# Classification Identification of Acoustic Emission Signals from Underground Metal Mine Rock by ICIMF Classifier

Authors: Hongyan Zuo; Zhouquan Luo; Chao Wu
Journal: Mathematical Problems in Engineering
 (2014)

---

## Abstract

To overcome the drawback that fuzzy classifier was sensitive to noises and outliers, Mamdani fuzzy classifier based on improved chaos immune algorithm was developed, in which bilateral Gaussian membership function parameters were set as constraint conditions and the indexes of fuzzy classification effectiveness and number of correct samples of fuzzy classification as the subgoal of fitness function. Moreover, Iris database was used for simulation experiment, classification, and recognition of acoustic emission signals and interference signals from stope wall rock of underground metal mines. The results showed that Mamdani fuzzy classifier based on improved chaos immune algorithm could effectively improve the prediction accuracy of classification of data sets with noises and outliers and the classification accuracy of acoustic emission signal and interference signal from stope wall rock of underground metal mines was 90.00%. It was obvious that the improved chaos immune Mamdani fuzzy (ICIMF) classifier was useful for accurate diagnosis of acoustic emission signal and interference signal from stope wall rock of underground metal mines.


---

## Body

## 1. Introduction

The mining damage of underground surrounding rock was caused by mining, changing the balance of underground rock [1, 2]; it was a common disaster that the impact of mining led to the occurrence of rock burst in underground works. Because evolution and formation of rock burst were a nonlinear process, the nonlinearity was the root cause of rock burst [3–6]. As shown in literature [3], the severities of roof fall accidents had been attempted to predict based on some major contributing parameters using the binary logistic regression model. The results revealed that wider gallery width was more prone to major and serious accidents than narrower gallery width. As shown in literature [4], Liu et al. had divided the roof caving hidden danger of roof area by roof structure detection instrumentation and the results showed that the division hidden danger of roof caving method based on the roof structure detection and peek into the roof had a higher similar rate to underground roof strata conditions. As shown in literature [5], rock samples were collected from horizontal stress-related roof fall material in coal mines for petrographic characterization and compressive strength testing and the results revealed that the great variability of strength, texture, and mineralogy documented in these samples may be an indication of their complexity and the need for specialized methodology in the study of shale strength. As shown in literature [6], a relative risk model for roof and side fall fatal accidents was developed using log-linear analysis of two-way contingency table. A few statistics such as potential fatalities (PF), relative risk of fatalities (RRF), and safety measure effectiveness (SME) were derived which can be used as key safety performance indicators of roof and side fall accidents in underground mines. The application reveals that the model and the statistics developed in this study were generic and can be applied to any industrial setting.Thus, the view of traditional deterministic was used to study mine roof fall which was a nonlinear dynamics process, as a stationary view was used to look at the evolving and changing problems [7–10]; Bobick et al. [7] had used a weighted manikin mounted to generated against the top rail and nine construction workers, who served as test subjects; each built five different guardrail configurations. The study results revealed that it was possible and effective methods for evaluation of guardrail systems for preventing falls through roof and floor holes. As shown in literature [8], fuzzy classification using features selected for computational ease was applied to the mine data. Both large roof fall events could be predicted successfully using a roof fall index (RFI) metric calculated from the results of the fuzzy classification. Zheng and Cai [9] had introduced an ANN subsystem to ensure technological and scale efficiencies of the training samples for ANN. The results revealed that the ANN subsystem was proved to be very efficient. As shown in literature [10], an extension to an established theory of cutoff grade was proposed herein to determine the optimal production capacities based on a stochastic framework relying on multiple grade-tonnage curves derived from a set of simulated orebody realizations. Application to an actual copper deposit demonstrates the benefits of the proposed model. The error of understanding and prediction even error were inevitable. Much information contained in the process of rock burst in underground metal mines was reflected by rock acoustic emission phenomenon [1]. By analyzing acoustic emission characteristics of rock rupture process in underground metal mines to identify rock fracture mechanism, theoretical basis would be provided for the acoustic emission monitoring techniques of underground metal mines rock. As a variety of sound and vibration led by production operations of the underground metal mine, such as drilling operations, blasting operations, locomotive motion, unloading ore, and ore drawing [11], these sounds or vibrations were easily confused with acoustic emission signals in rock fracture process; so the validity and accuracy of the acoustic emission monitoring results were greatly affected [12]; multiangle comparative study on acoustic emission characteristics of underground metal mines and multifeature integrated recognition technology theory which was different from the noise signal were still worthy of further discussion and study.Therefore, in the paper, it was proposed that bilateral Gaussian membership function parameters were made to be constraints; the validity index [13] and the corrected sample number [14] of fuzzy classification were made to be subobjective of the fitness function; Mamdani fuzzy classifier using improved chaos immune algorithm [15–17] to optimize was established; the disadvantage which was adjusting the weights of rule to change the parameters of fuzzy systems was avoided; good technical support and theoretical support for the monitoring signal classification identification of underground metal mines rock were provided.


