Prognostics for tool condition monitoring based on long term and short term prognostic approaches 2

Arising from variations in material characteristics of the workpiece and tool, there might be unexpected or pre-matured tool wear occurring before the failure time expected from the long

Thanks to Mr.Simon Tan, and all the technicians at Advanced Manufacturing Lab of NUS for their kind and quick technical assistance during my experiments

I have also benefitted from discussion with many of seniors and colleagues In particular Dr.Kommisetti V R S Manyam, Dr Yu Deping, Ms Wang Qing, Dr Wu Jiayun and others in the Control and Mechatronics Lab

I also would like to thank National University of Singapore for offering me research scholarship and research facilities I benefitted from the abundant professional books and technical Journal collection at NUS library

Finally, I would like to devote the thesis to my family for their love and understanding

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Table of Content

Acknowledgements ii

Table of Content iii

Summary vii

List of Table ix

List of Figures xi

List of Symbols xiv

Nomenclature xv

Chapter 1 Introduction 1

1.1 Tool Condition Monitoring 1

1.2 Motivation and Challenges 3

1.3 Objectives 5

1.4 Organization of the Thesis 6

Chapter 2 Literature Review 9

2.1 TCM Review 9

2.1.1 Background 9

2.1.2 Overview of Tool Condition Monitoring 12

iv

2.2 Prognostic Methodologies for General Health Monitoring Review 15

2.2.1 Reliability Analysis 16

2.2.2 Condition Monitoring Based Prognostic 18

2.3 Review for TCM Prognostics and its Challenge 23

Chapter 3 Long-term Prognostics 29

3.1 Introduction 29

3.2 The Feasibility of Using VDHMM to Model the Machining Process 32 3.2.1 HMM Based Prognostics 34

3.2.2 Modeling the tool wear as stationary Markov process and Markov process with explicit state duration 37

3.2.3 VDHMM parameter estimation 42

3.2.4 Case study results and discussion 53

3.3 Adaptive VDHMM based prognostics 65

3.3.1 Adaptive VDHMM Fundamentals 66

3.3.2 Experimental setup 72

3.3.3 Results and discussion 73 3.4 Adaptive-VDHMM based feature selections for different number of states 81

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3.4.2 Results and discussion 87

3.5 Conclusion 94

Chapter 4 Short-term Prognostics 99

4.1 Introduction 99

4.2 Theoretical background 104

4.2.1 Delay Coordinate Embedding 104

4.2.2 Function Approximation Methodologies 105

4.2.3 Bayesian MLP for regression 108

4.3 Results and discussion 109

4.3.1 Force prediction 109

4.4 Combination of Short term and long term prognostics 118

4.5 Conclusions 121

Chapter 5 Conclusions and Future Work 123

5.1 Conclusions and Contributions 123

5.2 Conclusions 123

5.3 Contributions 124

vi

5.4 Future work 126

5.4.1 Variable cutting condition study for long-term prognostics 126

5.4.2 Study the signal properties for short-term prognostics 127

References 128

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Summary

Tool condition monitoring (TCM) plays an important role in modern manufacturing system At present, the researches in TCM focus mainly on diagnostics of different tool conditions Such detection approaches may sometime be too late in avoiding damage or quality issues associated with the worn or broken tool Hence, this thesis proposes a TCM prognostic system which aims to enable a future scheduling decision as well as optimal tool replacement time

The proposed TCM prognostic system consists of two parts: long term prognostics, and short term prognostics In the long term prognostics, the remaining useful life (RUL) is prognosticated by utilizing variable duration Hidden Markov model (VDHMM) VDHMM overcomes the state duration limitation of the traditional HMM The relation between the model structure and the tool wear process

is studied to understand and address issues regarding the factors that affect the prognostic results It is found that VDHMM with Gaussian distribution as the state duration offers effective prognosis for the machining conditions studied

Several features have been derived from the force signal captured during the machining process and identified to correlate with tool conditions As appropriate selection of these features affects the prognostic results, a feature selection method is proposed The method identifies and selects a sub-set of complementary and supportive features The proposed method is compared with the feature ranking methods, which rank the features based on their relevance with tool wear progress

viii

The result shows that features considered relevant to tool wear may worsen the prognostic results, while those considered not relevant to tool wear could improve the prognostic results, when the latter features complement and support other features Arising from variations in material characteristics of the workpiece and tool, there might be unexpected or pre-matured tool wear occurring before the failure time expected from the long-term prognostics Hence, a short term prognostics capturing the short term dynamics of the tool wear is proposed This is achieved by adding a cutting force prediction part to a diagnostic system Different cutting force prediction structures are analyzed It is found that Sauer’s local linear model can achieve reasonable prediction accuracy and the shortest computation time

