Efstathios Bakolas

Highlights from the literature on accident causation and system safety: Review of major ideas, recent contributions, and challenges

Abstract This work constitutes a short guide to the extensive but fragmented literature on accident causation and system safety. After briefly motivating the interest in accident causation and discussing the notion of a safety value chain, we delve into our multi-disciplinary review with discussions of Man Made Disasters, Normal Accident, and the High Reliability Organizations (HRO) paradigm. The HRO literature intersects an extensive literature on safety culture, a subject we then briefly touch upon. Following this discussion, we note that while these social and organizational contributions have significantly enriched our understanding of accident causation and system safety, they have important deficiencies and are lacking in their understanding of technical and design drivers of system safety and accident causation. These missing ingredients, we argue, were provided in part by the development of Probabilistic Risk Assessment (PRA). The idea of anticipating possible accident scenarios, based on the system design and configuration, as well as its technical and operational characteristics, constitutes an important contribution of PRA, which builds on and extends earlier contributions made by the development of Fault Tree and Event Tree Analysis. We follow the discussion of PRA with an exposition of the concept of safety barriers and the principle of defense-in-depth, both of which emphasize the functions and “safety elements [that should be] deliberately inserted” along potential accident trajectories to prevent, contain, or mitigate accidents. Finally, we discuss two ideas that are emerging as foundational in the literature on system safety and accident causation, namely that system safety is a “control problem”, and that it requires a “system theoretic” approach to be dealt with. We clarify these characterizations and indicate research opportunities to be pursued along these directions. We conclude this work with two general recommendations: (1) that more fundamental research and cross-talk across several academic disciplines must be supported and incentivized for tackling the multi-disciplinary issues of accident causation and system safety (e.g., through the creation “academic hubs” or “centers of excellence” dedicated to system safety); and (2) that more interactions and partnerships between academia, industry, and government (especially accident investigation agencies) on accident causation and system safety issues would be particularly useful for all involved in advancing the safety agenda, from both research and education perspectives, and for disseminating research results, safety recommendations, and lessons learned from accident investigations.

Brief paper: The Zermelo-Voronoi diagram: A dynamic partition problem

We consider a Dirichlet-Voronoi like partition problem for a small airplane operating in the horizontal plane in the presence of winds that vary uniformly with time. It is shown that the problem can be interpreted as a Dynamic Voronoi Diagram problem, where the generators are not fixed, but rather they are moving targets to be reached in minimum time. The problem is solved by reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation.

Optimal pursuit of moving targets using dynamic Voronoi diagrams

We consider Voronoi-like partitions for a team of moving targets distributed in the plane, such that each set in this partition is uniquely associated with a particular moving target in the following sense: a pursuer residing inside a given set of the partition can intercept this moving target faster than any other pursuer outside this set. It is assumed that each moving target employs its own “evading” strategy in response to the pursuer actions. In contrast to standard formulations of problems of this kind in the literature, the evading strategy does necessarily restrict the evader to be slower than its pursuer. In the special case when all moving targets employ a uniform evading strategy, the previous problem reduces to the characterization of the Zermelo-Voronoi diagram.

Optimal feedback guidance of a small aerial vehicle in a stochastic wind

The navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem of minimizing the expected time required to drive a Dubins vehicle to a prescribed target set in the presence of a stochastically varying wind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected tim...

Augmenting defense-in-depth with the concepts of observability and diagnosability from Control Theory and Discrete Event Systems

