This paper advances the use of the ranked nodes method (RNM) to portray probabilistic relationships of continuous quantities in Bayesian networks (BNs). In RNM, continuous quantities are represented by ranked nodes with discrete ordinal scales. The probabilistic relationships of the nodes are quantified in conditional probability tables (CPTs) generated with expert-elicited parameters. When ranked nodes are formed by discretizing continuous scales, ignorance about the functioning of RNM can lead to discretizations that make the generation of sensible CPTs impossible. While a guideline exists on this matter, it is limited by a requirement to define an equal number of ordinal states for all the nodes. This paper presents two novel discretization approaches that consider the functioning of RNM and allow the nodes to have non-equal numbers of ordinal states. In the first one, called the “static discretization approach”, the nodes can be given any desired discretizations that stay unchanged during the use of the BN. In the second one, called the “dynamic discretization approach”, the discretizations are algorithmically updated during the use of the BN to help manage the sizes of the generated CPTs. Both approaches are based on the original idea that, besides the RNM parameters, the nodes probabilistic relationship is defined by initial RNM-compatible discretizations elicited from the domain expert. Overall, the new approaches offer an easier and more versatile way of using RNM to depict the probabilistic relationships of continuous quantities. In doing so, they also facilitate the effective and diverse use of BNs in decision support systems.

This paper provides new insight into the theoretical principle and the practical applicability of the ranked nodes method (RNM) that is used to construct conditional probability tables (CPTs) for Bayesian networks (BNs) by expert elicitation. RNM is designed for specific types of discrete random variables called ranked nodes that are common in real-world applications of BNs. Despite its active use in recent years, there remains ambiguity about the exact theoretical basis of RNM which can hamper its effective employment. In addition, there are a lack of studies about the general ability of CPTs generated with RNM to represent probabilistic relationships in real-world applications. In this paper, it is shown how the generation of probabilities with RNM is underpinned by a regression model of continuous random variables. Then, it is experimentally determined that in typical applications of RNM, one can generate in a matter of seconds CPTs whose elements reflect well probabilities given by the underlying regression model. Another experiment discovers that CPTs generated with RNM provide a good average fit to a large portion of various real-world CPTs investigated. This confirms the usefulness of RNM in practical applications. The results of the experiment also indicate that choices made by the user of RNM can considerably impact the ability of a generated CPT to represent a given probabilistic relationship. This paper then provides practical advice on the efficient use of RNM with regard to the user-controlled features explored in the experiment.

The purpose of this study was to demonstrate how the inclusion of a tactical task goal awareness measure complemented mental workload and performance measures in a simulated air combat mission. It was hypothesized that the evaluation of the tactical task goal awareness could provide additional information concerning the cognitive demands a pilot is exposed to during a complex air combat task. A test setting was developed to test this hypothesis in a virtual flight training device. To highlight the impact of task complexity, high performance aircraft pilots' heart rate (HR), interbeat-interval (IBI), and performance in two simple flying tasks were first compared. Then, a similar comparison, complemented with the tactical task goal awareness measure, was made with two complex flying tasks. It was found that when the pilot's awareness of the tactical goals was low, a combination of low performance and low mental workload occurred. It was concluded that when the pilots' performance is evaluated on a complex air combat task, the awareness of the tactical goals, performance, and mental workload should be studied together as the pilot's awareness can explain some of HR/IBI responses that could be otherwise misinterpreted. More generally, mental workload, performance, and task goal awareness should all be considered when the operator's performance in any complex human-machine system is assessed.

This paper presents two new computationally efficient direct methods for fitting n-dimensional ellipsoids to noisy data. They conduct the fitting by minimizing the algebraic distance in subject to suitable quadratic constraints. The hyperellipsoid-specific (HES) method is an elaboration of existing ellipse and 3D ellipsoid-specific fitting methods. It is shown that HES is ellipsoid-specific in n-dimensional space. A limitation of HES is that it may provide biased fitting results with data originating from an ellipsoid with a large ratio between the longest and shortest main axis. The sum-of-discriminants (SOD) method does not have such a limitation. The constraint used by SOD rejects a subset of non-ellipsoidal quadrics, which enables a high tendency to produce ellipsoidal solutions. Moreover, a regularization technique is presented to force the solutions towards ellipsoids with SOD. The regularization technique is compatible also with several existing 2D and 3D fitting methods. The new methods are compared through extensive numerical experiments with n-dimensional variants of three commonly used direct fitting approaches for quadratic surfaces. The results of the experiments imply that in addition to the superior capability to create ellipsoidal solutions, the estimation accuracy of the new methods is better or equal to that of the reference approaches.

