# An Advanced System for the Visualisation and Prediction of Equipment Ageing

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## Abstract

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## 1. Introduction

## 2. The Virtual Sensor of Ageing

#### 2.1. Dataset

- Thickness measurements carried out by means of ultrasonic thickness measurement (UTM) or magnetic flux leakage (MFL) techniques.
- Real-time data (e.g., acoustic emissions) coming from the diagnosis of anomalies.
- Complete information regarding the management of the ageing state according to the ageing fishbone model, which was recently adopted by the Italian Competent Authorities to satisfy the requirements of the Seveso Directive [6] regarding the control and management of the ageing of critical equipment.

#### 2.2. Models

- Ageing fishbone model for the assessment of the overall adequacy index (or simply ageing index).
- Failure frequency model for the assessment of the frequency of failure due to the equipment ageing (frequency of release).
- Probability distribution of pits model based on the extreme value theory for the assessment of the probability of the critical pit and the combination with the Bayesian inference for the assessment of the corrosion rate and the residual useful lifetime (RUL).

#### 2.2.1. Ageing Fishbone Model

_{overall}) is assessed after a score is assigned to the 12 factors, identified to be relevant for equipment ageing, in the sense that they can accelerate or slow down the phenomenon [9]. The index is the sum of the average score of accelerating factors (with a negative sign) and the average score of decelerating factors (with a positive sign).

_{k}is the score for the k-th factor, w

_{k}is the weight of the k-th factor (−1/M for accelerating factors and +1/M for decelerating factors).

#### 2.2.2. Failure Frequency Model

_{mod}is the modified frequency of failure, f

_{generic}is the generic frequency of failure from the literature, a

_{i}is the weight of factor affecting ageing, and x

_{i}is the score assigned to the factor according to [9] after normalisation to the range between −1 and 1.

#### 2.2.3. Probability Distribution of Pits Model and Combination with the Bayesian Inference

_{max}) and λ″(β|x

_{max}) are a posteriori probability distributions of α and β after a certain time, f(α|x

_{max}) and f(β|x

_{max}) are likelihood functions, and x

_{max}is the maximum corrosion value detected during the inspection.

#### 2.2.4. Interpolation Model

_{i}is the weight assigned to each measured value at the i-th location.

#### 2.3. Software

#### 2.3.1. App Desktop

#### 2.3.2. App Mobile

#### 2.4. AR Visualisation Tool

## 3. Case Study

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**View in AR: (

**a**) overlapped 3D model, (

**b**) table box information; (

**c**) bottom thickness map; (

**d**) colour scale of the map; (

**e**) example of graph given; (

**f**) scrolling of one of the pop-up menus. Note that the notation for decimal number uses comma as the software is Italian.

**Figure 8.**Iso-level thickness map obtained by the virtual sensor for the case study for (

**a**) the year 1990, (

**b**) the year 2019, (

**c**) +1 year, (

**d**) +2 years, (

**e**) +5 years, and (

**f**) +10 years. Note that the notation for decimal number uses comma as the software is Italian.

Year | Average Thickness (mm) | Minimum Thickness (mm) | Maximum Thickness (mm) | Standard Deviation | Technique |
---|---|---|---|---|---|

1990 | 7.15 | 6.1 | 9.2 | 0.733 | Visual inspection UTM |

2019 | 5.43 | 2.8 | 8 | 1.546 | MFL |

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**MDPI and ACS Style**

Ancione, G.; Saitta, R.; Bragatto, P.; Fiumara, G.; Milazzo, M.F.
An Advanced System for the Visualisation and Prediction of Equipment Ageing. *Sustainability* **2022**, *14*, 6156.
https://doi.org/10.3390/su14106156

**AMA Style**

Ancione G, Saitta R, Bragatto P, Fiumara G, Milazzo MF.
An Advanced System for the Visualisation and Prediction of Equipment Ageing. *Sustainability*. 2022; 14(10):6156.
https://doi.org/10.3390/su14106156

**Chicago/Turabian Style**

Ancione, Giuseppa, Rebecca Saitta, Paolo Bragatto, Giacomo Fiumara, and Maria Francesca Milazzo.
2022. "An Advanced System for the Visualisation and Prediction of Equipment Ageing" *Sustainability* 14, no. 10: 6156.
https://doi.org/10.3390/su14106156