Machine fault diagnois and condition prognois using adaptive neuro fuzzy inference system and classification and regression trees

Thesis for the Degree of Doctor of Philosophy Machine Fault Diagnosis and Condition Prognosis using Adaptive Neuro-Fuzzy Inference System and Classification and Regression Trees by Van Tung Tran Department of Mechanical Engineering The Graduate School Pukyong National University February 2009 Machine Fault Diagnosis and Condition Prognosis using Adaptive Neuro-Fuzzy Inference System and Classification and Regression Trees 기계 결함진단 및 예지를 위한 ANFIS 와 CART Advisor: Prof Bo-Suk Yang by Van Tung Tran A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mechanical Engineering, The Graduate School, Pukyong National University February 2009 Contents List of Figures v List of Tables viii List of Symbols ix Abstract I Introduction 1 Background Motivation of This Research Research Objectives Tools and Approaches Scientific Contribution of This Research Organization of Thesis References II The State-of-The-Art of Machine Fault Diagnosis and Prognosis 11 Machine Fault Diagnosis 11 1.1 Model-based approaches 11 1.2 Knowledge-based approaches 13 1.3 Pattern recognition-based approaches 15 Machine Fault Prognosis 19 2.1 Statistical approaches .20 2.2 Model-based approaches 21 2.3 Data-driven based approaches .22 References 22 i III Background Knowledge 36 Feature-Based Diagnosis and Prognosis: a Review 36 1.1 Feature extraction techniques 37 1.2 Feature selection techniques 39 Feature Representation 40 2.1 Features in time domain 40 2.1.1 Cumulants .40 2.1.2 Upper and lower bound histogram 44 2.1.3 Entropy estimation and error 45 2.1.4 Auto-regression coefficients 45 2.2 Feature in frequency domain 46 2.2.1 Fourier transform 46 2.2.2 Spectral analysis .47 2.2.3 Frequency parameter indices 48 Classification and Regression Trees (CART) 49 3.1 Introduction 49 3.2 Tree growing 50 3.2.1 Classification tree 50 3.2.2 Regression tree .52 3.3 Tree pruning 54 3.3.1 Classification tree 54 3.3.2 Regression tree .55 3.4 Cross-validation for selecting the best tree 56 Adaptive Neuro-Fuzzy Inference System (ANFIS) 57 4.1 Architecture of ANFIS 57 4.2 Learning algorithm of ANFIS 60 Conclusions 61 ii References 61 IV CART and ANFIS Based Fault Diagnosis for Induction Motors 67 Introduction 67 Induction Motor Faults 67 2.1 Bearing faults 70 2.2 Stator or armature faults 72 2.3 Broken rotor bar and end ring faults 74 2.4 Eccentricity related faults 75 The Proposed Fault Diagnosis System for Induction Motors 77 3.1 Experiment and data acquisition 79 3.2 Feature calculation 81 3.3 Feature selection and classification .83 Conclusion 90 References 91 V Machine Condition Prognosis 94 Introduction 94 Prediction Strategies 97 2.1 Recursive prediction strategy .97 2.2 DirRec prediction strategy .98 2.3 Direct prediction strategy .98 Time Delay Estimation 99 Determining Embedding Dimension 100 4.1 Cao’s method .100 4.2 False nearest neighbor method (FNN) 101 Proposed System for Machine Condition Prognosis 103 Experiment 105 iii Case Studies of Machine Condition Prognosis 108 7.1 Case study 1: CART and OS prediction 108 7.2 Case study 2: parallel CART and MS direct prediction 115 7.2.1 Parallel structure of CART 115 7.2.2 Results and discussions 116 7.3 Case study 3: ANFIS and MS direct prediction 124 Conclusions 130 References 132 VI Conclusions and Future Works 134 Conclusions 134 Future Works 135 Acknowledgements iv List of Figures Fig 1.1 System costs depending on type of maintenance strategy Fig 1.2 Architecture of a CBM system .4 Fig 3.1 Histogram for bearing signal with different condition .44 Fig 3.2 Classification tree .51 Fig 3.3 Regression tree 53 Fig 3.4 Schematic of ANFIS architecture .58 Fig 4.1 View of a squirrel cage induction motor 68 Fig 4.2 Four types of rolling-element bearing misalignment 70 Fig 4.3 Bearing sizes marked 71 Fig 4.4 Proposed system for fault diagnosis 78 Fig 4.5 Test rig for experiment .79 Fig 4.6 Faults on the induction motors 80 Fig 4.7 Vibration and current signals of each fault condition .81 Fig 4.8 Decision tree of features obtained from vibration signal 84 Fig 4.9 Decision