Data-driven extraction and analysis of repairable fault trees from time series data

Fault tree analysis is a probability-based technique for estimating the risk of an undesired top event, typically a system failure. Traditionally, building a fault tree requires involvement of knowledgeable experts from different fields, relevant for the system under study. Nowadays’ systems, however, integrate numerous Internet of Things (IoT) devices and are able to generate large amounts of data that can be utilized to extract fault trees that reflect the true fault-related behavior of the corresponding systems. This is especially relevant as systems typically change their behaviors during their lifetimes, rendering initial fault trees obsolete. For this reason, we are interested in extracting fault trees from data that is generated from systems during their lifetimes. We present DDFTAnb algorithm for learning fault trees of systems using time series data from observed faults, enhanced with Naïve Bayes classifiers for estimating the future fault-related behavior of the system for unobserved combinations of basic events, where the state of the top event is unknown. Our proposed algorithm extracts repairable fault trees from multinomial time series data, classifies the top event for the unseen combinations of basic events, and then uses proxel-based simulation to estimate the system’s reliability. We, furthermore, assess the sensitivity of our algorithm to different percentages of data availabilities. Results indicate DDFTAnb’s high performance for low levels of data availability, however, when there are sufficient or high amounts of data, there is no need for classifying the top event

Applications of Bayesian networks and Petri nets in safety, reliability, and risk assessments: A review

YesSystem safety, reliability and risk analysis are important tasks that are performed throughout the system lifecycle to ensure the dependability of safety-critical systems. Probabilistic risk assessment (PRA) approaches are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to, Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). Growing complexity of modern systems and their capability of behaving dynamically make it challenging for classical PRA techniques to analyse such systems accurately. For a comprehensive and accurate analysis of complex systems, different characteristics such as functional dependencies among components, temporal behaviour of systems, multiple failure modes/states for components/systems, and uncertainty in system behaviour and failure data are needed to be considered. Unfortunately, classical approaches are not capable of accounting for these aspects. Bayesian networks (BNs) have gained popularity in risk assessment applications due to their flexible structure and capability of incorporating most of the above mentioned aspects during analysis. Furthermore, BNs have the ability to perform diagnostic analysis. Petri Nets are another formal graphical and mathematical tool capable of modelling and analysing dynamic behaviour of systems. They are also increasingly used for system safety, reliability and risk evaluation. This paper presents a review of the applications of Bayesian networks and Petri nets in system safety, reliability and risk assessments. The review highlights the potential usefulness of the BN and PN based approaches over other classical approaches, and relative strengths and weaknesses in different practical application scenarios.This work was funded by the DEIS H2020 project (Grant Agreement 732242)