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List of Table

Table 3.1 Experimental conditions and equipment 53

Table 3.2 The tool wear table 57

Table 3.3 The A-D test for the 8 samples 60

Table 3.4 The residual lives take each state as the initial state of the 8 life tests 61 Table 3.5 The natural mean residual life 61

Table 3.6 Cutting conditions 73

Table 3.7 average model for the training sets 74

Table 3.8 the transformation matrix for the training sets 74

Table 3.9 The MAPE of MRL taking each state as the initial 78

Table 3.10 The cross validation 81

Table 3.11 Summary of features 87

Table 3.12 The feature sets selected by the proposed method 90

Table 3.13 feature selection by LDA 91

Table 4.1 The smallest embedding dimension for all the test and their average 110 Table 4.2 Compare the ASIE and calculation time for Sauer’s local linear approach, Global linear approach and non-linear (MLP) approach 112

x

Table 4.3 Selected features 113

Table 4.4 Successful rate for each testing sets 115

Table 4.5 Two prognostic scenarios 118

Table_Apx A-1Cutting condition 142

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List of Figures

Figure 2.1 Tool wear definition 9

Figure 2.2 Tool wear measurement 10

Figure 2.3 TCM process 13

Figure 3.1 The on-line prognostic process for a target test at time t 37

Figure 3.2 a left-to-write Markov process 39

Figure 3.3 A Markov process with the explicit state duration distribution 40

Figure 3.4 the feature 1 & 2 and its GMM model for fresh, moderately worn and worn tool 45

Figure 3.5 feature 9 & 10 and its GMM model for fresh, moderately worn and worn tool 45

Figure 3.6 The probability of features vectors belongs to fresh, moderately worn and worn tools 46

Figure 3.7 different combinatiosn of k0 and λ0 and their corresponding log-likelihood 52

Figure 3.8 experimental setup 54

Figure 3.9 Geometry of a face milling operation 54

Figure 3.10 Cutting force sample for fresh cutting tool 55

xii

Figure 3.11 Cutting force sample for worn cutting tool 55

Figure 3.12 normalized maximum resultant force per revolution 56

Figure 3.13 normalized average resultant force per revolution 56

Figure 3.14 Eight life tests under the same cutting condition for testing the state duration distribution type 57

Figure 3.15 The natural MRL compared with the MRL estimated by Conventional HMM (Exponential), VDHMM with Gaussian and Weibull distributions 63

Figure 3.16 the state duration mean changes with the number of training set changes 64

Figure 3.17 VDHMM-based adaptive training 68

Figure 3.18 Adaptive HSMM based prognostics for tests under new cutting condition (f) 72

Figure 3.19 log-likelihood for each training iteration 75

Figure 3.20 Prognostic results for T1 76

Figure 3.21 Prognostic results for T4 77

Figure 3.22 Prognostic results for T6 77

Figure 3.23 Prognostic results for T7 78

Figure 3.24 prognostic results for T12 78

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Figure 3.26 The proposed feature selection process 89

Figure 3.27 The MAPE for different number of states 93

Figure 3.28 MAPE for ball nose milling prognostics 94

Figure 4.1 TCM diagnostic system architecture 101

Figure 4.2 The proposed prognosis process 101

Figure 4.3 The architecture of MLP in this study 108

Figure 4.4 Illustration of predicted tool wear, confidence interval, and tool failure probability 114

Figure 4.5 compares of true tool wear and predicted tool wear with its 95% confidence interval 115

Figure 4.6 risk cost and profit cost 117

Figure 4.7The usage of long-term and short-term prognostic system 120

Figure_Apx A-1The machining process………137

Figure_Apx A-2 Cutting force sample for fresh cutting tool……….138

Figure_Apx A-3 Cutting force sample for worn cutting tool……….138

Figure_Apx A-4 Experiment setup……… …… 138

Figure_Apx A-5 Tool wear of a cutter after a period of cutting ……… 139

xiv

List of Symbols

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Nomenclature

N j i j

i j

a

A { },1, The state transition probability

α t (i) Forward probability

N i

i k b

B{ ( )}1 Output probability distribution, which is the probability of

the observation k in state i

b(t) Delay coordinate vector at time unit t, with time delay 

b * Delay coordinate vector for observation series

N i

p

D{ ( )}1 State duration probability distribution (Gaussian or

Weibull distribution), which is the probability of staying in

state i for d time units

D 0 max(y 1 ,y 2 …,y N )

