Intelligent Prognostic Framework for Degradation Assessment and Remaining Useful Life Estimation of Photovoltaic Module

All industrial systems and machines are subjected to degradation processes, which can be related to the operating conditions. This degradation can cause unwanted stops at any time and major maintenance work sometimes. The accurate prediction of the remaining useful life (RUL) is an important challenge in condition-based maintenance. Prognostic activity allows estimating the RUL before failure occurs and triggering actions to mitigate faults in time when needed. In this study, a new smart prognostic method for photovoltaic module health degradation was developed based on two approaches to achieve more accurate predictions: online diagnosis and data-driven prognosis. This framework of forecasting integrates the strengths of real-time monitoring in the first approach and relevant vector machine in the second. The results show that the proposed method is plausible due to its good prediction of RUL and can be effectively applied to many systems for monitoring and prognostics

Machine learning model for event-based prognostics in gas circulator condition monitoring

Gas circulator (GC) units are an important rotating asset used in the Advanced Gas-cooled Reactor (AGR) design, facilitating the flow of CO2 gas through the reactor core. The ongoing maintenance and examination of these machines is important for operators in order to maintain safe and economic generation. GCs experience a dynamic duty cycle with periods of non-steady state behavior at regular refuelling intervals, posing a unique analysis problem for reliability engineers. In line with the increased data volumes and sophistication of available the technologies, the investigation of predictive and prognostic measurements has become a central interest in rotating asset condition monitoring. However, many of the state-of-the-art approaches finding success deal with the extrapolation of stationary time series feeds, with little to no consideration of more-complex but expected events in the data. In this paper we demonstrate a novel modelling approach for examining refuelling behaviors in GCs, with a focus on estimating their health state from vibration data. A machine learning model was constructed using the operational history of a unit experiencing an eventual inspection-based failure. This new approach to examining GC condition is shown to correspond well with explicit remaining useful life (RUL) measurements of the case study, improving on the existing rudimentary extrapolation methods often employed in rotating machinery health monitoring

A multi-state physics modeling for estimating the size- and location-dependent loss of coolant accident initiating event probability

Multi-State Physics Modeling (MSPM) integrates multi-state modeling to describe a component degradation process by transitions among discrete states (e.g., no damage, micro-crack, flaw, rupture, etc.), with physics modeling by (physic) equations to describe the continuous degradation process within the states. In this work, we propose MSPM to describe the degradation dynamics of a piping system, accounting for the dependence on the size and location of the Loss of Coolant Accident (LOCA) initiating event of the Reactor Coolant System (RCS) of a Pressurized Water Reactor (PWR). Estimated frequencies of LOCA as a function of break size are used in a variety of regulatory applications and for the Probabilistic Risk Assessment (PRA) of Nuclear Power Plants (NPPs). Traditionally, two approaches have been used to assess LOCA frequencies as a function of pipe break size: estimates based on statistical analysis of field data collected from piping systems service experience and Probabilistic Fracture Mechanics (PFM) analysis of specific, postulated, physical damage mechanisms. However, due to the high reliability of NPP piping systems, it is difficult to construct a comprehensive service database based on which perform statistical analysis. On the other hand, it is difficult to utilize PFM models for calculating LOCA frequencies because many of the input variables and model assumptions are over-simplified and may not adequately represent the true plant conditions. We overcome these challenges and propose a size- and location-dependent LOCA initiating event frequencies estimation by resorting to the novel MSPM modeling scheme. Benchmarking is done with respect to the results obtained with the Generic Safety Issue (GSI) 191 framework that makes use of field data for LOCA initiating event probability calculation

A locally adaptive ensemble approach for data-driven prognostics of heterogeneous fleets

In this work, we consider the problem of predicting the remaining useful life of a piece of equipment, based on data collected from a heterogeneous fleet working under different operating conditions. When the equipment experiences variable operating conditions, individual data-driven prognostic models are not able to accurately predict the remaining useful life during the entire equipment life. The objective of this work is to develop an ensemble approach of different prognostic models for aggregating their remaining useful life predictions in an adaptive way, for good performance throughout the degradation progression. Two data-driven prognostic models are considered, a homogeneous discrete-time finite-state semi-Markov model and a fuzzy similarity-based model. The ensemble approach is based on a locally weighted strategy that aggregates the outcomes of the two prognostic models of the ensemble by assigning to each model a weight and a bias related to its local performance, that is, the accuracy in predicting the remaining useful life of patterns of a validation set similar to the one under study. The proposed approach is applied to a case study regarding a heterogeneous fleet of aluminum electrolytic capacitors used in electric vehicle powertrains. The results have shown that the proposed ensemble approach is able to provide more accurate remaining useful life predictions throughout the entire life of the equipment compared to an alternative ensemble approach and to each individual homogeneous discrete-time finite-state semi-Markov model and fuzzy similarity-based models

