# Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Symbolic Dynamic Entropy (SDE)

#### 2.2. Modified Multi-Scale Symbolic Dynamic Entropy (MMSDE)

#### 2.3. Damage Index

## 3. Numerical simulation

#### 3.1. Database of Numerical Simulation

#### 3.2. MMSDE of Numerical Simulation

#### 3.3. Damage Index

#### 3.4. Confusion Matrix Verification

## 4. Experimental Verification

#### 4.1. Experimental Database

#### 4.2. Results of Experimental Verification

- (I)
- One-story damage

- (II)
- Two-story damage

- (III)
- Three-story damage

#### 4.3. Damage Index

#### 4.4. Confusion Matrix Verification

#### 4.5. Comparison between Numerical Simulation and Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Three−dimensional seven-story numerical model; (

**b**) velocity response under ambient vibration (undamaged case).

**Figure 5.**MMSDE diagram of single-story damage cases; (

**a**) second floor damaged; (

**b**) fifth floor damaged; (

**c**) sixth floor damaged.

**Figure 6.**MMSDE diagram of two-story damage; (

**a**) first and second floors damaged; (

**b**) third and fourth floors damaged; (

**c**) fourth and fifth floors damaged; (

**d**) sixth and seventh floors damaged.

**Figure 7.**MMSDE diagram of three-story damage; (

**a**) first, second, and third floors damaged; (

**b**) third, fourth, and fifth floors damaged; (

**c**) fourth, fifth, and sixth floors damaged; (

**d**) fifth, sixth, and seventh floors damaged.

**Figure 9.**Detection result of the four- and five-story damage case; (

**a**) MMSDE curve; (

**b**) damage index.

**Figure 10.**Detection result of the fourth- to the sixth-story damage case. (

**a**) MMSDE curve; (

**b**) damage index.

**Figure 11.**Experimental setup. (

**a**) Seven-story steel frame model; (

**b**) location of the sensor and mass block.

**Figure 12.**Experimental installation of destructive and non-destructive structures; (

**a**) undamaged condition (no bracing removed); (

**b**) damaged condition (bracing removed).

**Figure 15.**The experimental MMSDE diagrams of damage on a single story; (

**a**) damage on the first floor; (

**b**) damage on the fourth floor; (

**c**) damage on the seventh floor.

**Figure 16.**The experimental MMSEE diagram of damage on two stories; (

**a**) damage on the first floor and second floor; (

**b**) damage on the third floor and fourth floor; (

**c**) damage on the fifth floor and sixth floor.

**Figure 17.**The experimental MMSDE diagram of damage on three stories; (

**a**) damage on the first floor, second floor, and third floor; (

**b**) damage on the fourth floor, fifth floor, and sixth floor.

**Figure 18.**The experimental MMSEE diagram of damage on four stories; (

**a**) damage on the first floor, second floor, third floor, and fourth floor; (

**b**) damage on the fourth floor, fifth floor, sixth floor, and seventh floor.

**Figure 19.**Damage index of damage on the fourth floor; (

**a**) four diagnosis results; (

**b**) the average diagnosis result.

**Figure 20.**Damage index of damage on the fifth floor and sixth floor; (

**a**) four diagnosis results; (

**b**) the average diagnosis result.

**Figure 21.**Damage index of damage from the fourth floor to the sixth floors; (

**a**) four diagnosis results; (

**b**) the average diagnosis result.

Case Number | Damage Group | Damaged Floors |
