State-Based Prognostics with State Duration
Information
O. F. Eker
a,band F. Camci
a,b*
†Failure prediction (i.e. prognostics) is critical for effective maintenance because it greatly impacts the competitiveness of organizations through its direct connection with operating and support costs, system availability, and operational safety. In recent years, research has focused on state-based prognostics that forecast future progression byfirst identifying the current state. The duration spent in a state is a factor that influences the expected time to be spent in that state in the future; however, previous works on state-based prognostics have ignored the effect of duration. Hidden Markov Models are the most famous state-based prognostics methods in the literature with practicality problems such as computational complexity, requirement of excessive data, and dependency on initialization. This paper presents a new, simple and easy to implement state-based prognostic method using state duration information. The presented method is applied to two real systems (railway turnout systems and drill bits), and the results are compared with the existing methods presented in the literature. The results show that the presented method outperforms the existing methods. Copyright © 2012 John Wiley & Sons, Ltd.
Keywords: fault diagnosis; failure analysis; forecasting; prognostics; remaining useful life estimation; condition-based maintenance
1. Introduction
A
n effective maintenance plan greatly impacts the competitiveness of organizations through its direct connection with operating and support costs, system availability, and operational safety. Many examples that quantify maintenance efficiency exist in the literature. For example, the cost of maintenance in medium-sized power utility companies will exceed their profits.1 The annual maintenance cost for domestic plants in the USA has increased from $600 billion to $1.2 trillion in almost 20 years (from 1981 to 2000).2The U.S. Department of Defense spends $40 billion annually for maintenance.3However, one-third to one-half of this cost could be saved with more effective maintenance.4Predictive maintenance is considered key to achieving effective maintenance and in recent years has attracted interest from academia and industry.5–17 In predictive maintenance, sensory information is collected in real time from machinery equipment, analyzed to identify an incipient failure, and used to predict the time left before the failure damages the system (i.e. remaining useful life (RUL)). The process of failure identification is called diagnostics, and the prediction of the RUL is called prognostics. RUL is the time left until the system or component will not perform its intended functionality with required safety and efficiency37and has been formulated in23as follows:
RUL¼ n; where St¼ i; Stþ1¼ j; . . . Stþn1¼ l; Stþn¼ f; (1)
t; t þ 1; . . . ; t þ n; represent the discrete time sequence; t is current time; i; j; . . . l; and f are the health states; and f is the failure state f > l⩾ . . . ⩾j⩾ið Þ:
Prognostics has the potential to play a critical role on maintenance planning, spare parts provision, operational performance, in the management of product reuse and recycle affecting energy consumption, raw material use, pollution, and the users’ profitability.5–9 Many different industrial components have been studied for prognostics such as rotating machinery,4batteries,10and electronics.11 The literature on diagnostics is relatively mature,29–31and the research trend now focuses on prognostics.
The goal of prognostic methods is to predict the degradation of the machinery under observation. In early studies, degradation was directly measured by extracting features from sensory information.12However, degradation is often too complex to predict without processing the features. Hence, statistical and computational intelligence methods are used to process the features for prediction.
a
IVHM Centre, Cranfield University, Cranfield, UK bMeliksah University, Kayseri, Turkey
*Correspondence to: F. Camci, IVHM Centre, Cranfield University, Cranfield, UK. †E-mail: f.camci@cranfield.ac.uk
Computational models for prognostics can be categorized by their degradation type: continuous or discrete degradation. Examples of continuous degradation measures include physical performance used in13, continuous failure progression states used in14,15, and failure probability used in16,17. In,13times series analysis was used for physical performance prediction but was found to be unsuitable for long-term prediction.18,19In,14a degradation path satisfying Brownian motion drift model was used to predict the RUL. In contrast, in15, the structure of the degradation path is assumed unknown, but the failure degradation is assumed to be linear. A linear degradation path is not suitable for applications in which cumulative damage has a significant effect on the rate of degradation.20In16, a neural network model is used to predict the RUL, where survival probabilities are used to predict the future sur-vival probabilities. Neural networks and kernel methods are used in17to estimate the conditional probability distribution of the sys-tem output. The general difficulty with using a continuous degradation measure is assuming a model for the degradation path.
