Complexity

Volume 2018, Article ID 7356189, 9 pages

https://doi.org/10.1155/2018/7356189

## Damage Detection of Refractory Based on Principle Component Analysis and Gaussian Mixture Model

Correspondence should be addressed to Gangbing Song; ude.hu@gnosg

Received 11 August 2017; Accepted 3 January 2018; Published 31 January 2018

Academic Editor: Michele Scarpiniti

Copyright © 2018 Changming Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Acoustic emission (AE) technique is a common approach to identify the damage of the refractories; however, there is a complex problem since there are as many as fifteen involved parameters, which calls for effective data processing and classification algorithms to reduce the level of complexity. In this paper, experiments involving three-point bending tests of refractories were conducted and AE signals were collected. A new data processing method of merging the similar parameters in the description of the damage and reducing the dimension was developed. By means of the principle component analysis (PCA) for dimension reduction, the fifteen related parameters can be reduced to two parameters. The parameters were the linear combinations of the fifteen original parameters and taken as the indexes for damage classification. Based on the proposed approach, the Gaussian mixture model was integrated with the Bayesian information criterion to group the AE signals into two damage categories, which accounted for 99% of all damage. Electronic microscope scanning of the refractories verified the two types of damage.

#### 1. Introduction

Structural health monitoring (SHM) has made significant advances in the past decades [1–8]. Monitoring of refractories, which are widely used in furnace, iron, and steel industries due to their ability to gain strength rapidly and to withstand aggressive environments and high temperature [9], receives increasing attention [10–13]. Temperature variations can lead to either interfacial separation between aggregates and matrix or microcracks, both depending on the range of coefficient of thermal expansion (CTE) mismatch between phases. Such effects modify all the thermomechanical properties of the material, especially Young’s modulus (E) [10, 11, 14]. The AE technique has been developed over the last two decades as a nondestructive evaluation technique and as a useful tool for material research [15–17]. It is an efficient method to monitor, in real time, damage growth in both structural components and laboratory specimens. This technique was often used to detect Young’s modulus because it was correlated to AE activity variations considering the specific types of damage induced by CTE mismatch [12, 13]. The acoustic emission technique and the ultrasonic pulse echography technique, both carried out at high temperature, were applied as nondestructive characterization methods to monitor the damage extension within the materials submitted to thermal stress and to follow the evolution of the associated elastic properties [18, 19]. With this as a basis, the study could provide an important reference for thermal stress analysis under the AE data processing method. However, the AE signals generated by the complex structure of the refractory are extremely complex even at normal temperature, which makes it difficult for the damage classification [20]. For this purpose, the AE signal parameters of the delay distribution, rise time, energy, and peak amplitude were selected to distinguish the effective features for different failure mechanism so that the two failure modes of fiber breakage and delamination can be distinguished [21, 22]. The related parameters can be modeled by a generative model, in particular a Gaussian mixture model (GMM) in the field of dimension processing [23, 24]. The global feature descriptor was formed by stacking the parameters of the adapted GMM (i.e., means, covariance, and weight) in a so-called supervector [25, 26]. Also, some scientists paid more attention to the parameter of the signal energy moment compared to the peak amplitude distribution in the study of the glass fiber composite materials and chose it to distinguish the fiber breakage and debonding crack. Moreover, the amplitude, ring count, and felicity ratio were found more suitable in the damage study of the B-Al composite [27]. However, much effort was put on the characterization of the overall parameters rather than on the data analysis of the damage mechanism.