Uncertainty in Engineering

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners

A Bayesian Network methodology for railway risk, safety and decision support

For railways, risk analysis is carried out to identify hazardous situations and their consequences. Until recently, classical methods such as Fault Tree Analysis (FTA) and Event Tree Analysis (ETA) were applied in modelling the linear and logically deterministic aspects of railway risks, safety and reliability. However, it has been proven that modern railway systems are rather complex, involving multi-dependencies between system variables and uncertainties about these dependencies. For train derailment accidents, for instance, high train speed is a common cause of failure; slip and failure of brake applications are disjoint events; failure dependency exists between the train protection and warning system and driver errors; driver errors are time dependent and there is functional uncertainty in derailment conditions. Failing to incorporate these aspects of a complex system leads to wrong estimations of the risks and safety, and, consequently, to wrong management decisions. Furthermore, a complex railway system integrates various technologies and is operated in an environment where the behaviour and failure modes of the system are difficult to model using probabilistic techniques. Modelling and quantification of the railway risk and safety problems that involve dependencies and uncertainties such as mentioned above are complex tasks. Importance measures are useful in the ranking of components, which are significant with respect to the risk, safety and reliability of a railway system. The computation of importance measures using FTA has limitation for complex railways. ALARP (As Low as Reasonably Possible) risk acceptance criteria are widely accepted as ’\'best practice’’ in the railways. According to the ALARP approach, a tolerable region exists between the regions of intolerable and negligible risks. In the tolerable region, risk is undertaken only if a benefit is desired. In this case, one needs to have additional criteria to identify the socio-economic benefits of adopting a safety measure for railway facilities. The Life Quality Index (LQI) is a rational way of establishing a relation between the financial resources utilized to improve the safety of an engineering system and the potential fatalities that can be avoided by safety improvement. This thesis shows the application of the LQI approach to quantifying the social benefits of a number of safety management plans for a railway facility. We apply Bayesian Networks and influence diagrams, which are extensions of Bayesian Networks, to model and assess the life safety risks associated with railways. Bayesian Networks are directed acyclic probabilistic graphical models that handle the joint distribution of random variables in a compact and flexible way. In influence diagrams, problems of probabilistic inference and decision making – based on utility functions – can be combined and optimized, especially, for systems with many dependencies and uncertainties. The optimal decision, which maximizes the total benefits to society, is obtained. In this thesis, the application of Bayesian Networks to the railway industry is investigated for the purpose of improving modelling and the analysis of risk, safety and reliability in railways. One example application and two real world applications are presented to show the usefulness and suitability of the Bayesian Networks for the quantitative risk assessment and risk-based decision support in reference to railways.:ACKNOWLEDGEMENTS IV ABSTRACT VI ZUSAMMENFASSUNG VIII LIST OF FIGURES XIV LIST OF TABLES XVI CHAPTER 1: Introduction 1 1.1 Need to model and quantify the causes and consequences of hazards on railways 1 1.2 State-of-the art techniques in the railway 2 1.3 Goals and scope of work 4 1.4 Existing work 6 1.5 Outline of the thesis 7 CHAPTER 2: Methods for safety and risk analysis 10 2.1 Introduction 10 2.1.1 Simplified risk analysis 12 2.1.2 Standard risk analysis 12 2.1.3 Model-based risk analysis 12 2.2 Risk Matrix 14 2.2.1 Determine the possible consequences 14 2.2.2 Likelihood of occurrence 15 2.2.3 Risk scoring matrix 15 2.3 Failure Modes & Effect Analysis – FMEA 16 2.3.1 Example application of FMEA 17 2.4 Fault Tree Analysis – FTA 19 2.5 Reliability Block Diagram – RBD 22 2.6 Event Tree Analysis – ETA 24 2.7 Safety Risk Model – SRM 25 2.8 Markov Model – MM 27 2.9 Quantification of expected values 31 2.9.1 Bayesian Analysis – BA 35 2.9.2 Hazard Function – HF 39 2.9.3 Monte Carlo (MC) Simulation 42 2.10 Summary 46 CHAPTER 3: Introduction to Bayesian Networks 48 3.1 Terminology in Bayesian Networks 48 3.2 Construction of Bayesian Networks 49 3.3 Conditional independence in Bayesian Networks 51 3.4 Joint probability distribution in Bayesian Networks 52 3.5 Probabilistic Inference in Bayesian Networks 53 3.6 Probabilistic inference by enumeration 54 3.7 Probabilistic inference by variable elimination 55 3.8 Approximate inference for Bayesian Networks 57 3.9 Dynamic Bayesian Networks 58 3.10 Influence diagrams (IDs) 60 CHAPTER 4: Risk acceptance criteria and safety targets 62 4.1 Introduction 62 4.2 ALARP (As Low As Reasonably Possible) criteria 62 4.3 MEM (Minimum Endogenous Mortality) criterion 63 4.4 MGS (Mindestens Gleiche Sicherheit) criteria 64 4.5 Safety Integrity Levels (SILs) 65 4.6 Importance Measures (IMs) 66 4.7 Life Quality Index (LQI) 68 4.8 Summary 72 CHAPTER 5: Application of Bayesian Networks to complex railways: A study on derailment accidents 73 5.1 Introduction 73 5.2 Fault Tree Analysis for train derailment due to SPAD 74 5.2.1 Computation of importance measures using FTA 75 5.3 Event Tree Analysis (ETA) 78 5.4 Mapping Fault Tree and Event Tree based risk model to Bayesian Networks 79 5.4.1 Computation of importance measures using Bayesian Networks 81 5.5 Risk quantification 82 5.6 Advanced aspects of example application 83 5.6.1 Advanced aspect 1: Common cause failures 83 5.6.2 Advanced aspect 2: Disjoint events 84 5.6.3 Advanced aspect 3: Multistate system and components 84 5.6.4 Advanced aspect 4: Failure dependency 85 5.6.5 Advanced aspect 5: Time dependencies 85 5.6.6 Advanced aspect 6: Functional uncertainty and factual knowledge 85 5.6.7 Advanced aspect 7: Uncertainty in expert knowledge 86 5.6.8 Advanced aspect 8: Simplifications and dependencies in Event Tree Analysis 86 5.7 Implementation of the advanced aspects of the train derailment model using Bayesian Networks. 88 5.8 Results and discussions 92 5.9 Summary 93 CHAPTER 6: Bayesian Networks for risk-informed safety requirements for platform screen doors in railways 94 6.1 Introduction 94 6.2 Components of the risk-informed safety requirement process for Platform Screen Door system in a mega city 97 6.2.1 Define objective and methodology 97 6.2.2 Familiarization of system and information gathering 97 6.2.3 Hazard identification and hazard classification 97 6.2.4 Hazard scenario analysis 98 6.2.5 Probability of occurrence and failure data 99 6.2.6 Quantification of the risks 105 6.2.6.1. Tolerable risks 105 6.2.6.2. Risk exposure 105 6.2.6.3. Risk assessment 106 6.3 Summary 107 CHAPTER 7: Influence diagrams based decision support for railway level crossings 108 7.1 Introduction 108 7.2 Level crossing accidents in railways 109 7.3 A case study of railway level crossing 110 7.4 Characteristics of the railway level crossing under investigation 111 7.5 Life quality index applied to railway level crossing risk problem 115 7.6 Summary 119 CHAPTER 8: Conclusions and outlook 120 8.1 Summary and important contributions 120 8.2 Originality of the work 122 8.3 Outlook 122 BIBLIOGRAPHY 124 APPENDIX 1 13