tree of features obtained from current signal .84 Fig 4.10 Topology of ANFIS architecture for vibration signals .85 Fig 4.11 The network RMS error convergence curve .86 Fig 4.12 Bell shaped membership functions for vibration signals 87 Fig 5.1 Hierarchy of prognostic approaches 96 Fig 5.2 Proposed system for machine fault prognosis 104 Fig 5.3 Low methane compressor: wet screw type .105 Fig 5.4 The entire of peak acceleration data of low methane compressor 106 v Fig 5.5 The entire of envelope acceleration data of low methane compressor 107 Fig 5.6 The faults of main bearings of compressor 108 Fig 5.7 Training and validating results of peak acceleration data (the first 300 points) .109 Fig 5.8 Predicted results of peak acceleration data .110 Fig 5.9 Peak acceleration of low methane compressor 110 Fig 5.10 The values of E1 and E2 of peak acceleration data of low methane compressor .111 Fig 5.11 Training and validating results of peak acceleration data 112 Fig 5.12 Predicted results of peak acceleration data .112 Fig 5.13 Data trending of envelope acceleration of low methane compressor 113 Fig 5.14 The values of E1 and E2 of envelope acceleration data 114 Fig 5.15 Training and validating results of envelope acceleration data 114 Fig 5.16 Predicted results of envelope acceleration data 115 Fig 5.17 Architecture and input values for sub-model of parallel-structure of CART .116 Fig 5.18 Time delay estimation 117 Fig.5.19 The relationship between FNN percentage and embedding dimension 118 Fig 5.20 Training and validating results of peak acceleration data 120 Fig 5.21 Training and validating results of envelop acceleration data 121 Fig 5.22 Predicted results of peak acceleration data .123 Fig 5.23 Predicted results of envelop acceleration data 124 Fig 5.24 Training and validating results of the ANFIS model for peak acceleration data .126 vi Fig 5.25 Training and validating results of the ANFIS model for envelope acceleration data .126 Fig 5.26 RMSE convergent curve 127 Fig 5.27 The changes of MFs after learning 128 Fig 5.28 Predicted results of ANFIS model for peak acceleration data 129 Fig 5.29 Predicted results of the ANFIS model for envelope acceleration data 130 Fig 6.1 The general hybrid system 136 vii (a) (b) Fig 5.26 RMSE convergent curve (a) Peak acceleration, (b) Envelope acceleration 127 0.5 Degree of membership 0.35 0.4 Input mf1 mf2 0.5 0.4 Input mf1 mf2 0.5 0.45 0.35 Degree of membership mf2 0.35 Degree of membership Degree of membership mf1 0.4 Input 0.45 mf1 mf2 0.5 0.45 0.35 0.4 Input ( ) 0.45 mf2 0.5 Degree of membership 0.5 1.5 Input mf1 mf2 0.5 1.5 Input mf1 mf2 0.5 0.5 Degree of membership mf1 0.5 Degree of membership Degree of membership (a) 1.5 Input mf1 mf2 0.5 0.5 (b) 1.5 Input (b) Fig 5.27 The changes of MFs after learning (a) Peak acceleration, (b) Envelope acceleration Figs 5.28 and 5.29 show the predicted results of the ANFIS model for peak acceleration and envelope acceleration data The RMSE values of the CART 128 model and the ANFIS model for those data are summarized in Table 5.4 Although, the RMSEs of ANFIS models are slightly higher than those of CART models in both cases of peak acceleration and envelope acceleration data, the predicted results of ANFIS models can keep track with the changes of the operating condition of machine more precisely This is of crucial importance in industrial application for estimating the time-to-failure of equipments As mentioned above, the predicted results of ANFIS models can be improved by adjusting the parameters of ANFIS However, these changes should take into consideration the increase of computational complexity and time-consumption of the training process which may lead to unrealistic application in real life 1.6 RMSE = 0.1708 Actual Predicted 1.4 1.2 0.8 0.6 0.4 0.2 -0.2 25 50 75 100 Time Fig 5.28 Predicted results of ANFIS model for peak acceleration data 129 Actual Predicted RMSE = 0.29379 3.5 Acceleration (g) 2.5 1.5 0.5 25 50 Time 75 100 Fig 5.29 Predicted results of the ANFIS model for envelope acceleration data Table 5.4 The RMSEs of CART and ANFIS Data type Peak acceleration Envelop acceleration Training Testing CART 