No such degradation model is assumed with a discrete degradation measure.1,21–24A discrete degradation measure consists of individual degradation levels called health states, and afinite number of health states exist, progressing from fault free to failure states. Hidden Markov Model (HMM)-based methods are mostly used in discrete degradation measures.1,21–23In1and21, a health state is represented by a distinct HMM within an HMM pool. Once the health state is identified as the HMM with the highest probability based on the signal collected from the system, the time to travel through the remaining healthy states is calculated.
In an HMM, the transition probability from one state to another does not depend on the time spent in that state, which is untrue in a real system. The transition probability to the next state increases as the time spent in that state increases. The more time spent in that state indicates that the state is more likely to jump to the consecutive states. Segmental Hidden Semi-Markov Model (HSMM) is presented in22to model this reality. Note that the duration modeling in22is for states that represent the non-stationary property of the collected data, not the system health states. However, prognostics are based on the system health states and their progression. These health states are represented by distinct independent HMMs in1and21. Although each HMM represents a distinct health state in this approach, the progression of the states cannot be modeled efficiently. In23, a Hierarchical HMM (HHMM) that integrates distinct HMMs into one model with transition probabilities between health states is employed with better prognostic results. In HHMM, the transition probabilities between health states are learned from the training data, and a Monte Carlo simulation estimates the RUL. Although integrating HMMs into one model (HHMM) allows health state transition probability to be calculated, the health state transition probabilities will be unaffected by the time spent in the health state. An aging factor is introduced in HMMs to create decreasing health state transition probability based with duration spent in the health state in.24Three kinds of aging factors have been used in 33 to obtain non-stationary state transition probabilities. Reference 32 presents Non-stationary Segmental Hidden SMM to model non-stationary state transition probabilities. These approaches increase the existing complexity of HMM-based prognostics methods by introducing extra parameters, new concepts, and algorithms.
Employment of standard HMMs for prognostics has some practicality issues such as computational difficulty in training,22excessive number of parameters to learn,36requirement of huge data for training, and dependency of results to parameter initialization.23,36 The driving force of this paper is the need of a simple and easy to implement state-based prognostics method that uses the duration information in health states without dealing with the complexity of HMM-based methods.
A simple, discrete state-based prognostics method is presented in;25 however, state duration information is not considered in the transition probability. The state transition probabilities are constant and independent of the time spent in that state. However, in a real system, the probability of leaving the state increases as the time spent in that state increases. In other words, it is more likely to jump to the‘failure state’ for a component that has been ‘close to failure state’ for a long time compared to the one that recently reached to‘close to failure state’.23 This concept has recently been modeled in HMM-based approaches in 24,32,33with aforementioned disadvantages of HHM. This paper presents a discrete-state prognostic method that uses state duration information to provide a more realistic model and better RUL estimation with ease of implementation and simple computational complexity.
Section 2 gives the presented method. Experiments and results are given in section 3. Section 4 provides a sensitivity analysis of the method, and section 5 concludes the paper.
2.
State-based prognostics with duration information (SBPD)
The presented State-Based Prognostics with Duration information (SBPD) consists of two steps: health state identification and RUL calculation.
Health states are the discrete states that progress from a failure-free state to a failure state. Discrete health states are not observa-ble, but the failure progression through the states will change the observed signal. Each health state changes the observed signal differently, which suggest that the failure health state might be understood by analyzing the observed signal. Given that the health states are not observable, health state identification is a clustering problem, not a classification problem. As in general clustering pro-blems, the number of clusters to be used for health state identification is unknown. Several cluster validity indexes to measure the goodness of clusters have been proposed in the literature.34,35They basically evaluate the closeness of data points within the clusters and distance between clusters. In this study, cluster validity indexes Silhouette, Davies-Bouldin, Calinski-Harabasz (CH), Dunn, C-index, and Krzanowski-Lai are used. CH index shown in (2) has been selected due its most robust results. kis number of clusters,ncis number of data in cluster c, zcis center of the cluster c, zis the center of the all data, xiis the ithdata point.
