17 Cluster Analysis of Acoustic Emission …
189
17.3.3 Evaluation Criteria of Clustering Effectiveness
Cluster validity evaluation is mainly a process of selecting the cluster validity index,
evaluating cluster quality and determining the best cluster number [15]. Davies
Bouldin index (DB) proposed by Davies et al. [16] is one of the most commonly
used clustering effectiveness indexes. DB indexes estimate the compactness within
a cluster by the distance between the sample points within the cluster and its cluster
center and express the level of separation between clusters by the distance between
the cluster centers. The relevant formula of DB value definition is shown in formula
(17.2)–(17.4) The smaller the DB, the smaller the distance within the cluster, and the
greater the distance between clusters, which means more clustering results. In this
paper, the DB index is selected as the evaluation index of clustering effectiveness.
D B =
1
k
K
i=1
( maxR i j
j=1,..., j =i
)
(17.2)
R i j =
s i + s j
D i j
(17.3)
s i =
1
n
x − m i
(17.4)
17.4 Results and Discussions
17.4.1 Tensile Test Results
The displacement loading curve of 2D-C/SiC specimen and the energy distribution
of AE signals during stretching are shown in Fig. 17.2.
17.4.2 Acoustic Emission Signal Clustering Results
The results of previous studies on 2D-C/SiC ceramic matrix composites [10–12, 17–
19] and SEM images of sample fracture (Fig. 17.3) show that there are five dominant
failure modes in the damage and failure process of the material, including matrix
cracking, interface failure, fiber fracture, interlayer peeling and fiber bundle fracture,
and the parameters of the clustering center can represent the characteristics of AE
signals under various damage modes [20, 21], so the cluster number K = 5 is selected
for cluster analysis, and the result shown in Fig. 17.4 is obtained.
189
17.3.3 Evaluation Criteria of Clustering Effectiveness
Cluster validity evaluation is mainly a process of selecting the cluster validity index,
evaluating cluster quality and determining the best cluster number [15]. Davies
Bouldin index (DB) proposed by Davies et al. [16] is one of the most commonly
used clustering effectiveness indexes. DB indexes estimate the compactness within
a cluster by the distance between the sample points within the cluster and its cluster
center and express the level of separation between clusters by the distance between
the cluster centers. The relevant formula of DB value definition is shown in formula
(17.2)–(17.4) The smaller the DB, the smaller the distance within the cluster, and the
greater the distance between clusters, which means more clustering results. In this
paper, the DB index is selected as the evaluation index of clustering effectiveness.
D B =
1
k
K
i=1
( maxR i j
j=1,..., j =i
)
(17.2)
R i j =
s i + s j
D i j
(17.3)
s i =
1
n
x − m i
(17.4)
17.4 Results and Discussions
17.4.1 Tensile Test Results
The displacement loading curve of 2D-C/SiC specimen and the energy distribution
of AE signals during stretching are shown in Fig. 17.2.
17.4.2 Acoustic Emission Signal Clustering Results
The results of previous studies on 2D-C/SiC ceramic matrix composites [10–12, 17–
19] and SEM images of sample fracture (Fig. 17.3) show that there are five dominant
failure modes in the damage and failure process of the material, including matrix
cracking, interface failure, fiber fracture, interlayer peeling and fiber bundle fracture,
and the parameters of the clustering center can represent the characteristics of AE
signals under various damage modes [20, 21], so the cluster number K = 5 is selected
for cluster analysis, and the result shown in Fig. 17.4 is obtained.