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At least 19 records

Multi-objective decision-making under uncertainty: Fuzzy logic methods

Fuzzy logic allows for quantitative representation of vague or fuzzy objectives, and therefore is well-suited for multi-objective decision-making. This paper presents methods employing fuzzy logic concepts to assist in the decision-making process. In addition, this paper describes software developed at NASA Lewis Research Center for assisting in the decision-making process. Two diverse examples are used to illustrate the use of fuzzy logic in choosing an alternative among many options and objectives. One example is the selection of a lunar lander ascent propulsion system, and the other example is the selection of an aeration system for improving the water quality of the Cuyahoga River in Cleveland, Ohio. The fuzzy logic techniques provided here are powerful tools which complement existing approaches, and therefore should be considered in future decision-making activities.

Hardy, Terry L.↗

Multi-objective decision-making under uncertainty: Fuzzy logic methods

Selecting the best option among alternatives is often a difficult process. This process becomes even more difficult when the evaluation criteria are vague or qualitative, and when the objectives vary in importance and scope. Fuzzy logic allows for quantitative representation of vague or fuzzy objectives, and therefore is well-suited for multi-objective decision-making. This paper presents methods employing fuzzy logic concepts to assist in the decision-making process. In addition, this paper describes software developed at NASA Lewis Research Center for assisting in the decision-making process. Two diverse examples are used to illustrate the use of fuzzy logic in choosing an alternative among many options and objectives. One example is the selection of a lunar lander ascent propulsion system, and the other example is the selection of an aeration system for improving the water quality of the Cuyahoga River in Cleveland, Ohio. The fuzzy logic techniques provided here are powerful tools which complement existing approaches, and therefore should be considered in future decision-making activities.

Hardy, Terry L.↗

The uncertainty threshold principle - Fundamental limitations of optimal decision making under dynamic uncertainty

The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.

Athans, M.↗

The uncertainty threshold principle - Some fundamental limitations of optimal decision making under dynamic uncertainty

This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.

Athans, M.↗

Considering Risk and Resilience in Decision-Making

This paper examines the concepts of decision-making, risk analysis, uncertainty and resilience analysis. The relation between risk, vulnerability, and resilience is analyzed. The paper describes how complexity, uncertainty, and ambiguity are the most critical factors in the definition of the approach and criteria for decision-making. Uncertainty in its various forms is what limits our ability to offer definitive answers to questions about the outcomes of alternatives in a decision-making process. It is shown that, although resilience-informed decision-making would seem fundamentally different from risk-informed decision-making, this is not the case as resilience-analysis can be easily incorporated within existing analytic-deliberative decision-making frameworks.

Torres-Pomales, Wilfredo↗

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗

Reliability-Aware Requirements Development for Autonomy Software

Autonomy is the ability of a system to make decisions and take actions in the presence of uncertainty. Validating autonomy, therefore, is a matter of validating that the system makes intelligent decisions even when there might be discrepancies between the observed and the expected state of the world as well as when the possible outcome of each of the possible courses of action is uncertain. During the requirements engineering phase, the functions, including those that are required to be autonomous and their expected behavior are specified. However, in the case of autonomous software system, it is challenging to specify all possible scenarios that the software may encounter. Additionally, since autonomous behaviors cannot always be fully predetermined, it is difficult to reason about their completeness and correctness. While these challenges are also faced with non-autonomous system, they are more prevalent for autonomous system due to their complexity and emergent behavior. Our efforts have been three-fold. On one hand, we have developed a goal-based method for requirements decomposition. We have embedded this approach into a higher-level systems engineering framework and then developed methods for decision and reliability analysis within this framework. And finally, we use simulation analysis to validate the more theoretical methods and provide a feedback mechanism. The decision analysis approach (DA) helps in identifying and mitigating the run-time risks, by bringing to the forefront the uncertainties, decisions, interactions, and other factors that may cause autonomous software to make erroneous decisions. The DA framework is used to quantify, for each decision that the software can make, failure risk due to uncertainties. The information about the key decisions and circumstances that can cause autonomous system to make incorrect decisions are used to generate test scenarios to be run in a simulator to ensure that the system can handle error-prone circumstances. The results or outcomes from decisions, based on the simulated scenarios, can then be leveraged to further gain insight of the assured system. We combine a goal-based approach with simulation analysis to facilitate requirements development for autonomous systems and further provide a method for run-time systems level reliability considerations during the autonomous software development process. The DA and the reliability analysis methods provide a formalism for the consideration of uncertainty in the run time decision-making process for autonomous software. This formalism considers the uncertainty involved in the outcome of different courses of action, in terms of performance and cost, as well as a method to consider the system level reliability implications. System level reliability considerations for autonomous software decision making contribute to the satisfaction of the system level goals over the lifecycle of a given mission. We demonstrate our approach using a hypothetical rover path planning example. The requirements for our rover simulator are based on existing literature about Mars rovers and lessons learned from real world observations at JPL. The specifics of the autonomy design for the Mars rovers, that have not been previously cleared for external release, are not used for our demonstrations.