CH¼ Pk c¼1nckzc zk2 k 1 " #. Pk c¼1Pni¼1c kxi zck2 n k " # (2)
For the SBPD, a simple k-means clustering method that groups the data by minimizing the sum of squares of distances between data and the corresponding cluster center is used.38The number of clusters, starting from two to ten, was tested and evaluated with a CH validity index. After determining the best number of clusters, any observed signal received was clustered, and then the expected RUL was calculated. Transition probabilities between health states are utilized to calculate the expected RUL. The transition probability (qi, j) in state i is defined as the probability of the transition to state j. In previous studies, the transition probability of a state is assumed to be inde-pendent of the time spent in that state.21,23–25However, this assumption is untrue for real systems. The probability of transition to the next state (the same state) increases (decreases) as the time spent in the state increases. Thus, in this paper, the transition probability of a state is described as (qd
i;j), the probability of transition from state i to state j given that the system stayed in state i for d times.
The transition probabilities are identified using the k-means clustering applied to a training dataset. qd
i;jis calculated as the ratio of the
number of transitions from state i to state j after staying at least d time to the total number of transitions occurred after staying at least d time from state i. For example, consider three samples of a component that were manufactured by the same company with the same specifications. All three samples have been used under the same operation conditions and have degraded with health states numbered sequentially from 1 to 3 (from the failure-free to the close-to-failure state) exist as shown in Table I. Due to uncontrollable variations, each sample has degraded and failed differently. Each row in Table I represents the failure progression of one sample. State 3 (close-to-failure state) is thefinal state before failure, and samples fail after 12, 9, and 11 time units. Table II gives the transition probabilities obtained from the given example in Table I. When the duration is 1, the transition probability from state 1 to state 2 is 3/12 because only three transitions occur from state 1 to state 2 out of 12 transitions. Similarly, the transition probability from state 1 to itself is defined as 9/12 for duration 1. When the duration is 2, the transitions that occurred in duration 1 are ignored. In other words, the total number of transitions is 9 after 2 units, and thus the transition probability from state 1 to state 2 (itself) for duration 2 is 3/9 (6/9). Similarly, transition probability from state 1 to state 2 (state 1 to itself) becomes 3/6 (3/6) when the duration is 3, since the total number of transitions from state 1 after duration 2 is reduced to 6. For duration 4, transition probability from state 1 to state 2 (state 1 to itself) becomes 2/3 (1/3). Because all samples transitioned to state 2 after spending 5 or less time units in state 1, the transition probability from state 1 to 2 is defined as 1 for duration values greater than 5. Similar to state 1, the transition probability from state 2 is calculated by considering all transitions from state 2. Total of 16 transitions, 3 of which to state 3 and the rest to itself, have occurred from state 2. Thus, state transition probabilities from state 2 with duration 1 are 3/16 to state 3 and 13/16 to state 2. Similar to the calculation above, the transitions that occurred before the duration under consideration have not been considered in transition probability calculation. Hence, the transition probabilities from state 2 to states 3 for durations 2, 3, 4, 5, and 6 are calculated as 3/13, 3/10, 3/7, 3/4, and 1, respectively.
To simplify the calculation, it is assumed that transition from a state can only occur to the same state or consecutive states. It is not allowed to jump over states. For example, a transition from state 1 to state 3 is not allowed (only a transition to itself or state 2 is allowed). Thus, transitions that are not allowed are restricted with zero transition probability.
The transition probabilities obtained are used to calculate the expected RUL. The current health state of the system is obtained by clustering and is represented by h. The time spent in state h and the age of the system are represented by d and t, respectively. Expected RUL can be defined as the sum of the expected time to be spent in the current and futures states until reaching the failure
Table I. Example of health states for three samples
Life
1 2 3 4 5 6 7 8 9 10 11 12
Sample 1 1 1 1 1 2 2 2 2 2 2 3 3
Sample 2 1 1 1 2 2 2 2 2 3
Sample 3 1 1 1 1 1 2 2 2 2 2 3
Table II. State transition probabilities with duration
Duration stayed in the states
d = 1 d = 2 d = 3 d = 4 d = 5 d = 6 qd 1;1 9/12 6/9 3/6 1/3 0/1 0 qd 1;2 3/12 3/9 3/6 2/3 1/1 1 qd 1;3 0 0 0 0 0 0 qd 2;1 0 0 0 0 0 0 qd 2;2 13/16 10/13 7/10 4/7 1/4 0/1 qd 2;3 3/16 3/13 3/10 3/7 3/4 1/1 qd 3;1 0 0 0 0 0 0 qd 3;2 0 0 0 0 0 0 qd 3;3 3/3 3/3 3/3 3/3 3/3 3/3
state as given in (3) based on RUL formulation given in (1). Tsis the time to be spent in the health state s, and Tcdis the time to be spent in the current health state given that dtime has already been spent in the current health state. crepresents the current state, and frepresents the last state before failure. The time spent in the health states increases until the transition to the other health state occurs with probabilities q1
s;sþ1and qdc;cþ1. Hence, TsandTcd follow geometric distribution with transition probabilities q1s;sand qdc;c,
respectively. Calculation of expected values of Td
c and Tsare given in (4) and (5), respectively, based on expected value calculation for geometric distribution.39Note that the exponent of q (duration) in Tsis 1 and in Tcd is d, since no time has been spent in state
s and d time has already been spent in current state. In other words, state transition probability calculation incorporates duration information after some time has been spent in a health state. The pseudo-code for calculating the transition probabilities is given in Figure 1. Figure 2 displays the pseudo-code for the RUL calculation using transition probabilities.
