MACHINE PROGNOSTICS BASED ON HEALTH STATE PROBABILITY ESTIMATION Hack-Eun Kim Master of Engineering (Mechanical) Bachelor of Engineering (Material) Thesis submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy SCHOOL OF ENGINEERING SYSTEMS FACULTY OF BUILT ENVIRONMENTAL ENGINEERING QUEENSLAND UNIVERSITY OF TECHNOLOGY 2010
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MACHINE PROGNOSTICS BASED ON HEALTH STATE PROBABILITY ESTIMATION
Hack-Eun Kim Master of Engineering (Mechanical)
Bachelor of Engineering (Material)
Thesis submitted in total fulfilment of the requirements of the degree of
Doctor of Philosophy
SCHOOL OF ENGINEERING SYSTEMS
FACULTY OF BUILT ENVIRONMENTAL ENGINEERING
QUEENSLAND UNIVERSITY OF TECHNOLOGY
2010
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ABSTRACT
The ability to accurately predict the remaining useful life of machine components
is critical for machine continuous operation and can also improve productivity and
enhance system’s safety. In condition-based maintenance (CBM), maintenance is
performed based on information collected through condition monitoring and
assessment of the machine health. Effective diagnostics and prognostics are
important aspects of CBM for maintenance engineers to schedule a repair and to
acquire replacement components before the components actually fail. Although a
variety of prognostic methodologies have been reported recently, their application in
industry is still relatively new and mostly focused on the prediction of specific
component degradations. Furthermore, they required significant and sufficient
number of fault indicators to accurately prognose the component faults. Hence,
sufficient usage of health indicators in prognostics for the effective interpretation of
machine degradation process is still required. Major challenges for accurate long-
term prediction of remaining useful life (RUL) still remain to be addressed.
Therefore, continuous development and improvement of a machine health
management system and accurate long-term prediction of machine remnant life is
required in real industry application.
This thesis presents an integrated diagnostics and prognostics framework based on
health state probability estimation for accurate and long-term prediction of machine
remnant life. In the proposed model, prior empirical (historical) knowledge is
embedded in the integrated diagnostics and prognostics system for classification of
impending faults in machine system and accurate probability estimation of discrete
degradation stages (health states). The methodology assumes that machine
degradation consists of a series of degraded states (health states) which effectively
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represent the dynamic and stochastic process of machine failure. The estimation of
discrete health state probability for the prediction of machine remnant life is
performed using the ability of classification algorithms.
To employ the appropriate classifier for health state probability estimation in the
proposed model, comparative intelligent diagnostic tests were conducted using five
different classifiers applied to the progressive fault data of three different faults in a
high pressure liquefied natural gas (HP-LNG) pump. As a result of this comparison
study, SVMs were employed in heath state probability estimation for the prediction
of machine failure in this research.
The proposed prognostic methodology has been successfully tested and validated
using a number of case studies from simulation tests to real industry applications.
The results from two actual failure case studies using simulations and experiments
indicate that accurate estimation of health states is achievable and the proposed
method provides accurate long-term prediction of machine remnant life. In addition,
the results of experimental tests show that the proposed model has the capability of
providing early warning of abnormal machine operating conditions by identifying the
transitional states of machine fault conditions. Finally, the proposed prognostic
model is validated through two industrial case studies. The optimal number of health
states which can minimise the model training error without significant decrease of
prediction accuracy was also examined through several health states of bearing
failure. The results were very encouraging and show that the proposed prognostic
model based on health state probability estimation has the potential to be used as a
generic and scalable asset health estimation tool in industrial machinery.
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KEYWORDS
Diagnostics, Prognostics, Condition-Based Maintenance (CBM), Support Vector
Machines (SVMs), Health State Probability Estimation
CHAPTER 1 INTRODUCTION ······················································ 1 1.1 Problem Statement ··································································· 4 1.2 Objective of Research ······························································ 5 1.3 Scope of Research ··································································· 6 1.4 Originality and Contribution···················································· 7 1.5 Organization of Thesis····························································· 10
CHAPTER 2 RESEARCH BACKGROUND AND LITERATURE REVIEW ······························································································ 13
2.1 Historical Maintenance Strategies and Philosophies ··············· 13 2.2 Key Aspects for Effective Implementing of CBM ·················· 16
2.4.2 Model-Based Approaches ··························································· 36 2.4.3 Comparison of data-driven and model-based approaches ··········· 37
2.5 Current Prognostics Approaches ········································ 39 2.5.1 Data-driven Approaches for Prognostics ····································· 39
2.5.1.1 Time Series Analysis Approaches ·········································· 40 2.5.1.2 Artificial Intelligence (AI) Approaches ·································· 44
2.5.2 Model-Based Approaches for Prognostics ·································· 49 2.5.3 Reliability-Based Approaches for Prognostics ···························· 51
2.6 Remaining Challenges of Prognostics for Real Industry Application ········································································· 53
CHAPTER 3 MACHINE PROGNOSTICS BASED ON HEALTH STATE PROBABILITY ESTIMATION ········································· 57
3.1 Closed Loop Architecture for Integrating Diagnostics and Prognostics System with Embedded Historical Knowledge ··· 57
3.2 Historical Knowledge ······························································ 60 3.3 Diagnostics ·············································································· 61 3.4 Health State Estimation and RUL Prediction ·························· 63
3.4.1 Health State Classification Using SVM Classifiers ····················· 65 3.4.1.1 One-Against-All (OAA) Strategy for health state estimation · 66 3.4.1.2 One-Against-One (OAO) Strategy for health state estimation ············································································································ 68 3.4.1.3 Direct Acyclic Graph (DAG) Strategy for health state estimation ············································································································ 68
3.4.2 Health State Probability Estimation ············································ 69 3.4.3 Prediction of Machine Remnant Life ·········································· 70
CHAPTER 4 COMPARATIVE STUDY ON FAULT DIAGNOSTICS USING MULTI-CLASSIFIERS ·························· 73
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4.1 HP-LNG Pumps ······································································ 73 4.2 Historical Failure Event and Data Analysis ································· 76
4.2.1 Bearing Fault ·················································································· 77 4.2.2 Rotor Bar Fault ··············································································· 80 4.2.3 Excessive rubbing of impeller wear-ring ········································· 84
4.3 Feature Calculation and Selection ··········································· 86 4.4 Brief Description of Employed Multi-Classifiers ·················· 88
4.4.1 Random Forests ·············································································· 89 4.4.2 Radial Basis Function Neural Networks (RBF-NNs) ······················ 90 4.4.3 Linear Regression ··········································································· 91
4.5 Result of Fault Classification Performance ····························· 93 4. 6 Summary ················································································ 94
CHAPTER 5 MODEL VALIDATION USING SIMULATED AND EXPERIMENTAL BEARING FAILURE DATA ······················· 95
5.1 Model Validation Using Simulated Bearing Fault Data ·········· 95 5.1.1 Simulation of Progressive Bearing Fault Data ································ 95 5.1.2 Feature Calculation and Selection ··················································· 99 5.1.3 Health State Estimation and Prediction of RUL ······························ 101
5.2 Model Validation Using Experimental Bearing Failure Data ·· 105 5.2.1 Design and Setup of Experimental Test Rig for Accelerated Bearing
Failure Test ····················································································· 105 5.2.2 Accelerated Bearing Run to Failure Test ········································ 107 5.2.3 Feature Calculation and Selection ··················································· 108 5.2.4 Health State Estimation and Prediction of RUL ······························ 109
5.3 Model Comparison Using PHM ·············································· 114 5.3.1 Proportional Hazard Model (PHM) ················································· 114 5.3.2 Prediction of Remnant Life Using PHM ········································· 116
CHAPTER 6 MODEL VALIDATION THROUGH INDUSTRY CASE STUDY ····················································································· 121
6.1 Prognostics of Impeller Rubbing Failure in HP-LNG Pump ··· 121 6.1.1 Data Acquisition of Excessive Impeller Rub in HP-LNG Pump ····· 121 6.1.2 Feature Calculation and Selection ··················································· 122 6.1.3 Health State Estimation ··································································· 123 6.1.4 RUL Prediction ··············································································· 125
6.2 Prognostics of Bearing Failure in HP-LNG Pump ··················· 127
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6.2.1 HP-LNG Pump ················································································ 127 6.2.2 Data Acquisition of Bearing Failure ················································ 128 6.2.3 Feature Calculation and Selection ··················································· 131 6.2.4 Selection of Number of Health States for Training ························· 133 6.2.5 RUL Prediction of Bearing Failure ················································· 135 6.2.6 Verification of Optimum Number of Health States ························· 138
fault detection and isolation techniques for adequate prognostic state awareness.
