Robust power series algorithm for epistemic uncertainty propagation in Markov chain models

In this article, we develop a new methodology for integrating epistemic uncertainties into the computation of performance measures of Markov chain models. We developed a power series algorithm that allows for combining perturbation analysis and uncertainty analysis in a joint framework. We characterize statistically several performance measures, given that distribution of the model parameter expressing the uncertainty about the exact parameter value is known. The technical part of the article provides convergence result, bounds for the remainder term of the power series, and bounds for the validity region of the approximation. In the algorithmic part of the article, an efficient implementation of the power series algorithm for propagating epistemic uncertainty in queueing models with breakdowns and repairs is discussed. Several numerical examples are presented to illustrate the performance of the proposed algorithm and are compared with the corresponding Monte Carlo simulations ones

基于概率盒演化的时变系统不确定性量化方法研究

为了研究时变系统的不确定性量化和传递问题,提出了一种概率盒演化方法。根据系统的时变规律,获取系统响应的累积分布函数随时间变化的规律。将认知不确定性参数和随机不确定性参数分离在外层和内层,用蒙特卡洛法量化外层的认知不确定性参数,用基于随机配点的非嵌入式混沌多项式法量化内层的随机不确定性参数,通过求取不同时刻系统响应的累积分布函数的上下边界,创建时变概率盒。最后,通过一延时电路性能退化算例,验证了该方法的有效性。研究表明,时变概率盒不仅表征了系统特定时刻的混合不确定性,而且反映了输出响应的时变规律和输出不确定性随时间变化的趋势。国家自然科学基金(Grant No.51505398);;\n国家自然科学基金委员会与中国工程物理研究院联合基金资助(Grant No.U1530122

Probabilistic assessment of performance under uncertain information using a generalised maximum entropy principle

When information about a distribution consists of statistical moments only, a self-consistent approach to deriving a subjective probability density function (pdf) is Maximum Entropy. Nonetheless, the available information may have uncertainty, and statistical moments maybe known only to lie in a certain domain. If Maximum Entropy is used to find the distribution with the largest entropy whose statistical moments lie within the domain, the information at only a single point in the domain would be used and other information would be discarded. In this paper, the bounded information on statistical moments is used to construct a family of Maximum Entropy distributions, leading to an uncertain probability function. This uncertainty description enables the investigation of how the uncertainty in the probabilistic assignment affects the predicted performance of an engineering system with respect to safety, quality and design constraints. It is shown that the pdf which maximizes (or equivalently minimizes) an engineering metric is potentially different from the pdf which maximizes the entropy. The feasibility of the proposed uncertainty model is shown through its app lication to: (i) fatigue failure analysis of a structural joint; (ii) evaluation of the probability that a response variable of an engineering system exceeds a critical level, and (iii) random vibration

Investigation of robust optimization and evidence theory with stochastic expansions for aerospace applications under mixed uncertainty

One of the primary objectives of this research is to develop a method to model and propagate mixed (aleatory and epistemic) uncertainty in aerospace simulations using DSTE. In order to avoid excessive computational cost associated with large scale applications and the evaluation of Dempster Shafer structures, stochastic expansions are implemented for efficient UQ. The mixed UQ with DSTE approach was demonstrated on an analytical example and high fidelity computational fluid dynamics (CFD) study of transonic flow over a RAE 2822 airfoil. Another objective is to devise a DSTE based performance assessment framework through the use of quantification of margins and uncertainties. Efficient uncertainty propagation in system design performance metrics and performance boundaries is achieved through the use of stochastic expansions. The technique is demonstrated on: (1) a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems and (2) a multi-disciplinary analysis of a supersonic civil transport. Finally, the stochastic expansions are applied to aerodynamic shape optimization under uncertainty. A robust optimization algorithm is presented for computationally efficient airfoil design under mixed uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions to create surrogate models utilized in the optimization process. To reduce the computational cost, output space mapping technique is implemented to replace the high-fidelity CFD model by a suitably corrected low-fidelity one. The proposed algorithm is demonstrated on the robust optimization of NACA 4-digit airfoils under mixed uncertainties in transonic flow. --Abstract, page iii

