Fault Class Prediction in Unsupervised Learning

Fault Class Prediction in Unsupervised Learning using Model-Based Clustering Approach Nagdev Amruthnath and Tarun Gupta  Abstract— Manufacturing industries have been on a steady path considering for new methods to achieve near-zero downtime to have flexibility in the manufacturing process and being economical. In the last decade with the availability of industrial internet of things (IIoT) devices, this has made it possible to monitor the machine continuously using wireless se nsors, assess the de gradation and predict the failures ahead of time . Condition-based predictive maintenance has made a significant influence in monitoring the asset and predicting the failure ahead of time. This has minimized the impact on production, quality, and maintenance cost. Numerous approaches have been in proposed over the years and implemented in supervised learning. In this paper, challenges of supervised learning such as need for historical data and incapable of classifying new faults accurately will be overcome with a new methodology using unsupervised learning for rapid implementation of predictive maintenance activity which includes fault prediction and fault class detection for known and unknown faults using density estimation via Gaussian Mixture Model Clustering and K-means algorithm and compare their results with a real case vibration data. Index Terms— Unsupervised learning, fault class detection, pre dictive maintenance , Gaussian Mixture Model, Clustering, Just-in-Time, TPM

I. INTRODUCTION Over the years, numerous machine maintenance methodologies have been proposed. But, the goal of maintenance methodologies has not changed. The major aim of maintenance methodology is to increase the productivity along with quality while reducing the unplanned downtime. Machine maintenance can be mainly classified as unplanned or unscheduled maintenance and planned or scheduled maintenance. Unplanned maintenance or run to failure maintenance is performed only when the machine breaks down. The major disadvantage of this type of maintenance is high downtime which includes investigation, component part replacement, and verification of repaired condition. This leads to high maintenance cost. Every year, it is estimated that U.S. industry spends $200 billion on maintenance of plant equipment and facilities and the result of ineffective maintenance leads to a loss of more than $60 billion [1]. During the evolution of Toyota Production System era, a concept of Total Preventive Maintenance (TPM) was introduced. TPM is also known as planned maintenance or time-based maintenance (TBM). In this type of maintenance, the machine failure rate, and component failure rates are Nagdev Amruthnath is with Industrial and Entrepreneuri al Engineering, Western Michigan University, Kalamazoo, MI, 49008, USA (e-mail: [email protected]). Dr. Tarun Gupta is with Industrial and Entrepreneurial Engineering, Western Michigan University, Kalamazoo, MI, 49008, USA (e-mail: [email protected]).

identified [2]. This data is used to inspect the machine and its components periodically and replaced if necessary. Implementing TPM have shown a significant improvement in productivity and quality, and decrease in maintenance cost. This type of maintenance is widely used in industry today. Although with many advantages with this approach, it is still difficult to monitor critical component degradation such as ball bearings, motor shaft, pneumatic components and many as such. By replacing these critical components based on reliability data, the remaining useful life is lost and hence increasing the cost of maintenance [2]. Predictive maintenance is the second type of planned maintenance. This type of maintenance is also called as the complement or opposite of planned maintenance. In this process, machine data is collected for a certain period of time and then this data is modeled in different learning algorithms such as regression, classification, neural networks, fuzzy logic and many as such. There is a number of architectures proposed over the years but, the main components of predictive maintenance such as data collection, data cleaning (process of removing incomplete, duplicate and missing values), feature extraction and selection (feature is synonymous of an attribute or input variable) [3], fault prediction, fault class prediction and time to failure (TTF) prediction have remained same. The data collected for predictive maintenance can be physics based data such as vibration, temperature, pressure, voltage, light dispersion, humidity [4] and process data such as process deviations, raw material quality, control settings, machine specification and as such. The implementation predictive maintenance can be performed using different learning methods such as supervised learning, unsupervised learning, deep learning and reinforcement learning. Learning methods can be mainly classified into 4 types; supervised learning, unsupervised learning, semi-supervised learning and reinforcement learning. Supervised and unsupervised learning methods are the most commonly used methods in predictive maintenance. Supervised learning is where the target variable or response variable is known. In unsupervised learning, the target variable or response variable is not known. II. LITERATURE REVIEW In today’s competitive market, attaining Just-in-Time (JIT) had become one of the biggest goals especially in manufacturing. There are many advantages to achieving JIT such as reduction in cost, increase in quality and shorter lead time. Over the years, it has become challenging to achieve this due to performance issues and equipment failures [5], control on inventory, line stoppages, poor process synchronization, and low volume operations [6]. To overcome poor process synchronization, an enhanced method

