite

**MDPI and ACS Style**

Hanák, T.; Tuscher, M.; Přibyl, O. Hybrid Genetic Algorithm-Based Approach for Estimating Flood Losses on Structures of Buildings. *Sustainability* **2020**, *12*, 3047.
https://doi.org/10.3390/su12073047

**AMA Style**

Hanák T, Tuscher M, Přibyl O. Hybrid Genetic Algorithm-Based Approach for Estimating Flood Losses on Structures of Buildings. *Sustainability*. 2020; 12(7):3047.
https://doi.org/10.3390/su12073047

**Chicago/Turabian Style**

Hanák, Tomáš, Martin Tuscher, and Oto Přibyl. 2020. "Hybrid Genetic Algorithm-Based Approach for Estimating Flood Losses on Structures of Buildings" *Sustainability* 12, no. 7: 3047.
https://doi.org/10.3390/su12073047