## 2. Design of Mamdani Fuzzy Classifier Based on Improved Chaos Immune Algorithm

### 2.1. Establishment of Mamdani Fuzzy Classifier

For Mamdani fuzzy classifier withn classified input samples and m rules, Mamdani fuzzy rule can be expressed by (1) as follows:
(1)
R
k
:
If
x
1
k
was
μ
1
k
,
x
2
k
was
μ
2
k
,
…
,
x
n
k
was
μ
n
k
,
then
y
k
was
μ
(
n
+
1
,
c
k
)
,
where μ
j
k was the membership of input sample x
j (j
=
1,2
,
…
,
n) to be classified under the kth rule; y
k (k
=
1,2
,
…
,
m) was the classified output variable under the kth rule; c
k was the output category number of Mamdani fuzzy classifier under the kth rule.To reach a better statistical property, Gaussian membership function with statistical nature was taken as the membership function of rule antecedent; that is, bilateral Gaussian membership function was used to represent the membership function of thejth variable x
j
k corresponding to the kth rule as
(2)
μ
j
k
=
{
exp
⁡
⁡
[
-
x
j
k
-
δ
j
k
α
j
k
]
2
x
j
k
≤
δ
j
k
exp
⁡
⁡
[
-
x
j
k
-
δ
j
k
β
j
k
]
2
x
j
k
>
δ
j
k
,
where δ
j
k (j
=
1,2
,
…
,
n), α
j
k (j
=
1,2
,
…
,
n), and β
j
k (j
=
1,2
,
…
,
n) denote the midpoint, the left width, and the right width of bilateral Gaussian membership function of the jth variable corresponding to the kth rule.To make Mamdani fuzzy classifier have better classification capability, single point membership function was adopted for the consequence of fuzzy rule as follows:(3)
μ
(
n
+
1
,
c
k
)
=
{
1
y
=
c
k
0
y
≠
c
k
.Assuming the total number of categories wasM, it can be known from the experiment that the output domain of Mamdani fuzzy logic system was [
1
,
M
], which was divided into M areas averagely and each area was a category. The output category of Mamdani fuzzy classifier can be calculated through (4) as
(4)
c
k
=
int
⁡
[
M
M
-
1
(
ω
-
1
)
]
,
where ω was the output of Mamdani fuzzy logic system and M was the total number of sample categories.


### 2.2. Indexes of Fuzzy Classification Effectiveness

ForX
=
{
x
1
,
x
2
,
…
,
x
n
}, the cut set d
k of fuzzy class c
k under the kth rule was set as
(5)
d
k
=
{
d
1
k
,
d
2
k
,
…
,
d
s
k
}
=
{
x
k
∣
x
k
∈
X
,
and
k
=
arg
max
⁡
1
≤
k
≤
c
{
μ
k
(
x
k
)
}
}
,
where arg
⁡
max
⁡
⁡
[
μ
k
(
x
k
)
] was the fuzzy class c
k which was assigned to the kth rule under mode x according to the principle of maximum membership; s was the number of effective samples under the kth rule.Then, using the cut set of fuzzy classc
k corresponding to the kth rule and fuzzy membership matrix U, the probability P
(
c
k
) of the kth fuzzy class can be calculated by
(6)
P
(
c
k
)
=
∑
d
j
k
∈
d
k
μ
k
(
d
j
k
)
∑
k
=
1
c
∑
d
j
k
∈
d
k
μ
k
(
d
j
k
)
,
where c was the number of fuzzy classification.ProbabilityP
(
d
j
k
) of mode d
j
k can be expressed as
(7)
P
(
d
j
k
)
=
∑
k
=
1
c
P
(
c
k
)
μ
k
(
d
j
k
)
.The probabilityP
(
c
k
∣
d
k
) of the cut set d
k of fuzzy class c
k corresponding to the kth rule can be expressed as
(8)
P
(
c
k
∣
d
k
)
=
∏
j
=
1
s
P
(
c
k
)
μ
k
(
d
j
k
)
P
(
d
j
k
)
.The occurring probability of fuzzy classification can be measured through the mean value of all the occurring probabilities of cut sets of fuzzy classes; then, the indexf
(
U
,
c
) of fuzzy classification effectiveness can be expressed as
(9)
f
(
U
,
c
)
=
∑
k
=
1
c
∏
j
=
1
s
P
(
c
k
)
μ
k
(
d
j
k
)
∑
i
=
1
c
P
(
c
k
)
μ
k
(
d
j
k
)
.The greater the value off
(
U
,
c
) was, the greater occurring probability of this fuzzy classification was. When its value reaches the maximum, the classification number it corresponds to was the optimal number c
* of data set.