Optionally, the dimensionality of the feature vectors can be reduced by a principal component analysis (PCA) [28]. The PCA was used to generate a new set of noncorrelated features to remove interference and to avoid using low variance variables (that was almost single-valued variables). Moreover, these new features were selected according to their discriminative capability. Subsequently, feature space modeling and classification were addressed by means of probabilistic self-organizing maps (SOM), a fuzzy version of classical SOM that allowed measuring the activation probability of each unit [29, 30]. Nevertheless, detecting not only an event but also the type was not a straightforward task, and previous approaches had not been able to obtain high per attack detection accuracy values. Scientists showed that the resulting GMM supervector encoding yielded an excellent representation for fuzzy parameters [31, 32]. This method was an outstanding technique for handling the description of multimodal data, making it robust with high computational efficiency [26]. Additionally, scientists employed support vector machines (SVM) to build individual classifiers per sample cluster [33, 34]. Such a SVM was a linear classifier trained by only one single positive sample and multiple negative samples; it was denoted as Exemplar-SVM. Therefore, secondly, using the features extracted by AE, the negative log likelihood was obtained by using the Bayesian GMM which was an outstanding technique for the multimodal distribution of the data with high computational efficiency [35, 36]. Among others, the PCA have been used successfully for object classification and scene classification. The PCA method is a statistical linear transformation selection from multiple variables to minor ones [28]. Meanwhile, the GMM is a Gauss probability density model, which can be used to accurately quantify matters and classify them into several models based on the Gauss probability density function [23].

Taking advantages of the PCA and GMM methods in the processing of the multidimensional models, especially the reduction of the AE parameters and pattern recognitions, this paper intends to reduce the correlation dimension of the 15 parameters of the AE signals emitted from the damage process of the materials and to obtain the two new parameters which could be used to describe the overall damage property without linear dependence. Afterwards, the GMM was used to classify the damage into two major categories. Finally, the results were verified experimentally by using scanning electron microscopy image based classification.

#### 2. Analysis to Construct the New Characterization

The PCA method shows obvious advantages in the multiparameter dimension reduction problems and the construction process is clear to operate. The observation matrix of the sample is discussed by Shang et al. [37],where the rows of the sample matrix represent the AE parameters and the columns correspond to different signals. The covariance matrix of the sample iswhich is the estimation of . Through the calculation of , the characteristic quantity of the original observation matrix can be easily reconstructed so as to facilitate the sort of the features.

*Step 1. *The covariance matrix of the sample is constructed by as follows:where the matrix is a and positive definite matrix, and there are characteristic values of which are not equal to each other and greater than zero. Each characteristic value corresponds to a unit feature vector.

*Step 2. *Compute the features and its characteristic vector. Set to be eigenvalues of . Meanwhile, are the corresponding unit feature vectors. Arranging eigenvalues in a descending order gives

*Step 3. *Define the contribution rate of the characteristic value and the accumulated contribution rate

*Step 4. *Based on the principle of the accumulated contribution , the former () principal components are picked, which means the former mutually orthogonal eigenvector matrices are retained.

*Step 5. *Conduct linear correlation transformation between the new feature vector matrix and the original one. In this way, the original dimension index will be reduced to , which contains the ultimate information with mutual linear independence.

#### 3. Classification with GMM

The GMM probability density function is set as follows:where is the mixed number of the model; is the weighting coefficient of the model, and ; is the th single Gauss probability density function, which is depicted as

The proper parameters were evaluated aswhich makes the max maximum likelihood estimator of the probability density function,

In order to obtain the maximum likelihood estimate, the GMM will be evaluated by the maximum expected value algorithm. The iteration steps are as follows.

*Step 1. *Initiate the parameters:

(1) Set the mean values to be random values.

(2) Set the covariance matrix to be the unit matrix.

(3) Set the weighting coefficient of each model to be the prior probability of each model:where was the number of GMM.

*Step 2. *Compute the prior probability of each item in the model:

*Step 3. *Update the parameters by the prior probability:

*Step 4. *Repeat Steps 2 and 3 until the convergence: where and are the parameters estimation of the previous and current step and is the set threshold, which is usually set to 10^{−5}.

#### 4. Experimentation and Verification

##### 4.1. Specimens and Experiment Setup

The industrial refractory tested in the study is composed of magnesia aggregates, carbon binder (phenolic resin and/or pitch), and other components. Figure 1 shows the microstructure of such a refractory without damage. The magnesia aggregates are formed by sintering of crystallites with weak interfaces. The size of magnesia grains varies from less than one half millimeters to five millimeters. The other grains impurities, such as SiO2 and Al2O3, with less than 5 mm sizes, are founded scattered in the matrix, the carbon binder.