Therefore, an integrated prognostics system should include effective feature
extraction and fault diagnostics, including historical (empirical) knowledge for
accurate long-term prediction of the machine remnant life.
In the proposed model, fault diagnostics (isolation) and health state probability
estimation are performed based on the abilities of classification algorithms. A
number of classifiers and pattern recognition techniques are explored to determine
appropriate classifiers, such as Neural Networks (NNs), Support Vector Machines
(SVMs), Classification and Regression Trees (CART), and others. To deal with high-
dimensional data, effective feature selection techniques are employed in this research
for the best possible prediction of RUL. Historical (empirical) knowledge will also
be used to provide qualitative understanding of the discrete machine degradation
stages and training data sets for the estimation of discrete health state probability.
Machine Prognostics Based on Health State Probability Estimation
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To validate the proposed prognostic model in a timely manner, bearing failure
data will be simulated and experimental tests will be conducted using the bearing-
run-to-failure test rig to facilitate accelerated bearing life. From the bearing failure
data, a number of features will be calculated, trained and tested for the validation of
the proposed model.
Since the primary research goal is the development of a practical prognostic
model, real life condition monitoring data and maintenance events of actual pumps in
industry will be analysed extensively and then employed for the model validation in
a real environment.
1.4 Originality and Contribution
This thesis presents a novel approach that can be used in asset health management
system for fault diagnostics and prognostics of machine failure. The principal
significance and contribution of the work include:
Integration of fault diagnostics and prognostics for accurate prediction of
machine remnant life
For accurate prediction of RUL, the proposed prognostic model has a closed loop
architecture consisting of an integrated diagnostics and prognostics system based on
health state probability estimation, with embedded historical knowledge for accurate
long-term prediction of the machine remnant life. Through the integrated system
with fault diagnostics, a more precise failure pattern from a number of empirical
degradation data stored as historical knowledge can be employed in the prognostics
model. The accumulated historical knowledge can then be used for system updating
and for improving the prognostics model by providing reliable posterior degradation
characteristics for diverse failure modes and fault types. Furthermore, this scheme
provides the guideline for the integration of the machine diagnosis and prognosis
architectures which is aimed at determining the remaining useful life of failing
components.
Machine Prognostics Based on Health State Probability Estimation
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Methodology to estimate the probability of machine health state in real time
A novel methodology for machine health state estimation by applying discrete
degradation process of machine failure is presented in this research. None of the
current prognostic models have considered using discrete health state probability,
which can effectively represent the dynamic and stochastic degradation of machine
failure. To compare with other existing prognostics approaches, the proposed model
not only provides accurate long-range prediction of machine remnant life, but also
enables a sufficient usage of a range of condition indicators to effectively represent
the complex nature of machine degradation by using the ability of classification
algorithms in health state probability estimation. Furthermore, this full utilization of
a range of features can lead to a generic and scalable prognostic model for practical
application in industry.
Comparative study of machine fault diagnostics using progressive fault data
A comparative study of five different classifiers was performed using progressive
fault data from three machine fault cases. Although many intelligent fault diagnostic
models have been validated using a number of fault data, none of them consider
different severity levels in fault propagation to estimate the fault diagnostic
performance. The result of a comparison test shows that the fault classification
accuracy is variable and depends on the severity of machine fault and on the type of
classifier. Through this comparative study, an appropriate classification algorithm is
employed in heath state probability estimation in this research.
Model validation through four case studies using simulated, experimental and
real industry data
A number of case studies, from simulation tests through to industry applications,
were conducted to validate the feasibility of the proposed model. The scalability of
the proposed model was validated by using different types of fault in real case
studies. The optimum number of health states for a machine failure is also
investigated to minimise the training error of health state estimation without
significant decrease in the prediction accuracy.
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Model comparison using Proportional Hazards Model
Through the model comparison study using PHM, it is verified that the proposed
prognostic model based on health state probability estimation can provide a more
accurate prediction capability than the commonly used PHM in the case of dynamic
and stochastic process of machine degradation.
Publications of research outcome
Several publications have been generated as part of the research work hereby
discussed. The results presented in the case studies of simulation, experiment and
industry case studies have been disclosed to the public in the following publications:
1. Hack-Eun Kim, Andy C. C. Tan, Joseph Mathew, Eric Y. H. Kim and Byeong-Keun Choi, 2010 “Machine Prognostics based on health state estimation using SVM”, Journal of Engineering Asset Management (Accepted 15 June, 2010).
2. Hack-Eun Kim, Andy C. C. Tan and Joseph Mathew, 2010 “New machine prognostics approach based on health state probability estimation” in Proceedings of 6th Australasian Congress on Applied Mechanics, ACAM 6, Perth, Australia.
3. Hack-Eun Kim, Andy C. C. Tan and Joseph Mathew, 2010 “Integrated approach for HP-LNG pump diagnostics and prognostics based on health state probability estimation” in Proceedings of the 5th World Congress on Engineering Asset Management (WCEAM-ICF/IQ-AGIC), Brisbane, Australia.
4. Hack-Eun Kim, Andy C. C. Tan, Joseph Mathew, Eric Y. H. Kim and Byeong-Keun Choi, 2009 “Prognosis of bearing failure based on health state estimation” in Proceedings of the 4th World Congress on Engineering Asset Management, Athens, Greece.
5. Hack-Eun Kim, Andy C. C. Tan, Joseph Mathew, Eric Y. H. Kim and Byeong-Keun Choi, 2009 “Integrated Diagnosis and Prognosis Model for High Pressure LNG Pump” in Proceedings of 13th Asia-Pacific Vibration Conference, Christchurch, New Zealand.
Machine Prognostics Based on Health State Probability Estimation
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6. Yifan Zhou, Lin Ma, Rodney C. Wolff and Hack-Eun Kim, 2009 “Asset life prediction using multiple degradation indicators and lifetime data: a Gamma-based state space model approach” in Proceedings of the 8th International Conference on Reliability, Maintainability and Safety, Chengdu, China.
7. H. E. Kim, A. C. C. Tan, J. Mathew, E. Y. H. Kim and B. K. Choi, 2008 “Machine Prognostics Based on Health State Estimation Using SVM”, in Proceedings of the World Congress on Engineering Asset Management, Beijing, China.
8. D. S. Gu, S. W. Cho, J. H. Lee, H. E. Kim and B. K. Choi, “Redesign of Cryogenic Pump in Liquefied Natural Gas Storage Tank Considering Thermal Effect” Journal of Computational and Theoretical Nanoscience, vol. 5, pp. 1534-1538, 2008.
9. H. E. Kim, B. G. Choi, H. J. Kim, H.E Jeong, D. S. Gu, 2007 “Vibration diagnosis case of primary LNG pumps”, in Proceedings of the World Congress on Engineering Asset Management, Harrogate, UK.
10. D. S. Gu, J. H. Lee, H. E. Kim and B. K. Choi, 2007 “Abnormal Vibration Diagnosis caused by Design Failure of Cryogenic Low-Pressure LNG Pump” in Proceedings of Korean Society for Noise and Vibration Engineering Autumn Annual Meeting.
11. Hack-Eun Kim, Andy C.C. Tan, Joseph Mathew and Byeong-Keun Choi, 2010 “Bearing fault prognosis based on health state probability estimation”, Journal of Expert Systems with Applications (Under review).
12. Hack-Eun Kim, Andy C.C. Tan, Joseph Mathew and Bo-Suk Yang, 2010, “Integrated approach for diagnosis and prognosis of HP-LNG pump based on health state probability estimation”, Journal of Sound and Vibration (In preparation).
1.5 Organisation of the Thesis
This thesis is composed of seven chapters. The subtopics contained in each chapter
are described as follow:
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Chapter 1 introduces a brief overview and the scope of the research area. This
chapter also presents the objective, significance and innovation of this research. It
shows how the research objective has grown out of the unresolved problem identified
in current research. The originality and principal contribution of this work are also
presented.
