# Predictive Maintenance: An Autoencoder Anomaly-Based Approach for a 3 DoF Delta Robot

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## Abstract

**:**

## 1. Introduction

- Given the semi-supervised nature of the method, there is no need for R2F data for training the model, which is vital when gathering such data can be dangerous or economically infeasible.
- The proposed method does not require hand designed features for training the models, which makes the training stage easier when no or too little domain knowledge about the system is available or when a large, high-dimensional dataset must be tackled.
- The proposed method can also be used to classify the task and determine which task is going to fail, based on the similarity of distribution of the signal sequence.
- By having the output of the proposed method, a probability can be assigned, which describes how probable it is that the system is going to fail. This probability includes a slack variable which determines how much deviation from reference values is allowed. Additionally, it is also possible to determine the sensitivity and rate of changes of the proposed method to deviation from the reference values or find optimal values by solving a minimax problem.
- Given the studied system, the proposed method is capable of pinpointing where the problem originates from, regardless of the number of motors misbehaving. Moreover, the output of fault localization shows that the trained model has learned some correlations between different parameters of the studied system.
- The trained GP does not require numerous data points to predict the anomaly values. Moreover, the dedicated GP for regression does not require a long time to be (re)trained. These characteristics make GP ideal for online prediction of anomaly values.

## 2. Material and Methods

#### 2.1. Autoencoder (AE)

- encoder f
- internal representation z
- decoder g

- AE does not require any labels as the input is the output of the neural network.
- AE can capture the underlying error-free signal sequence distribution.
- Data shifts from the learned distributions can easily be acquired from the reconstruction error at the output of the AE.

#### 2.2. Convolutional Layer

#### 2.3. Delta Robot Dynamics and Parameters

#### 2.4. Gathering and Preprocessing Data from Delta Robot

#### 2.5. Architecture of the Proposed Method

- Convolution with 32 filters and kernel size of $4\times 4$
- Dropout
- Convolution with 16 filters and kernel size of $12\times 12$
- Transpose (a.k.a. deconvolution) with 16 filters and kernel size of $12\times 12$
- Dropout
- Transpose with 32 filters and kernel size of $4\times 4$

#### 2.6. GP

## 3. Results

#### 3.1. Setting up the Model

#### 3.2. Binary Classification and Predicting Anomaly Probability

#### 3.3. Robustness Testing

#### 3.4. Comparison of the Convolutional, LSTM and Dense AE

- AE with dense feed-forward layers: This architecture has the lowest performance and simply is not capable of handling sequential data. Even by increasing the model complexity, this architecture does not show any improvement in the performance. The number of trainable parameters in this case is 475,200. Moreover, the minimum validation loss for this structure is 0.8266.
- AE with LSTM layers: This model has a much better performance than the previous scenario. However, this model cannot outperform the results of the AE with convolutional layers. This simulation results proves that as expected, this structure is capable of handling sequential data, but not as good as the AE with convolutional layers. In this case, the number of trainable parameters is 254,347. It is worth noting that the minimum validation loss for AE with LSTM layers is $0.0637$.
- AE with convolutional layers: The best performing among the test models with the fewest parameters. The proposed method has successfully found all the spatial information and acquired features for reconstructing the given signal sequences. The number of parameters in this case is 125,665. Lastly, the minimum validation loss for the chosen AE structure is 0.0281

#### 3.5. Optimization of Sigmoid Function

#### 3.6. Fault Localization

#### 3.7. RUL

- Exp-Sine-Squared kernel$$k(x,{x}^{\prime})=exp(-{\displaystyle \frac{2si{n}^{2}(\pi d(x,{x}^{\prime})/p)}{{l}^{2}}})$$
- Radial basis function$$k(x,{x}^{\prime})=exp(-{\displaystyle \frac{d{(x,{x}^{\prime})}^{2}}{2{l}^{2}}})$$
- Matern$$k(x,{x}^{\prime})=\frac{{2}^{1-\nu}}{\Gamma \left(\nu \right)}{\left(\right)}^{\sqrt{2\nu}}\nu $$
- Constant kernel$$k(x,{x}^{\prime})=constant\phantom{\rule{3.33333pt}{0ex}}value\phantom{\rule{3.33333pt}{0ex}}\forall x,{x}^{\prime}\in X$$

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

PdM | Predictive maintenance |

R2F | Run-to-failure |

CI | Condition indicator |

HI | Health index |

RUL | Remaining useful lifetime |

AE | Autoencoder |

GP | Gaussian process |

LSTM | Long short-term memory |

MSE | Mean squared error |

AFFC | Adaptive feed-forward controller |

MAE | Mean absolute error |

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**Figure 2.**AFFC block diagram. The feed-forward control block contains the parameters the of the delta robot. The parameters will be updated given the output of the feedback controller.

**Figure 3.**Architecture of the proposed method. Convolutional layers in AE are used to capture information in signal sequences. This architecture tries to replicate the input signal at its output based on the learned data distribution.

**Figure 6.**Distribution of reconstruction error given the normalized input data. For the binary classification case, given these data, a threshold can be determined for PdM.

**Figure 7.**Indices of detected anomalies. Reconstruction errors above a given threshold are depicted as anomaly (1) and otherwise are set to normal (0).

**Figure 10.**Results of simulation from incremental disturbance. HI values tend to oscillate, due to the partly non-representative training data.

**Figure 11.**Learning curve of the different AEs for the barrel movement. AE with convolutional layers has the highest generalization power given the validation curves.

**Figure 12.**Results of simulation from optimized sigmoid function. Lower oscillation in HI values due to the optimization, which makes the HI time-series more informative.

Parameter | Learning Rate |
---|---|

Motor inertia [gm${}^{2}$] | 0.0005 |

Gravity [mN] | 0.08 |

Mass [g] | 0.09 |

Spring offset [mN m] | 0.07 |

Coulomb friction 0 [mNm] | 0.1 |

Coulomb friction 1 [mNm] | 0.1 |

Coulomb friction 2 [mNm] | 0.1 |

Spring constant [mNm/rad] | 0.2 |

Viscose friction 0 [mNm s/rad] | 0.01 |

Viscose friction 1 [mNm s/rad] | 0.01 |

Viscose friction 2 [mNm s/rad] | 0.01 |

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**MDPI and ACS Style**

Fathi, K.; van de Venn, H.W.; Honegger, M.
Predictive Maintenance: An Autoencoder Anomaly-Based Approach for a 3 DoF Delta Robot. *Sensors* **2021**, *21*, 6979.
https://doi.org/10.3390/s21216979

**AMA Style**

Fathi K, van de Venn HW, Honegger M.
Predictive Maintenance: An Autoencoder Anomaly-Based Approach for a 3 DoF Delta Robot. *Sensors*. 2021; 21(21):6979.
https://doi.org/10.3390/s21216979

**Chicago/Turabian Style**

Fathi, Kiavash, Hans Wernher van de Venn, and Marcel Honegger.
2021. "Predictive Maintenance: An Autoencoder Anomaly-Based Approach for a 3 DoF Delta Robot" *Sensors* 21, no. 21: 6979.
https://doi.org/10.3390/s21216979