Efficient Reliability Modelling & Analysis of Complex Systems with Application to Nuclear Power Plant Safety

Nuclear power may be our best chance at a permanent solution to the world's energy challenges, owing to its sustainability and environmental friendliness. However, it also poses a great risk to life, property, and the economy, given the possibility of severe accidents during its generation. These accidents are a result of the susceptibility of the generating plants to component failure, human error, extreme environmental events, targeted attacks, and natural disasters. Given the complexity and high interconnectivity of the systems in question, a small glitch, otherwise known as an initiating event, could cascade to catastrophic consequences. It is, therefore, vital that the vulnerability of a plant to these glitches and their ensuing consequences be ascertained, to ensure that the appropriate mitigating actions are taken. The reliability of a system is the likelihood that it survives a defined period and its availability is the likelihood of it being capable of performing its required functions on demand. These quantities are important to a nuclear power plant's safety because, a nuclear power plant by default is equipped with safety systems to inhibit the propagation of an initiating event. An accident ensues if the safety systems required to mitigate some initiating event are unavailable or incapacitated by the initiating event. It is, therefore, easy to see that the reliability, as well as the availability of these systems, shape the safety of the plant. These crucial quantities, currently, are estimated using legacy techniques like static fault and event tree analyses or their derivatives. Despite their popularity and widely acclaimed success, these legacy techniques lack the flexibility to implement fully the operational dynamics of the majority of systems. Most importantly, their ease of application deteriorates with increasing system size and complexity, such that the analyst is often forced to make unrealistic assumptions. These unrealistic assumptions sometimes compromise the accuracy of the results obtained and subsequently, the quality of the risk management decisions reached. Their inadequacy is often amplified if the system is composed of multi-state components or characterised by epistemic uncertainties, induced by vague or imprecise data. The ideal approach, therefore, should be sufficiently robust to not necessitate unrealistic assumptions but flexible enough to accommodate realistic system attributes, while guaranteeing accuracy. This dissertation provides a detailed account of a series of computationally efficient system reliability analysis techniques proposed to address the limitations of the existing probabilistic risk assessment approaches. The proposed techniques are based mainly, on an advanced hybrid event-driven Monte Carlo simulation technique that invokes load-flow principles to resolve, intuitively, the difficulties associated with the topological complexity of systems and the multi-state attributes of their components. In addition to their intuitiveness and relative completeness, a key advantage of the proposed techniques is their general applicability. They have been applied, for instance, to a variety of problems, ranging from the production availability of an offshore oil installation and the maintenance strategy optimization of the IEEE-24 bus test system to the probabilistic risk assessment of station blackout accidents at the Maanshan nuclear power plant in Taiwan. The proposed techniques, therefore, should influence robust decisions in the risk management of not only nuclear power plants but other critical systems as well. They have been incorporated into the open-source uncertainty quantification tool, OpenCossan, to render them readily available to industry and other researchers

