# The Adaptive Seismic Resilience of Infrastructure Systems: A Bayesian Networks Analysis

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## Abstract

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## 1. Introduction

#### 1.1. Related Research in Resilience

#### 1.2. Existing Literature Related to Bayesian Networks in Seismic Resilience

- Lack of research on infrastructure adaptability as a critical feature of resilience.
- Lack of understanding on how to quantify adaptability and account for interdependencies between different infrastructure systems and factors, as may be provided by a Bayesian network BN analysis.

- Classifying the underlying factors of interdependent networks with respect to the concept of adaptability.
- Developing a new conceptual BN framework for interdependent networks.
- Using different types of inferences to provide a better insight regarding the result of the BN model.

## 2. Background

#### 2.1. Background of Bayes Theorem

#### 2.2. Background of Bayesian Network

#### 2.3. The Methodology

- Undergo adaptability modeling: the adaptability key variables and link of the BN are acquired from expert knowledge and published studies.
- Determine the parameters of Bayesian networks: the unconditional probability of the root node, the conditional probability of intermediate nodes and leaf nodes all derive from historical data, published literature and expert judgment.
- Conduct an inference: calculate the adaptability of the infrastructure system in the target area by way of forward reasoning of the Bayesian network model in order to identify important influencing factors of the adaptability through the unique backward reasoning of the Bayesian network. This is done so as to propose targeted adaptability improvement measures.

## 3. Adaptability Modeling Using Bayesian Networks

#### 3.1. Variables Selection

**Step 1**: Identify the factor. Identify a list of key factors affecting the adaptability of infrastructure systems from the existing literature.**Step 2**: Cluster the factor. The identified 19 key factors affecting the adaptability of infrastructure systems were divided into five categories.**Step 3**: Construct a Bayesian network structure. Apply the parent-child structure and causal relationship to construct the Bayesian network structure.

#### 3.2. Variables Connectivity

- Factors associated with seismic events are clustered to determine response capabilities matched to magnitude of earthquake damage.
- The basic elements and operational specifications required to maintain the normal service of the infrastructure system are clustered, which support daily supply services and provide technical support in the event of an earthquake.
- Policy and mechanism factors are clustered and conduct coordinated drills between systems to ensure effective integration of resources from all parties for rapid recovery when the next earthquake occurs.
- Factors related to economic reserves are clustered for possible economic support.
- The potential support factors of stakeholders in the assessed area are clustered to determine the degree of cooperation of stakeholders when the next earthquake occurs.

#### 3.2.1. Earthquake Intensity

#### 3.2.2. Technology

#### 3.2.3. Organization

#### 3.2.4. Economic Variables

#### 3.2.5. Social

#### 3.3. Interdependent Infrastructure

## 4. Conditional Probabilities

#### 4.1. Unconditional Probabilities

#### 4.2. Conditional Probabilities

## 5. Case Study and Inference

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Factor | State | Performance Measure | Reference |
---|---|---|---|