### 2.3. Optimization of the Fitness Function by Improved Chaos Immune Algorithm

The midpointδ
j
k, left width α
j
k, and right width β
j
k of the bilateral Gaussian membership function of Mamdani fuzzy classifier can be optimized by improved chaos immune algorithm. Considering that the key to improved chaos immune algorithm was to determine the fitness function, in this study, the fitness function was expressed as follows:
(10)
F
(
δ
i
k
,
α
i
k
,
β
i
k
)
=
w
1
f
(
U
,
c
)
f
0
(
U
,
c
)
+
w
2
N
N
0
,
where f
0
(
U
,
c
) was the initial value of fuzzy classification effectiveness index before optimization, N was the number of samples which were fuzzy classified correctly after optimization, and N
0 was the number of samples with correct fuzzy classification before optimization. w
1 was the weight coefficient corresponding to the index of fuzzy classification effectiveness, w
2 was the weight coefficient corresponding to the number of samples which were fuzzy classified correctly, and w
1
+
w
2
=
1.Figure1 showed flow chart of optimizing parameters of Mamdani fuzzy classifier using improved chaos immune algorithm, and the specific steps were expressed as follows.Figure 1
Flow chart of optimizing parameters of Mamdani fuzzy classifier using improved chaos immune algorithm.Step 1.
Inputkth antigens {
A
g
1
k
,
A
g
2
k
,
…
,
A
g
l
k
,
…
,
A
g
L
k
} (k
=
1,2
,
…
,
m) and carry out the standardization process.Step 2.
Select the logistic modelx
r
+
1
=
4
x
r
(
1
-
x
r
) as R chaotic variables of the kth initialization antibodies {
A
b
1
k
,
A
b
2
k
,
…
,
A
b
r
k
,
…
,
A
b
R
k
} (k
=
1,2
,
…
,
m) in interval (
0,1
), which were generated randomly by chaotic model.Step 3.
For each antigenA
g
l
k (l
=
1,2
,
…
,
L; k
=
1,2
,
…
,
m), it was operated as follows.Step  3.1. Calculate the affinity β
r
l of each antibody A
b
r
k and antigen A
g
l
k, respectively, using (11) as follows:
(11)
β
r
l
=
∑
k
=
1
m
(
A
b
r
k
-
A
g
l
k
)
2
.Step  3.2. Select R
0 antibodies with highest affinity as network cells and clone them and then obtain the corresponding number of clonal antibody cells C
0.Step  3.3. For the clonal cells, equation C
i
+
1
=
C
i
-
α
(
C
i
-
X
) (i
=
1,2
,
…
,
R
0) was used for their mutation, where C
i was the number of clonal antibody cells, X
0 was the number of clonal antigen cells, and α was the mutation rate.Step  3.4. Recalculate the affinity β
r
l of each antibody A
b
r
k and antigen A
g
l
k after mutation using (11).Step  3.5. Select 30% of the cells with highest affinity as the memory cell data set M
p.Step  3.6. Calculate the similarity degree λ
r
(
R
-
r
) (r
≠
R
-
r) between each antibody A
b
r and A
b
(
R
-
r
) using (12); eliminate the individuals whose similarity degree λ
r
(
R
-
r
) was greater than the threshold value σ
s in the data set M
p as follows:
(12)
λ
r
(
R
-
r
)
=
∑
k
=
1
m
[
A
b
r
k
-
A
b
(
R
-
r
)
k
]
2
.Step 4.
Insert the memory cell data setM
p into the memory dataset M.Step 5.
Select better antibody and antigen individuals for chaotic search.Select 10% of the individuals whose fitness value was relatively large for chaotic fine search and set optimum individual asT
=
(
T
1
,
T
2
,
…
,
T
k
); the search interval of chaotic variables was narrowed as follows:
(13)
a
i
′
=
T
i
-
ϕ
(
b
i
-
a
i
)
b
i
′
=
T
i
+
ϕ
(
b
i
-
a
i
)
,
where ϕ was the shrinkage factor and ϕ
∈
(
0,0.5
).To ensure that the new range is not out of bound, deal with it as follows: ifa
i
′
<
a
i,  a
i
′
=
a
i; if b
i
′
>
b
i,  b
i
′
=
b
i.Therefore, vectorY
i of T
i after reduction in the new interval [
a
i
′
,
b
i
′
] can be determined by (14) as follows:
(14)
Y
i
=
T
i
-
a
i
′
b
i
′
-
a
i
′
.Set the linear combination ofY
i and T
i
,
n
+
1 as a new chaotic variable and use it for search. Consider
(15)
T
i
,
n
+
1
′
=
(
1
-
δ
i
)
Y
i
+
δ
i
T
i
,
n
+
1
,
where δ
i was the adaptive control coefficient and 0
<
δ
i
<
1.Adaptive control coefficientδ
i was determined adaptively as follows:
(16)
δ
i
=
1
-
(
K
-
1
K
)
θ
,
where θ was a positive integer and was determined according to the objective function (in this paper, it was taken as 2.5); K was the evolutional generation.Eliminate the individuals whose similarity was greater thanσ
s in 10% of individuals with larger fitness value in the memory base.Step 6.
Selectx
r
+
1
=
4
x
r
(
1
-
x
r
) for generating N
′ individuals in (
0,1
) to replace the individuals with poor affinity; then, they were set as the antibodies for next immune computing together with the memory dataset M
p which was obtained from last immune computing; return to Step 3 until the network reaches convergence.Step 7.
Use the fitness functionf
(
δ
j
k
,
α
j
k
,
β
j
k
) to evaluate δ
j
k
*
,
α
j
k
*
,
β
j
k
* and calculate the corresponding f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
); if f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
)
>
f
(
δ
j
k
,
α
j
k
,
β
j
k
), then f
(
δ
j
k
,
α
j
k
,
β
j
k
)
=
f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
); or else, abandon δ
j
k
*
,
α
j
k
*
,
β
j
k
*.Step 8.
If the fitness function was the maximum which was greater than 1.0, then stop searching and output the optimal solutionδ
j
k
*
,
α
j
k
*
,
β
j
k
*; otherwise, return to Step 1.