Lindvall, Mikael↗

MAGE: Alleviating Uncertainty in Real-Time Decision-Making as a Function of Problem Complexity

In this paper, we discuss a critical aspect of uncertainty in the operation of complex systems, such as the future air traffic: the ability of agents in the system to arrive at satisfactory decisions and the attendant actions as a function of problem complexity. Intuitively, when the problem complexity is manageable, given an appropriate decision problem formulation and solution tools, an agent (computational or human) has no trouble arriving at a solution that yields good outcomes for the agent and the system. Growing problem complexity results in progressively larger computational problems that may yield suboptimal solutions or even be intractable within required time limits or at all. We propose a measurable representation of complexity in terms of problem tractability and quality of solutions. We also propose a computational scheme, MAGE (Monitor, Anticipate, Guide, Evolve), for detecting approaching transitions from efficient decision-making states to inefficient to unsafe ones, so that operations based on decision-making can be reconfigured to forestall unfavorable transitions, returning to efficient modes when complexity diminishes. Maintaining tractable complexity reduces the uncertainty in the outcomes of decision-making. We describe the general scheme, an outline of MAGE applied to managing airspace complexity, and initial examples of investigating the tractability of problem-solving schemes.

complexity management↗

SafeMAP: Safe Multi-Agent Planning Framework Based on Dynamic Probabilistic Risk Assessment

This paper proposes a risk-aware framework for Safe Multi-Agent Planning (SafeMAP) that unifies disparate models for multi-agent systems in a Markovian process that allows for simultaneous system health monitoring, decision making under uncertainty, and multi-agent system collaboration. As operations beyond low earth orbit mature, there is an increased need for autonomous cyber-physical systems with onboard decision making capabilities. Multi-agent cyber-physical systems in particular offer the potential of increased efficiency, resiliency, and mission capabilities for future applications such as multi-rover terrain operations, distributed satellite operations, and management of smart lunar habitats. SafeMAP utilizes physics-based models of each agent and the relevant components, probability models of the environment and component operational states, and reward models for mission-specific objectives such as scientific task completion or resource consumption. The output of SafeMAP is a set of mission plans that satisfy the mission objective under specified risk/reward constraints. A readable interpretation of each of these generated mission plans is provided as an additional output. SafeMAP has been demonstrated on a simulated case study involving a four-rover system performing surface mapping operations and science tasks. Results of this paper demonstrate SafeMAP’s ability to generate explainable mission plans that satisfy the mission objective while minimizing risk under nominal and off-nominal conditions.

