# Switching Kalman Filtering-Based Corrosion Detection and Prognostics for Offshore Wind-Turbine Structures

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## Abstract

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## 1. Introduction

## 2. Bayesian Filtering

#### 2.1. Kalman Filtering

#### 2.2. Extensions of Kalman Filtering

## 3. Proposed Methodology

#### 3.1. Corrosion Detection

#### 3.2. Corrosion Prognosis

#### 3.2.1. Prognosis Algorithms

#### 3.2.2. Wall Thickness Estimation during Steel Corrosion

- Linear corrosion model;
- Power-law corrosion model;
- Bi-modal corrosion model.

#### 3.2.3. Implementation

#### Linear Corrosion Model

#### Bi-Modal and Power-Law Corrosion Models

#### Model Complexitity vs. State Estimation

## 4. Results

#### 4.1. Performance Metric

#### 4.2. Datasets

#### 4.3. Corrosion Detection

#### 4.4. Corrosion Prognosis

#### 4.5. Accuracy of Remaining Useful Life Estimates

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A dataset of simulated wall thickness measurements (a Gaussian measurement noise with a standard deviation of 20 μm is used here) along with the ground truth and the corresponding corrosion rate and corrosion loss. Only the wall thickness measurements are used in the corrosion detection and corrosion prognosis [24].

**Figure 2.**Output of the corrosion detection algorithm on simulated measurement data of a single position, along with the ground truth for reference. Again, a Gaussian measurement noise with a standard deviation of 20 μm is used here.

**Figure 3.**Output of the corrosion prognosis algorithm based on the power-law corrosion model on (simulated) measurement data, along with the ground truth for reference, see also [13].

**Figure 4.**Remaining useful life estimates over time, along with the ground truth and an illustration of the computation of the corresponding $\alpha $-$\lambda $-accuracy.

**Table 1.**Comparison of the accuracy of the prognosis algorithms based on the three corrosion models. Highest mean accuracy in bold.

Prognosis Algorithm | Mean Accuracy |
---|---|

Linear | 0.400 |

Power law | 0.415 |

Bimodal | 0.376 |

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**MDPI and ACS Style**

Brijder, R.; Helsen, S.; Ompusunggu, A.P.
Switching Kalman Filtering-Based Corrosion Detection and Prognostics for Offshore Wind-Turbine Structures. *Wind* **2023**, *3*, 1-13.
https://doi.org/10.3390/wind3010001

**AMA Style**

Brijder R, Helsen S, Ompusunggu AP.
Switching Kalman Filtering-Based Corrosion Detection and Prognostics for Offshore Wind-Turbine Structures. *Wind*. 2023; 3(1):1-13.
https://doi.org/10.3390/wind3010001

**Chicago/Turabian Style**

Brijder, Robert, Stijn Helsen, and Agusmian Partogi Ompusunggu.
2023. "Switching Kalman Filtering-Based Corrosion Detection and Prognostics for Offshore Wind-Turbine Structures" *Wind* 3, no. 1: 1-13.
https://doi.org/10.3390/wind3010001