Uncertainty in Engineering

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners

Propuesta de herramientas basadas en fiabilidad para el modelado de sistemas productivos complejos.

La importancia de los costes de mantenimiento en procesos intensivos en el uso de activos, puede alcanzar hasta el 40% de los costes de producción, como, por ejemplo, en los procesos de la gran minería del Cobre (Consejo Minero, 2015). Dada su relevancia, resulta indispensable un estudio acabado de cada uno de los procesos, bajo un enfoque de mantenimiento y de coste de ciclo de vida. El estudio y modelado de fiabilidad, es la piedra angular para un análisis de mantenimiento, ya que se relaciona directamente con el comportamiento de fallos de cada uno de los componentes hasta establecer la relación de dependencia dinámica de cada uno de los equipos en estudio, aspectos que son fundamentales para evaluar criticidad y proyectar costes en fases de inversión y operación (CAPEX y OPEX) (Parra et al., 2012). El modelado de fiabilidad, basa su análisis en la ocurrencia de los fallos de un equipo, a través de distribuciones probabilísticas que permiten ajustar los tiempos de buen funcionamiento, las que dan origen a la función de fiabilidad. Dentro de las distribuciones más utilizadas, están la Exponencial y la Weibull, que permiten modelar el comportamiento de un componente durante todo su ciclo de vida; con fases de rodaje, vida útil y degaste, a través de la curva de la bañera (Dhillon, 2006). El modelado de fiabilidad por componentes se hace extensivo a procesos productivos, lo que permite conocer la fiabilidad por componente y sistemas en su conjunto. Sobre este punto, existen diversas metodologías como Reliability Block Diagram (RBD) (Rausand and Hoyland, 2003; Guo and Yang, 2007), Cadenas de Markov (Welte, 2009), Árboles de Fallo (Rauzy et al., 2007), Gráficos de Fiabilidad (Distefano and Puliafito, 2009), Redes de Petri (PNs) (Volovoi, 2014), entre otros. No obstante a lo anterior, existen relaciones de equipos que, dada su configuración, no es posible modelarlas con las técnicas tradicionales. La realidad de los procesos industriales evidencia que una mayor flexibilidad en dichos procesos mejora la productividad, la eficiencia del propio proceso y, en definitiva, los resultados generales de la empresa. En ese contexto, los sistemas dinámicos alcanzan una gran importancia en el modelado de los procesos productivos. Los sistemas dinámicos son aquellos que cambian con el tiempo, es decir, pueden variar sus relaciones de dependencia con el entorno o bien, su habilidad de funcionar en diversos escenarios. El tema de investigación principal de la presente Tesis Doctoral, presentado en el formato por Compendio de Publicaciones, se desarrolla en la revisión y proposición de las técnicas de modelado de fiabilidad, para la evaluación de impacto de fiabilidad y fallos de elementos individuales que se encuentren inmersos en procesos productivos complejos, permitiendo evaluar la criticidad operacional de cada uno de ellos. La determinación del indicador de criticidad operacional es de vital importancia para la identificación de riesgos operacionales en el interior de los procesos productivos de las empresas, permitiendo facilitar el proceso de toma de decisión de manera efectiva. Actualmente , en la literatura existen diversas investigaciones desarrolladas para identificar los factores que afectan directamente la maximización de beneficios. Estos factores se fundamentan en la consideración empírica de los indicadores de fiabilidad, mantenibilidad y disponibilidad (RAM) (Viveros et al., 2012). Como resultado principal del trabajo de doctorado, se obtienen 3 artículos ISI – JCR y la presentación de 4 artículos en congresos internacionales con proceedings. En cada una de estas publicaciones, el candidato a doctor es el primer autor y su tutor, el segundo. El proyecto de Tesis Doctoral que se presenta, se enmarca dentro de la línea de investigación del grupo Sistemas Inteligentes de Mantenimiento - SIM, perteneciente al Departamento de Organización Industrial y Gestión de Empresas de la Universidad de Sevilla