This paper elaborates on the ranked nodes method (RNM) that is used for constructing conditional probability tables (CPTs) for Bayesian networks consisting of a class of nodes called ranked nodes. Such nodes typically represent continuous quantities that lack well-established interval scales and are hence expressed by ordinal scales. Based on expert elicitation, the CPT of a child node is generated in RNM by aggregating weighted states of parent nodes with a weight expression. RNM is also applied to nodes that are expressed by interval scales. However, the use of the method in this way may be ineffective due to challenges which are not addressed in the existing literature but are demonstrated through an illustrative example in this paper. To overcome the challenges, the paper introduces a novel approach that facilitates the use of RNM. It consists of guidelines concerning the discretization of the interval scales into ordinal ones and the determination of a weight expression and weights based on assessments of the expert about the mode of the child node. The determination is premised on interpretations and feasibility conditions of the weights derived in the paper. The utilization of the approach is demonstrated with the illustrative example throughout the paper.

This paper presents a new game-theoretic approach toward the validation of discrete-event air combat (AC) simulation models and simulation-based optimization. In this approach, statistical techniques are applied for estimating games based on data produced by a simulation model. The estimation procedure is presented in cases involving games with both discrete and continuous decision variables. The validity of the simulation model is assessed by comparing the properties of the estimated games to actual practices in AC. These games are also applied for simulation-based optimization in a two-sided setting in which the action of the opponent is taken into account. In optimization, the estimated games enable the study of effectiveness of AC tactics as well as aircraft, weapons, and avionics configurations. The game-theoretic approach enhances existing methods for the validation of discrete-event simulation models and techniques for simulation-based optimization by incorporating the inherent game setting of AC into the analysis. It also provides a novel game-theoretic perspective to simulation metamodeling which is used to facilitate simulation analysis. The utilization of the game-theoretic approach is illustrated by analyzing simulation data obtained with an existing AC simulation model.

The paper presents a new game theoretic approach towards the validation of discrete event air combat simulation models. In the approach, statistical techniques are applied for estimating game models based on simulation data. The estimation procedure is presented in cases involving games with both discrete and continuous decision variables. The validity of the simulation model is assessed by comparing the properties of the estimated games to actual practices in air combat. The approach enhances existing methods for the validation of discrete event simulation models by incorporating the inherent game setting of air combat into the analysis. The estimated games also provide a novel game theoretic perspective to simulation metamodeling which is used to facilitate simulation analysis. The utilization of the game theoretic approach is illustrated by analyzing simulation data produced with an existing air combat simulation model.

Modern fighter aircraft are equipped with a data link system for relaying encrypted messages containing information on the states of friendly or hostile aircraft within a team of friendly aircraft. During a many-versus-many air combat, only the most important and essential information must be transmitted in order to achieve the best possible situation awareness of pilots. In this paper, we introduce a prioritization approach for solving the team optimal signaling strategy referring to the best sequence of relayed information with respect to the overall goals of the friendly pilots. The approach is based on a value function that captures the preferences of the pilots and prioritizes the existing information. Uncertainty about the states of the aircraft as well as about incomplete preference statements is incorporated into the prioritization by utilizing interval analysis. We also describe a software that is designed for simulating the evolution of team members' information and trajectories in an air-combat game. The prioritization approach is illustrated by numerical examples

Modern fighter aircraft are equipped with a data communications system for relaying information within a group of friendly aircraft. During many-versus-many air combat, the most important and essential information must be transmitted in order to achieve the best possible outcome of the combat. In this paper, we introduce a prioritization model for selecting optimal signaling strategies with respect to the overall goals of the friendly group. The model is based on a decision analytical value function which tries to capture the preferences of pilots. Uncertainty about the states of the aircraft as well as incomplete preference statements is incorporated into the model by utilizing an interval approach.

An approach toward the automated solution of aircraft trajectory optimization problems is introduced and implemented in an interactive program called visual interactive aircraft trajectory optimization (VIATO). This MS Windows-compatible software produces minimum time trajectories to a fixed or moving target. It is easy to use by nonexperts as no previous knowledge of the methods of optimal control theory or mathematical modeling are needed. VIATO consists of a graphical user interface, an optimization server, and a model server. In VIATO, different aircraft types are represented by a set of parameters. The equations of motion and state as well as control constraints are fixed in advance. Since the objective function is also specified, the user avoids the modeling and explicit formulation of optimal control problems. Reliable convergence to an approximate optimal solution is achieved by converting the original optimal control problem into a finite dimensional optimization problem. The parameterized problem is solved using nonlinear programming.