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.
The mining damage of underground surrounding rock was caused by mining, changing the balance of underground rock [
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 [
Therefore, in the paper, it was proposed that bilateral Gaussian membership function parameters were made to be constraints; the validity index [
For Mamdani fuzzy classifier with
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 the
To make Mamdani fuzzy classifier have better classification capability, single point membership function was adopted for the consequence of fuzzy rule as follows:
Assuming the total number of categories was
For
Then, using the cut set of fuzzy class
Probability
The probability
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 index
The greater the value of
The midpoint
Figure
Flow chart of optimizing parameters of Mamdani fuzzy classifier using improved chaos immune algorithm.
Input
Select the logistic model
For each antigen
Insert the memory cell data set
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 as
To ensure that the new range is not out of bound, deal with it as follows: if
Therefore, vector
Set the linear combination of
Adaptive control coefficient
Eliminate the individuals whose similarity was greater than
Select
Use the fitness function
If the fitness function was the maximum which was greater than 1.0, then stop searching and output the optimal solution
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 [
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.
Parameters
Parameter values of the optimized three kinds of fuzzy classifiers.
Classifier | Rule |
|
|
|
Category |
---|---|---|---|---|---|
|
1 | 0.5844 | 0.4218 | 0.6656 | 1 |
2 | 1.367 | 0.6789 | 0.9706 | 2 | |
3 | 2.4655 | 0.8996 | 0.1646 | 3 | |
|
|||||
|
1 | 0.5732 | 0.4312 | 0.6472 | 1 |
2 | 1.283 | 0.6472 | 0.9493 | 2 | |
3 | 2.325 | 0.9493 | 0.1592 | 3 | |
|
|||||
|
1 | 0.5823 | 0.4224 | 0.6627 | 1 |
2 | 1.335 | 0.6753 | 0.9675 | 2 | |
3 | 2.452 | 0.8956 | 0.1629 | 3 |
Comparison of classification accuracy of three kinds of fuzzy classifiers.
Name of classifier |
|
|
|
---|---|---|---|
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 | 97.33 |
The results in Table
The computational complexity measured by CPU time was also compared with three kinds of fuzzy classifiers. As shown in Table
The CPU time of three kinds of the fuzzy classifiers.
Data | CPU time (s) | ||
---|---|---|---|
|
|
|
|
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 |
Interference signals of acoustic emission signals from stope wall rock of underground metal mines mainly include mechanical vibration and blasting signals [
Classified results of measurement data1.
Classifier | Number of misclassified samples | Classification accuracy/% | ||
---|---|---|---|---|
|
|
|
||
|
3 | 4 | 4 | 81.67 |
|
2 | 3 | 3 | 86.67 |
|
2 | 2 | 2 | 90.00 |
|
2 | 2 | 2 | 90.00 |
Acoustic emission signals and their interference signals from stope wall rock of underground metal mines.
Rock blasting signals
Mechanical vibration signals
Acoustic emission signals
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. 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.
The authors declare that there was no conflict of interests regarding the publishing of this paper.
The authors would like to acknowledge Project (51274250) supported by the National Natural Science Foundation of China and Project (2012BAK09B02-05) supported by National “Twelfth Five-Year” Science & Technology Support Plan.