# Self-Supervised Health Index Curve Generation for Condition-Based Predictive Maintenance

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## Abstract

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## 1. Introduction

## 2. Related Literature, Problem Statement and Contribution

- The capability of self-supervised learning to estimate coherent HI curves of a device.
- The enhanced self-supervised HI performance of CNN- over LSTM autoencoder.
- That self-supervised HI curves indicate wear in the device prior to human experts.
- The effects of imperfect weak labels on our proposed self-supervised HI method.

## 3. Methods

#### 3.1. Generating Unsupervised Weak Labels Applying Autoencoder

#### 3.1.1. Data Preprocessing

#### 3.1.2. Autoencoder Topologies

#### 3.1.3. Autoencoder Optimization Details

#### 3.1.4. Reconstruction Error-Based Generation of Weak Labels

#### 3.2. Self-Supervised HI Generation Using Weakly Labeled Data

## 4. Experimental Setup and Evaluation Metrics

#### 4.1. Dataset Description

#### 4.2. Comparison of Different Weak Labeling Architectures

## 5. Results and Discussion

#### 5.1. Unsupervised Generation of Preliminary Labels

#### 5.1.1. Evaluation of the Autoencoder Training Quality

#### 5.1.2. Influence of the Input Vector Window Size ${w}_{s}$ and Compression ${c}_{s}$

#### 5.1.3. Visualization of the Trained Features Encoded in the Latent Vector

#### 5.2. Self-Supervised HI Generation

#### 5.2.1. Results Using Expert-Based Initial Fault Detection

#### 5.2.2. Impact of Non-Ideal Initial Fault Detection

#### 5.3. Implications, Limitations, and Outlook

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Illustration of the HI scaling mismatch induced by unsupervised learning (

**left**) and conventional RUL estimation methods based on curve fitting (

**middle**). The introduction of a time shift in the estimation of RUL is intended to reflect the initial wear of the device caused by manufacturing tolerances. However, the true initial asset condition is unknown. In addition, a schematic of our proposed time-shift independent HI is shown (

**right**).

**Figure 4.**An illustration of the topology of our studied CNN autoencoder. In the encoder, the given input training sample of size ${w}_{s}$ is narrowed by a factor of two between layers using max-pooling. The process is repeated until a compression factor ${c}_{s}$ is achieved. The bottleneck vector is called the latent. An opposing decoder network is trained simultaneously to unravel the encoder compression in order to reconstruct the input.

**Figure 5.**Schematic of the wear-induced deterioration trend monitored by the autoencoder reconstruction error over time. The initial fault is used to weakly label the unlabeled measurement data.

**Figure 6.**Simple 1D-CNN and fully connected (MLP) layer-based classifier architecture used to estimate the HI based on the weakly labeled data. Note that other supervised architectures are adoptable.

**Figure 7.**Sensor positions (

**left**) and test rig structure (

**right**) in our test-to-failure bearing monitoring scenario: (1) motor clutch, (2) back gear, (3) load clutch, (4) coupling gear, (5) tested bearing.

**Figure 8.**Illustration on the evaluation of different weak labeling architectures based on their AUC. The required ROC is determined by continuously selecting thresholds in the deterioration curve (

**left**) and calculating its TPR/FPR with respect to an expert ground truth (

**right**).

**Figure 9.**Examples of normalized input signals and their corresponding reconstructed signal of the 1D-CNN autoencoders for a damaged and an undamaged bearing measurement.

**Figure 10.**Initial fault estimation comparison of our 1D-CNN autoencoder (

**left**) for ${w}_{s}=128$, ${c}_{s}=50\%$ and the LSTM model (

**right**) from Malhotra et al. [26], for bearing 1 from our dataset.

**Figure 11.**AUC analysis for the deterioration curve of the CNN (

**left**) and LSTM (

**right**) based autoencoder from Figure 10.

**Figure 12.**Latent space visualization based on PCA (

**top**) t-SNE (

**bottom**) for the lifecycle of bearing 1.

**Figure 13.**The proposed self-supervised device HI curve depicted for bearing 1 (

**left**) and bearing 2 (

**right**). The provided RSD curve represents the model’s uncertainty that the provided measurement belongs to the ‘functional’ class.

**Figure 14.**Overall accuracy of the HI classifier for bearing 1 (

**left**) and bearing 2 (

**right**) as the initial fault detection timing is shifted. Each individual shift corresponds to a delayed (negative shift) or early (positive shift) initial fault estimation compared to the expert initial fault decision at shift zero.

Bearing 1 | Bearing 2 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Window Size ${w}_{s}$ | ||||||||||||||

Compression ${c}_{s}$ | 128 | 256 | 512 | 1024 | 2048 | 4096 | 6144 | 128 | 256 | 512 | 1024 | 2048 | 4096 | 6144 |

$50\%$ | 0.98 | 0.92 | 0.91 | 0.82 | 0.87 | 0.70 | 0.67 | 0.97 | 0.83 | 0.64 | 0.72 | 0.75 | 0.80 | 0.77 |

$25\%$ | 0.94 | 0.87 | 0.91 | 0.93 | 0.82 | 0.84 | 0.71 | 0.82 | 0.59 | 0.47 | 0.57 | 0.62 | 0.75 | 0.73 |

$12.5\%$ | 0.91 | 0.96 | 0.72 | 0.88 | 0.93 | 0.84 | 0.73 | 0.57 | 0.51 | 0.47 | 0.50 | 0.03 | 0.67 | 0.64 |

LSTM [26] | 0.78 | (best) | 0.74 | (best) |

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**MDPI and ACS Style**

Seitz, S.; Arnold, M.; Tetzlaff, R.; Holstein, P.
Self-Supervised Health Index Curve Generation for Condition-Based Predictive Maintenance. *Electronics* **2023**, *12*, 4941.
https://doi.org/10.3390/electronics12244941

**AMA Style**

Seitz S, Arnold M, Tetzlaff R, Holstein P.
Self-Supervised Health Index Curve Generation for Condition-Based Predictive Maintenance. *Electronics*. 2023; 12(24):4941.
https://doi.org/10.3390/electronics12244941

**Chicago/Turabian Style**

Seitz, Steffen, Marvin Arnold, Ronald Tetzlaff, and Peter Holstein.
2023. "Self-Supervised Health Index Curve Generation for Condition-Based Predictive Maintenance" *Electronics* 12, no. 24: 4941.
https://doi.org/10.3390/electronics12244941