Chapter 2 presents a comprehensive literature review on current condition
monitoring techniques, diagnostics and prognostics approaches. First, the
background information of machine maintenance strategy is reviewed to show how it
has evolved to the present state. Then, the overviews of key techniques for the
effective implement of CBM strategy are explored in Section 2.2. Section 2.3
describes the existing signal processing techniques as a fundamental step prior to
fault diagnostics and prognostics. Current research on machine fault diagnostics and
prognostics are reviewed respectively in Sections 2.4 and 2.5. Finally, unresolved
current research issues and remaining challenges for machine diagnostics and
prognostics in real industrial applications are summarised in Section 2.6. The
following four chapters present the research contribution to fulfil the remaining
challenges derived from the research review.
Chapter 3 describes the development of the prognostic model proposed by the
candidate to address the unresolved issues identified in chapter 2. Section 3.1
introduces the proposed prognostic system which is integrated with diagnostics and
based on health state probability estimation. Three key elements in the proposed
system, historical knowledge, diagnostics, health state estimation and prognostics are
detailed in Sections 3.2, 3.3 3.4 and 3.5 respectively. The methodology of the health
state probability estimation and remnant life prediction using SVM classifiers is
presented in this chapter.
Chapter 4 presents a comparative study on intelligent fault diagnostics using five
different classifiers to investigate appropriate classifiers to be employed in the
proposed prognostic model. Section 4.1 describes the High-Pressure Liquefied
Natural Gas (HP-LNG) Pump as an object of this diagnostics test. The historical
maintenance event and failure data analysis are presented in Section 4.2. The feature
selection method and comparison test results are presented in the remaining sections
which includes a brief description of the five classifiers employed.
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In Chapter 5, the proposed model is validated using simulation data of progressive
bearing failure and experimental bearing run-to-failure data. Section 5.1 describes
the bearing fault simulation methodology and the model validation using simulated
bearing failure data. Section 5.2 describes the designed experimental test rig for
accelerated bearing failure test and how these experimental data are used for
validating the prognostic model including prediction results. The model comparison
with the Proportional Hazards Model (PHM) using identical experimental data is
presented in Section 5.3.
Chapter 6 presents the validation of the proposed model through two industry case
studies. To verify the applicability of the proposed model in a real environment,
these model validations are conducted using two different failure data from HP-LNG
pumps. Section 6.1 presents the prognostics of impeller rubbing failure. In this case
study, two sets of impeller-rub data are analysed and employed to predict the
remnant life of the pump based on estimation of health state probability using the
SVM classifier. In Section 6.2, the second case study is conducted using two data
sets of bearing failure. The optimal number of health states of bearing failure is also
investigated through comparison tests of a range of health states.
The last part of the thesis, in Chapter 7, presents conclusions and future work to
improve the proposed model for real application in industry.
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CHAPTER 2 RESEARCH BACKGROUND AND LITERATURE REVIEW
This Chapter presents the research background and current technologies in
machine diagnostics and prognostics used in condition-based maintenance (CBM)
and it is divided into five sections. Section 2.1 covers the historical aspects and
evolution of maintenance strategies. The overviews of key techniques for the
effective implement of CBM strategy are explored in Section 2.2. Section 2.3
describes existing signal processing techniques as a fundamental step prior to fault
diagnostics and prognostics. In Sections 2.4 and 2.5, current research on machine
fault diagnostics and prognostics in focus throughout the thesis are reviewed
respectively. Section 2.6 summarises current challenges on machine prognostics for
real industrial application.
2.1 Historical Maintenance Strategies and Philosophies
Machinery is a critical asset for business success in the fiercely competitive global
economy. Recent advancement in technology has resulted in improvements to
machinery so that output, productivity and efficiency have increased rapidly.
Maintenance is a combination of all technical, administrative and managerial actions
during the life cycle of an item intended to keep a machine or restore it to a state in
which it can perform the required function [3]. Previously, maintenance has been
considered as an expense account with performance measures developed to track
direct costs or surrogates such as the headcount of tradesmen and the total duration
of forced outages during a specified period. However, this recognition has been
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changed. Nowadays, maintenance is acknowledged as a major contributor to the
performance and profitability of business organizations [4]. Therefore today
maintenance is confronted with a wide range of challenges that include quality
improvement, reduced lead times, set up time and cost reductions, capacity
expansion, managing complex technology and innovation, improving the reliability
of systems, and related environmental issues [5]. A good maintenance policy not
only prevents system failures, but leads to maximum capacity utilization, improved
product quality, customer satisfaction and adequate equipment life span, among other
benefits.
Maintenance philosophies can be broadly classified as reactive and proactive.
Figure 2.1 shows the taxonomy of maintenance philosophies. The earliest and
conventional maintenance strategies consist of break-down (or collective) and
preventive maintenance. In break-down maintenance, a machine is fixed when it fails
[6]. The advantage of this strategy is that no analysis or planning is required.
However, one of the problems with this strategy includes the occurrence of
unexpected downtime at times that may be inconvenient, and preventing
accomplishment of committed production schedules.
Figure 2.1 Taxonomy of maintenance philosophies [6]
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Proactive or planned maintenance can be further classified as preventive and
predictive maintenance. As the name suggests it does not wait for the equipment to
fail before commencing the maintenance operations. In preventive maintenance,
components are replaced based on a conservative schedule to “prevent” commonly
occurring failures. Although preventive maintenance programs increase system
availability, they can be expensive because of frequent replacement of costly parts
before the end of their life. Another disadvantage of preventive maintenance is that it
is time-based and is not related to the age of the machine. Moreover, this strategy is
neither incorporated into the design of the system, nor is the impact of maintenance
on system and business performance duly recognised.
Since the 1970s, a more integrated approach to maintenance evolved in both the
government and private sectors. Maintenance cost was considered a significant
component through the life cycle costing approach in new costly defence acquisitions.
The close connection between “reliability” and “maintainability” was recognised in
so called reliability centred maintenance (RCM). RCM has been developed for the
aircraft industry sector. For aircraft and other safety-related applications, cost-
effectiveness is balanced with safety and availability, with the goal of minimizing
cost and downtime by eliminating the chance of a failure [6]. In RCM strategy,
maintenance is carried out at the component level and the maintenance effort for a
component is a function of the reliability of the component and the consequence of
its failure under normal operation. This approach uses failure mode effects analysis
(FMEA) and utilizes reliability estimates of the system to formulate a cost-effective
schedule for maintenance [7]. RCM views maintenance in the broader business
context and takes into account the link between component failures and their impact
on the business performance. However, this approach only assumes a normal
operating condition and the optimal maintenance strategies do not consider the load
on the equipment and its effect on the degradation process in real life.
To minimize both maintenance and repair costs and have maintenance based on
probability of failure requires ongoing assessment of machine health, prediction of
failures based on current health, operation and maintenance history. It is known as
predictive maintenance. Therefore, predictive maintenance directly monitors the
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operating condition, efficiency and other indicators of critical components in the
machine to determine the mean-time-to-failure or cost of efficiency.
Condition-based maintenance (CBM) is a method used to reduce the uncertainty
of maintenance activities and is carried out according to the need indicated by the
equipment condition [8]. CBM assumes that existing indicative prognostic
parameters can be detected and used to quantify possible failure of equipment before
it actually occurs. Prognostic parameters provide the indication of potential problems
and incipient faults which would cause the equipment or component to deviate from
the acceptable performance level. The conditions of a system are quantified by
parameters that are continuously monitored. Some of the advantages of CBM include
prior warning of impending failure and increased precision in failure prediction. It
also aids in diagnostic procedures as it is relatively easy to associate the failure to
specific components through the monitored parameters. To develop solutions for
CBM effectively and efficiently will require a wide-ranging effort to coordinate all
levels of management, from engineers to project officers to program managers to top
corporate level.
2.2 Key Aspects for Effective Implementation of CBM
A complete CBM system is composed of a number of functional capabilities:
sensing and data acquisition, data manipulation, condition monitoring, health
assessment/diagnostics, prognostics and decision reasoning. In addition, some form
of human system interface is required to provide user access to the system and
provide a means of displaying vital information. Currently, in order to develop and
encourage the adoption of open information standards for operations and
maintenance in industry, the Machinery Information Management Open Standards
Alliance (MIMOSA) provides the standardized architecture for a CBM system called
Open Systems Architecture for Condition-Based Maintenance (OSA-CBM) [9]. The
OSA-CBM system must be broken down into generalized components or functions.
This architecture has been described in terms of functional layers: from sensing and
data acquisition to decision support. The general functions of the layers are specified
below:
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Layer 1 – Data Acquisition: The data acquisition module has been generalized to
represent the software module that provides system access to digitized sensors or
transducer data. The data acquisition module is basically a server of calibrated
digitized sensor data records.