E RUL½ ¼ E T cd þ X f s¼cþ1 E T½ s (3) E T cd ¼ nc; Sc¼ i; Scþ1¼ i; . . . Sccþnc¼ i; Scþncþ1¼ j; where i 6¼ j E T½ ¼ ns;where Ss s¼ i; Ssþ1¼ i; . . . Ssþns¼ i; Stþnsþ1¼ j;where i 6¼ j E T½ ¼ 1 qs 1s;s 1 ¼ q1 s;sþ1 1 (4) E T cd ¼ 1 q dc;c1¼ q dc;cþ11 (5) Td
c and Tsfollow geometric distribution with parameters qdc;cand q1s;s.
3.
Experiment and results
The presented method was applied to two different systems: railway turnout systems and drilling machines. Data from both systems have been previously used for prognostics in the literature.23,25The results of the presented method are compared to the existing results in the literature.
% Expected RUL Calculation for a sample in health % state c with duration d
expected RUL = 1/TP(s, d) for i from c+1 to f
expected RUL = expected RUL + 1/TP( i, 1) end
Figure 2. Pseudo-code for expected RUL calculation.
% Transition probability calculations
% hsTable: Sample health states as shown in Table 1
% Ns, s+1 :The number of transitions from state s to s+1 % Ns : The number of all transitions from state s % TP(s,d) : Transition probability of state s & duration d
for s from 1 to all states for d from 1 to all durations TP(s, d) = Ns,s+1 / Ns
delete values in hsTable where state = s & duration = d update Ns and Ns+1 based on new hsTable
end end
3.1. Railway turnout system
Railway turnout systems move the tracks to change the route of the train, as shown in Figure 3. The turnout system is a relatively complex system with a motor, reduction gear, and several other components, as shown in Figure 4. Although there are several types of turnout systems, such as electro-mechanic, hydraulic, and pneumatic systems, the data are collected from an electro-mechanical turnout system. Sensors were installed on the turnout system, and data were collected when the tracks were being moved back and forth as shown in Figure 4. An electric motor applies force to the drive rods of the railway turnout. When a failure occurs, the symptoms can be observed through the force sensor since more or less than normal force might be required to move the tracks. There are several fail-ure modes in railway turnout systems, and dry slide chair failfail-ure mode, which is one of the most important failfail-ure modes, is used for experiments. The details of the failure progression and data collection are discussed in.25
Figure 5 displays the effect of failure progression on the force data collected for one turnout sample through 15 moves of the track. Each move takes approximately 10 s, during which the sensory information related to turnout health has been collected. Total of ten turnout samples with varying number of moves from‘failure-free state’ to ‘close-to-failure state’ are used. Two of the turnout samples were left for testing, and the rest was used for training. Total of 109 move data obtained from 8 turnout samples have been used for
Figure 3. Railway and turnout system.
training in k-means clustering model. After training, all data containing training and testing data are used for RUL calculation. When sensory data from a move is given for failure prediction, the current state to which the data belongs is identified using the trained k-means clustering algorithm. Then, the RUL is calculated.
The same dataset used in25was employed for the experiments. Figure 6 displays the RUL predictions of the presented method (SBPD) and the method (SSBP) used in25for ten samples. The x-axis in thefigures represents the age of the system, and the y-axis represents the RUL for the corresponding age. Real RUL is also presented in thefigure as linear line. As seen from the figures, the RUL prediction of SDBP is more accurate than the SSBP, as the RUL estimates match the real RUL values more closely.