was proposed using modified rank order clustering using manufacturing data [7]. Condition-based maintenance (CBM) is a process of monitoring the system or a machine based on physical parameters or process parameters or both continuously to predict the health of the machine, predict faults, predict the type of faults and predict the time to failure of the machine. Initially termed as predictive maintenance, the concept of CBM was first introduced by the Rio Grande Railway Company in the late 1940s [8]. The process of CBM involves various domains such as data mining, artificial intelligence, and statistics. CBM has been used in various applications such as automotive, manufacturing, aviation, defense and other industries [8]. CBM is majorly implemented using supervised learning algorithms such as regression and classification. CBM systems can be applied when there is the availability of historical data as well as when no historical data is not available using machine learning. Unsupervised learning approach requires building a reference model identifying normal and abnormal situations. Supervised learning and reinforcement learning approach could be applied to make the CBM algorithms more accurate [21]. One of the key advantages of CBM is the ability to observe the machine component degradation before failing. One the most common learning approaches used today for fault diagnosis is supervised learning. This is wholly based on the predictor variable and response variable. One of the challenges in this method is the time required to collect the data and train the model. To overcome this challenge, unsupervised learning can be used where the class structure can be detected without any previous knowledge of the data. These methods can be classified into two techniques (i) subspace structure of data and its (ii) clustering characteristics [27]. To summarize the first approach, objects use a smaller number of features than the total population, and in clustering approach, the data set uses a smaller number of objects than the original number [27]. With the need for flexibility and cost-effectiveness, in a CBM system fault classification has an important role. Fault classification or fault diagnosis is a process of identifying the current state of the system or the machine. This process can be achieved by the data-driven approach, qualitative model approach or quantitative model approach [18]. Due to the need for precise mathematical models and a significant amount of expert knowledge, the data-driven method has been widely used in the last two decades [15]. Some of the common algorithms used in fault classification is support vector machine (SVM) [15], artificial neural network [15], Kohonen Feature Mapping [10], fuzzy logic [9], self-organizing map [17], k- means [24], fuzzy c-means, hierarchical clustering [27]. Among different learning methods, supervised learning is widely used mainly because of its high prediction accuracy [21]. This also comes with a disadvantage of longer implementation time which involves capturing all the machine states. In this paper, we have proposed an unsupervised learning methodology for rapid implementation of predictive maintenance activity. This implementation involves the major components of predictive maintenance such as collection of physics-based data, predicting faults and

predicting the type of fault using different machine learning algorithms such as principal component analysis (PCA) for dimensionality reduction, Hotelling T2 statistic for fault detection, density estimation via Gaussian Mixture Model Clustering Algorithm [14] and K-means clustering for fault class prediction [11]. All the above algorithms are implemented using Rprogramming, open-source statistical software and are visualized in real time using a BI tool called SISENSE. Density estimation via Gaussian Mixture Model Clustering Algorithm is implemented using mclust package [29] [30], silhouette optimal cluster identification is implemented using NbClust package [31]. III. UNSUPERVISED FAULT CLASS DETECTION A. Model Building A model using Gaussian Mixture Model and K-Means approach was developed next for detecting the faults while using minimal/no historical data which would serve as a metric to separate normal operating condition from abnormal, and no class labels. Following important assumptions applied to the model development process. Assumption 1: It is assumed that the model is working in ideal condition where, voltage, current, temperature of the machine, ambient temperature are not significant Assumption 2: It is assumed that vibration of the machine is the only significant attribute of the machine Assumption 3: the probabilistic model used here assumes that all vibration data obtained is generated obtained from a mixture of finite number of Gaussian distributions of unknown parameters An unsupervised fault prediction model is conceptualized and developed. Later on, we demonstrate how this model works while using minimal historical data accurately predicts known and unknown faults. Limitations: this model is developed, evaluated and validated only for rotating machinery such as cooling fan where vibration is the significant attribute. Hence, at this point of time in research, this model cannot be validated for machines where other physics-based data such as pressure and temperature are significant