---|---|---|

0 | Undamaged | None |

1 | 1 F | |

2 | 2 F | |

3 | 3 F | |

4 | One-story damage | 4 F |

5 | 5 F | |

6 | 6 F | |

7 | 7 F | |

8 | 1 F and 2 F | |

9 | 2 F and 3 F | |

10 | Two-story damage | 3 F and 4 F |

11 | 4 F and 5 F | |

12 | 5 F and 6 F | |

13 | 6 F and 7 F | |

14 | 1 F and 2 F and 3 F | |

15 | 2 F and 3 F and 4 F | |

16 | Three-story damage | 3 F and 4 F and 5 F |

17 | 4 F and 5 F and 6 F | |

18 | 5 F and 6 F and 7 F |

Case | Damage | MMSDE | |||
---|---|---|---|---|---|

Number | Floors | TP | FP | TN | FN |

1 | 1 F | 1 | 0 | 6 | 0 |

2 | 2 F | 1 | 1 | 5 | 0 |

3 | 3 F | 1 | 0 | 6 | 0 |

4 | 4 F | 1 | 0 | 6 | 0 |

5 | 5 F | 1 | 0 | 6 | 0 |

6 | 6 F | 1 | 0 | 6 | 0 |

7 | 7 F | 1 | 0 | 6 | 0 |

8 | 1 F and 2 F | 1 | 0 | 5 | 1 |

9 | 2 F and 3 F | 2 | 1 | 4 | 0 |

10 | 3 F and 4 F | 2 | 0 | 5 | 0 |

11 | 4 F and 5 F | 2 | 0 | 5 | 0 |

12 | 5 F and 6 F | 2 | 0 | 5 | 0 |

13 | 6 F and 7 F | 1 | 1 | 4 | 1 |

14 | 1 F and 2 F and 3 F | 1 | 0 | 4 | 2 |

15 | 2 F and 3 F and 4 F | 2 | 0 | 4 | 1 |

16 | 3 F and 4 F and 5 F | 2 | 0 | 4 | 1 |

17 | 4 F and 5 F and 6 F | 3 | 0 | 4 | 0 |

18 | 5 F and 6 F and 7 F | 3 | 0 | 4 | 0 |

Total | 28 | 3 | 89 | 6 | |

Accuracy | 92.80% | ||||

Precision | 90.30% | ||||

Recall | 82.30% |

The Number of Case | Damaged Case Group | Damage Floors | Frequency (Hz) |
---|---|---|---|

0 | Undamaged | None | 3.34 |

1 | One-story damage | 1 F | 2.08 |

2 | 2 F | 2.13 | |

3 | 3 F | 2.12 | |

4 | 4 F | 2.29 | |

5 | 5 F | 2.61 | |

6 | 6 F | 2.88 | |

7 | 7 F | 3.2 | |

8 | Two-story damage | 1F, 2 F | 1.64 |

9 | 3 F, 4 F | 1.83 | |

10 | 5 F,6 F | 2.32 | |

11 | Three-story damage | 1 F, 2 F, 3 F | 1.44 |

12 | 4 F, 5 F, 6 F | 1.88 | |

13 | Multi-story damage | 1 F, 2 F, 3 F, 4 F | 1.33 |

14 | 4 F, 5 F, 6 F, 7 F | 1.86 |

Case | Damage | MMSDE | |||
---|---|---|---|---|---|

Number | Floors | TP | FP | TN | FN |

1 | 1 Floor | 1 | 0 | 6 | 0 |

2 | 2 Floor | 1 | 0 | 6 | 0 |

3 | 3 Floor | 1 | 0 | 6 | 0 |

4 | 4 Floor | 1 | 0 | 6 | 0 |

5 | 5 Floor | 1 | 0 | 6 | 0 |

6 | 6 Floor | 1 | 0 | 5 | 1 |

7 | 7 Floor | 1 | 1 | 5 | 0 |

8 | 1 F and 2 F | 2 | 0 | 5 | 0 |

9 | 3 F and 4 F | 2 | 0 | 5 | 0 |

10 | 5 F and 6 F | 2 | 1 | 4 | 0 |

11 | 1 F and 2 F and 3 F | 2 | 1 | 3 | 1 |

12 | 4 F and 5 F and 6 F | 3 | 0 | 4 | 0 |

13 | 1 F and 2 F and 3 F and 4 F | 2 | 0 | 3 | 2 |

14 | 4 F and 5 F and 6 F and 7 F | 4 | 0 | 3 | 0 |

Total | 24 | 3 | 67 | 4 | |

Accuracy | 93.8% | ||||

Precision | 88% | ||||

Recall | 85.7% |

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**MDPI and ACS Style**

Lin, T.-K.; Lee, D.-Y.; Hsu, Y.-C.; Kuo, K.-W.
Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy. *Entropy* **2022**, *24*, 987.
https://doi.org/10.3390/e24070987

**AMA Style**

Lin T-K, Lee D-Y, Hsu Y-C, Kuo K-W.
Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy. *Entropy*. 2022; 24(7):987.
https://doi.org/10.3390/e24070987

**Chicago/Turabian Style**

Lin, Tzu-Kang, Dong-You Lee, Yu-Chung Hsu, and Kai-Wei Kuo.
2022. "Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy" *Entropy* 24, no. 7: 987.
https://doi.org/10.3390/e24070987