Degradation Modeling and RUL Prediction Using Wiener Process Subject to Multiple Change Points and Unit Heterogeneity

Degradation modeling is critical for health condition monitoring and remaining useful life prediction (RUL). The prognostic accuracy highly depends on the capability of modeling the evolution of degradation signals. In many practical applications, however, the degradation signals show multiple phases, where the conventional degradation models are often inadequate. To better characterize the degradation signals of multiple-phase characteristics, we propose a multiple change-point Wiener process as a degradation model. To take into account the between-unit heterogeneity, a fully Bayesian approach is developed where all model parameters are assumed random. At the offline stage, an empirical two-stage process is proposed for model estimation, and a cross-validation approach is adopted for model selection. At the online stage, an exact recursive model updating algorithm is developed for online individual model estimation, and an effective Monte Carlo simulation approach is proposed for RUL prediction. The effectiveness of the proposed method is demonstrated through thorough simulation studies and real case study

Predictive maintenance: a novel framework for a data-driven, semi-supervised, and partially online prognostic health management application in industries

Prognostic Health Management (PHM) is a predictive maintenance strategy, which is based on Condition Monitoring (CM) data and aims to predict the future states of machinery. The existing literature reports the PHM at two levels: methodological and applicative. From the methodological point of view, there are many publications and standards of a PHM system design. From the applicative point of view, many papers address the improvement of techniques adopted for realizing PHM tasks without covering the whole process. In these cases, most applications rely on a large amount of historical data to train models for diagnostic and prognostic purposes. Industries, very often, are not able to obtain these data. Thus, the most adopted approaches, based on batch and off-line analysis, cannot be adopted. In this paper, we present a novel framework and architecture that support the initial application of PHM from the machinery producers’ perspective. The proposed framework is based on an edge-cloud infrastructure that allows performing streaming analysis at the edge to reduce the quantity of the data to store in permanent memory, to know the health status of the machinery at any point in time, and to discover novel and anomalous behaviors. The collection of the data from multiple machines into a cloud server allows training more accurate diagnostic and prognostic models using a higher amount of data, whose results will serve to predict the health status in real-time at the edge. The so-built PHM system would allow industries to monitor and supervise a machinery network placed in different locations and can thus bring several benefits to both machinery producers and users. After a brief literature review of signal processing, feature extraction, diagnostics, and prognostics, including incremental and semi-supervised approaches for anomaly and novelty detection applied to data streams, a case study is presented. It was conducted on data collected from a test rig and shows the potential of the proposed framework in terms of the ability to detect changes in the operating conditions and abrupt faults and storage memory saving. The outcomes of our work, as well as its major novel aspect, is the design of a framework for a PHM system based on specific requirements that directly originate from the industrial field, together with indications on which techniques can be adopted to achieve such goals

Reliability modeling and analysis of load-sharing systems with continuously degrading components

This paper presents a reliability modeling and analysis framework for load-sharing systems with identical components subject to continuous degradation. It is assumed that the components in the system suffer from degradation through an additive impact under increased workload caused by consecutive failures. A log-linear link function is used to describe the relationship between the degradation rate and load stress levels. By assuming that the component degradation is well modeled by a step-wise drifted Wiener process, we construct maximum likelihood estimates (MLEs) for unknown parameters and related reliability characteristics by combining analytical and numerical methods. Approximate initial guesses are proposed to lessen the computational burden in numerical estimation. The estimated distribution of MLE is given in the form of multivariate normal distribution with the aid of Fisher information. Alternative confidence intervals are provided by bootstrapping methods. A simulation study with various sample sizes and inspection intervals is presented to analyze the estimation accuracy. Finally, the proposed approach is illustrated by track degradation data from an application example