F a (j) average cutting force in j th rotation



Fa ( j) The first order differencing of the average cutting force



 2F a ( j) The second order differencing of the average cutting force

F The cumulative distribution function of the specified

F i Reliability function for state i

F med (j) Median cutting force for in the jth rotation period

F v (j) variable force in j th rotation period

f a (j) average resultant force for j th revolution



f i initial (t) Probability density function (pdf) of the residual life

taking state i as the initial state

f m (j) maximum resultant force for j th revolution

f(t) Probability density function

G(m) Power at the fundamental tooth frequency and its

harmonics

h T (t) Hazard rate function at time T

m i state duration mean of state i

P i (d) Probability of remaining in state i for d time units

P TH (j) Total harmonic power

p i (t) Probability density function (pdf) of the duration in state i

) , ' (  

Q Auxiliary function of current parameters λ’ and new

parameter λ

r a (j) Amplitude ratio of cutting force in j th rotation period

s(j) Skewness of the cutting force in the j th rotation period

W Transformation matrix of the extended state duration

variance

W f Transformation matrix of the extended state duration

variance for new target

X Transformation matrix for extended mean vector

X f Transformation matrix for extended mean vector of new

target

i

y

Predicted cutting force

{i } N i=1 The initial state probability, which means the probability

of staying in state i at the beginning (t=0)

T i

  Extended state duration variance

(j) Standard deviation of the cutting force in j th rotation

period

i mean of the i th feature vector

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i standard deviation of the i feature vector

Chapter 1 Introduction 1

1.1 Tool Condition Monitoring

A cutting tool is a mechanical device which is used to fabricate components by machining The failure of a cutting tool can cause catastrophic damage to the workpiece, as well as much machining downtime Therefore, replacing the failed or failing cutting tool in time is of vital importance

Before 1980’s, two approaches are used to avoid damage caused by a worn cutting tool The first are empirical methods used to determine the tool life The Taylor’s tool life equation is a popular empirical method used to predict the general cutting tool life for a given machining condition However, it does not model the stochastic property of the cutting tool wear process In the second, the tool wear measurement is made directly The cutting tool is to be replaced when the tool wear exceeds a certain level Both approaches tend to be conservative in determining the usable life of the tool, affecting the efficiency of the machining system Therefore, an on-line and indirect TCM system, which aims to continuously monitor the cutting tool situation and indicate the need to terminate the machining process only when the tool is detected to be ineffective, is considered more suitable, especially for a highly automated machining system

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Recently, with increasing sophistication and performance in sensor technology, tool condition monitoring systems based on suitable intelligent sensors can be developed, such as those for cutting force or torque monitoring, vibration monitoring, spindle/drive power or current monitoring, acoustic emission monitoring, and temperature monitoring Most of the existing on-line TCM systems tend to focus on the acquisition of relevant tool wear degradation information and the detection or classification of tool wear state based on the acquired data These technologies enable

an existing problem of the cutting tool to be detected, diagnosed and corrected before serious consequences occur However, a more productive approach is to utilize the tool condition information for maximizing the machining schedule efficiency and optimizing the tool replacement time This potentially can be achieved through prognosis An effective prognostic system could forecast a cutting tool’s remaining useful life (RUL), future condition, or risk of failure The prognostic system has two advantages over a diagnostic system Firstly, the prognostic system can provide more information than the diagnostic system For example, by prognosis of the remaining useful life, the machines and workpiece can be pre-scheduled to achieve an optimal asset arrangement Secondly, prognostics can provide lead time for the decision on tool replacement In conclusion, the prognostic system can help to minimize production downtime and to plan inventory, thereby reducing machining costs

Chapter 1 Introduction 3

1.2 Motivation and Challenges

As discussed in the aforementioned, a prognostic system has two advantages compared with a diagnostic system These are optimal asset management, and optimal tool replacement time Therefore, the aims of a prognostic system are prognostics of 1) the remaining useful life (RUL), and 2) probability of failure (POF)

In this section, the motivations and challenges of the research approaches for both prognostics of RUL and POF are discussed