0.002217 1.3314×10 -5 ANFIS CART ANFIS 0.00876 0.14809 0.1708 0.08886 0.2772 0.2938 Conclusions Machine condition prognosis is extremely essential in foretelling the degradation of operating conditions and trends of fault propagation before they reach the final failure threshold In this chapter, three data-driven case studies in turn are introduced to machine operating condition prognosis, in which the CART and ANFIS prediction models are associated with OS and MS strategies In the first case study, CART which is used as a prediction model in the 130 combination with OS prediction methodology is applied to forecast the future operating condition value of low methane compressor Alternatively, this case study also presents the Cao’s method which is a technique to estimate the embedding dimension or the number of inputs of prediction model By using 10 cross-validations to find the optimum tree size and embedded dimension of 6, the results give a prediction error of 1.43% with peak acceleration data, and 6% with the enveloped acceleration data These errors are sufficiently small in statistical sense The results confirm that the proposed method offers a potential for foretelling the operating condition of machine Estimating the RUL is a final objective of machine prognosis, in which RUL is the interval between the current operating condition point and the point where the predicted values fall within the alarm region or reach the predetermined failure threshold Consequently, the more future operating conditions of machine are predicted precisely, the easier and faster RUL is determined For that reason, MS prediction methodology is remarkably considered in machine condition prognosis as well as in the second case study In this circumstance, parallel-structure of CART is proposed for the predicting purpose Furthermore, the number of observations (inputs of predictor) and predicted steps (outputs of predictor) are calculated by FNN and AMI methods, respectively The results obtained from parallel-structure CART are compared with those of traditional CART It shows that the former model is slightly better than the latter one Nonetheless, more substantial improvements should be pursued through further researches to ameliorate the forecasted results The third case study is an alternative investigation in which the ANFIS model is employed as a predictor A comparison between predicted results of CART model and ANFIS model is also carried out From the comparative study, the predicted results of CART models are slightly better than those of ANFIS Nevertheless, they are lack of tracking change capabilities of machines’ operating 131 conditions which is of crucial importance in estimating the RUL with high accuracy as compared to ANFIS models This means that ANFIS has the potential for using as a tool to machine condition prognosis References [1] A.H.C Tsang, Condition-based maintenance: tools and decision making, Journal of Quality in Maintenance Engineering (1995) 3-17 [2] M Bengtsson, Condition based maintenance system technology – where is development heading, Proceeding of the 17th European Maintenance Congress, Barcelona, Spain, 2004 [3] M Abbas, A.A Ferri, M.E Orchard, G.J Vachtsevanos, An intelligent diagnostic/ prognostic framework for automotive electrical systems, IEEE Intelligent Vehicles Symposium, pp 352–357, 2007 [4] J Luo, M Namburu, K Pattipati, L Qiao, M Kawamoto, S Chigusa, Model-based prognostic techniques, AUTOTESTCON Proceedings, IEEE Systems Readiness Technology Conference, 2003, pp 330-340 [5] G Vachtsevanos, F Lewis, M Roemer, A Hess, B Wu, Intelligent fault diagnosis and prognosis for engineering system, Wiley, 2006 [6] M.B Kennel, R Brown, H.D.I Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A 45 (1992) 3403-3411 [7] L Cao, Practical method for determining the minimum embedding dimension of a scalar time series, Physica D 110 (1997) 43-50 [8] D.S Broomhead, Extracting qualitative dynamics from experimental data, Physica D 20 (1986) 217 [9] M.T Rosenstein, J.J Collins, C.J.D Luca, Reconstruction expansion as a geometry-based framework for choosing proper delay time, Physica D 73 132 (1994) 