### 2.4. Simulation Experiment of Mamdani Fuzzy Classifier Based on Improved Chaos Immune Algorithm

To validate the robustness of the Mamdani fuzzy classifier (denoted by C1) based on improved chaos immune algorithm to noises and outliers, Iris database was used for simulation experiment and its classification result was compared with those of the Mamdani fuzzy classifier (denoted by C2) in [14] based on improved genetic algorithm and the classifier (denoted by C3) in [18].150 groups of Iris data were a very typical classification data proposed by the famous British statistician Fisher R. A. and can be used as evaluation criteria of various classification algorithms. Iris data was composed of 150 four-dimensional (pental length, pental width, sepal length, and sepal width) samples and consists of a total of three categories (1-Iris-setosa, 2-Iris-versicolor, and 3-Iris-virginica), with 50 samples in each category. Category 1 was completely separate from the other 2 categories, while some cross exists between Category 2 and Category 3.Parametersδ
j
k, α
j
k, and β
j
k of fuzzy classifiers C1, C2, and C3 after optimization were shown in Table 1 and the classification accuracy was compared in Table 2.Table 1
Parameter values of the optimized three kinds of fuzzy classifiers.
Classifier
Rule
δ
j
k
α
j
k
β
j
k
Category
C1
1
0.5844
0.4218
0.6656
1
2
1.367
0.6789
0.9706
2
3
2.4655
0.8996
0.1646
3
C2
1
0.5732
0.4312
0.6472
1
2
1.283
0.6472
0.9493
2
3
2.325
0.9493
0.1592
3
C3
1
0.5823
0.4224
0.6627
1
2
1.335
0.6753
0.9675
2
3
2.452
0.8956
0.1629
3Table 2
Comparison of classification accuracy of three kinds of fuzzy classifiers.
Name of classifier
C1
C2
C
3
Number of variables
1
1
2
Number of rules
3
3
12
Number of samples correctly classified
147
144
146
Classification accuracy/%
98.00
96.00
97.33The results in Table2 indicate that, for fuzzy classifier C3 after optimization, the number of variables was 2, the number of rules was 12, the number of samples correctly classified was 146, that is, the number of samples misclassified was 4, and the classification accuracy was 97.33%; for fuzzy classifier C2 after optimization, the number of variables was 1, the number of rules was 3, the number of samples correctly classified was 144, that is, the number of samples misclassified was 6, and the classification accuracy was 96.00%; for fuzzy classifier C1 after optimization, the number of variables was 1, the number of rules was 3, the number of samples correctly classified was 147, that is, the number of samples misclassified was 3, and the classification accuracy was 98.00%. It can be concluded that the Mamdani fuzzy classifier based on improved chaos immune algorithm proposed in this paper has higher classification accuracy for Iris data.The computational complexity measured by CPU time was also compared with three kinds of fuzzy classifiers. As shown in Table3, compared with the CPU time of the fuzzy classifier C2 and the fuzzy classifier C3, the CPU time of the fuzzy classifier C1 was the shortest. Obviously, it was easy to simply conclude that the fuzzy classifier C1 was less computationally expensive than the fuzzy classifier C2 or the fuzzy classifier C3.Table 3
The CPU time of three kinds of the fuzzy classifiers.
Data
CPU time (s)
C1
C2
C
3
SPECTF
0.007631
0.315737
0.016842
Iris
0.002986
0.015712
0.005712
Lymphography
0.005756
0.139592
0.010951
Heart-disease-cleverland
0.016427
0.312738
0.015944
Pendigits (test)
0.275628
3.127292
0.535523