The prognostic of the RUL is useful for determining the future machining schedule The prior information for future schedule is the tool life distribution [1-8] Before TCM was implemented in the industry, the prior information was achieved by off-line analysis [9-11] This tool life distribution is determined before the cutting tool is used for machining However, the tool wear process is a stochastic process, which can be affected by many unpredicted factors, such as the uneven constituent of the workpiece, the machine vibration and the unsteady motor current Therefore, the actual tool life distribution may differ much from the pre-determined tool life distribution A hybrid model, which combines the reliability model with the Condition Monitoring (CM) information, aims to narrow down the uncertainty In the literature, these hybrid models [12-14] are established for equipment health monitoring systems However, in TCM application, the literatures are quite limited There are two challenges Firstly, some existing models have been established for a

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different type of wear process, which may not be suitable for tool wear process For example, an exponential wear profile is used to describe a component in hot strip steel mill [12] However, the exponential wear profile is not applicable for tool wear process[15] Secondly, some hybrid models have its own limitations, which need to

be improved For example, HMM, which is a popular statistical model, has been used for prognostic purpose [14, 16] However, the limitation of the exponential state duration distribution deters the way for application of TCM This is because exponential state duration has a constant hazard rate, which represents a constant tool wear rate However, tool wear rate increase rapidly at the initial and finally wear stage Therefore, there is a need to study the machining process and the model structure to identify and develop a hybrid model which combines the reliability theory and CM information and is capable of prognosticating the RUL of the cutting tool There are two motivations to determine POF Firstly, it can ensure the safety issue, such as premature and unexpected tool failure Secondly, it can help in deciding on the optimal tool replacement time Although some diagnostic systems are also capable of detecting the POF at present, it does not provide much information or lead time for optimal tool replacement decision Prognosticating the POF in the future

is able to offer enough reaction time The prognostics of the RUL can be considered

as long-term prognostics, as the prediction horizon is from the present time until the tool failure The prognostic of POF has a shorter prediction horizon, and so can be considered as short-term prognostics The challenge for short-term prognostics lies in

Chapter 1 Introduction 5

the computation time The tool life is relative short compared with the machine or equipment Therefore, if the prognostic algorithm is quite complex, the computation time might exceed the prediction horizon In this case, the prognostic is not achieved, regardless of the accuracy of the result

1.3 Objectives

The purpose of a tool condition monitoring system (TCM) is primarily to provide tool condition information for making decision on tool replacement It can also enable optimal decision to maximize profit rate, and minimize machine downtime and inventory, while avoiding damage to tool, workpiece and machine As discussed earlier, a diagnostic system can only estimate the tool wear at present, so this system does not offer enough reaction time for making optimal decision Hence, there is the trend towards research in prognostic systems for TCM

The prognostic system has two parts: long-term and short-term The long-term prognostics determine the remaining useful tool life as a random variable, and could contribute to the scheduling of future machining requirements The short-term prognostics target at tool failure occurring before the expected tool life obtained by long-term prognostics, with emphasis on the damage avoidance and optimal tool replacement time Therefore, the objectives of this thesis are to:

 Establish a prognostic system capable of long-term and short-term prognostics

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 Verify the prognostic results by case studies

 Analyze the factors which affect the prognostic results

The long-term prognostics are achieved by a variable duration Hidden Markov model (VDHMM) and adaptive-VDHMM This VDHMM is an update of conventional HMM by assuming the state duration as an explicit duration function This assumption overcomes the limitations of conventional HMM [1] The prognostic result of the variable duration Hidden Markov model (VDHMM) is compared with conventional Hidden Markov model (HMM) The adaptive-VDHMM adapts the model information to a targeted test under different cutting conditions, which broadens the application area for the prognostic system

The short-term prognostics are achieved by a combination of the delay coordinate embedding technique and the Bayesian neural networks This short-term prognostic system is to provide fast and accurate prognosis

The overall study aims to demonstrate the feasible application of the prognostic system that offers enhanced capability and performance compared to a diagnostic system in TCM Establishing the prognostic system is also helpful in the understanding of the machining process

1.4 Organization of the Thesis

The thesis is organized as follows:

Chapter 1 Introduction 7

Chapter 2 first looks at current TCM methodologies, which include sensor signals, feature extraction methods, and diagnostic methods The prognostic methodologies for general health monitoring applications are then reviewed These methodologies involve reliability analysis, and condition monitoring based prognostics Finally, the prognostic methodologies for TCM applications are discussed

Chapter 3 presents the establishment of a long-term prognostic system, which aims at prognosticating the RUL of the cutting tool Firstly, the modeling of the tool wear process as a non-stationary Markov Chain is discussed A VDHMM is established for the prognostic of the RUL The prognostic results are verified using data from the experimental study of a face milling process Secondly, an adaptive algorithm is combined with VDHMM to adapt the training information to the target tests, which are under different cutting conditions The factors, which affect the prognostic performance, are discussed The prognostic results are verified by face milling experiments