Accelerated Fatigue Reliability Analysis of Stiffened Sections Using Deep Learning

Fatigue is one of the main failure mechanisms in structures subjected to fluctuating loads such as bridges and ships. If inadequately designed for such loads, fatigue can be detrimental to the safety of the structure. When fatigue cracks reach a certain size, sudden fracture failure or yielding of the reduced section can occur. Accordingly, quantifying the critical crack size is essential for determining the reliability of fatigue critical structures under growing cracks. Failure Assessment Diagrams (FADs) can be used to determine the critical crack size or whether the state of the crack is acceptable or not at a particular instant in time. Due to the presence of uncertainties in loads, material properties and crack growth behavior, probabilistic analysis is essential to understand the fatigue performance of the structure over its service life. A time dependent reliability profile for the structure can be established to help schedule maintenance and repair activities. However, probabilistic analysis of crack growth under complex geometrical and loading conditions can be very expensive computationally. Deep learning is a useful tool that is used in this study to curtail this lengthy process by establishing multi-variate non-linear approximations for complex fatigue crack growth profiles. This study proposes a framework for establishing the fatigue reliability profiles of stiffened panels under uncertainty. Monte Carlo simulation is used to draw samples from relevant probabilistic parameters and establish the time dependent reliability profile of the structure under propagating cracks. Deep learning is adopted to improve the computational efficiency of the probabilistic analysis in establishing the probabilistic crack growth profiles. The proposed framework is illustrated on a bridge with stiffened tub girders subjected to fatigue loading.Civil Engineerin

Investigation on Statistical Model Calibration and Updating of Physics and Data-driven Modeling for Hybrid Digital Twin