## 2.1. Establishment of Mamdani Fuzzy Classifier

For Mamdani fuzzy classifier withn classified input samples and m rules, Mamdani fuzzy rule can be expressed by (1) as follows:
(1)
R
k
:
If
x
1
k
was
μ
1
k
,
x
2
k
was
μ
2
k
,
…
,
x
n
k
was
μ
n
k
,
then
y
k
was
μ
(
n
+
1
,
c
k
)
,
where μ
j
k was the membership of input sample x
j (j
=
1,2
,
…
,
n) to be classified under the kth rule; y
k (k
=
1,2
,
…
,
m) was the classified output variable under the kth rule; c
k was the output category number of Mamdani fuzzy classifier under the kth rule.To reach a better statistical property, Gaussian membership function with statistical nature was taken as the membership function of rule antecedent; that is, bilateral Gaussian membership function was used to represent the membership function of thejth variable x
j
k corresponding to the kth rule as
(2)
μ
j
k
=
{
exp
⁡
⁡
[
-
x
j
k
-
δ
j
k
α
j
k
]
2
x
j
k
≤
δ
j
k
exp
⁡
⁡
[
-
x
j
k
-
δ
j
k
β
j
k
]
2
x
j
k
>
δ
j
k
,
where δ
j
k (j
=
1,2
,
…
,
n), α
j
k (j
=
1,2
,
…
,
n), and β
j
k (j
=
1,2
,
…
,
n) denote the midpoint, the left width, and the right width of bilateral Gaussian membership function of the jth variable corresponding to the kth rule.To make Mamdani fuzzy classifier have better classification capability, single point membership function was adopted for the consequence of fuzzy rule as follows:(3)
μ
(
n
+
1
,
c
k
)
=
{
1
y
=
c
k
0
y
≠
c
k
.Assuming the total number of categories wasM, it can be known from the experiment that the output domain of Mamdani fuzzy logic system was [
1
,
M
], which was divided into M areas averagely and each area was a category. The output category of Mamdani fuzzy classifier can be calculated through (4) as
(4)
c
k
=
int
⁡
[
M
M
-
1
(
ω
-
1
)
]
,
where ω was the output of Mamdani fuzzy logic system and M was the total number of sample categories.


## 2.2. Indexes of Fuzzy Classification Effectiveness

ForX
=
{
x
1
,
x
2
,
…
,
x
n
}, the cut set d
k of fuzzy class c
k under the kth rule was set as
(5)
d
k
=
{
d
1
k
,
d
2
k
,
…
,
d
s
k
}
=
{
x
k
∣
x
k
∈
X
,
and
k
=
arg
max
⁡
1
≤
k
≤
c
{
μ
k
(
x
k
)
}
}
,
where arg
⁡
max
⁡
⁡
[
μ
k
(
x
k
)
] was the fuzzy class c
k which was assigned to the kth rule under mode x according to the principle of maximum membership; s was the number of effective samples under the kth rule.Then, using the cut set of fuzzy classc
k corresponding to the kth rule and fuzzy membership matrix U, the probability P
(
c
k
) of the kth fuzzy class can be calculated by
(6)
P
(
c
k
)
=
∑
d
j
k
∈
d
k
μ
k
(
d
j
k
)
∑
k
=
1
c
∑
d
j
k
∈
d
k
μ
k
(
d
j
k
)
,
where c was the number of fuzzy classification.ProbabilityP
(
d
j
k
) of mode d
j
k can be expressed as
(7)
P
(
d
j
k
)
=
∑
k
=
1
c
P
(
c
k
)
μ
k
(
d
j
k
)
.The probabilityP
(
c
k
∣
d
k
) of the cut set d
k of fuzzy class c
k corresponding to the kth rule can be expressed as
(8)
P
(
c
k
∣
d
k
)
=
∏
j
=
1
s
P
(
c
k
)
μ
k
(
d
j
k
)
P
(
d
j
k
)
.The occurring probability of fuzzy classification can be measured through the mean value of all the occurring probabilities of cut sets of fuzzy classes; then, the indexf
(
U
,
c
) of fuzzy classification effectiveness can be expressed as
(9)
f
(
U
,
c
)
=
∑
k
=
1
c
∏
j
=
1
s
P
(
c
k
)
μ
k
(
d
j
k
)
∑
i
=
1
c
P
(
c
k
)
μ
k
(
d
j
k
)
.The greater the value off
(
U
,
c
) was, the greater occurring probability of this fuzzy classification was. When its value reaches the maximum, the classification number it corresponds to was the optimal number c
* of data set.