Figure 1: Model for fault detection and fault type prediction

B. Understanding the current system A furnace fan was used as a test subject for performing this predictive maintenance activity as shown in Figure 2. This fan operates in a non-fluctuating environment, and due to moving parts and no process data availability, vibration data

was chosen to monitor. Also, due to the sensitivity of the vibration spectrum of equipment failures, the vibration signal is commonly used as the data source [15]. It can also be noted that about 99% of mechanical faults have some noticeable vibration and acoustic signals.

limits are obtained at 99.99% confidence interval using the formula 1 and 2. Here, the significant components obtained using PCA are used for calculating the statistic [19]. T2 statistic 𝑇 2 = ∑𝑙𝑖=𝑙

C. Data Collection Vibration monitors were mounted both on x-axis and y-axis. Vibration data was collected in the time domain at 2048 Hz and for 0.8 seconds every 5 minutes. This raw data is used for feature extraction, feature selection, fault prediction and fault class prediction. The methodology for this research study is as shown in Table 1. D. Feature Extraction Every instance of raw data collected consists of approximately 1600 data point in the time domain. It is important to capture different features both in the time domain and frequency domain [11]. Here, the time domain features such as min, max, median, mean, standard deviation, kurtosis, skewness, range, and RMS [25] for both x-axis and y-axis are collected. The raw data in time domain was later transformed to frequency domain using Fourier transforms [16] to capture the same features in x-axis and y-axis at 25 Hz to minimize the noise at a higher frequency. E. Feature Selection In the feature extraction process, a total of 36 features were extracted both in the time domain and frequency domain. To avoid the curse of dimensionality, dimensionality reduction algorithm called PCA [28] is used. In this algorithm, the data is linearly mapped into lower dimension space to maximize the variance of the data. Here, the covariance matrix for the data is constructed, and Eigenvalues are computed. Optimal components are computed by using a scree plot for Eigenvalues. The Eigenvalues and components are plotted in a scree plot as shown in Figure 3.

𝑡2 𝑖

(1)

𝜆𝑖

Upper confidence limit 𝑙(𝑛−1) 2 𝑇𝑙,𝑛,∝ = 𝐹𝑙,𝑛−𝑙,∝

(2)

𝑛−𝑙

Figure 4 is the fault detection system for monitoring the state of the fan. This system was calibrated for July 31 and August 1. The obtained statistics were used for monitoring the system. Upper limit obtained was 15.83. It can be noticed that on August 26 there was a sharp trend in the graph which indicated that there was a fault detected. Upon investigation, it was found that the fan housing had displaced by 2 inches and the fan was replaced. Upon replacement of the fan, we were able to confirm that the model had to be recalibrated for the new fan. But, our research goal was to detect these changes in our new fault class detection model. Hence, the fan was not recalibrated and was left to continue to use the same statistics as the previous fan. This behavior can be observed in Figure 4. T able 1: Unsupervised predictive maintenance methodology for fault class Prediction Physical Parameter Vibration

Data type T ime Domain Frequency Domain

Features Min Max Mean Standard Deviation Kurtosis RMS Skewness Range Median

Fault prediction Hotelling T 2 Statistic

Fault class Prediction GMM K-Means

The primary objective of this research was to predict fault class in unsupervised learning enabling the architecture for rapid implementation. To achieve this, two unsupervised clustering algorithms, density estimation via Gaussian Mixture model clustering and K-means algorithm were used. The main objective of these to detect the following