Mohammad Hejase↗

SafeMAP: Safe Multi-Agent Planning framework based on Dynamic Probabilistic Risk Assessment

This paper proposes a risk-aware framework for Safe Multi-Agent Planning (SafeMAP) that unifies disparate models for multi-agent systems in a Markovian process that allows for simultaneous system health monitoring, decision making under uncertainty, and multi-agent system collaboration. As operations beyond low earth orbit mature, there is an increased need for autonomous cyber-physical systems with onboard decision making capabilities. Multi-agent cyber-physical systems in particular offer the potential of increased efficiency, resiliency, and mission capabilities for future applications such as multi-rover terrain operations, distributed satellite operations, and management of smart lunar habitats. SafeMAP utilizes physics-based models of each agent and the relevant components, probability models of the environment and component operational states, and reward models for mission-specific objectives such as scientific task completion or resource consumption. The output of SafeMAP is a set of mission plans that satisfy the mission objective under specified risk/reward constraints. A readable interpretation of each of these generated mission plans is provided as an additional output. SafeMAP has been demonstrated on a simulated case study involving a four-rover system performing surface mapping operations and science tasks. Results of this paper demonstrate SafeMAP’s ability to generate explainable mission plans that satisfy the mission objective while minimizing risk under nominal and off-nominal conditions.

Mohammad Hejase↗

Role of PHM in Autonomous Decision-Making: Aerospace applications

There is an increased need for onboard decision-making capabilities in cyber-physical systems be it in energy, automotive, aviation, space, or other industries as they aim for increased efficiency, resiliency, and mission assurance capabilities. Emerging next-gen technologies such as multi-rover planetary missions, distributed satellites, unmanned ground and aerial vehicle operations and smart grid systems rely on in-time risk assessment and autonomous decision-making. One critical piece of the autonomy puzzle is reliable prediction of system behavior under time-varying and potentially uncertain environmental conditions. Further, if agent states change during operation such as initiation of faults or degradation, reliable diagnostic tools need to be investigated. In this tutorial, we will revise approaches that integrates existing physics-based and data-driven models of agents interacting with probability models of the environment and component operation state. Role of existing PHM methodologies as they feed into decision-making under uncertainty will be studied. Balancing critical trade-offs between high-fidelity prognostic models, prediction time-horizons and the computational requirements for in-time cost-effective decision-making will be discussed through the implementation of surrogate models. Finally, the audience will be introduced to a real-time application of in-time trajectory planning of an unmanned aerial system (UAS) based on its PHM assessments under uncertain and varying wind conditions.

decision-making↗

Markov Decision Process based Trajectory Planning for UAVs under Uncertain Wind Conditions

In this paper we propose a Markov Decision Process (MDP) algorithm for path-planning of Unmanned Aviation Vehicles (UAVs) under varying wind conditions. Solutions to path-planning for UAVs are becoming increasingly necessary as autonomous UAVs continue to enter commercial and government spaces. Path-planning is inherently challenging, as UAVs needs to account for dynamically changing flying conditions such as weather, obstacle or no-fly zones, degraded vehicle health and off-nominal battery power consumption. Machine learning methods such as Markov Decision Process (MDPs) have the potential to revolutionize how vehicles navigate in such uncertain environments. Previous papers have demonstrated the use of MDPs to optimize UAV path-planning for energy consumption under time-varying wind distribution. In this study, UAV trajectories from a pre-determined waypoint to target cell, will be computed on a 7X7 grid environment by optimizing parameters for mission assurance and safety limits in addition to the energy consumption, and operation time. The UAV navigates the grid by taking actions to move in either of the eight cardinal and intercardinal directions, under constant thrust profile. The next state of the UAV is calculated by considering its action, transition probability, obstacle cells and the wind speed magnitude and direction. Both constant and stochastic wind will be considered in this paper, the parameters being extracted from real wind measurements in proximity to an experimental UAV flight. One of the studies to be demonstrated in this paper is that as the unmanned airspace gets more complex with multiple vehicles and environmental uncertainties, trade-offs between energy consumption, operation time, risk tolerance, and mission assurance needs to be made. Further, MDPs are capable of fast computation of UAV trajectories under varying wind, hence making them suitable for in-flight path planners.