## 2.3. Optimization of the Fitness Function by Improved Chaos Immune Algorithm

The midpointδ
j
k, left width α
j
k, and right width β
j
k of the bilateral Gaussian membership function of Mamdani fuzzy classifier can be optimized by improved chaos immune algorithm. Considering that the key to improved chaos immune algorithm was to determine the fitness function, in this study, the fitness function was expressed as follows:
(10)
F
(
δ
i
k
,
α
i
k
,
β
i
k
)
=
w
1
f
(
U
,
c
)
f
0
(
U
,
c
)
+
w
2
N
N
0
,
where f
0
(
U
,
c
) was the initial value of fuzzy classification effectiveness index before optimization, N was the number of samples which were fuzzy classified correctly after optimization, and N
0 was the number of samples with correct fuzzy classification before optimization. w
1 was the weight coefficient corresponding to the index of fuzzy classification effectiveness, w
2 was the weight coefficient corresponding to the number of samples which were fuzzy classified correctly, and w
1
+
w
2
=
1.Figure1 showed flow chart of optimizing parameters of Mamdani fuzzy classifier using improved chaos immune algorithm, and the specific steps were expressed as follows.Figure 1
Flow chart of optimizing parameters of Mamdani fuzzy classifier using improved chaos immune algorithm.Step 1.
Inputkth antigens {
A
g
1
k
,
A
g
2
k
,
…
,
A
g
l
k
,
…
,
A
g
L
k
} (k
=
1,2
,
…
,
m) and carry out the standardization process.Step 2.
Select the logistic modelx
r
+
1
=
4
x
r
(
1
-
x
r
) as R chaotic variables of the kth initialization antibodies {
A
b
1
k
,
A
b
2
k
,
…
,
A
b
r
k
,
…
,
A
b
R
k
} (k
=
1,2
,
…
,
m) in interval (
0,1
), which were generated randomly by chaotic model.Step 3.
For each antigenA
g
l
k (l
=
1,2
,
…
,
L; k
=
1,2
,
…
,
m), it was operated as follows.Step  3.1. Calculate the affinity β
r
l of each antibody A
b
r
k and antigen A
g
l
k, respectively, using (11) as follows:
(11)
β
r
l
=
∑
k
=
1
m
(
A
b
r
k
-
A
g
l
k
)
2
.Step  3.2. Select R
0 antibodies with highest affinity as network cells and clone them and then obtain the corresponding number of clonal antibody cells C
0.Step  3.3. For the clonal cells, equation C
i
+
1
=
C
i
-
α
(
C
i
-
X
) (i
=
1,2
,
…
,
R
0) was used for their mutation, where C
i was the number of clonal antibody cells, X
0 was the number of clonal antigen cells, and α was the mutation rate.Step  3.4. Recalculate the affinity β
r
l of each antibody A
b
r
k and antigen A
g
l
k after mutation using (11).Step  3.5. Select 30% of the cells with highest affinity as the memory cell data set M
p.Step  3.6. Calculate the similarity degree λ
r
(
R
-
r
) (r
≠
R
-
r) between each antibody A
b
r and A
b
(
R
-
r
) using (12); eliminate the individuals whose similarity degree λ
r
(
R
-
r
) was greater than the threshold value σ
s in the data set M
p as follows:
(12)
λ
r
(
R
-
r
)
=
∑
k
=
1
m
[
A
b
r
k
-
A
b
(
R
-
r
)
k
]
2
.Step 4.
Insert the memory cell data setM
p into the memory dataset M.Step 5.
Select better antibody and antigen individuals for chaotic search.Select 10% of the individuals whose fitness value was relatively large for chaotic fine search and set optimum individual asT
=
(
T
1
,
T
2
,
…
,
T
k
); the search interval of chaotic variables was narrowed as follows:
(13)
a
i
′
=
T
i
-
ϕ
(
b
i
-
a
i
)
b
i
′
=
T
i
+
ϕ
(
b
i
-
a
i
)
,
where ϕ was the shrinkage factor and ϕ
∈
(
0,0.5
).To ensure that the new range is not out of bound, deal with it as follows: ifa
i
′
<
a
i,  a
i
′
=
a
i; if b
i
′
>
b
i,  b
i
′
=
b
i.Therefore, vectorY
i of T
i after reduction in the new interval [
a
i
′
,
b
i
′
] can be determined by (14) as follows:
(14)
Y
i
=
T
i
-
a
i
′
b
i
′
-
a
i
′
.Set the linear combination ofY
i and T
i
,
n
+
1 as a new chaotic variable and use it for search. Consider
(15)
T
i
,
n
+
1
′
=
(
1
-
δ
i
)
Y
i
+
δ
i
T
i
,
n
+
1
,
where δ
i was the adaptive control coefficient and 0
<
δ
i
<
1.Adaptive control coefficientδ
i was determined adaptively as follows:
(16)
δ
i
=
1
-
(
K
-
1
K
)
θ
,
where θ was a positive integer and was determined according to the objective function (in this paper, it was taken as 2.5); K was the evolutional generation.Eliminate the individuals whose similarity was greater thanσ
s in 10% of individuals with larger fitness value in the memory base.Step 6.
Selectx
r
+
1
=
4
x
r
(
1
-
x
r
) for generating N
′ individuals in (
0,1
) to replace the individuals with poor affinity; then, they were set as the antibodies for next immune computing together with the memory dataset M
p which was obtained from last immune computing; return to Step 3 until the network reaches convergence.Step 7.
Use the fitness functionf
(
δ
j
k
,
α
j
k
,
β
j
k
) to evaluate δ
j
k
*
,
α
j
k
*
,
β
j
k
* and calculate the corresponding f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
); if f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
)
>
f
(
δ
j
k
,
α
j
k
,
β
j
k
), then f
(
δ
j
k
,
α
j
k
,
β
j
k
)
=
f
(
δ
j
k
*
,
α
j
k
*
,
β
j
k
*
); or else, abandon δ
j
k
*
,
α
j
k
*
,
β
j
k
*.Step 8.
If the fitness function was the maximum which was greater than 1.0, then stop searching and output the optimal solutionδ
j
k
*
,
α
j
k
*
,
β
j
k
*; otherwise, return to Step 1.