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2022.2. 윤병동.실제 운행중인 공학 시스템의 가상 디지털 객체를 구축하여 시스템의 관측 데이터를 기반으로 실제 시스템의 다양한 상황을 모사할 수 있는 디지털 트윈 기술은 설계, 제조 및 시스템 상태 관리와 같은 공학적 의사 결정을 지원할 수 있는 솔루션을 제공합니다. 디지털 트윈 접근 방식은 1) 데이터 기반 접근 방식, 2) 물리 기반 접근 방식, 3) 융합형 접근 방식의 세 가지 범주로 나눌 수 있습니다. 융합형 디지털 트윈은 데이터 기반 모델과 물리 기반 모델을 모두 활용하여 이 두 가지 접근 방식의 단점을 극복하기 때문에 관찰된 데이터를 바탕으로 신뢰할 수 있는 공학적 의사 결정을 가능하게 합니다. 그러나 이를 적용하기 위해 필요한 시스템에 대한 사전 정보들은 대부분의 공학 시스템에서 제한적으로 이용 가능합니다. 이러한 사전 정보에는 모델 입력 변수의 통계적 정보, 데이터 기반 혹은 물리 기반 모델링에 필요한 모델링 정보, 시스템 이상 상태에 대한 물리적 사전 지식이 포함됩니다. 많은 경우, 주어진 사전 정보가 충분하지 않은 상황에서 디지털 트윈을 활용한 의사 결정의 신뢰성 문제가 발생합니다. 통계적 모델 보정 및 갱신 방법은 불충분한 사전 정보 하에서 디지털 트윈 분석을 검증 및 고도화하는 데 사용할 수 있습니다. 본 박사 학위 논문은 사전 정보가 부족한 상황에서 융합형 디지털 트윈을 구축하기 위해 모델 보정 및 갱신에서 세 가지 필수 및 관련 연구 분야를 발전시키는 것을 목표로 합니다. 유효한 디지털 트윈 모델을 구축하기 위해서는 다양한 운행 조건에서 충분한 관측 데이터와 시스템 형상, 재료 속성, 작동 조건과 같은 사전 지식이 필요합니다. 그러나 복잡한 엔지니어링 시스템에서는 모델 구축을 위한 사전 정보를 얻기가 어렵습니다. 첫번째 연구에서는 모델 구축에 필요한 사전 지식 부족 시에도 활용 가능한 데이터 기반 동적 모델 갱신 방법을 제안합니다. 제안된 신호 전 처리를 사용하여 관측된 신호에서 시스템 이상 감지를 위한 시간-주파수 영역 특성을 추출합니다. 다양한 작동 조건에서의 시스템 구동 상태를 예측하기 위해 부분 공간 상태 공간 시스템 식별 방법을 이용하여 상태 공간 모델을 구축합니다. 시스템 작동 조건은 시스템 모델의 매개변수화된 입력 신호로 정의됩니다. 다음으로, 신호 관측 시점에서의 시스템 작동 조건과 이상 상태를 추정하기 위해 입력 신호 매개변수는 기준 신호와 관측 신호의 오차를 최소화하도록 갱신됩니다. 모델 입력 변수의 통계적 정보 부족할 경우 최적화 기반 통계 모델 보정을 통해 미지 입력 변수를 추정하여 모델의 예측 능력을 향상시킬 수 있습니다. 최적화 기반 통계 모델 보정은 가상 모델의 예측 응답과 실제 시스템의 관측 응답 간의 통계적 유사성을 최대화하여 모델에 존재하는 미지 입력 변수의 통계적 모수를 추정하는 최적화 문제로 공식화 됩니다. 이때 보정 척도는 통계적 유사성을 정량화하는 목적 함수로 정의됩니다. 두 번째 연구에서는 모델 보정의 정확도와 효율성을 높이기 위해 통계적 상관관계를 고려한 새로운 보정 메트릭인 Marginal Probability and Correlation Residual (MPCR)을 제안합니다. MPCR의 기본 아이디어는 출력 응답 간의 통계적 상관 관계를 고려하면서 다 변량 결합 확률 분포를 수치적 계산 비용이 낮은 다중 주변 확률 분포로 분해하는 것입니다. 디지털 트윈을 이용하여 고장 상태에 대한 사전 지식 부재한 공학 시스템의 고장 상태를 예측하기 위해, 제조 및 실험 조건의 불확실성들이 고려되어야 합니다. 세 번째 연구 방향은 고장 상태에 대한 사전 지식이 부재한 시스템의 피로 균열 시작 및 성장을 추정하기 위한 융합형 디지털 트윈 접근 방식을 제안하였습니다. 본 연구에서는 피로 균열의 시작과 성장을 추정하기 위해 두 가지 기술: (i) 통계적 모델 보정과 (ii) 확률적 요소 갱신을 제안합니다. 통계 모델 보정에서는 균열 시작 조건과 관련된 관찰된 응답을 기반으로 제조 및 실험 조건의 불확실성을 나타내는 입력 변수의 통계적 매개변수를 추정합니다. 통계적 보정을 통해 불확실성을 고려한 확률론적 물리 기반 해석을 통해 균열 시작 및 성장을 나타내는 주요 취약 요소를 예측할 수 있습니다. 확률적 요소 갱신에서는 시스템의 피로 균열 시작 및 성장을 추정하기 위해 균열 성장 조건에서 관찰된 응답을 이용한 최대 우도 법을 갱신 기준으로 모델을 갱신합니다.Digital Twin technology, a virtual representation of the physical entity, has been explored toward providing a solution that could support engineering decisions, such as design, manufacturing, and system health management. Digital twin approaches can be divided into three categories: 1) data-driven, 2) physics-based, and 3) hybrid approaches. The hybrid digital twin is recognized as a promising solution for reliable engineering decisions based on the observed data because it utilizes both the data-driven and physics-based models to overcome the disadvantages of these two approaches. However, the applicability of the digital twin approach has been limited by a lack of prior information. The prior information includes the statistics of model input parameters, required information for (data-driven, physics-based, and hybrid) modeling, and prior knowledge about system failure. Now, a question of fundamental importance arises how to help decision-making using a digital twin under a given insufficient prior information. Statistical model calibration and updating can be used to validate the digital twin analysis under insufficient prior information. In order to build a hybrid digital twin under insufficient prior information, this doctoral dissertation aims the investigation on three co-related research areas in model calibration and updating: Research Thrust 1 – Data-driven dynamic model updating for anomaly detection with an insufficient prior information Research Thrust 2 – A new calibration metric formulation considering the statistical correlation Research Thrust 3 – Hybrid model calibration and updating considering system failure A sufficient prior knowledge such as observed data in various conditions, geometry, material properties, and operating conditions for data-driven / physics-based modeling are required to build a valid digital twin model. However, the prior information for modeling is hard to obtain for complex engineering system. Research Thrust 1 proposes Data-driven dynamic model updating for anomaly detection with insufficient prior knowledge. The time-frequency domain features are extracted from the observed signal using signal pre-processing. The state-space model is driven by a numerical algorithm for subspace state-space system identification (N4SID) to predict the extracted features under different operating conditions. In the model, the operating condition is defined as a parameterized input signal of a system model. Next, the input signal parameters are updated to minimize the prediction error that quantify the discrepancy between the target observed signal and reference model