Developing Methods of Obtaining Quality Failure Information from Complex Systems

The complexity in most engineering systems is constantly growing due to ever-increasing technological advancements. This result in a corresponding need for methods that adequately account for the reliability of such systems based on failure information from components that make up these systems. This dissertation presents an approach to validating qualitative function failure results from model abstraction details. The impact of the level of detail available to a system designer during conceptual stages of design is considered for failure space exploration in a complex system. Specifically, the study develops an efficient approach towards detailed function and behavior modeling required for complex system analyses. In addition, a comprehensive research and documentation of existing function failure analysis methodologies is also synthesized into identified structural groupings. Using simulations, known governing equations are evaluated for components and system models to study responses to faults by accounting for detailed failure scenarios, component behaviors, fault propagation paths, and overall system performance. The components were simulated at nominal states and varying degrees of fault representing actual modes of operation. Information on product design and provisions on expected working conditions of components were used in the simulations to address normally overlooked areas during installation. The results of system model simulations were investigated using clustering analysis to develop an efficient grouping method and measure of confidence for the obtained results. The intellectual merit of this work is the use of a simulation based approach in studying how generated failure scenarios reveal component fault interactions leading to a better understanding of fault propagation within design models. The information from using varying fidelity models for system analysis help in identifying models that are sufficient enough at the conceptual design stages to highlight potential faults. This will reduce resources such as cost, manpower and time spent during system design. A broader impact of the project is to help design engineers identifying critical components, quantifying risks associated with using particular components in their prototypes early in the design process and help improving fault tolerant system designs. This research looks to eventually establishing a baseline for validating and comparing theories of complex systems analysis

An Integrated Framework to Evaluate Off-Nominal Requirements and Reliability of Novel Aircraft Architectures in Early Design

One of the barriers to the development of novel aircraft architectures and technologies is the uncertainty related to their reliability and the safety risk they pose. In the conceptual and preliminary design stages, traditional system safety techniques rely on heuristics, experience, and historical data to assess these requirements. The limitations and off-nominal operational considerations generally postulated during traditional safety analysis may not be complete or correct for new concepts. Additionally, dearth of available reliability data results in poor treatments of epistemic and aleatory uncertainty for novel aircraft architectures. Two performance-based methods are demonstrated to solve the problem of improving the identification and characterization of safety related off-nominal requirements in early design. The problem of allocating requirements to the unit level is solved using a network-based bottom-up analysis algorithm combined with the Critical Flow Method. A Bayesian probability approach is utilized to better deal with epistemic and aleatory uncertainty while assessing unit level failure rates. When combined with a Bayesian decision theoretic approach, it provides a mathematically backed framework for compliance finding under uncertainty. To estimate multi-state reliability of complex systems, this dissertation contributes a modified Monte-Carlo algorithm that uses the Bayesian failure rate posteriors previously generated. Finally, multi-state importance measures are introduced to determine the sensitivity of different hazard severity to unit reliability. The developed tools, techniques, and methods of this dissertation are combined into an integrated framework with the capability to perform trade-studies informed by safety and reliability considerations for novel aircraft architectures in early preliminary design. A test distributed electric propulsion (T-DEP) aircraft inspired by the X-57 is utilized as a test problem to demonstrate this frameworkPh.D