Tài liệu 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 1. Background ........................................................................................... 1 2. Motivation of This Research ................................................................. 6 3. Research Objectives .............................................................................. 6 4. Tools and Approaches........................................................................... 7 5. Scientific Contribution of This Research.............................................. 7 6. Organization of Thesis .......................................................................... 8 References .................................................................................................. 9 II. The State-of-The-Art of Machine Fault Diagnosis and Prognosis ......... 11 1. Machine Fault Diagnosis .................................................................... 11 1.1. Model-based approaches........................................................................11 1.2. Knowledge-based approaches................................................................13 1.3. Pattern recognition-based approaches ...................................................15 2. 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 1. Feature-Based Diagnosis and Prognosis: a Review ............................ 36 1.1. Feature extraction techniques ................................................................37 1.2. Feature selection techniques ..................................................................39 2. 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 3. 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 4. Adaptive Neuro-Fuzzy Inference System (ANFIS)............................ 57 4.1. Architecture of ANFIS...........................................................................57 4.2. Learning algorithm of ANFIS................................................................60 5. Conclusions ......................................................................................... 61 ii References ................................................................................................ 61 IV. CART and ANFIS Based Fault Diagnosis for Induction Motors ......... 67 1. Introduction ......................................................................................... 67 2. 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 3. 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 4. Conclusion .......................................................................................... 90 References ................................................................................................ 91 V. Machine Condition Prognosis ................................................................ 94 1. Introduction ......................................................................................... 94 2. Prediction Strategies ........................................................................... 97 2.1. Recursive prediction strategy.................................................................97 2.2. DirRec prediction strategy .....................................................................98 2.3. Direct prediction strategy.......................................................................98 3. Time Delay Estimation ....................................................................... 99 4. Determining Embedding Dimension ................................................ 100 4.1. Cao’s method .......................................................................................100 4.2. False nearest neighbor method (FNN) .................................................101 5. Proposed System for Machine Condition Prognosis ........................ 103 6. Experiment ........................................................................................ 105 iii 7. 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 8. Conclusions ....................................................................................... 130 References .............................................................................................. 132 VI. Conclusions and Future Works ........................................................... 134 1. Conclusions ....................................................................................... 134 2. Future Works..................................................................................... 135 Acknowledgements ......................................................................................... iv List of Figures Fig. 1.1 System costs depending on type of maintenance strategy ....................3 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 List of Tables Table 3.1 Cumulants for bearing signal with different condition .......................42 Table 4.1 Comparison of detection technologies ...............................................69 Table 4.2 The description of faulty motors ........................................................80 Table 4.3 Feature parameters ..............................................................................82 Table 4.4 Descriptions of data sets .....................................................................83 Table 4.5 The confusion matrix for CART-ANFIS of 800 epochs ....................88 Table 4.6 The value of statistical parameters .....................................................90 Table 5.1 Training set D for direct prediction strategy ......................................99 Table 5.2 Information of the system .................................................................105 Table 5.3 The RMSEs of CART and parallel-structure CART ........................119 Table 5.4 The RMSEs of CART and ANFIS ...................................................130 viii List of Symbols Chapter III Background Knowledge ai Auto-regression coefficients {ai, bi, ci} Modifiable parameters B(f1, f2) Bispectrum c1 Mean c2 Standard deviation c3 Skewness c4 Kutosis CF Crest factor d Number of divisions E{.