Chapter 4 presents the process of establishing a short-term prognostic system This system first predicts the future cutting force signal Then this predicted cutting force signal is passed through a Bayesian Neural network to obtain the probability of failure in the future A face milling case study verifies the prognostic results

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Chapter 5 concludes the study and the development of the prognostic system The limitation and future works are also presented

Chapter 2 Literature Review 9

2.1 TCM Review

2.1.1 Background

In the machining process, three failure modes of the cutting tool can be observed: tool wear, tool breakage and build up edge The TCM research is usually focused on monitoring the first two failure modes, as these two modes are important and critical

to be identified[17]

Tool wear is defined as the change in shape of the cutting edges and their neighboring regions, resulting in moderately loss of tool material during cutting[17] The geometry and wear definition are shown in Figure 2.1 and the measurement

criteria in Figure 2.2Error! Reference source not found

Figure 2.1 Tool wear definition

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Figure 2.2 Tool wear measurement

Tool wear can be categorized in two ways [18] One is based on the place, where the wear happens; the other one is based on the wear mechanisms For the first category, there are flank wear, crater wear, notch wear, chipping and breakage[18] Flank wear occurs on the tool flank face, and is measured by average wear land width (VB) and maximum wear land width (VBmax) as Figure 2.2 Three stages of flank wear process are observed in a typical tool life curve The first stage is a rapid initial wear process, in which the wear develops rapidly to a certain wear level This

is caused by micro cracking, surface oxidation and carbon loss, and micro roughness

at the cutting edge in tool manufacturing This wear stage usually experience only for

a short time The second stage is the moderate wear, the wear progresses linearly and comparatively longer time Most of the tool’s useful life is in this stage, where the micro roughness around the cutting edge progresses Finally, this roughness progression leads the tool wear to the third stage, which is a rapid wear stage In this stage, the flank wear increases rapidly to a critical value such that the surface quality

of the machined surface degrades, cutting force and temperature increases severely It

is recommended that the tool needs to be replaced before this stage

Chapter 2 Literature Review 11

Crater wear is caused by the friction between the rake face and chip flowing across the rake face The development of crater wear is closely related to the cutting temperature and pressure The parameters used to measure the crater wear is shown in Figure 2.2 (1)

Notch wear is a combination of flank and crater wear, which occurs close to the point where the major cutting edge intersects the workpiece surface It happens when the materials has high work hardening characteristics

Instead of wear, when a relatively large discrete particle of tool material is removed in the machining process, chipping or breakage happens This is usually caused by sudden loading with intermittent or temperature gradients Moreover, the buildup edge also contributes to chipping and breakage Based on the size of the removed particles, three kinds of chipping terms are defined They are micro chipping, macro chipping, and breakage (with length of more than 1mm)

For the second category, there are adhesive wear, abrasive wear, oxidative wear, diffusive wear, superficial plastic deformation and plastic deformation

Adhesive wear arises from molecular adhesion happening between the tool and the workpiece This kind of wear occurs at any cutting speed

Abrasive wear involves the removal of the tool material by the scoring action of the inherently hard particles in the workpiece, such as inclusions and carbide, causing

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continuous wear on the surface of the tool This kind of wear also occurs at any cutting speed

The oxidation wear occurs at high cutting temperature, in particular at the contact zone of tool and workpiece, where there is free atmospheric contact The oxidation process at this region weakens the tool material, facilitating the tool wear

Diffusive wear also happens at high cutting temperature When the temperature

is high, the mutual dissolution of material occurs between the workpiece and tool, and hence weakens the tool material

Superficial plastic deformation is the major cause of crater wear In high speed machining, the chip deforms at high strain rate and can exert sufficient shear stress on the surface layer of the tool This effect removes tool material from the crater zone Plastic deformation of the cutting edge occurs at high cutting temperature, which causes the thermal weakening of the cutting edge region This weakening causes plastic deformation under normally applied load Once this deformation occurs, the blunt edge causes additional heating due to rubbing Hence, weaken the tool material further and eventually leading to tool failure

2.1.2 Overview of Tool Condition Monitoring

Tool condition monitoring (TCM) aims at identifying and predicting the cutting tool state, by apply appropriate sensor signal processing and pattern recognition