Layer 2 – Data Manipulation: The data manipulation module may perform single
and/or multi-channel signal transformations along with specialized CBM feature
extraction algorithms.
Layer 3 – Condition Monitor: The primary function of the condition monitor is to
compare features against expected values or operational limits and output
estimation error{8}, Histogram upper{9} and Histogram lower{10}
RMS frequency value{11}, Frequency centre value{12},
Root variance frequency{13} andPeak value{14}
For the better performance of SVM and the reduction of computational effort,
effective features were also selected using the evaluation method of feature
effectiveness introduced by Knerr et al. [149, 150], as depicted Chapter 4.
The distance evaluation criteria (α ) of the 14 features in this work are shown
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in Figure 5.3. In order to select the effective features, a value of greater than 1.1
of a normalized distance evaluation criterion, αα 1.1 was used, where
α is distance evaluation criterion and α is mean value of α . From the results,
six features were selected as effective features as the distance evaluation criterion
value (α ) exceeded the threshold level. They meet the large distance evaluation
criterion (α ) as compared with other features. The selected six features were
Skewness, Kurtosis, Entropy estimation error, RMS frequency value, Frequency
centre value and Root variance frequency value. These features have a low
dispersibility in the same state and high dispersibility among different states.
Therefore, it could minimize the classification training error in each bearing
health state.
Figure 5.4 presents the trends of the selected features for health state
estimation of bearing failure. As shown in Figure 5.4, most of the selected
features are well represented with gradual progression of bearing degradation.
Skewness, Kurtosis and Entropy estimation error values were increased as time
passes, on the contrary, other features were formed to decrease.
Figure 5.3 Feature selection using distance evaluation criterion (Simulation test)
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Figure 5.4 Trends of selected features for simulation test
5.1.3 Health State Estimation and Prediction of RUL
In this simulation test, the degradation steps of bearing failure were simply
divided into ten health stages for health state estimation without prior analysis of
failure pattern because the trends of selected features are not highly fluctuating
but are observed to be growing exponentially as shown in Figure 5.4.
The polynomial function was used as the basic kernel function of SVM. As a
multi-class classification method of SVM, the one-against-one (OAO) method
was applied to perform the health state probability estimation of bearing
degradation, as described in Chapter 3. Sequential minimal optimization (SMO)
proposed by Platt [163] was used to solve the SVM classification problem. For
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selection of optimal kernel parameters (C, γ, d), the cross-validation technique
was used in order to obtain effective classification performance suggested by Hsu
et al. [164] so as to avoid over-fitting or under-fitting.
In this work, simulated bearing degradation data were divided into ten
degradation stages for the estimation of health state probability and prediction of
remnant life using the six selected features. In this RUL prediction of bearing
failure, closed and open tests were conducted. The closed test was conducted
using identical data sets for model training and test. On the other hand, different
test data sets were applied in the open test using identical training data sets which
were used in the closed test.
Closed Test of Simulation Data
In the closed test, once the ten states were trained using the six selected
features from Data1, the full data sets of Data1 (100 samples) were tested to
obtain each health state probabilities using the result of SVMs multi-
classification as described in Chapter 3.
Figure 5.5 shows the probability distribution of each health state of simulated
data1 that was also used for training of the ten degradation states. The first stage
probability started with 100% and decreased as long the as next state probability
increased.
Figure 5.5 Probability distribution of each health state
(Closed Test Using Simulation Data 1)
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Although there were some overlaps in the middle zone of the display, the
probabilities of each health state well explain the sequence of ten degradation
states over the entire sample. Especially, the initial and final states are distinctly
separated.
For the prediction of RUL, the expected life was calculated using the time of
each training data set ( ) and their probabilities of each health state as expressed
in Eq. (3.7). Figure 5.6 shows the result of remnant life prediction and the
comparison between actual remaining life and estimated life. As shown in Figure
5.6, the overall trend of the estimated life follows the real remaining life of the
bearing failure. And the average prediction value was 95.05% over the entire
range of the data set. The average prediction value was calculated using the
following equation.
(5.6)
where is number of sample, : is actual RUL(%), and is estimated
RUL(%).
Figure 5.6 Comparison of actual RUL and estimated RUL
(Closed Test Using Simulation Data 1)
Open Test of Simulation Data
The open test on the second set of simulated bearing failure data (Data2)
consists of 100 sample sets was conducted using identical training data (Data1).
Figure 5.7 shows the probabilities of each health state of Data2. Compared with
% 1∑ ′
100
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the closed test result from Data1, the first state probability shows a long-deferred
interval, and the final state probability does not reached higher probability than
the former state.
Figure 5.7 Probability distribution of each health state
(Open Test Using Simulation Data 2)
The RUL is also estimated by using the time of each training data set and their
probabilities of each health state as depicted in Eq. (3.7). Figure 5.8 shows
comparison result between the estimated RUL and the actual RUL. Although
there are some margins of error in initial states, the estimated life in the latter half
of samples matches closely with the real remaining life of bearing failure. The
average prediction value was also calculated using Eq. (5.6). The average
prediction value was 92.5% over the entire range of the data set.
Figure 5.8 Comparison of actual RUL and estimated RUL
(Open Test Using Simulation Data 2)
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5.2 Model Validation Using Experimental Bearing Failure Data
5.2.1 Design and Setup of Experimental Test Rig for Accelerated
Bearing Failure Test
In order to study the capabilities of the proposed prognostic model in a timely
manner, a test rig was designed to facilitate accelerated bearing life tests. The
schematic of the test rig is depicted in Figure 5.9.
Figure 5.9 Schematic of the bearing test rig
Figure 5.10 The test rig after assembly of all components
Bearing 2 Bearing 3
Motor
Radial load
Bearing 1 Bearing 4
Accelerometers Thermocouple
AE sensors
Spring load system
Bearing 4
Bearing 1 Coupling
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This test rig has four test bearings on a shaft driven by an AC motor.
Couplings were used so that when a bearing fails, it can be extracted and replaced
easily without having to move the other bearings on the shaft. Figure 5.10 shows
the test rig after assembly of all components. As shown in Figure 5.10, a spring
was designed to apply a spring load on the two middle bearings (Bearings 2 and
3). The load can be adjusted accordingly by tightening or loosening the screw on
the spring mechanism. The two bearings at each shaft end will undergo the same
amount of load as the middle bearings due to the reaction force at the support.
Another advantage of being able to run four bearings at once is the option to
run bearings from brand new, defect-free condition to failure in a timely manner.
In this way, when a bearing is failing, the degradation of the other three is also
accumulating. Therefore the test will take a shorter time than one that runs from
brand new to failure one by one. Two accelerometers, two acoustic emission
(AE) sensors and a thermocouple were attached on each bearing housing
(Bearings 2 and 3) for measurement reading. Figure 5.11 shows the close-view of
the middle bearing assembly.
Figure 5.11 Close view of the middle bearing assembly
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5.2.2 Accelerated Bearing Run-to-Failure Test
Prognostic experiments with test bearings that are induced with a prominent
crack or hole are less likely to develop natural defect propagation in the early
stages. Therefore, the accelerated bearing run-to-failure tests were conducted
with defect-free condition of bearings and excessive overloading conditions. In
this experimental test, SMT 61806 single row deep groove ball bearings were
used for the run-to-failure test at constant 1300 rpm of rotation speed. Table 5.3
summarizes the bearing specifications.
Table 5.3 Test bearing specifications for experiment
Inner Diameter
Outer Diameter Width
Dynamic Load
Rating
Static Load
Rating
Fatigue Load Limit
Reference Speed Rating
30 mm 42 mm 7 mm 4.29 kN 2.9 kN 0.146 kN 3200 rpm
Ball bearings were selected because of their lower load capacity and
premature failure with an over-load of the bearing. The 61806 bearings were
chosen because they have small balls but relatively large bore diameter. This
feature will ensure that the high load will be able to degrade the bearings without
bending and damage of the shaft.
Figure 5.12 shows the failed bearing after the run-to-failure test. In this
bearing run-to-failure test, two sets of bearing failure data were collected with
identical condition for the proposed model validation. The data sampling rate was
250 kHz and data collections were conducted by a National Instruments
LabVIEW program. The two collected vibration data sets are summarised in
Table 5.4.
