Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability
Abstract
:1. Introduction
2. Background
2.1. Demand Patterns
- (1)
- Stable demand (): this category of demand is relatively stable with few zero demand periods.
- (2)
- Unstable demand (): the demand is unstable with high variability and occurs frequently.
- (3)
- Intermittent demand (): the demand is irregular and scattered, but relatively stable.
- (4)
- Blocky demand (): this category has a random demand pattern, with a large number of time periods having no demand and the demands varying greatly from period to period, accompanied by a significant number of zero demand stages.
2.2. Multi-Way Delay Embedding Transform
2.3. Tucker Tensor Decomposition
3. The Proposed Method
3.1. Data Pre-Processing
3.2. Anomaly Detection Based on Dual-Tailed Probability
Algorithm 1: Unsupervised anomaly detection of intermittent demand for spare parts based on dual-tailed probability. |
Input: An SPD sequence . |
Output: Detected anomalous demands . |
Step1: Run Tucker tensor decomposition to obtain the reconstructed sequence by Equation (12). |
Step2: Split X to obtain a sequence of non-zero demand quantity , and perform the following steps for X and Q: |
(1) Calculate the empirical left-tailed cumulative distribution function and the empirical right-tailed cumulative distribution function by Equations (13) and (14), approximated as the tail probability. |
(2) Calculate by Equation (17) the outlier score for each data point in X and for each data point in Q. |
Step3: Obtain the anomaly detection results and on X and Q based on the relative values of and . Calculate the final result R by Equation (19). |
4. Experimental Results
4.1. Dataset Introduction
4.2. Evaluation Metric
4.3. Comparative Experiment
4.4. Ablation Experiment
5. Conclusions
- (1)
- The dual-tailed probability is suitable to detect anomalous demand from real-world SPD sequences since it does not require label information. Both false alarms and missing alarms can be effectively recognized in unsupervised mode, which can broaden the application range.
- (2)
- The proposed method has a very low computational cost by avoiding complex model training like deep learning techniques. A fast anomaly-detection method is of great importance to practical applications.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Original Sequence | Sequence after Segmentation | Category of Sequence | |
---|---|---|---|
0.733 | 1.000 | Unstable sequence | |
0.878 | 0.373 | Stable sequence |
Type | Name |
---|---|
Probability Model | COPOD [32] |
Probability Model | ECOD [34] |
Probability Model | PCA [35] |
Partition-Based Method | IForest [8] |
Distance-Based Method | KNN [7] |
Density-Based Method | LOFs [6] |
Classification-Based Method | OCSVM [5] |
Deep Learning Method | DeepSVDD [9] |
Dataset | COPOD | ECOD | IForest | KNN | LOFs | OCSVM | PCA | DeepSVDD | Proposed Method |
---|---|---|---|---|---|---|---|---|---|
Dataset 1 | 0.4548 | 0.4538 | 85.608 | 1.7463 | 1.7154 | 2.2751 | 1.7513 | 1064.5993 | 1.131 |
Dataset 2 | 0.2204 | 0.1865 | 50.1218 | 0.9828 | 0.8273 | 0.6951 | 1.166 | 449.343 | 0.4708 |
Group | Fixed Part | Implementation |
---|---|---|
Experiment 1 | Remove sequence segmentation and tensor decomposition | The original SPD sequences are dealt with only by COPOD |
Experiment 2 | Remove tensor decomposition | The original SPD sequences and the non-zero quantity sequences are dealt with by COPOD. |
Experiment 3 | Remove sequence segmentation | The sequences after tensor decomposition are dealt with by COPOD. |
Experiment 4 | None | The proposed method |
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Hong, K.; Ren, Y.; Li, F.; Mao, W.; Liu, Y. Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability. Electronics 2024, 13, 195. https://doi.org/10.3390/electronics13010195
Hong K, Ren Y, Li F, Mao W, Liu Y. Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability. Electronics. 2024; 13(1):195. https://doi.org/10.3390/electronics13010195
Chicago/Turabian StyleHong, Kairong, Yingying Ren, Fengyuan Li, Wentao Mao, and Yangshuo Liu. 2024. "Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability" Electronics 13, no. 1: 195. https://doi.org/10.3390/electronics13010195
APA StyleHong, K., Ren, Y., Li, F., Mao, W., & Liu, Y. (2024). Unsupervised Anomaly Detection of Intermittent Demand for Spare Parts Based on Dual-Tailed Probability. Electronics, 13(1), 195. https://doi.org/10.3390/electronics13010195