Figure 2: Furnace Fan and sensors mounted on x-axis and y-axis

F. Fault Prediction Fault prediction is a process of detecting an abnormal behavior of the system. Some of the most commonly used algorithms are Hotelling T2 statistic [28] [20], Q statistic [28] [20], K-means algorithm, and hierarchical clustering analysis [32] in unsupervised learning. In this research study, Hotelling T2 statistic, a multivariate statistic is used for the analysis. Test data or calibration data is captured during a healthy state of the machine and T2 statistics, and prediction

1. Healthy state of the machine 2. Faulty state of the machine 3. New fan replacement G. Density Estimation via Gaussian Mixture Model GMM algorithm is used in various applications such as image classification [12], speaker verification [26], speech recognition, medicine, etc. Density estimation is a process of fitting a distribution. Data distributions are usually identified by plotting density plots. If a set of random numbers are generated based on a known distribution such as normal, uniform or binomial, then it is known as parametric way of density estimation. If a set of random numbers are fitted to a

known distribution such as Gaussian Mixture model then, it is known as a non-parametric method of density estimation. In our research, when the feature data was plotted onto density plot to identify the distribution, multimodal distributions were identified. Hence, it was concluded to use non-parametric density estimation.

Where P(j) is the mixture proportion and is non-negative. Its sum must be equal to one. The Gaussian centers can be defined by their centers cj and their covariance matrix ∑j. [13] 𝑑

𝑝(𝑥|𝑗) = (2𝜋) −2|∑j|

−

1 2

1 . exp [− 2

(𝑥 − 𝑐𝑗 ) 𝑇 ∑−1 𝑗 (𝑥 − 𝑐𝑗 )] (4)

Based on our above mixture model (equation 4), we can define the log-likelihood function as (equation 5) [13] 𝐿(𝜃) = log ∏ 𝑁 𝑛−1 𝑝(𝑥𝑛 )

(5)

Where, 𝜃 is the model parameter of P(j), cj and ∑j . Using Expectation and Maximization approach the maximum likelihood estimate of 𝜃 can be obtained iteratively. Expectation or E-step involves computing the expected value of some unobserved data using current parameter estimates and observed data. Maximization or M-step involves using the expected values from E-step to compute the maximum likelihood estimates. Upon achieving this model parameters are updated. At a given iteration step t,

Figure 3: PCA scree plot to identify the optimal number of components

Fan 1: PCA-T2-Health

40 10

20

30

T2-Health

50

60

70

T2-Health T2-Limit

Aug 01

Aug 15

Sep 01

Sep 15

Date

Figure 4: Hotelling T2 statistic for fault detection H. Fault Class Prediction

E-step: [13] 𝑝 (𝑡) (𝑗|𝑥𝑛) =

In this section, we will recall the density functions, log-likelihood function and E and M steps for Gaussian Mixture Modeling [13]. Here, we have considered a D-dimensional continuous random vector X 𝜖 Rd. From the reference (equation 3 to 9), the probability density function for a mixture model which is a linear combination of M Gaussian component densities is defined as [13] 𝑝(𝑥) = ∑𝑀 𝑗=1 𝑃(𝑗 )𝑝(𝑥|𝑗)

(3)

𝑝 (𝑡)(𝑥𝑛 |𝑗)𝑃(𝑡)(𝑗) 𝑝 (𝑡)(𝑥𝑛)

(6)

M-step: [13] (𝑡+1)

𝑐𝑗

(

)

∑𝑗𝑡+1 =

=

(𝑡) ∑𝑁 𝑛=1 𝑝 (𝑗|𝑥𝑛 )𝑥𝑛 (𝑡) ∑𝑁 𝑛=1 𝑃 (𝑗|𝑥𝑛 )

(𝑡+1))(𝑥 −𝑐(𝑡+1)) 𝑇 (𝑡) ∑𝑁 𝑛 𝑗 𝑛=1 𝑃 (𝑥𝑛 −𝑐𝑗 (𝑡) ∑𝑁 𝑛=1 𝑃 ( 𝑗|𝑥𝑛 )

(7)

(8)

𝑃

Raw Features

(𝑡+1) (

𝑗) =

1 𝑁

(𝑡) ∑𝑁 (𝑗|𝑥𝑛 ) 𝑛=1 𝑃

PCA Analysis

(9)

2.