82-89 [10] A.M Fraser, H.L Swinney, Independent coordinates for strange attractors from mutual information, Physical Review A 33 (1986) 1134 [11] A Sorjamaa, A Lendasse, Time series prediction as a problem of missing values: application to ESTSP and NN3 competition benchmarks, European Symposium on Time Series Prediction, 2007, pp 165-174 [12] A Sorjamaa, J Hao, N Reyhani, Y Ji, A Lendasse, Methodology for long-term prediction of time series, Neurocomputing 70 (2007) 2861-2869 [13] S.E Shoura, M.E Sherif, A Atiya, S Shaheen, Neural networks in forecasting model: Nile river application, Proceeding of Circuits and Systems, 1998, pp 600-603 [14] Y Ji, J Hao, N Reyhani, A Lendasse, Direct and recursive prediction of time series using mutual information selection, Lecture Notes in Computer Science 3512 (2005) 1010-1017 [15] J Jeong, J.C Gore, B.S Peterson, Mutual information analysis of the EEG in patients with Alzheimer’s disease, Clinical Neurophysiology 112 (2001) 827-835 [16] V.T Tran, B.S Yang, M.S Oh, A.C.C Tan, Machine condition prognosis based on regression trees and one-step-ahead prediction, Mechanical Systems and Signal Processing 22 (5) (2008) 1179-1193 [17] L Breiman, J.H Friedman, R.A Olshen, C.J Stone, Classification and regression trees, Chapman & Hall, 1984 [18] J.S.R Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans System, Man and Cybernetics 23 (3) (1993) 665-685 133 VI Conclusions and Future Works Conclusions This dissertation presents an investigation of fault diagnosis and condition prognosis, which are two crucial components of condition-based maintenance system, based on two well-known methods: classification and regression trees (CART) and adaptive neuro-fuzzy inference system (ANFIS) It also provides a review of history and approachable methods for machine fault diagnosis as well as machine condition prognosis Generally, raw data obtained from transducer devices is rarely usable due to the huge dimensionality The huge dimensionality causes not only difficulties of data storage but also data transfer Feature-based technique which is one of the powerful techniques to represent the raw data as features is the best solution for solving this problem It extracts the useful information from the raw data to remove artifacts and reduce the dimensionality of data However, it must preserve as much as possible the characteristic features which indicate the fault event Feature-based technique is briefly introduced in this dissertation to supply the preliminary knowledge of fault diagnosis Feature representation, feature extraction, and feature selection are some of the feature-based technique Feature representation is a process where the features are calculated on time domain, frequency domain and auto-regression estimation to keep the information at the highest level Feature extraction and feature selection are to reduce the dimension of data and select an optimal subset of features that maximizes information content to improve the accuracy of classification process In case of fault diagnosis, CART and ANFIS are used as a feature selection tool to 134 select pertinent features which can characterize the machine conditions and a classifier, respectively This integrated system is validated to diagnose the faults of induction motor, which is an indispensable part in several industrial applications, based upon vibration and current signals There are several types of faults of induction motor such as bent rotor, broken rotor bar, bearing fault, mass unbalance, eccentricity fault, etc The high performance results indicate that this system can serve as a potential for machine fault diagnosis Predicting the future states of machine as well as estimating the remaining useful life of component is the capability of prognosis Nevertheless, prognosis is a relatively new area and needs more contribution to be developed In this dissertation, several case studies are proposed by using CART and ANFIS prediction model in association with some time series techniques These proposed methods are evaluated by trending data of a low methane compressor The predicted results show that CART and ANFIS