Table 5.4 Experimental bearing failure data set
Test No Number of Sample
Bearing Position RPM Sampling
frequency Total
operation time1 912 3 1300 250K 683 Min
2 810 3 1300 250K 579 Min
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Figure 5.12 The picture of failed bearing after run-to-failure test
5.2.3 Feature Calculation and Selection
Using vibration and AE data from the experimental test, a total of 28 features
were calculated from the time domain and the frequency domain. The same
features evaluation method as depicted in Chapter 4 was used for the selection of
effective features for the estimation of health state probability.
Figure 5.13 shows the distance evaluation criterion (α ) of 28 features in this
work. In order to select the effective features, the candidate defined a value
greater than 1.9 of normalized distance evaluation criterion, αα 1.9.
From the results, four features were selected as effective features compared with
the other features. The four selected features were RMS, entropy estimation value,
histogram upper value from vibration data and peak value from AE data. The
detailed descriptions of selected features are described in Chapter 2.3. Figure
5.14 presents the trends of each of the selected four features. The trends of the
four selected features show the dynamic and stochastic process of the real
bearing failure.
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Figure 5.13 Feature selection using distance evaluation criterion (Experimental Test)
Figure 5.14 Trends of selected features for experimental test
5.2.4 Health State Estimation and Prediction of RUL
Through the prior analysis of failure patterns, six discrete degradation stages
were determined as the number of health states of bearing failure in this
experimental test because they indicated discrete health states relating to bearing
failure over the time of test. The prediction tests of bearing failure were
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performed using the four selected features above. The training data sets for health
state estimation are summarized in Table 5.5.
Table 5.5 Training data sets for health state probability estimation of experimental test
State No. No. of samples ( )
Average operationtime ( , ) RUL (%) No. of
features 1 1 ~ 10 9 98.7% 4
2 301 ~ 310 571 16.4% 4
3 501 ~ 510 608 11.0% 4
4 701 ~ 710 645 5.6% 4
5 801 ~ 810 663 2.9% 4
6 903 ~ 912 682 0.1% 4
The polynomial function was used as the basic kernel function of SVM. In
multi-class classification method using SVMs, the OAO method was applied to
perform the health state probability estimation of bearing failure as described in
Chapter 3. In this experimental test of bearing failure, closed and open tests were
also conducted.
Closed Test of Experimental Data
Once the six health states were trained using the four selected features from
experimental data1 as depicted in Table 5.5, the full data sets of data1 (912
samples) were tested to obtain each health state’s probabilities.
Figure 5.15 shows the probabilities of each state of the experimental data1 that
was also used for training of the health states. The probability variation of health
state was perceived after 278 samples because an abnormal condition of bearing
was detected at this point of time. In general, the abnormal condition of the
bearings suddenly occurred at the early stage of defect development and
degraded rapidly. The probability distribution of the bearing health state
effectively presented the transition of bearing conditions as shown in Figure 5.14.
The entire probabilities of each stage explain the sequence of six degradation
states after starting at the abnormal condition, and are distinctly separated as
shown in Figure 5.15. The training error value was about 1.7% for the six health
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states.
Figure 5.15 Probability distribution of each health state
(Closed Test Using Experimental Data 1)
The expected life was also calculated by using the time of each training data
set ( ) and their probabilities of each health state as has be expressed in Eq. (3.7).
Figure 5.16 Comparison of actual RUL and estimated RUL
(Closed Test Using Experimental Data 1)
Figure 5.16 shows the closed test result with comparison between actual RUL
and estimated RUL. As shown in Figure 5.16, there were high margins of error
between the actual remaining useful life and the estimated life in the initial state
because of the long duration time of the normal condition. However, the
estimated life closely followed the actual remaining life after the beginning of
abnormal condition (540 minutes). The accuracy of prediction was also gauged
using the Eq. (5.6). The average prediction value was 86.32% over the entire
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range of data set.
Figure 5.17 Close view of the period of bearing fault condition
(Closed Test Using Experimental Data 1)
Figure 5.17 shows the close view of the period of bearing fault condition with
comparison between actual remaining useful life and estimated life. After the
start of the bearing fault, the estimated RUL was closely matched with the actual
remaining life. The average prediction value after the beginning of the abnormal
condition (from 540 minutes) was 97.67%.
Open Test of Experimental Data
The second experimental test data consisted of the 810 sample sets employed
for the open test using identical training data as depicted in Table 5.5. Figure 5.18
shows the test results of probabilities of each health state.
As shown in Figure 5.18, the probability variations began after around 600
samples because an abnormal condition started at the time of about 600 samples
in the case of the second bearing test. Compared with the former result (Closed
Test), the probability of five states indicated relatively low values and was hard
to find out in the probability distribution. However, the probability distribution of
each health state effectively represented the dynamic degradation process of the
bearing health state after the beginning of the abnormal condition.
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Figure 5.18 Probability distribution of each health state
(Open Test Using Experimental Data 2)
Figure 5.19 shows the comparison between the actual RUL and the estimated
RUL. The estimated life of open test (data 2) also started to follow the actual
remaining life after the beginning of the abnormal bearing condition. The average
prediction value was 38.93% over the entire range of data set.
Figure 5.19 Comparison of actual RUL and estimated RUL
(Open Test Using Experimental Data 2)
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Figure 5.20 Close view of the period of bearing fault condition
(Open Test Using Experimental Data 2)
Figure 5.20 shows the close view of the period of bearing fault condition for
the open test. Compared with the result of the closed test as shown in Figure 5.17,
the prediction result showed some low accuracy until after the starting of the
abnormal condition at 540 minutes. Furthermore, the difference between the
actual RUL time and the estimated RUL time at initial health state originated
from the different life time between training data (First Data Set, 683 minutes)
and test data (Second Data Set, 579 minutes) as described in Table 5.4. These
results indicate that accurate estimation of health states is achievable for
prediction of machine remnant life. Moreover, the proposed model also has the
capability to indicate abnormal machine conditions.
5.3 Model Comparison Using PHM
5.3.1 Proportional Hazard Model (PHM)
The proportional hazard model (PHM), which was originally proposed in the
medical research field, can model the uncertain relationships between multiple
indicators and time dependent failure rate. Cox's PH model [165] is a widely
accepted semi-parametric model for analysis of failures with covariates. It has
been successfully used for survival analyses in medical areas and reliability
predictions in accelerated life testing. In this case study, to compare the
performance of the proposed model, a model comparison was conducted using
the commonly used PHM because this model is also performed based on
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historical failure data.
PHM is developed based on the hazard rate function and assumes that the
hazard rate under the covariate is the product of an unspecified
baseline hazard rate and a relative risk ratio, , where is the
regression coefficient vector. The model can be generally expressed as:
(5.7)
The significant flexibility of PHM is that the regression coefficients can be
estimated by maximizing the corresponding partial likelihood function without
specifying the baseline . On the other hand, if the baseline hazard is
specified, the usual maximum likelihood approach can be carried out to estimate
the parameters in the model.
Considering the hard failure by the baseline function and degradation
simultaneously, the hazard rate in the form of PHM can be expressed as:
(5.8)
where , , … consists of n degradation features at
given time . Note that the conditional hazard rate in Eq. (5.7) is a
function of time only. The corresponding reliability function conditional on the
history of degradation features up to time is:
: 0 (5.9)
For failure time distribution, the Weibull distribution is widely used. In a
special case, assuming the baseline hazard has the form of two-parameter,
Weibull yields:
(5.10)
where 0 and 0 are the shape and scale parameters of Weibull
respectively. The model is referred to as the Weibull PH model. This model is
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utilized in this case study.
In order to estimate the parameters in the PHM, it is necessary to have the
historical data collected under the given operating conditions. The data consist of
aging times, feature sample paths and indicators of events (failure versus
censored). Then the likelihood function of the collected data is given by:
, , : 0
(5.11)
where is the set of failure times, is the set of surviving times, is
the failure time of the th unit and is either the failure time or the surviving
time of the th unit. The loglikelihood function can be expressed as:
, ,
(5.12)
where ln is the log-hazard rate and the integration
is implemented using the adaptive Simpson quadrature rule. The , ̂ and in
maximum likelihood estimate (MLE) can be obtained by maximizing the
loglikelihood function using Nelder-Mead’s algorithm. Then, the MLEs of the
reliability indices of interest can be obtained by substituting the MLEs of the
model parameters.
