# Identification of Bridge Key Performance Indicators Using Survival Analysis for Future Network-Wide Structural Health Monitoring

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## Abstract

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## 1. Introduction

## 2. Methodologies Adopted for Current Bridge Predictive Maintenance Methods

#### 2.1. Markov Theory and Its Application in the Current State-Of-The-Art Bridge Management Systems

#### Methods for Calculating Transition Probabilities

#### 2.2. Deterioration Model in the Current BMS

#### 2.3. Improvements to the Markov Model

#### 2.4. Semi-Markov Model

#### 2.5. Survival Analysis

#### 2.6. Artifical Intelligence (AI), Machine Learning and Data Mining Techniques

## 3. Case Study: Application to Visual Inspection Data from the Northern Ireland (NI) Road Network

#### Application of Survival Analysis Techniques

## 4. Discussion, Conclusions and Further Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of bridge stock on Northern Ireland road network: (

**a**) span construction type; (

**b**) number of spans; (

**c**) cumulative span range; (

**d**) bridge function.

**Figure 3.**Kaplan–Meier survival curve for time spent in condition state 1 stratified by: (

**a**) the bridge being masonry arch or not; (

**b**) the bridges function being road over river or not; (

**c**) the bridge being single span or not; (

**d**) the road class.

Condition Rating | BCI Boundaries |
---|---|

1 | [83,100] |

2 | [73,83) |

3 | [53,73) |

4 | [0,53) |

**Table 2.**A table showing the results of the hypothesis test for each of the characteristics for the time spent in condition states 1, 2 and 3 where * indicates significance at 5% level, ** highly significant, *** very highly significant and $\times $ denotes the test was insignificant at the 5% level.

Bridge Characteristic | State 1 | State 2 | State 3 |
---|---|---|---|

Masonry Arch and Not Masonry Arch | *** | $\times $ | $\times $ |

Road Over River and Not Road Over River | *** | $\ast \ast \ast $ | $\times $ |

Single Span and Not Single Span | $\ast $ | $\times $ | $\times $ |

Road Class | $\ast \ast \ast $ | $\ast \ast \ast $ | $\times $ |

**Table 3.**A table showing the value of coefficients, the exponential of these coefficients and the confidence intervals of the exponential of the coefficient for the significant variables in Cox Proportional Hazards model for time in condition state 1.

Variable | Coefficient (to 3sf) | Exp(coef) to 3sf | Confidence Interval for Exp(coef) |
---|---|---|---|

Single Span | −0.125 | 0.883 | [0.778,1.00] |

Road Class—A | 0.0822 | 1.09 | [0.998,1.18] |

Road Class—B | 0.0490 | 1.05 | [0.967,1.14] |

Road Class—C | 0.0143 | 1.01 | [0.94,1.09] |

Road Class—M | −0.570 | 0.566 | [0.402,0.797] |

Road over River | 0.102 | 1.11 | [1.02,1.21] |

Masonry Arch | 0.572 | 1.77 | [1.66,1.89] |

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**MDPI and ACS Style**

Stevens, N.-A.; Lydon, M.; Marshall, A.H.; Taylor, S.
Identification of Bridge Key Performance Indicators Using Survival Analysis for Future Network-Wide Structural Health Monitoring. *Sensors* **2020**, *20*, 6894.
https://doi.org/10.3390/s20236894

**AMA Style**

Stevens N-A, Lydon M, Marshall AH, Taylor S.
Identification of Bridge Key Performance Indicators Using Survival Analysis for Future Network-Wide Structural Health Monitoring. *Sensors*. 2020; 20(23):6894.
https://doi.org/10.3390/s20236894

**Chicago/Turabian Style**

Stevens, Nicola-Ann, Myra Lydon, Adele H. Marshall, and Su Taylor.
2020. "Identification of Bridge Key Performance Indicators Using Survival Analysis for Future Network-Wide Structural Health Monitoring" *Sensors* 20, no. 23: 6894.
https://doi.org/10.3390/s20236894