predictors are reliable and promising tools in machine condition prognosis However, more substantial improvements which should be pursued through further researches to ameliorate the forecasted results are of necessary Future Works Obviously, machine fault prognosis plays a crucial role for the foreseeable future of condition-based maintenance However, further researches in several aspects on fault prognosis involved statistical-based, driven-based, and model-based are necessary to be considered Even though prognosis techniques based data-driven devote their flexibility to generate the prediction model, the improvement of predicting accuracy is the issue needed to pursue so that these techniques can be employed for real industrial applications As mentioned in several published approaches, the model-based techniques 135 give the high potential for fault prognosis even though they are challenging to obtain the precise mathematic model for mimicking the dynamic system behavior The hybridization of model-based and data-driven based techniques is a novel approach to fault prognosis area This hybrid technique will inherit the advantages from each technique so that the reliability and accuracy of prediction model is significantly gained Two such models proposed in this dissertation for long-term prediction are the combination of (1) autoregressive moving average (ARMA) [1] and ANFIS, (2) grey model (GM) [2] and ANFIS The general system for these hybrid approaches is depicted in Fig 6.1 In this system, the forecasted values obtained from ARMA model or GM model are treated as inputs values of ANFIS model in training process The actual values of machine’s operating condition are regarded as supervised values for generating ANFIS prediction model After training, the final predicted values are the outputs of ANFIS model Fig 6.1 The general hybrid system The motivation of this hybridization comes from the following perspective Firstly, it is difficult to determine whether an operating condition of machine is a linear or nonlinear underlying process or whether one particular method is more effective than the others in out-of-sample forecasting Thus, choosing the right 136 technique is a challenging task Typically, a number of different models are utilized and the one with the most accurate result is selected However, the final selected model is not necessarily the best for future uses due to many potential influencing factors such as sampling variation, model uncertainty, and structure change By hybridizing different methods, the problem of model selection can be eased with little extra effort Secondly, machine’s operating condition is rarely pure linear or nonlinear It normally contains both linear and nonlinear patterns Therefore, neither model-based nor data-driven based techniques can be adequate in modeling and forecasting due to its disadvantages For instance, ARMA model cannot deal with nonlinear relationships while ANFIS model by itself is not able to handle both linear and nonlinear patterns equally well Hence, combining different models can increase the chance to capture different patterns in the data and improve forecasting performance In addition, the combined model is more robust with regard to the possible structure change in the data Another problem that should be considered as future work is to estimate the remaining useful life (RUL) which is the core of machine prognosis As mentioned in the previous chapters, predicting the RUL allows for improving the reliability of machine, scheduling of maintenance to prevent machine downtime and removing the cost of unscheduled maintenance However, forecasting RUL problems are still at preliminary stage in research and published results Therefore, it is a challenge of machine prognosis in further investigation References [1] G.E.P Box, G.M Jenkins, Time series analysis: forecasting and control, Holden-Day, San Francisco, 1970 [2] J.L Deng, Introduction to grey system theory, Journal of Grey Systems (1989) 1-24 137 기계 결함진단 및 예지를 위한 ANFIS 와 CART Van Tung Tran 부경대학교 대학원 기계공학부 요약 세계 시장 경쟁체제에서 생산성은 중요한 경영전략이다 경영자들은 생산 성을 유지하기 위해서 전체생산비용에서 많은 부분을 차지하는 설비유지보 수 