GMM 3.

Classification Data Figure 5: Approach used in fault diagnosis using unsupervised learning

The process of implementation is as shown in Figure 5. The raw data features are loaded onto PCA function to obtain the optimal number of principal components. These components are loaded to densityMclust [29] [30] function from Mclust package to obtain the classification data. Figure 6 represents the Gaussian Mixture Model Clustering fitted by Expectation-maximization (GMM-EM model) results grouped by dates on the x-axis and cluster number on the y-axis. The clusters are color-coded, and size of the cluster represents some data points clustered to a certain cluster on that day. Bigger the size of the cluster, the certain state was majorly observed and smaller the size fewer times that state was observed. In our model, we found a total of 6 states. Without any previous knowledge of the data, it is difficult to interpret the results. But, when we compare 1. From July 7 to August 25, cluster 4, 3 and 2 had major state occurrence. From T2 statistic we can hypothesize

4.

that this could be normal state From August 26 to August 30, cluster 1 has a major state occurrence. We can observe the deviation from the normal state. Since in unsupervised learning, we do not have class labels from historical data we can only hypothesize this as a failed state. Upon investigation we by the maintenance crew, it was found that it was a shaft housing had displaced by two inches From August 31 to September 19, cluster 5 had significant occurrence. As mentioned in the above section, this was the period when the old fan was replaced with a new fan. We can confirm this change here. Quite interestingly, there was yet another cluster formed. Cluster 6 occurred majorly on September 3 and September 10. The machine was completely shut down on September 3 and for a shift on September 10. These states could represent the machine shutdown state.

I. K-means Algorithm K-Means Algorithm is one of the most commonly used in fault detection and fault class prediction in unsupervised learning. This algorithm uses Euclidian distance to form the clusters, and the number of clusters is determined using silhouette method. K-means clustering is an unsupervised learning procedure; the method can be directly implemented to measured vibration data, and thus the need for training process for identification for the faulty process is eliminated [11]. Figure 7 is the final result obtained from the raw features extracted using K-means algorithm. There were two ideal clusters based on silhouette method. In the results, we can positively identify the faulty state as cluster 1 in purple. But,

Figure 6: Fault type detection using density estimation via GMM

Figure 7: K-Means clustering results grouped based on date

this algorithm fails to detect the replaced fan.

IV. A NALYSIS AND RESULTS Hotelling T statistic was used for detecting the faults. In this phase, we were able to detect the normal or healthy condition as well as abnormal condition based on the test statistic and statistical limit at 99.9% confidence interval. Based on the results the following test statistic was found to be 82.96% accurate in predicting the faults accurately. The accuracy was calculated based on the information in Table 2. 2

Based on the results from fault detection phase we were able to detect three states in the data. The states are a healthy state, faulty state, and reset state (new fan state). To predict the classes accurately, two unsupervised algorithms were used; K-means clustering and Gaussian Mixture Model Clustering. The results of both the algorithms are as shown in Table 3. Based the results, we can analyze that GMM method was able to predict all the states within the data along with redundant three healthy states. On the other hand, K-means algorithm was able to detect healthy and faulty state, but, it failed to identify new fan state and machine turned off state. T able 2: Confusion Matrix for fault detection using Hotelling T 2 Statistic

Predicted Positive Negative Positive A=1215 B=993 Negative C=1113 D=9041

Actual

T able 3: machine state detection comparison between algorithms

State Healthy or Normal Shaft Housing Fault New fan replacement Machine shutdown

Number of States GMM-EM K-Means 3 1 1 1 1 0 1 0

We were able to use our expert judgment to identify and name each cluster and create a confusion matrix as shown in Table 4 to predict the accuracy of density estimation via GMM. From the results, we were able to estimate the accuracy of about 90.01% in predicting the states accurately using confusion matrix from table 2 and Equation 11. 𝑇𝑃 + 𝐹𝑁 𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁 1215 + 9041 = = 82.96% 1215 + 993 + 1113 + 9041 (10)