Determinism Enhancement and Reliability Assessment in Safety Critical AFDX Networks

RÉSUMÉ AFDX est une technologie basée sur Ethernet, qui a été développée pour répondre aux défis qui découlent du nombre croissant d’applications qui transmettent des données de criticité variable dans les systèmes modernes d’avionique modulaire intégrée (Integrated Modular Avionics). Cette technologie de sécurité critique a été notamment normalisée dans la partie 7 de la norme ARINC 664, dont le but est de définir un réseau déterministe fournissant des garanties de performance prévisibles. En particulier, AFDX est composé de deux réseaux redondants, qui fournissent la haute fiabilité requise pour assurer son déterminisme. Le déterminisme de AFDX est principalement réalisé par le concept de liens virtuels (Virtual Links), qui définit une connexion unidirectionnelle logique entre les points terminaux (End Systems). Pour les liens virtuels, les limites supérieures des délais de bout en bout peuvent être obtenues en utilisant des approches comme calcul réseau, mieux connu sous l’appellation Network Calculus. Cependant, il a été prouvé que ces limites supérieures sont pessimistes dans de nombreux cas, ce qui peut conduire à une utilisation inefficace des ressources et augmenter la complexité de la conception du réseau. En outre, en raison de l’asynchronisme de leur fonctionnement, il existe plusieurs sources de non-déterminisme dans les réseaux AFDX. Ceci introduit un problème en lien avec la détection des défauts en temps réel. En outre, même si un mécanisme de gestion de la redondance est utilisé pour améliorer la fiabilité des réseaux AFDX, il y a un risque potentiel souligné dans la partie 7 de la norme ARINC 664. La situation citée peut causer une panne en dépit des transmissions redondantes dans certains cas particuliers. Par conséquent, l’objectif de cette thèse est d’améliorer la performance et la fiabilité des réseaux AFDX. Tout d’abord, un mécanisme fondé sur l’insertion de trames est proposé pour renforcer le déterminisme de l’arrivée des trames au sein des réseaux AFDX. Parce que la charge du réseau et la bande passante moyenne utilisée augmente due à l’insertion de trames, une stratégie d’agrégation des Sub-Virtual Links est introduite et formulée comme un problème d’optimisation multi-objectif. En outre, trois algorithmes ont été développés pour résoudre le problème d’optimisation multi-objectif correspondant. Ensuite, une approche est introduite pour incorporer l’analyse de la performance dans l’évaluation de la fiabilité en considérant les violations des délais comme des pannes.----------ABSTRACT AFDX is an Ethernet-based technology that has been developed to meet the challenges due to the growing number of data-intensive applications in modern Integrated Modular Avionics systems. This safety critical technology has been standardized in ARINC 664 Part 7, whose purpose is to define a deterministic network by providing predictable performance guarantees. In particular, AFDX is composed of two redundant networks, which provide the determinism required to obtain the desired high reliability. The determinism of AFDX is mainly achieved by the concept of Virtual Link, which defines a logical unidirectional connection from one source End System to one or more destination End Systems. For Virtual Links, the end-to-end delay upper bounds can be obtained by using the Network Calculus. However, it has been proved that such upper bounds are pessimistic in many cases, which may lead to an inefficient use of resources and aggravate network design complexity. Besides, due to asynchronism, there exists a source of non-determinism in AFDX networks, namely frame arrival uncertainty in a destination End System. This issue introduces a problem in terms of real-time fault detection. Furthermore, although a redundancy management mechanism is employed to enhance the reliability of AFDX networks, there still exist potential risks as pointed out in ARINC 664 Part 7, which may fail redundant transmissions in some special cases. Therefore, the purpose of this thesis is to improve the performance and the reliability of AFDX networks. First, a mechanism based on frame insertion is proposed to enhance the determinism of frame arrival within AFDX networks. As the network load and the average bandwidth used by a Virtual Link increase due to frame insertion, a Sub-Virtual Link aggregation strategy, formulated as a multi-objective optimization problem, is introduced. In addition, three algorithms have been developed to solve the corresponding multi-objective optimization problem. Next, an approach is introduced to incorporate performance analysis into reliability assessment by considering delay violations as failures. This allowed deriving tighter probabilistic upper bounds for Virtual Links that could be applied in AFDX network certification. In order to conduct the necessary reliability analysis, the well-known Fault-Tree Analysis technique is employed and Stochastic Network Calculus is applied to compute the upper bounds with various probability limits