## 2.4. Simulation Experiment of Mamdani Fuzzy Classifier Based on Improved Chaos Immune Algorithm

To validate the robustness of the Mamdani fuzzy classifier (denoted by C1) based on improved chaos immune algorithm to noises and outliers, Iris database was used for simulation experiment and its classification result was compared with those of the Mamdani fuzzy classifier (denoted by C2) in [14] based on improved genetic algorithm and the classifier (denoted by C3) in [18].150 groups of Iris data were a very typical classification data proposed by the famous British statistician Fisher R. A. and can be used as evaluation criteria of various classification algorithms. Iris data was composed of 150 four-dimensional (pental length, pental width, sepal length, and sepal width) samples and consists of a total of three categories (1-Iris-setosa, 2-Iris-versicolor, and 3-Iris-virginica), with 50 samples in each category. Category 1 was completely separate from the other 2 categories, while some cross exists between Category 2 and Category 3.Parametersδ
j
k, α
j
k, and β
j
k of fuzzy classifiers C1, C2, and C3 after optimization were shown in Table 1 and the classification accuracy was compared in Table 2.Table 1
Parameter values of the optimized three kinds of fuzzy classifiers.
Classifier
Rule
δ
j
k
α
j
k
β
j
k
Category
C1
1
0.5844
0.4218
0.6656
1
2
1.367
0.6789
0.9706
2
3
2.4655
0.8996
0.1646
3
C2
1
0.5732
0.4312
0.6472
1
2
1.283
0.6472
0.9493
2
3
2.325
0.9493
0.1592
3
C3
1
0.5823
0.4224
0.6627
1
2
1.335
0.6753
0.9675
2
3
2.452
0.8956
0.1629
3Table 2
Comparison of classification accuracy of three kinds of fuzzy classifiers.
Name of classifier
C1
C2
C
3
Number of variables
1
1
2
Number of rules
3
3
12
Number of samples correctly classified
147
144
146
Classification accuracy/%
98.00
96.00
97.33The results in Table2 indicate that, for fuzzy classifier C3 after optimization, the number of variables was 2, the number of rules was 12, the number of samples correctly classified was 146, that is, the number of samples misclassified was 4, and the classification accuracy was 97.33%; for fuzzy classifier C2 after optimization, the number of variables was 1, the number of rules was 3, the number of samples correctly classified was 144, that is, the number of samples misclassified was 6, and the classification accuracy was 96.00%; for fuzzy classifier C1 after optimization, the number of variables was 1, the number of rules was 3, the number of samples correctly classified was 147, that is, the number of samples misclassified was 3, and the classification accuracy was 98.00%. It can be concluded that the Mamdani fuzzy classifier based on improved chaos immune algorithm proposed in this paper has higher classification accuracy for Iris data.The computational complexity measured by CPU time was also compared with three kinds of fuzzy classifiers. As shown in Table3, compared with the CPU time of the fuzzy classifier C2 and the fuzzy classifier C3, the CPU time of the fuzzy classifier C1 was the shortest. Obviously, it was easy to simply conclude that the fuzzy classifier C1 was less computationally expensive than the fuzzy classifier C2 or the fuzzy classifier C3.Table 3
The CPU time of three kinds of the fuzzy classifiers.
Data
CPU time (s)
C1
C2
C
3
SPECTF
0.007631
0.315737
0.016842
Iris
0.002986
0.015712
0.005712