Accuracy for T2 =

T able 4: Confusion matrix for fault type prediction using density estimation via GMM

Actual True False

Predicted Positive Negative 934 142 1051 10340

𝑇𝑃 + 𝐹𝑁 𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁 934 + 10340 = = 90.01% 934 + 142 + 1051 + 10340 (11)

Accuracy for T2 =

V. CONCLUSION In the recent years, the wide availability of secure wireless sensor has made it more viable option to monitor the machine regularly and continuously [33]. The core objective of this paper was to propose, develop and implement the predictive maintenance methodology rapidly using unsupervised learning for a furnace fan as a case. With the following implementation, we were able to predict the faults with 82.96% accuracy and determine the different states of the machine based on domain knowledge. In order predict the state of the machine, GMM, and K-means algorithms were used. Based on the analysis and results we found that GMM methodology works better in predicting the states of the fault accurately compared to K-means algorithm. In conclusion, in this research, we were able to rapidly implement a predictive maintenance activity using unsupervised learning methodology with no historical data for fault class prediction algorithms and minimal historical data for fault detection algorithms. VI. FUTURE SCOPE OF W ORK The current work possibly will be extended to different physics-based data such as temperature, pressure, humidity, acoustics, voltage, and current across different domains. This would also help in determining the correlation between the need for dimensionality reduction algorithms such as PCA and the accuracy of clustering algorithms. REFERENCES [1] R. K. Mobley, An Introduction to predictive maintenance, 2 ed., 2002. [2] I. Guyon, "Design of experiments of the NIPS 2003 variable selection benchmark," 2003. [3] Y. Peng, M. Dong and M. J. Zuo, "Current status of machine prognostics in condition-based maintenance: a review," The International Journal of Advanced Manufacturing Technology, vol. 50, no. 1-4, pp. 297-313, 2010. [4] K. Javed, R. Gouriveau, N. Zerhouni and P. Nectoux, "Enabling Health Monitoring Approach Based on Vibration Data for Accurate Prognostics," IEEE Transactions on Industrial Electronics , vol. 62, no. 1, pp. 647-656, 2015. [5] E. Gundogar, A. Yilmaz and B. Erkayman, "A solution approach to a synchronization problem in a JIT production system," Production Planning and Control. , vol. 25, 2014. [6] R. C. Walleigh, "What’s Your Excuse for Not Using JIT?”,," Harvard Business Review, 1983. [7] N. Amruthnath and T. Gupta, "Modified Rank Order Clustering Algorithm Approach by Including Manufacturing Data," in 4th IFAC International Conference on Intelligent Control and Automation Sciences, Reims, 2016. [8] A. Prajapati, J. Bechtel and S. Ganesan, "Condition based maintenance: a survey," Journal of Quality in Maintenance Engineering, vol. 18, no. 4, pp. 384-400, 2012. [9] B. Das and J. Reddy, "Fuzzy-logic-based fault classification scheme for digital distance protection," IEEE Transactions on Power Deliver y , vol. 20, no. 2, 2005. [10] B. H. Chowdhury and K. Wang, "Fault Classification Using Kohonen Feature Mapping," in Proceedings of the International Conference on