Chapter 2 Literature Review 13

techniques Effective TCM system can improve productivity and ensure workpiece quality, and has a major influence in machining economics[19] [17] The generic structure of TCM is illustrated in Figure 2.3 A typical TCM system consists of signal collection, feature extraction, and diagnostics Recently, prognostics is also considered as part of TCM systems

TCM research has a history since late 1980s For a successful TCM system, the sensor signals should be sensitive to tool conditions in the harsh machining environment Various sensors are suitable to detect the tool wear, either directly from the tool or indirectly from the workpiece or machine table Direct monitoring methods involves optical approaches, which measure the geometric parameters of the cutting tool[20] (Figure 2.3) Indirect measurement involves cutting force [21-29], vibrations [30-32], acoustic emission [32-36], and motor/feed current [37-39]

Figure 2.3 TCM process

Feature extraction aims at processing the signals to yield useful features that are highly correlated to tool conditions The feature extraction methods can be divided into three categories: time domain, frequency domain and time-frequency domain The time-domain feature extraction method involves statistical and time-series

machining

Signals

Force

AE Vibration Current

Feature Extraction

Time domain Frequency domain Time-frequency domain

Diagnostics

Clustering NN HMM Linear regression

Prognostics

NN HMM

(image) direct

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modeling methodologies These features are popular in the early TCM research There are many successful TCM approaches using time-domain features, such as in references [40-43] Frequency domain features involve analysis of the power spectrum density and harmonics of the signals Elbestawi [40] is one of the earliest researchers employing fast Fourier Transform to compute the ratio of the magnitudes

of cutting force harmonics that are sensitive to flank wear Due to the non-stationary property of the cutting force signals, the time-domain and frequency-domain feature extraction methodologies are not enough to extract some potential features Hence, the interest in research of feature extraction is in the time-frequency domain The methodologies applied are mainly Wavelet Transform[39] and Hilbert Huang Transform[44-46]

The diagnostic approach aims to estimate the cutting tool condition given the effective features There is a wide range of methods for diagnostics The following briefly reviews the most popular diagnostic methodologies, which are based on artificial neural networks (ANN)

Several artificial neural networks are used for diagnostics in TCM, such as multilayer perceptron (MLP), self-organizing map, and support vector machine (SVM) MLP represent the most prominent and well researched class of neural networks in classification and function approximation, implementing a feed forward, supervised and hetero-associative paradigm It has several successful applications in

Chapter 2 Literature Review 15

TCM, such as in references [47-50] Support vector machine is another popular neural network It uses a kernel function to project low dimensional input features into high dimensions to achieve better classification Support vector machine maximizes the margin between classes with minimum number of support vectors, hence its name

‘Support Vector Machine’ References [43, 51] give examples of Support vector machine in TCM diagnostics Multilayer perceptrons and Support vector machine are supervised classification methodologies In the absence of wear measurements, there are no training pairs for supervised methodologies In this case, unsupervised classification and clustering methods such as self-organizing maps [52-54] are developed to meet the requirements

2.2 Prognostic Methodologies for General Health Monitoring Review

Prognostic concerns the prediction of the RUL and the POF in the future time unit[55] It can help in the making of early maintenance decision to achieve zero down time or maximum profit Prognostic methodologies in general health monitoring system have a longer history than in TCM applications Moreover, some

of these methodologies may be suitable for TCM, but some need to be modified to achieve a better performance in TCM Before the interest in the development of prognostic systems for general health condition monitoring, reliability analysis can provide related long-term prognostic information In this section, both reliability

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analysis and condition monitoring based prognostic methodologies for general health monitoring are reviewed

2.2.1 Reliability Analysis

The reliability analysis for the machining process involves modeling the failure times using different probability distribution functions and considering the process as stochastic For probability functions, exponential distribution, Weibull distribution, Normal distribution, Gamma distribution and mixtures of distributions[56, 57] are commonly used Among these distributions, the most common function is Weibull distribution, because Weibull distribution can fit a greater variety of data and life characteristics by changing its shape parameters[9, 11]

For the stochastic process, renewal process, non-homogenous Poisson process, and Markov process are most popular Among these stochastic processes, Markov process plays the most important role in the reliability evaluation of systems In 1907, Russian mathematician A.A Markov introduced a type of stochastic process whose future probability behavior is uniquely determined by its present state This non-hereditary or memory-less assumption suits a variety of physical systems [10] If a Markov stochastic process consists of a discrete state space and discrete time space, it

is referred to as a Markov chain If the time space is continuous, it is referred to as the Markov process It is fairly common using Markov process to model the accumulative damage process [58] The conventional Markov process has been