Though it is clear from thefigure above that the presented method outperforms SSBP, two quantitative measures (i.e. r-square and root mean square error (RMSE)) were used to evaluate the effectiveness of RUL prediction. R-square measures the similarity of the
0 50 100 150 200 250 300 350 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
Life of the turnout
Force A sample Close to Failure state Fault Free State Failure Progresses
Figure 5. Force signals from‘fault-free’ to ‘failure’ state.
5 10 15 0 5 10 15 20 Turnout System 1
System Current Age
Expected RUL 2 4 6 8 10 12 0 5 10 15 Turnout System 2 2 4 6 8 10 12 14 0 5 10 15 Turnout System 3 2 4 6 8 10 12 14 0 5 10 15 Turnout System 4 2 4 6 8 10 12 0 5 10 15 Turnout System 5 2 4 6 8 10 12 0 5 10 15 Turnout System 6 2 4 6 8 10 12 0 5 10 15 Turnout System 7 2 4 6 8 10 12 14 0 5 10 15 Turnout System 8 2 4 6 8 10 12 14 0 5 10 15 Turnout System 9 2 4 6 8 10 12 14 0 5 10 15
Turnout System 10 Real RUL SBPD SSBP
time series of predicted and real RUL values. RMSE is square root of the differences between real (yi)nd estimated (fi)UL values. The formulation of r-square and RMSE are shown in (6) and (7), respectively.
R square ¼ 1 P iðyi fiÞ2 P iðyi yÞ2 (6) RMSE¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn i¼1ðyi fiÞ2 n s (7)
Where,ys mean of real RUL values and in formula 2, ns number of observations.
Both parameters measure the similarity of the estimated RULs and real RULs. A high r-square value and low RMSE indicate better prediction. Figure 7 displays the RMSE and r-square values of SSBP and SBPD. As seen from thefigures, SBPD outperforms SSBD.
Figure 8 displays the average r-square values of all samples with different numbers of states. As seen from thefigure, the r-square values of the SSBP are low for a small number of states, increase up to a point as the number of states increases, and then decrease.
(a)
(b) Figure 7. Comparison of SSBP and SBPD using a) RMSE b) R-square.
Thus, the number of states in SSBP is critical and should be optimized. However, the number of states is not as critical in SBPD because duration information is considered in RUL calculation.
The effect of the size of the training data is illustrated in Table III. As seen from the table, the accuracy of the method increases with the increase in the size of the training dataset. 80% of the dataset gives good results leaving reasonable amount of data for testing.
3.2. Drill bits
The drilling process is one of the most commonly used processes in machining [26], [27]. For example, up to 50% of all machining operations in the U.S. involve drilling.28Drill bit breakage and/or excessive wear during the drilling process may cause fatal defects in the product. The quality of drilled holes may affect the quality of the product. For example, approximately 60% of rejected parts are often attributed to the poor quality of the hole.27Thus, it is important to predict the failure of drill bits to produce good products. The failure prediction for drill bits has been reported in,1,12,21and.23Among these methods, HMM-based methods are used for failure prediction. The same dataset will be used to compare the presented method with the results of the HHMM, which gave the best results of the HMM-based methods.
Figure 9 illustrates the data acquisition system for the drilling process. Thrust force and torque signals are collected during the actual drilling process as shown in Figure 10. The signals collected during the life of a drill bit are displayed in Figure 11, and the degradation
Table III. RMSE and r-square values with training size Training
size (%) 10% 20% 30% 40% 50% 60% 70% 80% 90%
RMSE 0.6 0.5 0.5 0.475 0.45 0.433333 0.446429 0.43125 0.438889
R-square 0.97937 0.985502 0.989579 0.990027 0.990182 0.990234 0.990187 0.990059 0.99044
Figure 9. Experimental setup for data collection during drilling process.
Standardized Torque Standardized Thrust-force
Rapid Increase
Trend RapidDecrease
HOLE START
HOLE END
of the drill bit from its brand new state to the failure state can be seen. The samples were taken as two-dimensional vectors, and distances have been measured within two dimensional space. Thus, both thrust force and torque are used in clustering.
Figure 12 displays the RUL values predicted by SBPD and HHMM. Table IV displays the r-square and RMSE values. As seen from the figure, SBPD outperforms HHMM. Time Thrust-force – Newtons Torque – Newton meters A hole
Figure 11. Thrust-force and torque data from a drill bit.