prediction. Optimization-based statistical model calibration (OBSMC) can be applied to estimate unknown input parameters of the digital twin. In OBSMC, the unknown statistical parameters of input variables associated with a digital twin model are inferred by maximizing the statistical similarity between predicted and observed output responses. A calibration metric is defined as the objective function to be maximized that quantifies statistical similarity. Research Thrust 2 proposes a new calibration metric: Marginal Probability and Correlation Residual (MPCR), to improve the accuracy and efficiency of model calibration considering statistical correlation. The foundational idea of the MPCR is to decompose a multivariate joint probability distribution into multiple marginal probability distributions while considering the statistical correlation between output responses. In order to diagnose and predict the system failure of a complex engineering system without prior knowledge about system failure using the digital twin, uncertainties in manufacturing and test conditions must be taken into account. Research Thrust 3 proposed a hybrid digital twin approach for estimating fatigue crack initiation and growth considering those uncertainties. The proposed approach for estimating fatigue crack initiation and growth is based on two techniques; (i) statistical model calibration and (ii) probabilistic element updating. In statistical model calibration, statistical parameters of input variables that indicate uncertainties in manufacturing and test conditions are estimated based on the observed response related to the crack initiation condition. Further, probabilistic analysis using estimated statistical parameters can predict possible critical elements that indicate crack initiation and growth. In probabilistic element updating procedures, the possible crack initiation and growth element is updated based on the Bayesian criteria using observed responses related to the crack growth condition.Abstract i List of Tables ix List of Figures xi Nomenclatures xvi Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Research Scope and Overview 4 1.3 Dissertation Layout 7 Chapter 2 Literature Review 9 2.1 Digital Twin Formulation 9 2.1.1 Data-driven Digital Twin 10 2.1.2 Physics-based Digital Twin 13 2.1.3 Hybrid Digital Twin 17 2.2 Digital Twin Calibration & Updating 18 2.2.1 Optimization-based Statistical Model Calibration 19 2.2.2 Parameter Estimation using Kalman/ Particle filter 24 2.2.3 Summary and Discussion 27 Chapter 3 Data-driven Dynamic Model Updating for Anomaly Detection with an Insufficient Prior Information 28 3.1 System Description of On-Load Tap Changer 30 3.2 Data-driven Dynamic Model Updating for Anomaly Detection with an Insufficient Prior Information 34 3.2.1 Preprocessing of Vibration Signal 37 3.2.2 Reference Model Formulation using N4SID 39 3.2.3 Optimization-based Parameter Updating 43 3.3 Case Study 45 3.3.1 Case Study 1: (Numerical) Vibration Analysis using Parameter Varying Cantilever Beam and Multi-DOF model 45 3.3.2 Case Study 2: Vibration Signal of On Load Tap Changer in Power Transformer 54 3.4 Summary and Discussion 59 Chapter 4 A New Calibration Metric that Considers Statistical Correlation : Marginal Probability and Correlation Residuals 61 4.1 Statistical correlation issue in calibration metric formulation 63 4.1.1 What happens if the statistical correlation is neglected in model calibration? 63 4.1.2 Comments on existing calibration metrics in terms of the statistical correlation 66 4.2 Proposed Method: Marginal probability and correlation residuals (MPCR) 69 4.3 Case Studies 73 4.3.1 Mathematical example 1: Bivariate output responses (Statistical correlation issue 73 4.3.2 Mathematical example 2: Multivariate output responses (Curse of dimensionality issue) 78 4.3.3 Engineering example 1: Modal analysis of a beam structure with uncertain rotational stiffness boundary conditions (Scale issue) 87 4.3.4 Engineering example 2: Crashworthiness of vehicle side impact (High dimensional & nonlinear problem) 93 4.4 Summary and Discussion 101 Chapter 5 Hybrid Model Calibration and Updating for Estimating System Failure 103 5.1 Brief Review of Digital Twin Approaches for Estimating Crack Initiation & Growth 105 5.2 Proposed Digital Twin Approach : Hybrid Model Calibration & Updating 109 5.2.1 Statistical Model Calibration using a Data-driven Twin 110 5.2.2 Probabilistic Element Updating with a Physics-based Twin 114 5.3 Case Study: Automotive Sub-Frame Structure 118 5.3.1 Experimental Fatigue Test 118 5.3.2 Statistical Model Calibration using a Data-driven Twin 121 5.3.3 Element Updating with a Physics-based Twin 127 5.4 Summary and Discussion 131 Chapter 6 Conclusions 133 6.1 Contributions and Significance 133 6.2 Suggestions for Future Research 135 References 138 국문 초록 155박