Lymphography
0.005756
0.139592
0.010951
Heart-disease-cleverland
0.016427
0.312738
0.015944
Pendigits (test)
0.275628
3.127292
0.535523


## 3. Practical Application of Mamdani Fuzzy Classifier Based on Improved Chaos Immune Algorithm

Interference signals of acoustic emission signals from stope wall rock of underground metal mines mainly include mechanical vibration and blasting signals [1]. Figure 2 shows the test data of mechanical vibration, blasting signals, and acoustic emission signals from stope wall rock collected during the exploitation process of underground metal mines, and each consists of 500 groups. 120 effective sample data were fetched from acoustic emission signals and interference signals from stope wall rock of underground metal mines, 60 of which were set as the training set (20 rock blasting signals, 20 mechanical vibration signals, and 20 acoustic emission signals) and 60 as the sample test set (20 rock blasting signals (mV), 20 mechanical vibration signals (mV), and 20 acoustic emission signals (103 mV2 s−1)). Classifier C2, classifier C3, and classifier C1 proposed in this paper were used, respectively, for the classification of test data of acoustic emission signals and interference signals from stope wall rock of underground metal mines and the results were shown in Table 4, from which it can be learned that the classification accuracy when using classifier C2, classifier C3, and classifier C1 proposed in this study is 81.67%, 86.67%, and 90.00%, respectively. It was thus clear that Mamdani fuzzy classifier optimized by improved chaos immune algorithm makes different samples have different contributions and, to a large extent, reduces the influence of noises and outliers on classification, making the learning algorithm more robust in the case of sensitive data or noisy data, for the indexes of fuzzy classification effectiveness and correct sample number of fuzzy classification were set as the subgoal of fitness function in classifier C1 when it constructs the fitness function.Table 4
Classified results of measurement data1.
Classifier
Number of misclassified samples
Classification accuracy/%
F
1
F
2
F
3
C
1
3
4
4
81.67
C
2
2
3
3
86.67
C
3
2
2
2
90.00
C
3
2
2
2
90.00
1
F
1-Rock blasting signals; F
2-mechanical vibration signals; F
3-acoustic emission signals.Acoustic emission signals and their interference signals from stope wall rock of underground metal mines.
(a)
Rock blasting signals
(b)
Mechanical vibration signals
(c)
Acoustic emission signals


## 4. Conclusions

(1)
Mamdani fuzzy classifier optimized by improved chaos immune algorithm was established and its simulation experimental results showed that the Mamdani fuzzy classifier could effectively improve the prediction accuracy of classification of data sets with noises and outliers.
(2)
Mamdani fuzzy classifier based on improved chaos immune algorithm proposed was used for classification and recognition of the acoustic emission signals and interference signals from stope wall rock of underground metal mines. The results showed that the classification accuracy of Mamdani fuzzy classifier based on improved chaos immune algorithm was 90.00%, which achieves to accurately diagnose the acoustic emission signals and interference signals from stope wall rock of underground metal mines.



---

*Source: 524304-2014-10-21.xml*