5.3.2 Prediction of Remnant Life Using PHM
This comparative study was conducted using the PHM algorithm developed in
[166]. Two vibration and AE data sets collected from the bearing test rig as
shown in Table 5.4 were also used for the model comparison. For the comparison
under identical conditions, the four selected features in the above section such as
RMS, entropy estimation value, histogram upper value from vibration data and
peak value from AE data were also used for the prediction of RUL using PHM.
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The parameters of the PHM model were identified using the likelihood
function given by Equation (5.12). In order to obtain a better fit, the features were
transformed by taking nature logarithm and denoted by ln RMS ,
ln Entropy Estimation , ln Histogram Upper and
ln Peak respectively. For the PHM:
(5.13)
The MLE’s of the parameters of the PHM are presented in Table 5.6.
Table 5.6 Estimated parameters of PHM using experimental data 1
2.3988 541.7 0.4717 0.5874 0.0025 3.678e-014
Using these parameters, the RULs of the bearing failure were estimated
respectively. In the closed test, Table 5.7 presents the prediction results both for
the PHM and the proposed model including comparison with the actual RUL
after stating abnormal condition of bearing (570 min).
Table 5.7 Comparison of RUL prediction between PHM and proposed model (Closed Test using experimental data 1) Time minute 570 580 590 600 610 620 630 640 650 660 670 680 683
In this Table, it can be seen that the estimated RUL from the proposed model
are in accordance with the actual remaining life of bearing, and outperform the
ones from the PHM model. Although the estimated RUL from PHM approached
the actual RUL closely according to the degradation of the bearing, the prediction
of the RUL still has significant difference between the actual RUL and the
estimated RUL compared to the results of the proposed model.
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Table 5.8 shows the open test result of the second experimental data using
identical training data (Data 1) after stating of bearing faulty condition. In the
case of the second experimental test, it had different bearing degradation pattern
with long duration of normal condition (around 540 minutes) and rapid failure
after the start of the faulty condition compared with the first experimental data.
As shown in Table 5.8, the PHM model cannot provide accurate prediction
results compared with the actual RUL and the results of the proposed model.
Although the estimated RULs of PHM matches with the actual RULs as the final
bearing failure approaches, the prediction of the RUL still has a significant
difference between the actual remaining life and the estimated life shown in
Table 5.8. For instance, the PHM still has high estimation error value (108
minutes) compared with the estimation error of the proposed model (32 minutes)
at the final bearing failure stage (578 minutes). In this case study, it can be seen
that the proposed model provides a more accurate prediction capability than the
PHM model in these bearing failure cases.
The above prediction result of PHM originates from insufficient historical
events in this case study. For better prediction using PHM, extensive data on a
substantial failure are required. However, in this case study, only one failure data
was available to be used for the prediction test. Moreover, the test data which has
considerably different life time from that of the training data can result in large
estimation error value in prediction of RUL.
Table 5.8 Comparison of RUL prediction between PHM and proposed model (Open Test using experimental data 2) Time minute 549 552 555 558 561 564 567 570 573 576 578
error{8}, Histogram upper{9} and Histogram lower{10}
RMS frequency value{11}, Frequency centre value{12},
Root variance frequency{13} andPeak value{14}
Acc.(B)
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To select the optimal parameters that can fully represent failure degradation,
effective features were selected using a feature selection method based on the
distance evaluation technique as discussed in Chapter 4. The reduction of feature
dimension leads to better performance of SVM and reduction in computational
effort.
In this work, a total 14 of features were used to extract effective features from
each signal sample measured at identical accelerometer positions. The distance
evaluation criterion (α ) of 14 features in this work are shown in Figure 6.9, with
almost zero value for histogram upper (No. 9). In order to select the effective
degradation features, the candidate defined a value greater than 1.3 of a
normalized distance evaluation criterion, αα 1.3, where α is distance
evaluation criterion and α is mean value of α . The ratio of 1.3 is selected
based on past historical records for this particular bearing/pump. From the results,
three features were selected for health state probability estimation, namely
Kurtosis {5}, Entropy estimation value {7} and Entropy estimation error value
{8}. They meet the large distance evaluation criterion (α ) as compared with
other features. These features could minimize the classification training and test
error of each health state.
Figure 6.9 Distance evaluation criterion of features.
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Figure 6.10 shows the selected feature trends of kurtosis, entropy estimation
and entropy estimation error value, respectively. All the selected features show
increasing trends which indicate the failure degradation process of the machine
over time as shown in the plots.
Figure 6.10 Feature trends of selected features
6.2.4 Selection of Number of Health States for Training
In this case study, to select the optimal number of health states of bearing
degradation, several health stages were investigated using the data sets of P301 D
for training and prediction tests. As the basic kernel function of SVM, a
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polynomial function was used in this work. Multi-class classification using the
OAO method was applied to perform the classification of bearing degradation as
described in Section 3. Sequential minimal optimization (SMO) was used to
solve the SVM classification problem. For the selection of optimal kernel
parameters (C, γ, d), the cross-validation technique was also used in order to
avoid over-fitting or under-fitting problems of classification performance. The
result of the investigation to select the optimal number of health states are plotted
in Figure 6.11. The average prediction value was estimated using Eq. (5.6).
Figure 6.11 Result of investigation to determine optimal number of health states.
A total of nine different states were investigated, ranging from two to ten
states. As shown in Figure 6.11, although low health states have low training
error values, they show high prediction error values compared with other higher
health states. On the contrary, high health states also have high training error
values but relatively low prediction error values. From this result, five health
states was selected as the optimal number of health states because beyond five
states the training error values increased rapidly and without significant decrease
in the prediction error values. The training error and prediction error values of the
five states were 10% and 5.6%, respectively.
Table 6.6 shows the training data sets of the selected five degradation states
used in this work and with eight sets of samples in each state using the three
selected features. Initially (Stage 1) the percentage of RUL was almost 100%
(99.89%) and progressively reduced to 28.77% in stage 4. At 5th stage, the
remaining bearing life was about 3.02%.
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Table 6.6 Training data sets for the health state probability estimation (P301D)
Stage No. No. of samples ( ) Average operation Hours ( ) RUL (%) No. of
features1 1 ~ 8 4 99.89% 3
2 25 ~ 32 503 85.67% 3
3 41 ~ 48 843 75.99% 3
4 81 ~ 88 2,501 28.77% 3
5 121 ~ 128 3,405 3.02% 3
6.2.5 RUL Prediction of Bearing Failure
In the RUL prediction of bearing failure, closed and open tests were conducted.
In the closed test, the five states were trained using the listed training data sets
shown in Table 6.6, and full data sets from P301 D (136 data sets) were tested to
obtain the probabilities of the five degradation states. Figure 6.12 shows the
probabilities of each state of P301 D. The first state probability started with
100% and decreased as long as the next state probability increased. For example,
the first state (solid lines) has the probabilities dropping and increasing again
until about 90% and eventually dropped to zero (at sample 30), while
simultaneously the second state (dotted lines) reached 100%. Some overlaps
between the states and also non uniformity of the distribution could be explained
due to the dynamic and stochastic degradation process and the uncertainty of
machine health condition or inappropriate data acquisitions in a real environment.
The entire probability of each state follow a non-linear degradation process and
are distinctly separated.
In the open test, similar bearing fault data (P301 C), which consisted of 120
sample sets, were tested to obtain the probability distribution of each health state
of P301 C using identical training data sets shown in Table 6.6. Figure 6.13
shows the probability distribution of each health state of P301 C. Similar non-
linear probability distribution and overlaps between states were also observed
due to reasons explained above.
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Figure 6.12 Probability distribution of each health state (Closed Test, P301 D)
Figure 6.13 Probability distribution of each health state (Open Test, P301 C)
The machine remnant life of bearing failure was estimated by using the
historical operation hours ( ) of each training data sets described in Table 6.6
and their probabilities evaluated using Eq.(3.5). Figure 6.14 shows the closed test
result of the estimated remnant life and the comparison between actual RUL and
estimated RUL. As shown in Figure 6.14, although there are some discrepancies
in the middle zone of the display, the overall trend of the estimated RUL follows
the gradient of actual remaining useful life of the machine. The average
prediction accuracy was 94.4%, calculated using Eq. (5.6) over the entire range
of the data set. Furthermore, the estimated RUL at the final state matched closely
to the actual RUL with less than 1% of remaining life.
