# LSTM-Autoencoder for Vibration Anomaly Detection in Vertical Carousel Storage and Retrieval System (VCSRS)

^{*}

## Abstract

**:**

## 1. Introduction

- A correlation coefficient approach of selecting the right features was adopted to ensure the selection of the right amount of sensors for the vibration study on the vertical carousel storage and retrieval system (VCSRS).
- Techniques such as filtering, normalization, and feature extraction are commonly used to improve the quality of the data and enhance the performance of the anomaly detection algorithms. These techniques have helped to remove noise and outliers, reduce dimensionality, and extract relevant features from the data, making it easier to detect patterns and anomalies. Overall, data preprocessing has played a crucial role in improving the accuracy and effectiveness of vibration anomaly detection for the vertical carousel module under study.
- The real-time multi-sensor vibration data from the vertical carousel storage and retrieval system have served as a prospect for the operational reliability of one of the AS/RS system module in a more efficient way.
- The PdM methodology assists with the current and future health monitoring status of the vertical carousel module under study, thereby predicting the anomalies as a result of misalignment from the brushless DC motor providing the rotational motion.

## 2. Literature Review and Related Works

## 3. Theoretical Backgrounds

#### 3.1. Modal Analysis

#### 3.1.1. Correlation Coefficient

#### 3.1.2. Fisher Information Matrix

#### 3.1.3. Effective Independence

#### 3.2. Vibration Signal Processing

#### 3.2.1. Fast Fourier Transform

#### 3.2.2. Power Spectral Density

_{PSD}(f), which is defined in Equation (8) as:

#### 3.3. Autoencoder

#### 3.4. Long Short-Term Memory (LSTM)

## 4. Proposed Anomaly Detection Model

- One-class classification: This involves training a model on a dataset containing only normal instances and then using the model to identify instances that are significantly different from the normal instances.
- Outlier detection: This involves identifying instances that are significantly different from the majority of the instances in the dataset.
- Clustering: This involves grouping the data into clusters and then identifying instances that do not belong to any of the clusters.
- Time series analysis: This involves analyzing the data over time to identify unusual patterns or trends.

## 5. Sensor Placement and Data Acquisition

#### 5.1. Modeling Analysis Procedure

- Use FEM to extract mode shapes of each node.
- Compute the correlation coefficient $\rho $ for each node’s mode shapes.
- Set the threshold and once it is greater than $\rho $, one eliminates nodes. If it is lesser, one continues further the optimal sensor selection process to either effective independence (Efi) or Fisher information matrix (FIM).
- Lastly, perform a comparison of the EFi and FIM results.

#### 5.2. Data Preprocessing

#### 5.3. Model Hyperparameter Function

#### 5.4. Metrics for Model Performance

- Accuracy:This is the most intuitive and straightforward metric, which measures the fraction of correctly predicted instances over the total number of instances.
- Precision: It measures the fraction of positive instances that the model correctly predicts. It is useful when the cost of false positives is high.
- Recall: It measures the fraction of positive instances correctly predicted by the model out of all the positive instances in the data. It is useful when the cost of false negatives is high.
- F1 Score: It is the harmonic mean of precision and recall, and it is a balanced measure that considers both false positives and false negatives.
- AUC-ROC: It stands for the “Area Under the Receiver Operating Characteristic” curve and is a popular metric to evaluate the performance of a binary classifier. It represents the probability that a randomly selected positive instance will be ranked higher than a randomly selected negative instance.
- Confusion Matrix: A table that shows the number of true positives, true negatives, false positives, and false negatives in a classification problem. It is helpful to understand the types of errors that the model is making and to identify patterns in the data that the model cannot capture.
- Classification Report: It summarizes the evaluation metrics for a classification problem, including precision, recall, f1-score, and support (number of instances for each class).

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AD | Anomaly Detection |

AE | Autoencoder |

AI | Artificial Intelligence |

AS/RS | Automatic Storage/Retrieval System |

CNN | Convolutional Neural Networks |

DFT | Discrete Fourier Transform |

EFI | Effective Independence |

FFT | Fast Fourier Transform |

FIM | Fisher Information Matrix |

FN | False Negative |

FP | False Positive |

IoT | Internet of Things |

LSTM | Long short term memory |

MSE | Mean Square Error |

NN | Neural Network |

PHM | Prognostics and Health Management |

PSD | Power Spectral Density |

RELU | Rectified Linear Unit |

RNN | recurrent Neural Networks |

RUL | Remaining Useful Life |

TN | True Negative |

TP | True Positive |

VA | Vibration Analysis |

VCSRS | Vertical Carousel Storage and Retrieval System |

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**Figure 3.**The LSTM-Autoencoder Model—a flowchart showing the steps from data acquisition to deployment.

**Figure 4.**The optimal sensor placement result: (

**a**) Pearson–Fisher Information Matrix, (

**b**) Pearson Effective Independence.

**Figure 5.**Identification of the vibration sensor placement on the vertical carousel storage and retrieval system.

**Figure 6.**Pictorial view of the vibration sensor placement on the vertical carousel storage and retrieval system.

**Figure 13.**The confusion matrix for the anomaly detection proposed model between the normal and abnormal class.

Model Architecture | Description |
---|---|

Number of Classes | 2 |

Number of Layers | 7 |

Batch Size | 128 |

Number of Epochs | 100 |

Dropout Rate | 0.001 |

Optimizer | Adam |

Activation Function | Softmax, ReLU, and Sigmoid |

Loss Function | MSE |

System | Item | Description |
---|---|---|

VCSRS Overall Spec. | Size | 2820 W × 1540 L × 3280 H |

Full Load | 2000 kg | |

Speed | 0.6 m/s | |

Size | 1900 W × 300 L × 200 H | |

Pallet Spec. | Quantity | 20 EA |

Load Capacity | 100 kg |

Algorithm | Accuracy (%) | Precision (%) | Recall (%) | F1-Score (%) | Cost (s) |
---|---|---|---|---|---|

AE-LSTM | 97.70 | 100.00 | 95.20 | 92.43 | 2517.8 |

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**MDPI and ACS Style**

Do, J.S.; Kareem, A.B.; Hur, J.-W.
LSTM-Autoencoder for Vibration Anomaly Detection in Vertical Carousel Storage and Retrieval System (VCSRS). *Sensors* **2023**, *23*, 1009.
https://doi.org/10.3390/s23021009

**AMA Style**

Do JS, Kareem AB, Hur J-W.
LSTM-Autoencoder for Vibration Anomaly Detection in Vertical Carousel Storage and Retrieval System (VCSRS). *Sensors*. 2023; 23(2):1009.
https://doi.org/10.3390/s23021009

**Chicago/Turabian Style**

Do, Jae Seok, Akeem Bayo Kareem, and Jang-Wook Hur.
2023. "LSTM-Autoencoder for Vibration Anomaly Detection in Vertical Carousel Storage and Retrieval System (VCSRS)" *Sensors* 23, no. 2: 1009.
https://doi.org/10.3390/s23021009