Data Management Framework & UAV Simulation Testbed for the Study of System-level Prognostics Technologies

Prognostics-enabled technologies have emerged over the last few years, primarily for Condition Based Maintenance (CBM+) applications, which are used for maintenance and operational scheduling. However, due to the challenges that arise from real-world systems and safety concerns, they have not been adopted for operational decision making based on system end of life estimates. It is typically cost-prohibitive or highly unsafe to run a system to complete failure and, therefore, engineers turn to simulation studies for analyzing system performance. Prognostics research has matured to a point where we can start putting pieces together to be deployed on real systems, but this reveals new problems. First, a lack of standardization exists within this body of research that hinders our ability to compose various technologies or study their joint interactions when used together. The second hindrance lies in data management and creates hurdles when trying to reproduce results for validation or use the data as input to machine learning algorithms. We propose an end-to-end object-oriented data management framework & simulation testbed that can be used for a wide variety of applications. In this paper, we describe the requirements, design, and implementation of the framework and provide a detailed case study involving a stochastic data collection experiment.

The analysis of Titan’s physical surface using multifractal geometry methods

Titan makes up 95% of the mass of all 82 satellites of Saturn. Titan’s diameter is 5152 km, which means that it is larger than the Moon by 50%, and it is also significantly larger than Mercury. On the satellite, a subsurface ocean is possible, the theory of the presence of which has already been advanced earlier by some scientists. It is located under a layer of ice and consists of 10% ammonia, which is a natural antifreeze for it and does not allow the ocean to freeze. On the one hand, the ocean contains a huge amount of salt, which makes the likelihood of life in it hardly possible. But on the other hand, since chemical processes constantly occur on Titan, forming molecules of complex hydrocarbon substances, this can lead to the emergence of the simplest forms of life. There are limitations on the probabilistic and statistical approaches, since not every process and not every result (form and structure of the system) is probabilistic in nature. In contrast to this, fractal analysis allows one to study the structure of complex objects, taking into account their qualitative specifics, for example, the relationship between the structure and the processes of its formation. When constructing a harmonic model of Titan, the method of decomposition of topographic information into spherical functions was used. As a result, based on the harmonic analysis of the Cassini mission data, a topographic model of Titan was created. In the final form, the model describing Titan’s surface includes the expansion of the height parameter depending on the spherical coordinates into a slowly converging regression series of spherical harmonics. For modeling surface details of the surface on a scale of 1 degree requires analysis of the (180 + 1)2 harmonic expansion coefficients. An over determined topographic information system was solved to meet the regression modelling conditions. In this case, a number of qualitative stochastic data, such as external measures, were used together with the standard postulation of the harmonic system of the Titan model. As a result of a sampling of self-similar regions (with close values of the self-similarity coefficients) on the surface of Titan, coinciding with the SRGB parameter (characterizes the color fractal dimension), the elements of the satellite’s surface were determined, which with a high degree of probability were evolutionarily formed under the action of the same selenochemical processes.

Sequential statistical decision making in problems of data flows analysis

In the problems of data flows analysis, the problems of statistical decision making on parameters of observed data flows are important. For their solution it is proposed to use sequential statistical decision rules. The rules are constructed for three models of observation flows: sequence of independent homogeneous observations; sequence of observations forming a time series with a trend; sequence of dependent observations forming a homogeneous Markov chain. For each case the situation is considered, where the model describes the observed stochastic data with a distortion. "Outliers" ("contamination") are used as the admissible distortions that adequately describe the majority of situations appear in practice. For such situations the families of sequential decision rules are proposed, and robust decision rules are constructed that allow to reduce influence of distortion to the efficiency characteristics. The results of computer experiments are given to illustrate the constructed decision rules.

Fitting deterministic population models to stochastic data: from trajectory matching to state-space models

Population and community ecology traditionally has a very strong theoretical foundation with well-known models, such as the logistic and its many variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are confronted to data via fitting to empirical time-series, from the field or from the laboratory, for purposes of projections or for estimating model parameters of interest. However, the interface between mathematical population or community models and data, provided by a statistical model, is far from trivial. In order to help empiricists make informed decisions, we here ask which error structure one should use when fitting classical deterministic ODE models to empirical data, from single species to community dynamics and trophic interactions. We use both realistically simulated data and empirical data from microcosms to answer this question in a Bayesian framework. We find that pure observation error models mostly perform adequately overall. However, state-space models clearly outperform simpler approaches when observation errors are sufficiently large or biological models sufficiently complex. Finally, we provide a comprehensive tutorial for fitting these models in R.

Inverse data envelopment analysis with stochastic data

The inverse Data Envelopment Analysis (InvDEA) is an exciting and significant topic in the DEA area. Also, uncertain data in various real-life applications can degrade the efficiency results. The current work addresses the InvDEA in the presence of stochastic data. Under maintaining the efficiency score, the inputs/outputs-estimation problem is investigated when some or all of its outputs/inputs increase. A novel optimality concept for multiple-objective programming problems, stochastic (weak) Pareto optimality in the level of significance α ∈[0,1], is introduced to derive necessary and sufficient conditions for input/output estimation. Furthermore, the performance of the developed theory in a banking sector application is verified.