Reliability Analysis By Considering Steel Physical Properties

Most customers today are pursuing engineering materials (e.g., steel) that not only can achieve their expected functions but also are highly reliable. As a result, reliability analysis of materials has been receiving increasing attention over the past few decades. Most existing studies in the reliability engineering field focus on developing model-based and data-driven approaches to analyze material reliability based on material failure data such as lifetime data and degradation data, without considering effects of material physical properties. Ignoring such effects may result in a biased estimation of material reliability, which in turn could incur higher operation or maintenance costs. Recently, with the advancement of sensor technology more information/data concerning various physical properties of materials are accessible to reliability researchers. In this dissertation, considering the significant impacts of steel physical properties on steel failures, we propose systematic methodologies for steel reliability analysis by integrating a set of steel physical properties. Specifically, three steel properties of various scales are considered: 1) a macro-scale property called overload retardation; 2) a local-scale property called dynamic local deformation; and 3) a micro-scale property called microstructure effect. For incorporating property 1), a novel physical-statistical model is proposed based on a modification of the current Paris law. To incorporate property 2), a novel statistical model named multivariate general path model is proposed, which is a generalization of an existing univariate general path model. For the integration of property 3), a novel statistical model named distribution-based functional linear model is proposed, which is a generalization of an existing functional linear model. Theoretical property analyses and statistical inferences of these three models are intensively developed. Various simulation studies are implemented to verify and illustrate the proposed methodologies. Multiple physical experiments are designed and conducted to demonstrate the proposed models. The results show that, through the integration of the aforementioned three steel physical properties, a significant improvement of steel reliability assessment is achieved in terms of failure prediction accuracy compared to traditional reliability studies

Novel Methods for Analyzing Longitudinal Data with Measurement Error in the Time Variable

In some longitudinal studies, the observed time points are often confounded with measurement error due to the sampling conditions, resulting into data with measurement error in the time variable. This type of data occurs mainly in observational studies when the onset of a longitudinal process is unknown or in clinical trials when individual visits do not take place as specified by the study protocol, but are often rounded to coincide with the study protocol. Methodological and inferential implications of error in time varying covariates for both linear and nonlinear models have been studied widely. In this dissertation, we shift attention to another source of measurement error in the time variable in longitudinal studies. Specifically, we develop statistical methods for analyzing longitudinal data when the onset of the process is unknown. This work has been motivated by a cervical dilation data from the Consortium on Safe Labor (CSL) study, a multi-center retrospective observational study conducted by the Eunice Kennedy Shriver National Institute of Child Health and Human Development. The uncertainty in onset of labor poses methodological challenges since the observed time variable is related to when women get to the hospital, not the biologic process of interest. In Chapter II, we present a Longitudinal Threshold Regression model for estimating the distribution of the time a woman’s cervical dilation takes to progress from one threshold to another (in cm). In Chapter III, we present a Semi-parametric model with random shift parameters for modeling labor curves prospectively. In Chapter IV, we extend Chapter III to predict women’s time to full dilation given their past measurements. We demonstrate the proposed methods using simulation studies and a data from the CSL study

