# Advancements in Optimal Sensor Placement for Enhanced Structural Health Monitoring: Current Insights and Future Prospects

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## Abstract

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## 1. Introduction

- The system should be as well constructed as possible at a low cost.
- The system is robust for continuous operation.
- The system can easily obtain and store large amounts of data for analysis.
- The system is sensitive to the vibration information of the structure and insensitive to noise.

- Determining monitoring objectives according to the structural application.
- Determining the type of sensor which is suitable according to the monitoring objective.
- Determining parameters such as the number of sensors and the candidate locations of sensors.
- Determining evaluation criteria for the optimal placement of sensors.
- Determining the optimization algorithm for the optimal arrangement of sensors.
- Determining the cost function and the input parameters for the optimization algorithm.
- Determining the optimal solution for the sensor placement employing numerous calculations.

## 2. Evaluation Criteria

#### 2.1. Maximum Vibration Signal

#### 2.1.1. Modal Kinetic Energy (MKE)

#### 2.1.2. Mode Shape Summation Plot (MSSP)

#### 2.1.3. Eigenvector Component Product (ECP)

#### 2.1.4. Driving Point Residue (DPR)

#### 2.2. Maximum Modal Identification

#### 2.2.1. Modal Assurance Criterion (MAC)

#### 2.2.2. Redundancy of Mode Shape (RMS)

#### 2.2.3. Singular Value Decomposition Ratio (SVDR)

#### 2.3. Minimum Parameter Identification Error

#### 2.3.1. Fisher Information Matrix (FIM)

#### 2.3.2. Information Entropy (IE)

#### 2.3.3. Mutual Information (MI)

#### 2.4. Data Reconstruction Error Minimization

#### 2.5. Probability-Based Damage Detection

#### 2.6. Minimum Energy Consumption

#### 2.7. Others

#### 2.7.1. Cost

#### 2.7.2. Coverage

#### 2.8. Summary of the Section

## 3. Optimization Methods

#### 3.1. Deterministic Sensor Placement Algorithm

#### 3.2. Sequential Sensor Placement Algorithm

#### 3.3. Meta-Heuristic Optimization Algorithm

#### 3.3.1. Genetic Algorithm (GA)

#### 3.3.2. Particle Swarm Optimization (PSO)

#### 3.3.3. Others

#### 3.4. Summary of the Section

## 4. Engineering Applications

#### 4.1. Bridges

#### 4.2. High-Rise Buildings

#### 4.3. Others

#### 4.4. Summary of the Section

## 5. Challenges and Prospects

#### 5.1. Challenges

#### 5.1.1. Interplay of Sensor Placement Sensing Techniques and Data Processing

#### 5.1.2. The Bottleneck of Optimization Algorithms

#### 5.1.3. Discrepancy between Research Advancements and Practical Applications

#### 5.2. Prospects

#### 5.2.1. Optimal Sensor Placement under Uncertainty

#### 5.2.2. Optimal Arrangement of Different Types of Sensors

#### 5.2.3. Optimal Sensor Placement under Multiple Objectives

#### 5.2.4. Optimal Sensor Placement with Emerging Technology

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Potential sensor placement for SHM. A: buildings on mountain site, B: buildings on the island within the river and C: buildings on the flat terrain.

**Figure 3.**Concept of critical-grid coverage model for indoor positioning: (

**a**) critical areas of a concept indoor environment and (

**b**) critical-grid coverage model [100].

**Figure 4.**Coverage of sensors influenced by the elevation [101].

**Figure 11.**Layout of Yingwuzhou Yangtze River Bridge. (

**a**) The real bridge overview, (

**b**) layout of monitoring sensors of the bridge [164].

**Figure 12.**Benchmark model of Canton Tower [175].

**Figure 13.**Sensors placement for Shenzhen Sports Center. (

**a**) Overview of the Center, up: steel roof, down: grandstand, (

**b**) locations of strain gauges.

Criterion | Description | Advantages | Disadvantages |
---|---|---|---|

Maximum Vibration Signal | Emphasis on high-intensity vibration signal acquisition. | Enhances signal clarity, pivotal for detecting significant structural changes. | Risk of neglecting subtle, yet crucial, structural signals. |

Maximum Modal Identification | Optimization towards comprehensive modal information capture. | Facilitates in-depth analysis of structural dynamics. | Involves high computational resource allocation and complexity. |

Minimum Parameter Identification Error | Precise estimation of structural parameters. | Increases reliability and accuracy in structural assessments. | Necessitates advanced computational algorithms, elevating operational intricacy. |

Data Reconstruction Error Minimization | Aimed at high fidelity in data interpretation and reconstruction. | Ensures integrity and reliability of the data reconstruction process. | Computationally demanding, requiring sophisticated data handling capabilities. |

Probability-Based Damage Detection | Utilizes probabilistic methods for early structural damage detection. | Facilitates early intervention and nuanced understanding of damage probabilities. | May yield non-definitive results due to inherent probabilistic nature. |

Minimum Energy Consumption | Focus on energy-efficient sensor placement and functioning. | Promotes sustainable and cost-effective monitoring, especially long term. | Could limit data collection scope in energy-constrained setups. |

Type of Algorithm | Features | Advantages | Disadvantages |
---|---|---|---|

Deterministic Sensor Placement | - Utilizes mathematical formulations to determine optimal sensor locations.
- Prioritizes accuracy and computational efficiency in less complex structural scenarios.
| Emphasizes data precision and algorithmic speed. | Not well-adapted for large-scale or highly complex structures due to scalability limitations. |

Sequential Sensor Placement | - Adopts an iterative procedure, adding or removing sensors in each step to enhance monitoring efficiency.
- Offers flexibility in accommodating structural features.
| Focuses on the comprehensiveness of coverage and the number of iterations required for convergence. | Computationally demanding for extensive structures, potentially leading to increased time and resource consumption. |

Meta-heuristic Optimization | - Employs adaptive algorithms inspired by natural processes.
- Offers flexibility and adaptability in diverse structural design.
| Assesses the optimization of sensor network coverage and overall computational efficiency. | Can be computationally intensive and may require extensive calibration and fine-tuning to achieve optimal results. |

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**MDPI and ACS Style**

Wang, Y.; Chen, Y.; Yao, Y.; Ou, J.
Advancements in Optimal Sensor Placement for Enhanced Structural Health Monitoring: Current Insights and Future Prospects. *Buildings* **2023**, *13*, 3129.
https://doi.org/10.3390/buildings13123129

**AMA Style**

Wang Y, Chen Y, Yao Y, Ou J.
Advancements in Optimal Sensor Placement for Enhanced Structural Health Monitoring: Current Insights and Future Prospects. *Buildings*. 2023; 13(12):3129.
https://doi.org/10.3390/buildings13123129

**Chicago/Turabian Style**

Wang, Ying, Yue Chen, Yuhan Yao, and Jinping Ou.
2023. "Advancements in Optimal Sensor Placement for Enhanced Structural Health Monitoring: Current Insights and Future Prospects" *Buildings* 13, no. 12: 3129.
https://doi.org/10.3390/buildings13123129