decision-making↗

Fuzzy set methods for object recognition in space applications

During the reporting period, the development of the theory and application of methodologies for decision making under uncertainty was addressed. Two subreports are included; the first on properties of general hybrid operators, while the second considers some new research on generalized threshold logic units. In the first part, the properties of the additive gamma-model, where the intersection part is first considered to be the product of the input values and the union part is obtained by an extension of De Morgan's law to fuzzy sets, is explored. Then the Yager's class of union and intersection is used in the additive gamma-model. The inputs are weighted to some power that represents their importance and thus their contribution to the compensation process. In the second part, the extension of binary logic synthesis methods to multiple valued logic synthesis methods to enable the synthesis of decision networks when the input/output variables are not binary is discussed.

Keller, James M.↗

A Markov Decision Process Framework for Optimal Airport Reconfiguration

The airport runway configuration is defined as a combination set of runways for arrivals and departures used at a point during operation of the airport. An optimal configuration of these runways depends on a number of factors, including traffic demand, wind magnitude and direction, other adverse weather conditions, and noise restrictions, among others. Based on the current state of these factors and predictions of traffic demand and weather conditions, runway configuration changes are made and coordinated between tower controller, other air traffic control facilities, pilots, and ground personnel. Reconfigurations can be quite disruptive to airport operations; minimizing their frequency and scheduling them well in advance is essential for mitigating some of the added workload for controllers and pilots. Unfortunately, deciding on an appropriate time to change is challenging for human decision makers. Not only do multiple factors need to be evaluated, but the uncertainty in their forecasts must also be considered. Previous optimization methods, such as mixed linear integer programming, have been proposed. Although these methods can reason over a large set of variables, they do not systematically handle the uncertainty associated with weather movement, traffic demands, and other variables. In this work, we introduce a Markov Decision Process (MDP)-based decision making framework which can reason effectively over the inherent uncertainties and make optimal decisions on if/when to change the airport configuration. In a prototype implementation, we present a single runway with three aircraft and utilize knowledge of the forecasted wind speed and direction to determine whether to keep or change the current runway configuration. Our aim through this work is to present a framework for airport reconfiguration which can be scalable to additional aircraft, multiple runways, and various input parameters. This technique will optimize the airport reconfiguration procedure by providing a proactive approach, optimizing not just at the next optimal opportunity for a reconfiguration based on varying atmospheric and traffic conditions in the terminal airspace, but also anticipating future necessary reconfigurations. This will eliminate the inefficiencies of frequent changes currently associated with runway reconfiguration procedures.

runway reconfiguration↗

NASA System Safety Handbook: System Safety Framework and Concepts for Implementation - Volume 1