유기발광 디스플레이 수명 모델 제안 및 모델 검증 체계 연구

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2018. 2. 윤병동.Despite the advantages of organic light-emitting diode (OLED) displays over liquid crystal displays, OLED displays suffer from reliability concerns related to luminance degradation and color shift. In particular, existing testing schemes are unable to reliably estimate the lifetime of large OLED displays (i.e., displays of 55 inches or larger). The limited number of test samples and the immature technology result in great hurdles for timely product development. This study proposes a statistical approach to develop a lifetime model for OLED panels. The proposed approach incorporates manufacturing and operational uncertainties, and accurately estimates the lifetime of the OLED panels under normal usage conditions. The proposed statistical analysis approach consists of: (1) design of accelerated degradation tests (ADTs) for OLED panels, (2) establishment of a systematic scheme to build bivariate lifetime models for OLED panels, (3) development of two bivariate lifetime models for OLED panels, and (4) statistical model validation for the heat dissipation analysis model for OLED TV design. This four-step statistical approach will help enable accurate lifetime prediction for large OLED panels subjected to various uncertainties. Thereby, this approach will foster efficient and effective OLED TV design to meet desired lifespan requirements. Furthermore, two bivariate acceleration models are proposed in this research to estimate the lifetime of OLED panels under real-world usage conditions, subject to manufacturing and operational uncertainties. These bivariate acceleration models take into account two main factors—temperature and initial luminance intensity. The first bivariate acceleration model estimates the luminance degradation of the OLED panelthe second estimates the panels color shift. The lifespan predicted by the proposed lifetime model shows a good agreement with experimental results. Ensuring the color shift lifetime is a great hurdle for OLED product development. However, at present, there is no effective way to estimate the color shift lifetime at the early stages of product development while the product design is still changing. The research described here proposes a novel scheme for color shift lifetime analysis. The proposed method consists of: (1) a finite element model for OLED thermal analysis that incorporates the uncertainty of the measured surface temperature, (2) statistical model validation, including model calibration, to verify agreement between the predicted results and a set of experimental data (achieved through adjustment of a set of physical input variables and hypothesis tests for validity checking to measure the degree of mismatch between the predicted and observed results), and (3) a regression model that can predict the color shift lifetime using the surface temperature at the early stages of product development. It is expected that the regression model can substantially shorten the product development time by predicting the color shift lifetime through OLED thermal analysis.Chapter 1. Introduction 1 1.1 Background and Motivation 1 1.2 Overview and Significance 2 1.3 Thesis Layout 6 Chapter 2. Literature Review 8 2.1 Accelerated Testing 8 2.2 Luminance Degradation Model for OLEDs 12 2.3 Color Shift of OLEDs 14 2.4 Verification and Validation Methodology 16 Chapter 3. OLED Degradation 28 3.1 Chromaticity and the Definition of Color Shift Lifetime 30 3.2 Degradation Mechanism 31 3.2.1 Luminance Degradation Mechanism 33 3.2.2 Color Shift Mechanism 34 3.3 Performance Degradation Models 36 3.3.1 Performance Degradation Model 36 3.3.2 Performance Color Shift Model 38 3.4 Acceleration Model 38 Chapter 4. Acceleration Degradation Testing (ADT) for OLEDs 42 4.1 Experimental Setup 42 4.2 Definition of the Time to Failure 46 4.2.1 The Time to Failure of Luminance 46 4.2.2 The Time to Failure of Color Shift 47 4.3 Lifespan Test Results 50 Chapter 5. Bivariate Lifetime Model for OLEDs 53 5.1 Fitting TTF Data to the Statistical Distribution 53 5.1.1 Estimation of Lifetime Distribution Parameters 53 5.1.2 Estimation of the Common Shape Parameter 58 5.1.3 Likelihood-Ratio Analysis 62 5.2 Bivariate Lifetime Model 64 5.2.1 Luminance Lifetime Model 64 5.2.2 Color Shift Lifetime Model 66 5.3 Validation of the Lifetime Model 67 Chapter 6. Statistical Model Validation of Heat Dissipation Analysis Model 77 6.1 Estimation Method for TTF using Surface Temperature 79 6.2 Thermal Analysis Model for OLED Displays 81 6.3 Statistical Calibration using the EDR Method 82 6.4 Validity Check 87 6.5 Results and Discussion 90 Chapter 7. Case Study 93 7.1 Computational Modeling 93 7.2 Estimation of Color Shift 95 7.3 Estimation of Luminance Degradation 96 Chapter 8. Contributions and Future Work 98 8.1 Contributions and Impacts 98 8.2 Suggestions for Future Research 103 References 104Docto

A Stochastic Approach to Measurement-Driven Damage Detection And Prognosis in Structural Health Monitoring