Intelligent Systems Applications to Power Systems, 1996. [11] C. T. Yiakopoulos, K. C. Gryllias and I. A. Antoniadis, "Rolling element bearing fault detection in industrial environments based on a K-means clustering approach," Expert Systems with Applications, vol. 38, no. 3, pp. 2888-2911, 2011. [12] Ç. Ari and S. Aksoy, "Unsupervised classification of remotely sensed images using Gaussian mixture models and particle swarm optimization," in Geoscience and Remote Sensing Symposium (IGARSS), 2010. [13] C. Archambeau and M. Verleysen, "Fully Nonparametric Probability Density Function Estimation with Finite Gaussian Mixture Models," in ICAPR'2003 proceedings - 5th International Conference on Advances in Pattern Recognition, Calcutta, 2003. [14] C. Biernacki, G. Celeux and Gérard Govaert, "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, vol. 41, no. 3-4, pp. 561-575, 2003. [15] F. Zhou, Y. Gao and C. Wen, "A Novel Multimode Fault Classification Method Based on Deep Learning," Journal of Control Science and Engineering , vol. 2017, 2017. [16] G. G. Yen and K.-C. Lin, "Wavelet packet feature extraction for vibration monitoring," IEEE Transactions on Industrial Electronics , vol. 47, no. 3, pp. 650-667, 2000. [17] H. Benitez-Perez, F. Garcia-Nocetti and H. Thompson, "Fault classi fication SOM and PCA for inertial sensor drift," in IEEE International Workshop on Intelligent Signal Processing, 2005. [18] H. Li and D. Y. Xiao, "Survey on data-driven fault classification methods," Control and Decision, vol. 26, no. 1, pp. 1-16, 2011. [19] H. Hotelling, "Analysis of a complex of statistical variables into principal components," Journal of Educational Psychology, vol. 24, pp. 417-441, 1933. [20] J.-H. Cho, J.-M. Lee, S. Wook, D.-w. Choi and I.-B. L. Lee, "Fault identification for process monitoring using kernel principal component analysis," Chemical Engineering Science, vol. 60, no. 1, pp. 279-288, 2005. [21] J.-H. Shin and H.-B. Jun, "On condition based maintenance policy," Journal of Computational Design and Engineering, vol. 2, no. 2, pp. 119-127, 2015. [22] M. Fujimoto and Y. Riki, "Robust speech recognition in additive and channel noise environments using GMM and EM algorithm," in IEEE International Conference on Acoustics, Speech, and Signal Processing, 2004. [23] D. Reynolds, "Gaussian Mixture Models," In Encyclopedia of Biometrics, pp. 659-663, 2009. [24] S. M. Zhang, F. L. Wang, S. Tan and S. Wang, "A fully automatic

online mode identification method for multi-mode processes”," Acta Automatica Sinica, vol. 42, no. 1, pp. 60-80, 2016. [25] S. Wegerich, A. Wilks and R. Pipke, "Nonparametric modeling of vibration signal features for equipment health monitoring," in Aerospace Conference, 2003. [26] S. Memon, M. Lech and N. Maddage, "Speaker Veri fication Based on Different Vector Quantization Techniques with Gaussian Mixture Models," in Third International Conference on Network and System Security, 2009. [27] S. M, C. P. and B. T., "Supervised and unsupervised learning process in damage classi fication of rolling element bearings," Diagnostyka, vol. 17, no. 2, pp. 71-80, 2016. [28] W. Ku, R. H. Storer and C. Georgakis, "Disturbance detection and isolation by dynamic principal component analysis," Chemometrics and Intelligent Laboratory Systems, , vol. 30, no. 1, pp. 179-196, 1995. [29] C. Fraley and A. E. Raftery, "Model-based Clustering, Discriminant Analysis and Density Estimation," Journal of the American Statistical Association, vol. 97, pp. 611-631, 2002. [30] C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca, "mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering," Classification, and Density Estimation Technical Report No. 597, Department of Statistics, University of Washington, 2012. [31] M. Charrad, N. Ghazzali, V. Boiteau and A. Niknafs, "NbClust: An R Package for Determining the Relevant Number of Clusters in a DataSet.," Journal of Statistical Software, vol. 61, no. 6, pp. 1-36, 2014. [32] N. Amruthnath and T. Gupta, "A Research Study on Unsupervised Machine Learning Algorithms for Early Fault Detection in Predictive Maintenance," in 5th International Conference on Industrial Engineering and Applications, Singapore, 2018. [33] N. Amruthnath and P. M. Prathibhavani, "Data Security in wireless Sensor Network using Multipath Randomized Dispersive Routes.," International Journal of Scientific & Engineering Research, vol. 5, no. 1, 2014.