Abstract Defense-in-depth is a fundamental principle/strategy for achieving system safety. First conceptualized within the nuclear industry, defense-in-depth is the basis for risk-informed decisions by the U.S. Nuclear Regulatory Commission, and is recognized under various names in other industries (e.g., layers of protection in the Chemical industry). Accidents typically result from the absence or breach of defenses or violation of safety constraints. Defense-in-depth is realized by a diversity of safety barriers and a network of redundancies. However, this same redundancy and the intrinsic nature of defense-in-depth – the multiple lines of defense or “protective layers” along a potential accident sequence – may enhance mechanisms concealing the occurrence of incidents, or that the system has transitioned to a hazardous state (accident pathogens) and that an accident is closer to being released. Consequently, the ability to safely operate the system may be hampered and the efficiency of defense-in-depth may be degraded or worse may backfire. Several accidents reports identified hidden failures or degraded observability of accidents pathogens as major contributing factors. In this work, we begin to address this potential theoretical deficiency in defense-in-depth by bringing concepts from Control Theory and Discrete Event Systems to bear on issues of system safety and accident prevention. We introduce the concepts of controllability, observability, and diagnosability, and frame the current understanding of system safety as a “control problem” handled by defense-in-depth and safety barriers (or safety constraints). Observability and diagnosability are information-theoretic concepts, and they provide important complements to the energy model of accident causation from which the defense-in-depth principle derives. We formulate a new safety-diagnosability principle for supporting accident prevention, and propose that defense-in-depth be augmented with this principle, without which defense-in-depth can degenerate into a defense-blind safety strategy. Finally, we provide a detailed discussion and illustrative modeling of the sequence of events that lead to the BP Texas City Refinery accident in 2005 and emphasize how a safety-diagnosable architecture of the refinery could have supported the prevention of this accident or mitigated its consequences. We hope the theoretical concepts here introduced and the safety-diagnosability principle become useful additions to the intellectual toolkit of risk analysts and safety professionals and stimulate further interaction/collaboration between the control and safety communities.

Time-optimal synthesis for the Zermelo-Markov-Dubins problem: The constant wind case

We consider a combination of the classical Markov-Dubins problem and Zermelos navigation problem. In particular, we consider the problem of characterizing minimum-time paths with prescribed positions and tangents for a vehicle with Dubins-type kinematics in the presence of uniform winds/currents. By utilizing optimal control theory, we characterize the structure of the optimal paths, and subsequently solve the time-optimal synthesis problem.

Optimal partitioning for spatiotemporal coverage in a drift field

Abstract We consider the problem of partitioning an area in the plane populated by a team of aerial/marine vehicles into a finite collection of non-overlapping sets. The sets of this partition are in an one-to-one correspondence with the vehicles under the following rule: each point in the given set of the partition can be reached by the corresponding vehicle in this set faster than any other vehicle in the presence of a spatiotemporal drift field. Consequently, a Voronoi-like partition results, which encodes the proximity relations between the vehicles and arbitrary points in the plane with respect to the minimum time-to-go. The construction of this Voronoi-like partition is based on its interpretation as the intersection of a forest of the cost (minimum time-to-go) surfaces emanating from each generator with their common lower envelope. The characterization of each cost surface is achieved by means of an efficient expansion scheme of the level sets of the minimum time-to-go function, which utilizes, in turn, the structure of the optimal synthesis of the minimum-time problem without resorting to exhaustive numerical techniques, e.g., fast marching methods. We examine the topological characteristics of the partition by using control/system theoretic concepts and tools. The theoretical developments are illustrated with a number of numerical examples.

Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov-Dubins Problem

We consider a variation of the classical Markov–Dubins problem dealing with curvature-constrained, shortest paths in the plane with prescribed initial and terminal positions and tangents, when the lower and upper bounds of the curvature of the path are not necessarily equal. The motivation for this problem stems from vehicle navigation applications, when a vehicle may be biased in taking turns at a particular direction due to hardware failures or environmental conditions. After formulating the shortest path problem as a minimum-time problem, a family of extremals, which is sufficient for optimality, is characterized, and subsequently the complete analytic solution of the optimal synthesis problem is presented. In addition, the synthesis problem, when the terminal tangent is free, is also considered, leading to the characterization of the set of points that can be reached in the plane by curves satisfying asymmetric curvature constraints.

Feedback Navigation in an Uncertain Flowfield and Connections with Pursuit Strategies

Copyright ©2012 by E. Bakolas and P. Tsiotras. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field

We consider the optimal synthesis of the Zermelo–Markov–Dubins problem, that is, the problem of steering a vehicle with the kinematics of the Isaacs–Dubins car in minimum time in the presence of a drift field. By using standard optimal control tools, we characterize the family of control sequences that are sufficient for complete controllability and necessary for optimality for the special case of a constant field. Furthermore, we present a semianalytic scheme for the characterization of an optimal synthesis of the minimum-time problem. Finally, we establish a direct correspondence between the optimal syntheses of the Markov–Dubins and the Zermelo–Markov–Dubins problems by means of a discontinuous mapping.