Networked Miscommunication: The Relationship Between Communication Networks, Misunderstandings, and Organizational Performance

In this dissertation, I introduce and define the concept of networked miscommunication – unintentional, aggregated effects of communication practices throughout an organization – and demonstrate its deleterious impacts on organizational performance through case studies and models. While “miscommunication” features prominently in accounts of high-profile complex system accidents, researchers have yet to demonstrate how communicative misunderstandings degrade organizational performance more generally. I show that while miscommunication costs can result from misunderstandings distributed throughout an organization’s communication networks, they also arise whenever a networked communicative interaction falls short of a desired organizational outcome. In my framework, miscommunication is not merely mistakes; practitioners can also be strategically ambiguous. Competitive environments make strategic ambiguity more likely than do cooperative organizational cultures. I therefore hypothesize that fostering cooperation over competition can improve organizational performance while also increasing equity. I begin by exploring the responsibilities organizations bear as they develop, operate, and manage the complex systems that pervade modern society – whether those systems involve manufacturing, healthcare, or finance. Complex systems contain large collections of highly interacting, tightly coupled elements, making them susceptible to “normal accidents” such as Three Mile Island (Perrow, 1981, 2011). Organizations that suppress dissent, as was the case with the Challenger Space Shuttle disaster, will be more prone to these accidents (Vaughan, 1997). More recently, the 2018 Hawaii Ballistic Missile False Alarm highlights how misunderstandings in organizational communication networks affect complex system performance and hence organizational performance. This last type of failure is the primary focus of this dissertation. After a review of the literature on communication and miscommunication, I dually define miscommunication: pragmatically as communication problems that negatively affect goal attainment, and integratively as misunderstandings that prevent participants from balancing their values. I then define networked miscommunication and present three studies that I use to identify a surprising and impactful type of unintentional communicative misunderstandings concerning the meaning of the term “estimates.” I demonstrate how heterogeneous meanings of the word estimate both do and don’t affect organizational performance. My first study reveals that expert practicing engineers use cognitive heuristics and strategic ambiguity to shape estimates of their designs. I then demonstrate how these behaviors increase system uncertainty via an Agent-Based Model and Monte Carlo simulation (Meluso & Austin-Breneman, 2018). To understand the strategic uses of estimates, I study a Fortune 500 company and find widespread variation among practicing engineers about what an “estimate” means independent of their division, title, and phase of product development. While some practitioners define estimates as approximations of current designs, others define them as approximations of future designs, points in a project which could be years apart. Importantly, engineers inadvertently aggregate estimates of different types into single values that inform programmatic decision-making, thereby constituting networked miscommunication (Meluso et al., 2020). The third study, however, reveals a nuanced picture in which varied estimate definitions conditionally degrade organizational performance. In particular, future estimates degrade complex system performance relative to current estimates, constituting networked miscommunication despite a lack of misunderstandings. I also find that some misunderstandings can protect an organization from performance degradation. In organizations with equal use of current and future estimates, current estimates buffer systems against degradation caused by future estimates, indicating that performance degradation depends on communication network structure (Meluso et al., 2019). Collectively, these studies demonstrate the potential of networked miscommunication to affect organizational performance.PHDDesign ScienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155145/1/jmeluso_1.pd