} Expected value of the function E[⋅] The statistical expectation E(t) Entropy impurity at node t E(tL) Impurity of the left branch node E(tR) Impurity of the right branch node Ee(xi) Standard error Es(xi) Entropy estimation Eα(T) Cost-complexity measure f Frequency index FC Frequency center f(t) Representation of a time signal F(ω) Frequency domain function hi Columns of the histogram hL Lower bound of histogram ix hU Upper bound of histogram L Learning sample MSF Mean square frequency n Order of the AR model N nij(v ) Number of data points Number of observations in Lv p(xi) Distribution on the whole signal p(wj|t) Fraction of patterns {pi, qi, ri} Consequent parameters RMSF R(T ) Root mean square frequency Total within-node sum of squares R(tL) Sum of squares of the left subset R(tR) Sum of squares of the right subset RVF Rˆ CV (Tk ) Rα (T ) Root variance frequency Misclassification error Error-complexity SEˆ ( Rˆ CV (Tk ) Standard error of misclassification error SF Shape factor t Temporal variable T Sub-tree tL Left branch nodes tR Right branch nodes Tmax T Wholly expanded tree in the growing phase {t1} T Set of current nodes of T Root of tree Number of terminal nodes in T T(v)(α) Sequence of trees T(f1, f2, f3) Trispectrum x VF Variance frequency V Mutually exclusive data sets xabs Absolute value xi Discrete time signals x(n) Discrete time series xp Peak value xrms RMS value X *( f ) Complex conjugate yt Time series under investigation α αk α k′ Complexity parameter Corresponding sequence Complexity parameter for the geometric midpoint ∆E(s,t) Drop of impurity εt Residual ω Frequency Chapter IV CART and ANFIS Based Fault Diagnosis for Induction Motors BD f fb fec fr fs fv Nb nd p PD Ball diameter Fundamental supply frequency Detectable broken bar frequency Frequency components of interest Rotor rotational frequency Supply frequency Characteristic vibration frequencies Number of balls Eccentricity order Number of pole pairs Pitch diameter xi s v β Slip Order of the stator time harmonics Contact angle Chapter V Machine Condition Prognosis Atol d E(d) MF PX ( x (t )) Threshold Embedding dimension Mean value Membership function Normalized histogram RA Rtol Size of the attractor Tolerance level RMSE X Y yi(d) yn(i,d)(d) Root-mean square error Input vector Output vector The ith reconstructed vector Nearest 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 Mechanical Engineering, The Graduate School, Pukyong National University Abstract Sustaining the productivity is a key strategy of manufacturers to exist on the drastic competition of global market. In order to keep up the productivity, manufacturers need to reduce the manufacturing costs by using maintenance due to its major part of the total costs of the manufacturing process. Consequently, a good maintenance strategy plays a crucial role in the existence and development of the organizations. Additionally, in accompany with the fast development of technology, the equipment becomes more and more complex. The traditional maintenance strategies such as corrective maintenance and prescheduled maintenance cannot guarantee the functional operation of equipments and are progressively replaced by intelligent maintenance strategies in which condition based maintenance is one of the delegates. Condition-based maintenance has been defined as maintenance actions which are based on actual conditions of equipments obtained from nondestructive inspections, operations and condition measurements. This means that the equipment condition is accessed under operation for making conclusions whether that equipment will be failed and the effective maintenance actions are necessary xiii to avoid the consequences of that failure or not. The use of condition-based maintenance systems ensures that the condition of equipment is always monitored and alarm limitations can be indicated if the condition exceeds predefined levels. In condition-based maintenance system, fault diagnosis and condition prognosis are crucial components which have been considerably received much attention from the community of researchers and maintainers. Fault diagnosis is the ability to detect fault, isolate the component which is failure, and decide on the potential impact of failed component on the health of the system; while condition prognosis is defined as a capability to foretell the future states, predict the remaining useful life – the time left for the normal 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 (ANFIS) will be developed as an effective intelligent system for performing machine fault diagnosis and condition prognosis. CART is known as one of the illustrious techniques of the decision tree induction and used for the purpose of either classification or regression depending on the output variable which is categorical or numerical. CART recursively partitions the entire data into binary descendant subsets which are as homogeneous as possible with respect to the response variables. High effective computation and reliability are the remarkable advantages of this algorithm. In the second technique, ANFIS is an excellent integration of the adaptive capability of neural networks and the modeling human knowledge ability of fuzzy logic. During the learning process, the parameters of fuzzy membership functions initially determined by experts are adapted to the relationship between the input and output. That combination makes the ANFIS model more systematic and less dependent on the expert knowledge. For implementing the fault diagnosis, CART and