Chapter 2 Literature Review 17

extended to the semi-Markov process model and hidden Markov model to deal with more generic reliability analysis [59-61]

To utilize the knowledge of maintenance expert system and to reduce the uncertainties and complexity of modeling, Bayesian model is applied together with the stochastic modeling The Bayesian model is based on Bayesian theorem which was introduced by Reverend Thomas Bayes in 1763 Researchers combined the Bayesian method with the Poisson process[62, 63]and the Bayesian method with the Markov process[63] The Bayesian model compensates the incomplete data input by the knowledge of designers, operators and maintenance engineers Bayesian models can be used to reduce the uncertainties and use the current observed data to update a priori Therefore, less life data is required However, there is no unique answer for how to choose the prior distribution

If the aging process involves more than one aging components, other methodologies are also developed, for example, Single Split Analysis[64] (SSA), Reliability block diagram (RBD)[65], and Fault Tree Analysis (FTA) Split Analysis predicts the reliability of complex systems with multiple preventive maintenance actions in the long-term Reliability block diagram is a logical network used to describe the constitution of the system This methodology calculates the system reliability based on its component reliability A Fault Tree is a model that graphically and logically represents the various combinations of possible events, both fault and

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normal, occurring in a system that leads to the top event[66] Fault Tree Analysis can also be used to find the most likely causes of system failure among various aging components

There are two challenges for reliability analysis Firstly, it requires statistically sufficient failure data which is often difficult to collect as systems attain less failure, and longer life Secondly, reliability analysis is accurate for the aging processes for the whole population However, without condition monitoring information, the reliability analysis is not accurate enough for a special aging process

2.2.2 Condition Monitoring Based Prognostic

As condition monitoring (CM) techniques were developed, prognostics began to involve CM information In the literature, a CM-based prognostic system is dependent on the following critical factors[67]:

Current health situation

Historical health situation

Past maintenance history

Expected usage of the equipment

The first two factors suggest a reliable diagnostic system As the diagnostic research is already matured, prognostics become workable The CM-based prognostic research began popular in the recent 10 years, especially in the area of air force, Navy,

Chapter 2 Literature Review 19

and army [68] At present, CM-based prognostics have been applied in areas such as, mechanical systems, power systems, and production process, where structural durability and operational reliability are critical

The prognostic techniques can be classified in four major approaches: physical model-based, expert system, data driven, and combined approaches

 Physical model-based approaches

Physical model-based approaches model the physical processes, which have direct or indirect effects on health of related components Once the physical model is established, the residuals between the physical model and the on-line monitoring information of the real systems can be used as the features Then statistical techniques are used to define thresholds for detecting the presence of faults

Physical model-based approaches have a lot of advantages The physical model can be used to simulate component failures without incurring any cost Physical models are useful in accounting for different operating conditions, any load profile, transient performance and unanticipated conditions Moreover, if the understanding

of system degradation improves, the physical models can be adapted to increase their accuracy Some of the successful physical model-based prognostics can be found in references [24, 69-78]

However, physical model-based approaches for prognostics require specific mechanistic knowledge and theories relevant to the monitored system Therefore,

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they are component sensitive, which means they cannot be applied to other types of components Moreover, in most cases, the physical model is difficult to build

 Expert System

Expert system (ES) has been used since 1960s It consists of a knowledge base with an inference engine in a particular domain area The domain knowledge extracted by human experts is stored in the form of rules Then the system simulates the way human experts think and infer Finally, generate solutions based on the rules The process of building expert system involves knowledge acquisition, knowledge representation, and the verification and validation of models [79, 80]

Recently, expert system has gained research interests for fault diagnostic and prognostic applications Successful research on applying expert system for CBM can

be found in the study of Garga[81]

The challenge in such approach is to obtain suitable domain knowledge and convert it to rules Moreover, it is difficult to handle new situations that are not covered explicitly in its knowledge bases

In order to measure the uncertainties in expert system’s knowledge and reasoning, researchers combine expert system with fuzzy member functions in fuzzy logic theory For example, [82] applied expert system together with fuzzy logic for bearing fault detection; [83] classify frequency spectra, which representing various rolling element bearing faults also by applying fuzzy logic