Physics-based approach to detect metal-metal contact in the hydrodynamic bearing of a planetary transmission

Health condition monitoring, commonly referred as Integrated Vehicle Health Management (IVHM) for fleets or vehicles, studies the current and future health state of a system. Health monitoring techniques based on data driven approaches have proven successful in several areas and are easily scalable; however they do not rely on the understating of the physics of failure; whereas Physics-based Model (PbM) approaches require expert knowledge of the failure modes and are based on the understanding of the component behaviour and degradation mechanisms. The development of IVHM is particularly challenging for legacy aircraft due to the restrictive regulations of the aerospace industry. This thesis proposes a novel PbM technique to detect metal-metal contact in hydrodynamic bearings. The planetary transmission of an aircraft’s Integrated Drive Generator (IDG) is used as a case study. Research on the detection of metal-metal contact in hydrodynamic bearings has focused on data driven approaches using vibration or acoustic emissions rather than on PbMs. The proposed technique estimates metal-metal contact by modelling the physical phenomena involved in the failure mechanism and only the speed, load and temperature are required as inputs, all of them available in the IDG and not requiring any additional sensors. The study of metal-metal in hydrodynamic bearings in the field of tribology has focused on mixed lubrication models of the whole bearing, or computational models accounting for local effect under the hydrodynamic lubrication region. In addition to the IVHM technique, this thesis contributes to the field of tribology by proposing a computational mixed lubrication model capable of studying metal-metal contact locally along the lubricated surface of the bearing. Experimental results of a plain journal bearing have been used to validate the PbM and a replica of the transmission of the IDG has been tested to evaluate the effectiveness of the proposed technique at detecting metal-metal contact