5 10 15 20 0 10 20 30 Drill Bit 1 5 10 15 0 10 20 30 Drill Bit 2 5 10 15 0 10 20 30 Drill Bit 3 2 4 6 8 10 12 0 10 20 30 Drill Bit 5 2 4 6 8 10 12 14 0 10 20 30 Drill Bit 7 5 10 15 20 0 10 20 30 Drill Bit 8 5 10 15 0 10 20 30 Drill Bit 9 5 10 15 0 10 20 30 Drill Bit 12
Life of drill-bit (holes)
Expected RUL
Real RUL SBPD HHMM
Figure 12. Real RUL and RUL predicted by HHMM and SBPD.
Table IV. R-square and RMSE values of predicted RUL by HHMM and SBPD
r-square RMSE
HHMM 0,91 4,04
4.
Discussion
This section discusses the robustness of the methods, where robustness is defined by the method sensitivity to the quality of the training data. Outliers in the training data do not represent the system behavior and may lead to poor prognostic results. The sensitivity of the method to the outliers is called the robustness of the method.
The datasets used in this paper represent two different aspects of data collection. In thefirst dataset (railway turnout systems), failure progression was obtained using a degradation model, and data were collected based on this failure progression by manually creating the health state. Thus, the dataset represented the failure progression with no outlier samples. In contrast, the second dataset (drill bit) was collected from a system that ran until failure. There was no pre-determined failure degradation model. Thus, this drill bit dataset included outlier samples that did not represent the failure progression. Figure 13 shows the failure progression of an outlier sample. As seen from thefigure, the failure occurs suddenly in hole number 7, which suggests a sudden failure rather than an incipient failure.
The results presented in previous sections removed these outliers from the dataset. When the outliers are not removed, the HMM-based methods outperform the presented method, as shown in Table V. Thus, we can conclude that SBPD is more sensitive to outliers than HMM-based methods and the data should be cleaned from outliers before applying SBPD. When the outliers are removed, SBPD outperforms the HMM-based methods. Hence, we recommend using the presented method on a dataset without outliers that do not represent the failure progression. Considering the aforementioned difficulties for practicality of HMM based methods, SBPD has more potential to be used.
5.
Conclusion
Prognostics is an important tool in effective maintenance management. In state-based prognostics, the time spent in each state affects the transition probability from its current state to the next. This transition is ignored in most state-based prognostic methods. This paper presents a state-based prognostic method that incorporates the state duration information. State transition probabilities are used to calculate the RUL. The presented method was applied to two real cases: railway turnout systems and drill bits. The results show the presented method outperforms other methods in the literature. The sensitivity analysis of the presented method was also reported in the paper. To obtain good prognostic results, the outliers that do not represent the failure degradation should be removed from the training data. The sensitivity of the presented method to the outliers should be studied as future work. The presented method should be enhanced to deal with outliers without using distinct outlier detection methods.
0 20 40 60 80 100 120 140 160 180 -2 -1 0 1 2 3 4 5
Life of the drill-bit
Thrust force (Newtons)
Hole #7
Figure 13. Failure progression of an outlier sample.
Table V. r-square values with entire dataset without removing outlier samples
r-square RMSE
No Outlier HHMM 0,91 4,04
SBPD 0,94 2,01
Outlier HHMM 0,91 3,96
Acknowledgements
This research was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under project number 108M275.
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Authors' biographies
Omer Faruk Eker is a PhD student in School of Applied Sciences and works as researcher at IVHM Centre, Cranfield University, UK. He received his B.Sc. degree in Mathematics from Marmara University and MSc. in Computer Engineering from Fatih University, Istanbul, Turkey. His research interests include failure diagnostics and prognostics, condition based maintenance, pattern recognition and data mining.
Fatih Camci received the B.S. degree in computer engineering from Istanbul University, Istanbul, Turkey, and the M.S. degree in com-puter engineering from Fatih University, Istanbul, and the Ph.D. degree in industrial engineering from Wayne State University, Detroit, MI. He is a senior research fellow at IVHM Centre, Cranfield University, UK. He worked in several projects related to prognostic health management in USA and Turkey. His expertise includes prognostics health management, intelligence engineering systems, engineer-ing optimization, and video processengineer-ing.