Chapter 2 Literature Review 21

 Data-Driven approaches

driven prognostic originated from the theory of pattern recognition driven approaches are usually developed from finding the relationship between input/output data These approaches can process a wide variety of data types and exploit the nuances in the data that cannot be discovered by physical model-based and expert system approaches Although reliability approaches needs huge data, they are not classified as data-Driven approaches The reliability analysis for the machining process involves modeling the failure time using different probability distribution functions and considering the process as stochastic Data-driven approaches are usually developed from finding the relationship between features (input) and tool wear or tool life (output) The input data required for reliability approach and data driven approach is different The reliability approaches uses the tool life data, such as the samples of the life time of the cutting tools, and the time spend in a specific wearing state However, data driven approach requires the condition monitoring (CM) data as the input data, such as the mean cutting force per revolution, the standard deviation of the cutting force per revolution Therefore, these two approaches are categorized separately Data-driven approaches can be classified into two categories: hybrid and AI models

Data-Hybrid models include state space models (e.g., hidden Markov models (HMM), hidden semi-Markov models (HSMM))[14, 16, 59, 84-90], and regressive models

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(e.g., logistic regression, Proportional Hazard rate (PHR), Gray models, auto regressive moving average, exponential smoothing)[91-95] These models combine the reliability analysis and the condition monitoring information Therefore, they can reach a relative long prediction horizon

AI models include Neural Network (NN) and its variants, for example, polynomial neural networks (PNN), dynamic wavelet neural network (DWNN), self-organizing feature maps, and Bayesian networks

There are two types of applications of NN for prognostics One is using NN as a nonlinear function approximation tool to predict system failure features and trends by estimating and classifying applications The other is using NN to model dynamic processes of system degradation and make expectation of RUL

 Combined Models

In the industrial prognostic processes, it is difficult to predict the trend of all characteristic parameters by using a single prediction method Therefore, a combination of prediction methods is adopted for prognostics For examples, the application of NN is usually incorporated with expert system and fuzzy logic[96] to form a neuro-fuzzy system These algorithms are particularly adaptive, lucid, robust, and highly flexible NN is also combined with Bayesian reasoning to form a Bayesian network Gray models are combined with NN to perform a good prediction in the study of[97]

Chapter 2 Literature Review 23

2.3 Review for TCM Prognostics and its Challenge

The research for TCM has a history of more than 20 years However, the prognostics for TCM are still at its infancy The same as the general prognostic approaches, reliability analysis has been extensively studied before 1980’s, when the on-line indirect tool condition information is not available With the development of condition monitoring (CM) techniques, prognostics began to incorporate the CM information of TCM For CM-based TCM, there are physical approaches, and data-driven approaches In this section, the reliability analysis and CM-based prognostics will be both reviewed for TCM applications

Researches on the determination of a proper cutting tool replacing time date back

to the beginning of the 20th century In 1907, W Taylor published his famous tool life equation However, this equation predetermined the cutting tool life before machining, and could not model the stochastic property of the cutting tool wear process S Ramalingam [9]studied the tool life distributions, he propose the Weibull distribution and Gama distribution are suitable for modeling the cutting tool life His study paved the way for reliability analysis of machining process Besides the tool life distribution modeling, stochastic process are also used for tool wear modeling, such

as reference [11, 58] However, the reliability analysis based prognostic has two limitations Firstly, the tool life distributions are predetermined Secondly, in order to establish a stochastic model for tool wear, huge life testing experiments are needed

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Similar to general prognostic methodology, physical model-based approaches are also applied for prognostics in machining process Prognostics can be achieved by establishing physical models for tool wear rate, tool life and wear itself Establishing these physical models involve the study of 1) different types of tool wear pattern, like abrasive wear, diffusive wear and adhesive wear; 2) contact surface parameters, like temperature, stress Takeyama and Murata [98] firstly establish a wear rate model by considering abrasive wear, which is proportional to cutting distance, and diffusive wear However, temperature, which affects the tool wear greatly, is not involved in this wear rate model Molinari and Mouari[99] proposed a new diffusion wear model

by considering the contact temperature Usui et al.[100-102] derived an adhesive tool wear model considering temperature, normal stress, and sliding velocity at the contact surface Instead of establishing the tool wear rate model, Hak Gu Lee and Dai Gil Lee[103] established a tool life physical mode considering abrasive wear In addition

to pure physical models, there are combined models, which combine the physical features with empirical experiences, such as [69, 72] For example, X Luo[104]estimated the tool wear rate by using cutting force, cutting temperature simulation A successful physical model can be easily adapted between different cutting conditions Moreover, physical model also gives us a better understanding of the machining process However, there are two limitations for physical model for TCM prognostics Firstly, since the model parameters in question are often unique for different cutting conditions and tool-workpiece materials, it is hard to identify these