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Figure 6.14 Comparison of actual RUL and estimated RUL (Closed Test, P301 D)
Figure 6.15 shows the open test result of estimated remnant life and the
comparison between actual RUL and estimated RUL. There is a large difference
in remnant life at the initial degradation states as shown in Figure 6.15. For the
open test, the estimated RUL time was obtained based on the training data sets
(P301 D) which had 3,511 hours in total operation. This caused the discrepancy
between actual RUL and estimated RUL in the beginning of the test. However, as
it approached final bearing failure, the estimated RUL matched more closely to
the actual remaining useful life than those in the initial and middle states.
Figure 6.15 Comparison of actual RUL and estimated RUL
(Open Test, P301 C)
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6.2.6 Verification of Optimum Number of Health States
In this case study, several tests of different health states were also conducted
to verify the optimum number of health states, ranging from two states to ten
states using same test data (P301 C).
Figure 6.16 shows the test result of training and prediction errors of these
health states. Health states from two to five show a high prediction error and
settled down at about 7.45% error at state No. 5, while the training error increases
as the number of states increases and stabilized between states Nos. 4 and 5.
However, beyond five states, the training error values increased rapidly in the
classification while the average prediction errors remain relatively constant.
Although states Nos. 4 and 5 have almost similar training error, the prediction
error at state No. 5 was much lower than state No. 4. Therefore, the selected five
health states were verified as optimal health states for the estimation of health
state probability in this case study. It has to be noted that different health stages
need to be evaluated for different case studies.
Figure 6.16 Training and prediction values of several health states (P301 C)
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6.3 Summary
The proposed prognostic model was successfully validated through two industry
case studies. Through prior analysis of historical data in terms of historical
knowledge, discrete failure degradation stages were employed to estimate discrete
health state probability for long term machine prognosis. In both case studies, for
optimum performance of the classifier, the prominent features were selected using
the distance evaluation method. The health state probability estimation was carried
out using a full failure degradation process of the machine over time from new to
final failure stages.
In the proposed model, the determination of the number of health states in
machine failure process plays a significant role for accurate estimation of machine
remnant life. Therefore, in the second case study of bearing failure prediction, the
optimal number of health states was selected through the investigation of several
health states. The selected optimum health states led to reduction of the training error
of health state estimation without significant decrease of the prediction error values
in this case study.
The results from two industrial case studies indicate that the proposed model has
the capability to provide accurate estimation of machine health condition for long-
term prediction of machine remnant life.
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CHAPTER 7 CONCLUSION AND FUTURE WORK
7.1 Conclusion
The ability to accurately predict the RUL of a machine is critical for its operation,
and can also be used to extend production capability; and to enhance the system’s
reliability. Effective diagnostics and prognostics are important aspects of CBM for
maintenance engineers to schedule a repair and to acquire replacement components
before the components eventually fail. Through an extensive literature review on
machine diagnostics and prognostics, this thesis addresses four critical challenges
and problems in machine fault prognostics such as accurate long term prediction,
sufficient usage of effective features, generality, scalability and the problem of
systematic incorporation of diagnostic information and historical knowledge.
With consideration to challenges in machine fault prognostics, the novel approach
to designing integrated diagnostic and prognostic systems based on health state
probability estimation has been presented in this thesis. This work concludes that:
The integration of fault diagnostic and prognostic system is confirmed to be
effective for accurate prediction of machine remnant life. The proposed model
has a closed loop architecture in configuration with an integrated diagnostics
and prognostics system based on health state probability estimation, with
embedded historical knowledge. Through the integrated system with fault
diagnostics, a more precise failure pattern from a number of historical
degradation data can be employed in prognostics through the prior verification
(isolation) of impending faults. With this scheme of the proposed model, a
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generic and scalable model is also established for the application of different
failing components. The proposed prognostic model has been successfully
tested and validated by applying it to a number of cases from a simulation test
to industry applications of HP-LNG pump failures. The results from case
studies indicate that accurate estimation of health states is achievable, which
would provide accurate prediction of machine remnant life. In addition, the
results of experimental tests show that the proposed model has the capability
to provide early warning of abnormal bearing conditions by indicating the
transitional health state of machine failure effectively.
The novel methodology of machine health state estimation applied to discrete
degradation process of machine failure enables accurate long-term prediction
of machine remnant life. None of the current prognostic models have
considered using discrete health state probability, which can effectively
represent the dynamic and stochastic degradation of the machine failure.
Current prognostic techniques only consider specific component degradations
and mainly applied in the laboratory environment for model validation. In this
research, the outcome of health state estimation provides an accurate real time
failure index for the prediction of machine remnant life. The proposed model
also enables a sufficient usage of a range of condition indicators to effectively
represent the complex nature of machine degradation by using the ability of
classification algorithms in health state probability estimation. In case studies,
a number of effective features (up to eight features) were used for health state
estimation. Furthermore, this full utilization of a range of features leads to a
generic and scalable prognostic model for the practical application in industry.
A systematic approach incorporating diagnostic information and historical
knowledge for accurate RUL prediction. The proposed prognostics model
integrates effective feature extraction and fault diagnostics to obtain the best
possible RUL prediction and to minimise the uncertainty in interpretation of
machine degradation. This scheme supports the prognostic system on how to
manage the historical knowledge in conjunction with machine fault
diagnostics and prognostics. In this thesis, the embedded historical knowledge
provides key references for real time fault diagnostics and health state
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estimation. The outcomes of integrated diagnostics and prognostics can then
be used for system updating and improving of the prognostics model by
providing reliable posterior degradation features for diverse failure modes and
fault types. The accumulated information also provides a good guideline to
solve the CM data management problems in many industries which are
suffering from huge storage of CM data. This scheme leads to improved
model scalability for applications of various faults and failure patterns. The
proposed prognostic model has been successively validated using two
different industrial fault data for the model scalability. The results from two
industrial case studies also indicate that the proposed model has the capability
to provide accurate estimation of health condition for accurate prediction of
machine remnant life.
The comparative study of intelligent diagnostics using five different
classification algorithms. The comparative diagnostic tests were conducted
using five different classifiers applied to progressive fault levels of three fault
types in the HP-LNG pump. Although many intelligent fault diagnostic
models have been validated using a number of machine fault data, none of
them consider different severity levels in fault propagation to estimate the
fault diagnostic performance. The result of a comparison test shows that the
fault classification accuracy is variable and depending on the severity of the
machine fault and the type of classifier. The SVMs show relatively
outstanding performance for intelligent fault classification in the range of fault
propagation among commonly used classifiers. Therefore the SVM technique
is employed in health state probability estimation for prediction of machine
failure in this research.
Investigation of the optimal number of health states for better prediction of
machine remnant life. In the industrial case study of bearing failure, the health
state probability estimation was carried out using a full failure degradation
process of the machine over time from new to final failure stages. The optimal
number of health states was validated through the investigation of several
number of health states in the case study of bearing failure prediction of HP-
LNG pumps. It has been confirmed that the selected optimum health states
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have led to minimising the training error of health state estimation without a
significant decrease in the prediction error values in this case study.
The results of model comparison indicate that the proposed model has a more
accurate prediction capability. The model comparison study with the
Proportional Hazards Model has been conducted under identical conditions
using experimental bearing failure data. Through the comparison between the
proposed model and the PHM with the actual remaining life of bearing, it is
verified that the proposed prognostic model based on health state probability
estimation provides a more accurate RUL prediction than the commonly used
PHM in the case of dynamic and stochastic process of machine degradation.
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7.2 Future Work
Through model validation using simulated and experimental data, and industry
case studies, several new research issues have been identified and described as
followings:
Although the proposed prognostic model is shown to be effective through
several case studies from simulation tests to industrial applications, further
validations of different machine system failures such as gear box, tool wear,
structural corrosion, motor and engines still remain as an area of future work
to establish a generic and scalable asset health management system.
The signal processing and feature extraction techniques are fundamental to
the development of a robust diagnostics and prognostics model for certain
fault types and failure patterns. In this thesis, the proposed model mainly
used conventional standard features from vibration CM data. Therefore,
other feature extraction methods from different CM data need to be explored
to extract appropriate health indicators.
One novelty of the proposed model is health state probability estimation for
accurate long term prediction of remaining useful life of a machine. The
selection of a number of optimal health states of component failure is vital in
order to avoid high training error with high prediction accuracy. Even
though the optimum health degradation stages were determined in this work
by using several health states in industry case study, new approaches using
current available optimization algorithms and pattern recognition techniques
for the optimization of health degradation stages is still required to be
developed. It is shown in this work that the number of health states plays a
significant role in providing accurate machine failure prognosis.