ANFIS are combined with another technique so-called feature-based technique. This technique is one of the powerful techniques to represent the raw data as features which are xiv representatives of values indicating the machine condition. By using features, the encountered problem in data transfer and data storage could be effortlessly solved. Feature-based technique consists of data acquisition, data preprocessing, feature representation, feature extraction, feature selection and classifiers. In the proposed system for fault diagnosis, CART is used as a feature selection tool to select pertinent features which can characterize the machine conditions from the whole feature set whilst ANFIS plays a role as a classifier. In order to be evaluated, this system is applied to diagnose the faults of induction motor, which is an indispensable part in several industrial applications. The high performance results indicate that this system offers a potential for machine fault diagnosis. Foretelling the future states of machine has become more and more significant in modern industry. It assists maintainers or system operators in monitoring, inspecting the machines’ operating conditions, and detecting the incipient faults so that they could opportunely perform remedial actions to avoid the catastrophic failures. Furthermore, it enables the scheduled maintenance to be more effective. In this study, the future machines’ operating conditions are predicted by using CART and ANFIS model in combination with time series techniques. These time series techniques consist of methods which are utilized to determine the optimal observations and the steps ahead as the inputs and outputs of predictors, respectively. The trending data of a low methane compressor is used to validate the proposed method. The predicted results show that CART and ANFIS predictors are reliable and promising tools in machine condition prognosis. xv I. Introduction 1. Background A failure in equipment of production line results in not only the loss of productivity but also timely services to customer, and may even lead to safety and environmental problems which destroy the organization image. This emphasizes the need of maintenance activities in manufacturing operations of organization. Maintenance activities can sustain the reliability and availability of product equipment, improve the product quality, increase productivity, and undertake the safety requirements. However, maintenance activities have been historically regarded as a necessary evil by the various management functions in an organization since maintenance costs form a large part of the total operating and production costs in capital-intensive industries. According to [1], the maintenance cost for industrial companies in the USA has increased 10-15% per year since 1979. Depending on the specific industry, maintenance costs can represent between 10 and more than 40% of the costs of goods produced. For example, maintenance costs as a percentage of total value-added costs could be 20-50% for mining, 15-25% for primary metal and 3-15% for processing and manufacturing industries [2]. In a study of Knights and Oyanader [3], in open-pit mining operations in Chile, the world’s primary copper producer, maintenance costs were estimated at 44% of total mine production costs. Similarly, 20-40% of these maintenance costs are related to the repair of major components. Therefore, major system repair costs indirectly account for 9-18% of the total operating costs of an open-pit mining operation. Also, for equipment manufacturers and distributors, system repair and maintenance costs are the major cause of liabilities through 1 warranty programs and repair and maintenance contracts, especially when taking into account that the use of rebuilt system is of growing interest to the industry, both on a rental or leasing basis. The recent surveys of maintenance management effectiveness in US manufacturing industry indicate that one third of all maintenance costs is wasted as the result of unnecessary and improper maintenance activities. Additionally, with the augment of mechanization and automation, many modern plants have installed flexible computer-controlled automatic and unmanned equipments, the maintenance costs have been increased substantially. Consequently, an efficient and reasonable maintenance strategy is in need of implementing so that organization’s overall goals and objectives can be attained at minimal costs. Traditionally, maintenance strategies in industry are broadly classified as two categories, namely corrective maintenance and preventive maintenance [4, 5]. Corrective maintenance, also known as breakdown maintenance, is carried out merely after the occurrence of an obvious functional failure, malfunction, or breakdown of equipment. Its actions are able to restore the functional capabilities of failed or malfunctioned equipment by either repairing or replacing the failed component. Corrective maintenance is reactive approach to maintenance because the action is triggered by the unplanned event of an equipment failure. Preventive maintenance involves scheduled maintenance and condition-based maintenance (CBM) [6]. Scheduled maintenance is performed periodically at predetermined interval to prevent the functional failure by replacing critical components before the end of their expected useful lives. CBM is a method used to reduce the uncertainty of maintenance activities, and is carried out according to the need indicated by equipment condition. Unlike the strategies mentioned above, CBM does not normally involve in an intrusion into the equipment and actual preventive action is taken only when an incipient failure is believed to have been detected. According to [7], the variation in costs with number of maintenance events is 2