Epicentral distance | Close | Visual inspection/Expert opinion | [21] |

Far | |||

Very far | |||

Earthquake magnitude | Strong | M5–5.9 | |

Major | M6–6.9 | ||

Severe | M7–7.9 | ||

Violent | M8-Above | ||

Earthquake intensity | Dangerous | Ⅴ–Ⅶ | [37] |

Severe | Ⅷ–Ⅸ | ||

Violent | Ⅹ–Ⅻ |

Factor | State | Performance Measure | References |
---|---|---|---|

Normative operation | Low | $\sigma $ ≤ 80% | [5] |

Medium | 80% < $\sigma $ ≤ 90% | ||

High | $\sigma $ > 90% | ||

Professional | No | Inadequate | [15,16,38,39] |

Yes | Adequate | ||

Maintenance routine | No | Irregular maintenance | [40,41] |

Yes | Regular maintenance | ||

Advanced technology | No | Inadequate | [31] |

Yes | Adequate | ||

Earthquake history | No | Did not happen | [42,43,44] |

Yes | Happened |

Factor | State | Performance Measure | References |
---|---|---|---|

Training drills and rehearsals | No | None | [17,24,45] |

Yes | Not less than once | ||

Leadership | No | Unsatisfied | [17,45,46,47] |

Yes | Satisfied | ||

Contingency mechanisms | No | Inadequate/No update | [24,46,48] |

Factor | State | Performance Measure | References |
---|---|---|---|

Operation and maintenance funds | No | Inadequate | [23,41,49,50] |

Yes | Adequate | ||

Government investment decisions | No | No special investment | [5,24,51] |

Yes | Special investment | ||

Financial reserves | Bad | Deficit | [23,24,41,49,52,53] |

Medium | Balance | ||

Good | Surplus | ||

Local economic development situation | Low | Below average | [52,54] |

Medium | Equal to average | ||

High | More than average |

Factor | State | Performance Measure | References |
---|---|---|---|

Social information sharing | No | None | [12,48] |

Yes | Done | ||

The level of residents’ culture | Low | Below average | [38,46,47,55] |

Medium | Equal to average | ||

High | More than average | ||

Public awareness | Low | Unwillingness | [24,52] |

Medium | Average | ||

High | Willingness | ||

Relevant information | Low | Inadequate/no communication | [24,56] |

Medium | Average but not sufficient | ||

High | Adequate/communicate sufficiently |

Node State | Probability |
---|---|

Operation and maintenance funds | |

No | 1/2 |

Yes | 1/2 |

Government investment decisions | |

No | 1/2 |

Yes | 1/2 |

Financial reserves | |

Bad | 1/3 |

Medium | 1/3 |

Good | 1/3 |

Local economic development situation | |

Low | 1/3 |

Medium | 1/3 |

High | 1/3 |

Father Nodes | $\mathit{s}$ | Son Node: Economic | |||||
---|---|---|---|---|---|---|---|

Operation and Maintenance Funds | Government Investment Decisions | Financial Reserves | Local Economic Development Situation | $s=\frac{{{\displaystyle \sum}}_{i=1}^{n}{p}_{i}}{n\times max}$ | High ${s}^{2}$ | Medium $2s\left(1-s\right)$ | Low ${\left(1-s\right)}^{2}$ |

1 | 1 | 2 | 2 | 1.0000 | 1.0000 | 0.0000 | 0.0000 |

1 | 1 | 2 | 1 | 0.8333 | 0.6944 | 0.2778 | 0.0278 |

1 | 1 | 2 | 0 | 0.6667 | 0.4444 | 0.4444 | 0.1111 |

0 | 0 | 1 | 1 | 0.3333 | 0.1111 | 0.4444 | 0.4444 |

0 | 0 | 1 | 0 | 0.1667 | 0.0278 | 0.2778 | 0.6944 |

0 | 1 | 2 | 0 | 0.5000 | 0.2500 | 0.5000 | 0.2500 |

… | … | … | … | … | … | … | … |

Scenario | Earthquake History | Relevant Information | Contingency Mechanisms | Adaptability (%) | ||
---|---|---|---|---|---|---|

Low | Medium | High | ||||

Base Case | yes | low | yes | 49 | 40 | 12 |

1 | no | low | yes | 63 | 30 | 7 |

2 | yes | medium | yes | 42 | 42 | 16 |

3 | yes | high | yes | 35 | 45 | 20 |

4 | yes | low | no | 59 | 32 | 9 |

5 | no | low | no | 75 | 21 | 4 |

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## Share and Cite

**MDPI and ACS Style**

Tang, H.; Zhong, Q.; Chen, C.; Martek, I.
The Adaptive Seismic Resilience of Infrastructure Systems: A Bayesian Networks Analysis. *Systems* **2023**, *11*, 84.
https://doi.org/10.3390/systems11020084

**AMA Style**

Tang H, Zhong Q, Chen C, Martek I.
The Adaptive Seismic Resilience of Infrastructure Systems: A Bayesian Networks Analysis. *Systems*. 2023; 11(2):84.
https://doi.org/10.3390/systems11020084

**Chicago/Turabian Style**

Tang, Hui, Qingping Zhong, Chuan Chen, and Igor Martek.
2023. "The Adaptive Seismic Resilience of Infrastructure Systems: A Bayesian Networks Analysis" *Systems* 11, no. 2: 84.
https://doi.org/10.3390/systems11020084