전략을 이용하여 생산비용을 줄이는 것이 필요하다 다시 말해서, 좋은 설비유지보수 전략이 현재 중요한 역할을 하고 있다 게다가 빠른 기술발전 과 함께, 기계들은 계속해서 복잡해지고 있다 과거의 사후정비, 예방정비는 기계의 기능적인 작동을 보장할 수 없고, 대표적인 상태기반정비인 인공지능 기법을 도입한 설비유지보수로 점차 대체되어가고 있다 상태기반 정비는 비파괴검사, 기계작동과 상태로부터 실제 기계의 상태에 근거하여 설비유지보수를 하는 것으로 정의된다 이것은 기계의 파손이 일어 나지 않도록 기계의 파손여부와 효과적인 정비방법에 대한 의사결정을 할 수 있다는 것이다 상태기반의 정비를 사용한다는 것은 기계상태가 항상 모 니터링(Monitoring)되고, 미리 설정된 알람(Alarm) 레벨을 나타낼 수 있어야 한다 상태기반정비에서 결함진단과 예지는 연구자들과 엔지니어들에게 관심 받을만한 중요한 요소이다 결함진단은 결함을 감지하는 것으로 시스템의 잠 재적인 결함요소를 결정하는 기술이다 그리고 예지진단은 기계의 미래의 상 태에 대해서 정상상태부터 파손이 일어나기 전까지의 잔여유용수명을 예측 할 수 있는 것으로 정의된다 이 연구에서는 기계결함진단과 예를 위해 CART(Classification and Regression Trees)와 ANFIS(Adaptive Neuro-fuzzy Inference System)가 개발되었다 CART는 결정목(Decision Tree) 기술중의 하나이고 명확하고 수치적인 결과변 수에 의존하여 분류하거나 회귀할 목적으로 사용한다 CART는 전체 데이터 를 반복적으로 반응할 변수에 대해 가능한 상동하도록 이진 하위집합을 분 할한다 이 알고리즘은 효율적인 계산과 신뢰성이 장점이다 다음으로 ANFIS 138 는 뉴럴 네트워크의 적응능력을 통합할수 있고, 퍼지논리의 인간지식을 모델 링할 수 있다 학습하는 동안에는 전문가에의해 초기화된 퍼지 멤버십 함수 의 파라미터는 입력과 출력 사이의 관계로 적응하게 된다 그것이 ANFIS 모 델을 시스템적이고 전문가 지식에 의존하지 않게 만드는 요소이다 결함진단에 사용하기 위해 CART와 ANFIS는 특징기반의 기술과 결합하 였다 이 기술은 원래의 신호를 기계의 상태를 나타낼 수 있는 특징값으로 나타내는 강력한 기법이다 특징을 이용하여 데이터 전송과 저장문제가 효과 적으로 해결된다 특징기반의 기술은 데이터취득, 데이터 전처리, 특징계산, 특징추출, 특징선택과 분류로 구성되어 있다 결함진단을 위해 제안된 CART 는 기계상태를 특징지을 수 있는 특징선택에 사용되었고 ANFIS는 특징분류 에 사용되었다 이 기술을 평가하기 위해 산업계에서 아주 중요하게 사용되 고 있는 유도전동기에 적용하였다 고성능의 분류결과는 기계결함진단에 잠 재력이 있다고 판단된다 기계의 미래상태를 예지하는 것은 현대 산업계에서 더욱더 중요해지고 있 다 그것은 엔지니어, 시스템관리자에게 도움을 주며, 재해를 예방할 수 있는 기회를 제공한다 게다가 설비유지보수 계획을 할 때 더욱 효과적으로 할 수 있다 이 연구에서는 미래의 기계상태를 CART와 ANFIS를 시간신호 예측에 사용하였다 이 기술은 예측할 때 최적의 예측구간을 결정하는 방법을 포함 하였다 메탄 압축기의 경향데이터는 제안된 시스템을 검증하는 좋은 예이다 예측된 결과는 CART와 ANFIS가 예지도구로서 신뢰할만한 도구인 것을 입 증한다 139 Acknowledgements First and foremost, I wish to express my deepest gratitude to my supervisor, Professor Bo-Suk Yang, for providing me with the opportunity to work in Intelligent Mechanics Laboratory and for his patient guidance during all stages of this study I am deeply indebted to him for teaching me about machine fault diagnosis and prognosis I would like to thank to Prof Soo-Jong Lee, Prof Byeong-Keun Choi, Prof InPil Kang and Prof Jung-Hwan Oh, the members of my dissertation committee, who have generously given their precious time and expertise to make my work better I would also like to acknowledge the research group member of Fault Diagnosis and Prognosis in laboratory, Dr Widodo, Jong-Yong Ha, Jong-Duk Son, Min-Chan Shim, Niu Gang, for warm discussion in and around research and life in Korea My special thanks go to seniors and juniors in laboratory: Jin-Dae Song, Ae-Hee Song, Sung-Do Tae, Sung-Won Jo, Won-Jung Cho, Jun-Seok Oh, Pham Hong Thom, Caesarendra, Younus, Seong-Yong Park, and Sung-Wook Yang They gave me spirit of brotherhood, help and supports during my study in Korea I would like to acknowledge my family who has been an inspiration throughout my life They have always supported my dreams and aspirations and consistently helped me keep my perspective A special thank is extended to them for all they are, and for all they have done for me My special thanks go to my fiancée, Ngoc Han Pham, for her love, care, understanding and encouragement throughout, as always, for which my mere 140 expression of thanks likewise does not suffice Thanks for always being there for me Last but not least, my thanks must go to friends who always stand by me through my ups and downs It is always impossible to personally thank everyone who has facilitated the completion of this dissertation To those of you I did not specifically name, I also give my thanks for moving me towards my goal Busan, Feb 2009 Van Tung Tran 141 .. .Machine Fault Diagnosis and Condition Prognosis using Adaptive Neuro- Fuzzy Inference System and Classification and Regression Trees 기계 결함진단 및 예지를 위한 ANFIS 와 CART... neighbor of yi(d) Time delay τ xii Machine Fault Diagnosis and Condition Prognosis using Adaptive Neuro- Fuzzy Inference System and Classification and Regression Trees Van Tung Tran Department of... operation of machine before breakdowns occur or machine condition reaches the critical failure value In this study, classification and regression trees (CART) and adaptive neuro- fuzzy inference systems