Accommodating maintenance in prognostics

Error on title page - year of award is 2021Steam turbines are an important asset of nuclear power plants, and are required to operate reliably and efficiently. Unplanned outages have a significant impact on the ability of the plant to generate electricity. Therefore, condition-based maintenance (CBM) can be used for predictive and proactive maintenance to avoid unplanned outages while reducing operating costs and increasing the reliability and availability of the plant. In CBM, the information gathered can be interpreted for prognostics (the prediction of failure time or remaining useful life (RUL)). The aim of this project was to address two areas of challenges in prognostics, the selection of predictive technique and accommodation of post-maintenance effects, to improve the efficacy of prognostics. The selection of an appropriate predictive algorithm is a key activity for an effective development of prognostics. In this research, a formal approach for the evaluation and selection of predictive techniques is developed to facilitate a methodic selection process of predictive techniques by engineering experts. This approach is then implemented for a case study provided by the engineering experts. Therefore, as a result of formal evaluation, a probabilistic technique the Bayesian Linear Regression (BLR) and a non-probabilistic technique the Support Vector Regression (SVR) were selected for prognostics implementation. In this project, the knowledge of prognostics implementation is extended by including post maintenance affects into prognostics. Maintenance aims to restore a machine into a state where it is safe and reliable to operate while recovering the health of the machine. However, such activities result in introduction of uncertainties that are associated with predictions due to deviations in degradation model. Thus, affecting accuracy and efficacy of predictions. Therefore, such vulnerabilities must be addressed by incorporating the information from maintenance events for accurate and reliable predictions. This thesis presents two frameworks which are adapted for probabilistic and non-probabilistic prognostic techniques to accommodate maintenance. Two case studies: a real-world case study from a nuclear power plant in the UK and a synthetic case study which was generated based on the characteristics of a real-world case study are used for the implementation and validation of the frameworks. The results of the implementation hold a promise for predicting remaining useful life while accommodating maintenance repairs. Therefore, ensuring increased asset availability with higher reliability, maintenance cost effectiveness and operational safety.Steam turbines are an important asset of nuclear power plants, and are required to operate reliably and efficiently. Unplanned outages have a significant impact on the ability of the plant to generate electricity. Therefore, condition-based maintenance (CBM) can be used for predictive and proactive maintenance to avoid unplanned outages while reducing operating costs and increasing the reliability and availability of the plant. In CBM, the information gathered can be interpreted for prognostics (the prediction of failure time or remaining useful life (RUL)). The aim of this project was to address two areas of challenges in prognostics, the selection of predictive technique and accommodation of post-maintenance effects, to improve the efficacy of prognostics. The selection of an appropriate predictive algorithm is a key activity for an effective development of prognostics. In this research, a formal approach for the evaluation and selection of predictive techniques is developed to facilitate a methodic selection process of predictive techniques by engineering experts. This approach is then implemented for a case study provided by the engineering experts. Therefore, as a result of formal evaluation, a probabilistic technique the Bayesian Linear Regression (BLR) and a non-probabilistic technique the Support Vector Regression (SVR) were selected for prognostics implementation. In this project, the knowledge of prognostics implementation is extended by including post maintenance affects into prognostics. Maintenance aims to restore a machine into a state where it is safe and reliable to operate while recovering the health of the machine. However, such activities result in introduction of uncertainties that are associated with predictions due to deviations in degradation model. Thus, affecting accuracy and efficacy of predictions. Therefore, such vulnerabilities must be addressed by incorporating the information from maintenance events for accurate and reliable predictions. This thesis presents two frameworks which are adapted for probabilistic and non-probabilistic prognostic techniques to accommodate maintenance. Two case studies: a real-world case study from a nuclear power plant in the UK and a synthetic case study which was generated based on the characteristics of a real-world case study are used for the implementation and validation of the frameworks. The results of the implementation hold a promise for predicting remaining useful life while accommodating maintenance repairs. Therefore, ensuring increased asset availability with higher reliability, maintenance cost effectiveness and operational safety

AGENT AUTONOMY APPROACH TO PROBABILISTIC PHYSICS-OF-FAILURE MODELING OF COMPLEX DYNAMIC SYSTEMS WITH INTERACTING FAILURE MECHANISMS

A novel computational and inference framework of the physics-of-failure (PoF) reliability modeling for complex dynamic systems has been established in this research. The PoF-based reliability models are used to perform a real time simulation of system failure processes, so that the system level reliability modeling would constitute inferences from checking the status of component level reliability at any given time. The "agent autonomy" concept is applied as a solution method for the system-level probabilistic PoF-based (i.e. PPoF-based) modeling. This concept originated from artificial intelligence (AI) as a leading intelligent computational inference in modeling of multi agents systems (MAS). The concept of agent autonomy in the context of reliability modeling was first proposed by M. Azarkhail [1], where a fundamentally new idea of system representation by autonomous intelligent agents for the purpose of reliability modeling was introduced. Contribution of the current work lies in the further development of the agent anatomy concept, particularly the refined agent classification within the scope of the PoF-based system reliability modeling, new approaches to the learning and the autonomy properties of the intelligent agents, and modeling interacting failure mechanisms within the dynamic engineering system. The autonomous property of intelligent agents is defined as agent's ability to self-activate, deactivate or completely redefine their role in the analysis. This property of agents and the ability to model interacting failure mechanisms of the system elements makes the agent autonomy fundamentally different from all existing methods of probabilistic PoF-based reliability modeling. 1. Azarkhail, M., "Agent Autonomy Approach to Physics-Based Reliability Modeling of Structures and Mechanical Systems", PhD thesis, University of Maryland, College Park, 2007