System safety assessment is defined in NPR 8715.3C, NASA General Safety Program Requirements as a disciplined, systematic approach to the analysis of risks resulting from hazards that can affect humans, the environment, and mission assets. Achievement of the highest practicable degree of system safety is one of NASA's highest priorities. Traditionally, system safety assessment at NASA and elsewhere has focused on the application of a set of safety analysis tools to identify safety risks and formulate effective controls.1 Familiar tools used for this purpose include various forms of hazard analyses, failure modes and effects analyses, and probabilistic safety assessment (commonly also referred to as probabilistic risk assessment (PRA)). In the past, it has been assumed that to show that a system is safe, it is sufficient to provide assurance that the process for identifying the hazards has been as comprehensive as possible and that each identified hazard has one or more associated controls. The NASA Aerospace Safety Advisory Panel (ASAP) has made several statements in its annual reports supporting a more holistic approach. In 2006, it recommended that "... a comprehensive risk assessment, communication and acceptance process be implemented to ensure that overall launch risk is considered in an integrated and consistent manner." In 2009, it advocated for "... a process for using a risk-informed design approach to produce a design that is optimally and sufficiently safe." As a rationale for the latter advocacy, it stated that "... the ASAP applauds switching to a performance-based approach because it emphasizes early risk identification to guide designs, thus enabling creative design approaches that might be more efficient, safer, or both." For purposes of this preface, it is worth mentioning three areas where the handbook emphasizes a more holistic type of thinking. First, the handbook takes the position that it is important to not just focus on risk on an individual basis but to consider measures of aggregate safety risk and to ensure wherever possible that there be quantitative measures for evaluating how effective the controls are in reducing these aggregate risks. The term aggregate risk, when used in this handbook, refers to the accumulation of risks from individual scenarios that lead to a shortfall in safety performance at a high level: e.g., an excessively high probability of loss of crew, loss of mission, planetary contamination, etc. Without aggregated quantitative measures such as these, it is not reasonable to expect that safety has been optimized with respect to other technical and programmatic objectives. At the same time, it is fully recognized that not all sources of risk are amenable to precise quantitative analysis and that the use of qualitative approaches and bounding estimates may be appropriate for those risk sources. Second, the handbook stresses the necessity of developing confidence that the controls derived for the purpose of achieving system safety not only handle risks that have been identified and properly characterized but also provide a general, more holistic means for protecting against unidentified or uncharacterized risks. For example, while it is not possible to be assured that all credible causes of risk have been identified, there are defenses that can provide protection against broad categories of risks and thereby increase the chances that individual causes are contained. Third, the handbook strives at all times to treat uncertainties as an integral aspect of risk and as a part of making decisions. The term "uncertainty" here does not refer to an actuarial type of data analysis, but rather to a characterization of our state of knowledge regarding results from logical and physical models that approximate reality. Uncertainty analysis finds how the output parameters of the models are related to plausible variations in the input parameters and in the modeling assumptions. The evaluation of unrtainties represents a method of probabilistic thinking wherein the analyst and decision makers recognize possible outcomes other than the outcome perceived to be "most likely." Without this type of analysis, it is not possible to determine the worth of an analysis product as a basis for making decisions related to safety and mission success. In line with these considerations the handbook does not take a hazard-analysis-centric approach to system safety. Hazard analysis remains a useful tool to facilitate brainstorming but does not substitute for a more holistic approach geared to a comprehensive identification and understanding of individual risk issues and their contributions to aggregate safety risks. The handbook strives to emphasize the importance of identifying the most critical scenarios that contribute to the risk of not meeting the agreed-upon safety objectives and requirements using all appropriate tools (including but not limited to hazard analysis). Thereafter, emphasis shifts to identifying the risk drivers that cause these scenarios to be critical and ensuring that there are controls directed toward preventing or mitigating the risk drivers. To address these and other areas, the handbook advocates a proactive, analytic-deliberative, risk-informed approach to system safety, enabling the integration of system safety activities with systems engineering and risk management processes. It emphasizes how one can systematically provide the necessary evidence to substantiate the claim that a system is safe to within an acceptable risk tolerance, and that safety has been achieved in a cost-effective manner. The methodology discussed in this handbook is part of a systems engineering process and is intended to be integral to the system safety practices being conducted by the NASA safety and mission assurance and systems engineering organizations. The handbook posits that to conclude that a system is adequately safe, it is necessary to consider a set of safety claims that derive from the safety objectives of the organization. The safety claims are developed from a hierarchy of safety objectives and are therefore hierarchical themselves. Assurance that all the claims are true within acceptable risk tolerance limits implies that all of the safety objectives have been satisfied, and therefore that the system is safe. The acceptable risk tolerance limits are provided by the authority who must make the decision whether or not to proceed to the next step in the life cycle. These tolerances are therefore referred to as the decision maker's risk tolerances. In general, the safety claims address two fundamental facets of safety: 1) whether required safety thresholds or goals have been achieved, and 2) whether the safety risk is as low as possible within reasonable impacts on cost, schedule, and performance. The latter facet includes consideration of controls that are collective in nature (i.e., apply generically to broad categories of risks) and thereby provide protection against unidentified or uncharacterized risks.

Dezfuli, Homayoon↗