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Wake vortices that are generated by an aircraft as a consequence of lift constitute a potential danger to the following aircraft. To predict and avoid dangerous situations, wake vortex transport and decay models have been developed. Being based on different model physics, they can complement each other with their individual strengths. This paper investigates the skill of a Multi-Model Ensemble (MME) approach to improve prediction performance. Therefore, this paper aims to use wake vortex models developed by NASA (APA3.2, APA3.4, TDP2.1) and by DLR (P2P). Furthermore, this paper analyzes the possibility to use the ensemble spread to compute uncertainty envelopes.

An MME approach called Reliability Ensemble Averaging (REA) is adapted and used to the wake vortex predictions. To train the ensemble, a set of wake vortex measurements accomplished at the airports of Frankfurt (WakeFRA), Munich (WakeMUC) and at a special airport Oberpfaffenhofen was applied.

The REA approach can outperform the best member of the ensemble, on average, regarding the root-mean-square error. Moreover, the ensemble delivers reasonable uncertainty envelopes.

Reliable wake vortex predictions may be applicable for both tactical optimization of aircraft separation at airports and airborne wake vortex prediction and avoidance.

Ensemble approaches are widely used in weather forecasting, but they have never been applied to wake vortex predictions. Until today, the uncertainty envelopes for wake vortex forecasts have been computed among others from perturbed initial conditions or perturbed physics as well as from uncertainties from environmental conditions or from safety margins but not from the spread of structurally independent model forecasts.

The use of the 4D trajectory operational concept in the future air traffic management (ATM) system will require the aircraft to meet very accurately an arrival time over a designated checkpoint. To do this, time intervals known as time windows (TW) are defined. The purpose of this paper is to develop a methodology to characterise these TWs and to manage the uncertainty associated with the evolution of 4D trajectories.

4D trajectories are modelled using a point mass model and EUROCONTROL’s BADA methodology. The authors stochastically evaluate the variability of the parameters that influence 4D trajectories using Monte Carlo simulation. This enables the authors to delimit TWs for several checkpoints. Finally, the authors set out a causal model, based on a Bayesian network approach, to evaluate the impact of variations in fundamental parameters at the chosen checkpoints.

The initial results show that the proposed TW model limits the deviation in time to less than 27 s at the checkpoints of an en-route segment (300 NM).

The objective of new trajectory-based operations is to efficiently and strategically manage the expected increase in air traffic volumes and to apply tactical interventions as a last resort only. We need new tools to support 4D trajectory management functions such as strategic and collaborative planning. The authors propose a novel approach for to ensure aircraft punctuality.

The main contribution of the paper is the development of a model to deal with uncertainty and to increase predictability in 4D trajectories, which are key elements of the future airspace operational environment.

Vibration of large membranes has great utility in engineering application such as in important parts of drums, pumps, microphones, telephones and other devices. So, to obtain a numerical solution of this type of problems is necessary and important. In general, in existing approaches, involved parameters and variables are defined exactly. Whereas in actual practice, it may contain uncertainty owing to error in observations, maintenance-induced error, etc. So, the main purpose of this paper is to solve this important problem numerically under fuzzy and interval uncertainty to have an uncertain solution and to study its behaviour.

In this study, the authors have considered a new approach is known as double parametric form of fuzzy number to model uncertain parameters. Along with this a semianalytical approach, i.e. variational iteration method, has been used to obtain uncertain bounds of the solution.

The variational iteration method has been successfully implemented along with the double parametric form of fuzzy number to find the uncertain solution of the vibration equation of a large membrane. The advantage of this approach is that the solution can be written in a power series or a compact form. Also, this method converges rapidly to obtain an accurate solution. Various cases depending on the functional value involved in the initial conditions have been studied and the behaviour has been analysed. Applying the double parametric form reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

The vibration equation of large membranes has been solved under fuzzy and interval uncertainty. Uncertainties have been considered in the initial conditions. New approaches, i.e. variational iteration method along with the double parametric form, have been applied to solve the vibration equation of large membranes.

The current air traffic management (ATM) operational approach is changing; “time” is now integrated as an additional fourth dimension on trajectories. This notion will impose on aircraft the compliance of accurate arrival times over designated checkpoints (CPs), called time windows (TWs). This paper aims to clarify the basic requirements and foundations for the practical implementation of this functional framework.

This paper reviews the operational deployment of 4D trajectories, by defining its relationship with other concepts and systems of the future ATM and communications, navigation and surveillance (CNS) context. This allows to establish the main tools that should be considered to ease the application of the 4D-trajectories approach. This paper appraises how 4D trajectories must be managed and planned (negotiation, synchronization, modification and verification processes). Then, based on the evolution of a simulated 4D trajectory, the necessary corrective measures by evaluating the degradation tolerances and conditions are described and introduced.

The proposed TWs model can control the time tolerance within less than 100 s along the passing CPs of a generic trajectory, which is in line with the expected future ATM time-performance requirements.

