Rail Steel Health Analysis Based on a Novel Genetic Density-based Clustering Technique and Manifold Representation of Acoustic Emission Signals

Figures & data

Figure 1. Illustrative diagram of the definitions in DBSCAN.

Figure 2. Flow chart of DBSCAN algorithm.

Figure 3. The flowchart for automatic and joint optimization of the feature fusion and clustering processes in AE signal analysis.

Table 1. Benchmark synthetic datasets and real-world datasets used in the validation

Dataset number	Dataset properties
	Name	Categories	Noise	Instances	Dimensions	Clusters
1	Aggregation	Synthetic (Rodriguez and Laio 2014;Wang et al. 2020)	×	1419	2	7
2	Synthetic4k		√	4000	2	5
3	Two moons		×	1502	2	2
4	T4.8k		√	8000	2	6
5	T5.8k		√	8000	2	6
6	Iris	real-world (UCI)	×	150	4	3
7	Wine		×	178	13	3
8	Seeds		×	210	7	3
9	WBC		×	683	9	2
10	Thyroid		×	215	5	3

Figure 4. Clustering results of the proposed method on two-dimensional synthetic benchmark datasets: (a) dataset 1, (b) dataset 2, (c) dataset 3, (d) dateset 4 and (e) dataset 5.

Figure 5. Clustering results of the proposed method on UCI real-world datasets: (a) dataset 6, (b) dataset 7, (c) dataset 8, (d) dataset 9 and (e) dataset 10.

Figure 6. (a) Purity, (b) F₁-measure and (c) ARIs of the comparing methods in the validating datasets (No. 1–10 in Table 1).

Figure 7. Region query in dataset 1 with (a) k-dist graph (Minpts = 10) and (b) GSI.

Table 2. Theoretical computational complexity of the mentioned clustering methods

Algorithms	k-means	AHC	FDBSCAN	OPTICS	DPC	Proposed method
Complexity	O(KIn)	O(n^3)	O(nlogn)	O(n^2logn)	O(n^2)	O(P^2nlogn)

Figure 8. (a) Schematic diagram of the tensile test system, (b) a closeup of the tensile testing machine and (c) a photo of the specimen and U75V rail steel.

Table 3. Discriminative features for AE signal clustering

Feature No.	Feature type	Feature name
1–6	Frequency domain	Wavelet packet coefficient energy ratio; Wavelet entropy
7–9	Time domain	Peak value; Absolute mean; Root mean square
10–15	Dimensionless	Skewness; Kurtosis; Crest factor; Waveform factor; Pulse factor; Clearance factor

Figure 9. Optimization of t-SNE based on GSI for test 1.

Figure 10. GSI distribution map for different parameters in clustering.

Figure 11. Visualization of clusters from (a) test 1, (b) test 2, (c) test 3 and (d) test 4 datasets in 2D features fused by t-SNE.

Figure 12. (a) Purities and (b) F1-measure of tensile tests in accordance with stage labels.

Figure 13. Clustering results of proposed method in random noise tests with a number of (a) 100, (b) 200 railway noise samples and (c) purities and F₁-measures for the proposed method, OPTICS and AHC under variant noise interference.

Rodriguez, A., and A. Laio. 2014. Clustering by fast search and find of density peaks. Science 344 (6191):1492–96. doi:10.1126/science.1242072.

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Wang, Y., D. Wang, W. Pang, C. Miao, A.-H. Tan, Y. Zhou. 2020. A systematic density-based clustering method using anchor points. Neurocomputing 400:352–70. doi:10.1016/j.neucom.2020.02.119.

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