Damage detection and prognosis are integral to asset management of critical mechanical and civil engineering infrastructure. In practice, these two aspects are often decoupled, where the former is carried out independently using sensor data (e.g., vibrations), while the latter is undertaken based on reliability principles using life time failure data of the system or the component of interest. Only in a few studies damage detection results are extended to remaining useful life estimation, which is achieved by modeling the underlying degradation process using a surrogate measure of degradation. However, an integrated framework which undertakes damage detection, prognosis, and maintenance planning in a systematic way is lacking in the literature. Furthermore, the parameters of degradation model which are utilized for prognosis are often solely estimated using the degradation data obtained from the monitored unit, which represents the degradation of a specific unit, but ignores the general population trend. The main objectives of this thesis are three-fold: first, a mathematical framework using surrogate measure of degradation is developed to undertake the damage detection and prognosis in a single framework; next, the prior knowledge obtained from the historical failed units are integrated in model parameter estimation and residual useful life (RUL) updating of a monitored unit using a Bayesian approach; finally, the proposed degradation modeling framework is applied for maintenance planning of civil and industrial systems, specifically, for reinforced concrete beams and rolling element bearings. The initiation of a fault in these applications is often followed by a sudden change in the degradation path. The location of a change-point can be associated with a sudden loss of stiffness in the case of structural members, or fault initiation in the case of bearings. Hence, in this thesis, the task of change point location identification is thought of as being synonymous with damage or fault detection in the context of structural health monitoring. Furthermore, the change point results are used for two-phase degradation modeling, future degradation level prediction and subsequent RUL estimation. The model parameters are updated using a Bayesian approach, which systematically integrates the prior knowledge obtained from historical failure-time data with monitored data obtained from an in-situ unit. Once such a model is established, it is projected to a failure threshold, thereby allowing for RUL estimation and maintenance planning. Results from the numerical as well as actual field data shows that the proposed degradation modeling framework is good in performing these two tasks. It was also found that as more degradation data is utilized from the monitoring unit, the progressing fault is detected in a timely manner and the model parameters estimates and the end life predictions become more accurate

Statistical Sample Size Determination Methods for Inspections of Engineering Systems

A statistical sample size determination (SSD) method is designed for the maintenance of engineering components of similar structure within an overall system. The maintenance problem is defined as a sequential decision-making process, in which the optimal sample sizes are derived by an approach based on the value of information (VoI) concept. Firstly, various sample size determination methods are summarized, and their advantages and disadvantages are discussed. This comparison highlights that, in many cases, the VoI-based approach is superior to traditionally used methods. Existing standards for engineering components are then categorized, based on the comparison, and the rationale behind each standard is described. Potential advantages of using a VoI-based approach are suggested and discussed. Secondly, the theoretical superiority of VoI-based methods is demonstrated in the context of a diagnostic inspection problem, in which the traditional SSD method, the hypothesis-testing approach, can be defined. After the hypothesis-testing context is translated into a sequential decision-making problem, theoretical and numerical results are compared for the VoI-based and traditional methods. Thirdly, the models for condition-based maintenance problems are defined with a time-dependent degradation process called the gamma process. The models mathematically describe how temporal and parameter uncertainties of the degradation process affect the VoI-based analysis. Computational calculation techniques are introduced and compared with each other. Additionally, the model is generalized as a dynamic programming problem and formulated as a multiple-inspection problem. Finally, the effectiveness of the SSD approach is demonstrated through application to an actual degrading system. Based on data from nuclear power plants, numerical analyses are shown for both single and two inspection cases. The results provide operators with guidelines for maintenance and inspection policies that minimize the expected cost throughout the remaining lifetime of the system

Statistical Sample Size Determination Methods for Inspections of Engineering Systems

A statistical sample size determination (SSD) method is designed for the maintenance of engineering components of similar structure within an overall system. The maintenance problem is defined as a sequential decision-making process, in which the optimal sample sizes are derived by an approach based on the value of information (VoI) concept. Firstly, various sample size determination methods are summarized, and their advantages and disadvantages are discussed. This comparison highlights that, in many cases, the VoI-based approach is superior to traditionally used methods. Existing standards for engineering components are then categorized, based on the comparison, and the rationale behind each standard is described. Potential advantages of using a VoI-based approach are suggested and discussed. Secondly, the theoretical superiority of VoI-based methods is demonstrated in the context of a diagnostic inspection problem, in which the traditional SSD method, the hypothesis-testing approach, can be defined. After the hypothesis-testing context is translated into a sequential decision-making problem, theoretical and numerical results are compared for the VoI-based and traditional methods. Thirdly, the models for condition-based maintenance problems are defined with a time-dependent degradation process called the gamma process. The models mathematically describe how temporal and parameter uncertainties of the degradation process affect the VoI-based analysis. Computational calculation techniques are introduced and compared with each other. Additionally, the model is generalized as a dynamic programming problem and formulated as a multiple-inspection problem. Finally, the effectiveness of the SSD approach is demonstrated through application to an actual degrading system. Based on data from nuclear power plants, numerical analyses are shown for both single and two inspection cases. The results provide operators with guidelines for maintenance and inspection policies that minimize the expected cost throughout the remaining lifetime of the system