Although the proposed model makes use of sufficient health indicators in the
prediction of machine remnant life, there is also a limitation in using many
features due to the problem of dimensionality in classification process,
which may cause computer overload and over-fitting of training data. In a
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supervised learning setting with many input features, over-fitting is a
potential problem unless there is ample training data.
To avoid this dimensionality problem in using a number of health indicators
in the proposed model, a tensor based method for health state probability
estimation can be used as an alternative to traditional classification
techniques. Most of the traditional learning/classification algorithms are
based on the Vector Space Model (VSM). That is, the data are represented as
vectors x . The learning algorithms aim at finding a linear (or
nonlinear) function wTx according to some pre-defined criteria,
where w , … , T are the parameters to estimate. However, in
Tensor Space Model (TSM), a data sample is represented as a tensor [167].
Each element in the tensor corresponds to a feature. For a data sample
x , it can be converted into the second order tensor (or matrix)
x , , where , . Tensor based approaches can perform
data analysis in high dimensional spaces. Therefore, the utilisation of TSM
for health state probability estimation is suggested as a possible future work
for full utilization of input parameters.
Finally, for real application and convenient implementation of the model in
industry, it is necessary to develop an integrated health management
software tool based on health state probability estimation which can be used
in fault detection, diagnostics and prognostics of machine components.
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APPENDIX
Basic binary classification theory of SVMs
Given a set of input data 1, 2, … , where M is the number of samples.
The ith sample in an n-dimension input space belongs to one of two classes
labelled by 1, 1 namely, positive class and negative class. For linear data, it
is possible to determine the hyperplane 0 that separates the given input data.
∑ 0 (A.1)
where is the coefficient vector and is the bias of the hyperplane. The vector
and scalar are used to define the position of the separating hyperplane. The
decision function is made using sign to create a separating hyperplane that
classify input data into either positive class or negative class. A distinctly separating
hyperplane should satisfy the constraints
1, if 11, if 1 (A.2)
or it can be presented in a complete equation
1 for 1, 2, … (A.3)
The separating hyperplane that creates the maximum distance between the plane
and the nearest data, i.e., the maximum margin, is called the optimal separating
hyperplane (OSH). An example of the optimal hyperplane of two data sets is
presented in Figure A.1.
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Figure A.1. Binary classification using SVMs[168]
By taking into account the noise with slack variables and error penalty , the
optimal hyperplane separating the data can be obtained as a solution to the following
optimization problem
minimise ∑ (A.4)
subject to 1 , 1, 2, … 0, 1, 2, … (A.5)
where is the measured distance between the margin and the samples that
lying on the wrong side of the margin. The calculation can be simplified by
converting the problem with the Kuhn-Tucker condition into the equivalent
Lagrangian dual problem, which will be
minimise , , ∑ ∑ (A.6)
The task is minimising Eq. (A.6) with respect to and , while requiring the
derivatives of to to vanish. At the optimal point, the following saddle point
equations are applied
Positive Class
Negative Class
{ }1H : | ( ) 1b⋅ + = +x w x
{ }H : | ( ) 0b⋅ + =x w x{ }2 : | ( ) 1H b⋅ + = −x w x
Margin
b−w
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0, 0 (A.7)
which can be replaced by
∑ , ∑ 0 (A.8)
From Eq. (A.8), is contained in the subspace spanned by the . By
substitution Eq. (A.8) into Eq. (A.7), the dual quadratic optimization problem is
obtained
maximise ∑ ∑ , (A.9)
subject to 0, 1, 2, … . ∑ 0 (A.10)
Thus, by solving the dual optimization problem, one obtains the coefficient
which is required to express so as to solve Eq. (A.4). This leads to the non-linear
decision function,
∑ , (A.11)
SVMs can also be used in non-linear classification tasks with the application of
Kernel functions. The data to be classified is mapped onto a high-dimensional feature
space, where linear classification can be applied.
Using the non-linear vector function, Eq. (A.12) to map the n-dimensional input
vector onto one-dimensional feature space
Φ , … (A.12)
The linear decision function in dual form is given by
∑ , Φ Φ (A.13)
Working in high-dimensional feature space enables the expression of complex
functions. But it can also generate other problems. Computational problems can
occur due to the large vectors and the overfitting problem can also exist due to the
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high-dimensionality. The latter problem can be solved by using Kernel functions.
The Kernels are a function that returns a dot product of the feature space mappings of
the original data points, as stated below
, Φ Φ (A.14)
When applying a Kernel function, learning in the feature space does not require
explicit evaluation of Φ and the decision function will be
∑ , , (A.15)
Any function that satisfies Mercer’s theorem [169] can be used as a Kernel
function to compute a dot product in feature space. There are different Kernel
functions used in SVMs, such as linear, polynomial and Gaussian RBF. The Kernel
defines the feature space in which the training set examples will be classified.
The selection of the appropriate Kernel function is very important, since the
Kernel defines the feature space in which training set examples will be classified.
The definition of a legitimate Kernel function is given by Mercer’s theorem, which
states that the function must be continuous and positive definite. Table A.1 shows the
formulation of linear, polynomial and Gaussian RBF functions respectively.
Table A.1 Formulation of Kernel functions
Kernel Linear Polynomial Gaussian RBF
Formulation, , · γ · , γ 0 – – /2γ
SVMs Quadratic Programming (QP) problem
Vapnik [170] presented a method which used the projected conjugate gradient
algorithm to solve the SVM-QP problem, which has been known as chunking. The
chunking algorithm uses the fact that the value of the quadratic form is the same if
you remove the rows and columns of the matrix that corresponds to zero Lagrange
multipliers. Therefore, chunking seriously reduces the size of the matrix from the
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number of training examples squared to approximately the number of non-zero
Lagrange multipliers squared. However, chunking still cannot handle large-scale
training problems, since even this reduced matrix cannot fit into memory. Osuna,
Freund and Girosi [171] presented the improved training algorithm which suggests a
whole new set of QP algorithms for SVM. The theorem proves that the large QP
problem can be broken down into a series of smaller QP sub-problems.
Sequential Minimum Optimization (SMO) for SVM-QP Problem
Sequential minimal optimization (SMO) proposed by Platt [163] is a simple
algorithm that can be used to solve the SVM-QP problem without any additional
matrix storage and without using the numerical QP optimization steps. This method
decomposes the overall QP problem into QP sub-problems using the Osuna’s
theorem to ensure convergence. In this dissertation, SMO is used as a solver and the
detail of SMO is readily available in reference [163].
In order to solve the two Lagrange multipliers , , SMO first computes the
constraints on these multipliers and then solves for the constrained minimum. For
convenience, all quantities that refer to the first multiplier will have a subscript 1,
while all quantities that refer to the second multiplier will have a subscript 2. The
new values of these multipliers must lie on a line in , space, and in the box
defined by 0 , .
(A.16)
Without loss of generality, the algorithm first computes the second Lagrange
multipliers and successively uses it to obtain . The box constraint
0 , , together with the linear equality constraint ∑ 0, provides a
more restrictive constraint on the feasible values for . The boundary of feasible
region for can be applied as follows
, 0, , , , (A.17)
, 0, , , ,
(A.18)
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The second derivative of the objective function along the diagonal line can be
expressed as:
, , 2 , (A.19)
Under normal circumstances, the objective function will be positive definite, there
will be a minimum along the direction of the linear equality constraint, and will
be greater than zero. In this case, SMO computes the minimum along the direction of
the constraint:
(A.20)
where is the prediction error on the ith training example. As a next step, the
constrained minimum is found by clipping the unconstrained minimum to the ends of
the line segment:
,H if H;
; L if ;
(A.21)
Now, let . The value of is computed from the new :
(A.22)
Solving Eq. (A.9) for the Lagrange multipliers does not determine the threshold
of the SVM, so must be computed separately. The following thresholds ,
are valid when the new , are not at the each bounds, because it forces the
output of the SVM to be , when the input is , respectively
, , ,
(A.23)
, , ,
(A.24)
When both and are valid, they are equal. When both new Lagrange
multipliers are at bound and if is not equal to , then the interval between
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and are all thresholds that are consistent with the Karush-Kuhn-Tucker
conditions which are necessary and sufficient conditions for an optimal point of a
positive definite QP problem. In this case, SMO chooses the threshold to be halfway
between and [163].
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