The main contribution of this work is the provision of a holistic vision of the systems and concepts that will be necessary to implement the new 4D-trajectory concept efficiently, thus enhancing performance. It also proposes tolerance windows for trajectory degradation, to understand both when an update is necessary and what are the conditions required for pilots and air traffic controllers to provide this update.

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

The purpose of this paper is to introduce a new conceptual framework for smallholder value chains based on complex adaptive systems.

The authors review the application of the framework to three case studies and explore their implications. The authors reflect on the value of a framework based on complex adaptive systems compared to alternative frameworks.

The authors argue that the dynamics of smallholder value chains have received insufficient attention.

By focusing on these dynamics and on the capacity for adaptation among value chain actors the framework provides a new perspective on smallholder value chains.

Complex adaptive systems provide a useful framework for analyzing value chain dynamics.

“The unexamined life is not worth living,” said Socrates. That is, without critically inquiring into the knowledge of life, which is well-being and valuable, life is not worth living. Critical thinking questions existing theories and their unexamined and obsessive assumptions and generalizations, constraints, and the so-called “best” practices of the prevailing system of management and tries to replace them with more valid assumptions and generalizations that uphold the dignity, uniqueness, and inalienable rights of every individual and the community. In our diverse and pluralistic cultural environment, the promise of a truly generative dialogue among occidental (western) and oriental (eastern) cultures and civilizations holds great hope for the future. Critical thinking can facilitate this dialogue such that all of us have a meaningful place in this universe. In this chapter, we explore introductory working definitions of critical thinking so that we can early enough understand its demanding domains, moral calls, and ramifications in its current critical applications. Specifically, in Part I, we examine the structured layers of our thinking and reasoning to dismantle them progressively, and in Part II, in support of our claims, we explore complexity and chaos theories as a new resource for critical thinking.

The problem of robotic co-manipulation is often addressed using impedance control based methods where the authors seek to establish a mathematical relation between the velocity of the human-robot interaction point and the force applied by the human operator (HO) at this point. This paper aims to address the problem of co-manipulation for handling tasks seen as a constrained optimal control problem.

The proposed point of view relies on the implementation of a specific online trajectory generator (OTG) associated with a kinematic feedback loop. This OTG is designed so as to translate the HO intentions to ideal trajectories that the robot must follow. It works as an automaton with two states of motion whose transitions are controlled by comparing the magnitude of the force to an adjustable threshold, in order to enable the operator to keep authority over the robot's states of motion.

To ensure the smoothness of the interaction, the authors propose to generate a velocity profile collinear to the force applied at the interaction point. The feedback control loop is then used to satisfy the requirements of stability and of trajectory tracking to guarantee assistance and operator security. The overall strategy is applied to the penducobot problem.

The approach stands out for the nature of the problem to be tackled (heavy load handling tasks) and for its vision on the co-manipulation. It is based on the implementation of two main ingredients. The first one lies in the online generation of an appropriate trajectory of the interaction point located at the end-effector and describing the HO intention. The other consists in the design of a control structure allowing a good tracking of the generated trajectory.

The earliest human societies relied for their subsistence on the hunting of animals and the gathering of food. The small bands of people who lived together pursuing these activities appear to have been the prototype of all human organisation. Hunting and gathering was the predominant type of social organisation until perhaps 12,000 years ago. Tools and weapons were not made of metal till around 4,000 B.C., the plough was not in use until about a thousand years later, and iron tools and weapons were not used until around 1,000 B.C. (Lenski and Lenski, 1978). The history of the human race has been intextricably bound up with that of engineering when this is very broadly defined as the making of tools and other contrivances as aids and adjuncts to life. From the Stone, Bronze and Iron Ages at one end of human experience to the Steam, Jet, Atomic and Computer Ages at the other, technical‐engineering achievements have defined and delimited whatever is possible for human beings. Thus throughout the long historical transition from a predominantly agricultural to a predominantly industrial society engineers, or rather anyone whose principal activity was making and tinkering with three‐ dimensional artefacts, played a crucial role.

This study examines how the distribution of opinions and social status combine in a collectively oriented task group to affect perceptions about the correctness of a final decision.

We relied on data from a controlled laboratory experiment to test a series of theoretically derived hypotheses.

The study shows that both the distribution of opinions and status affect perceptions of correctness. It also establishes that the effects of status on uncertainty are strongest when the group is initially evenly split about the correctness of an opinion, and that like the distribution of opinions, the effects of status on uncertainty are curvilinear.

Previous research shows that by integrating research on faction sizes with status characteristics theory (SCT), more accurate predictions of social influence are possible. Assumed therein is that people use information about the distribution of opinions and status to reduce uncertainty about correctness of a choice. The current study establishes this point empirically by examining the effects of the distribution of opinions and status in a four-person, collectively oriented task group. Future research should consider groups of different sizes and other moderating factors.

This study advances and elaborates upon previous research on social influence that integrates research on faction sizes with SCT.