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- ItemVanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point(De Gruyter, 2024-02-05) Diblík, Josef; Růžičková, MiroslavaA singular nonlinear differential equation z(sigma) dw/dz = aw + zwf(z , w), where sigma > 1, is considered in a neighbourhood of the point z = 0 z=0 located either in the complex plane C if sigma is a natural number, in a Riemann surface of a rational function if sigma is a rational number, or in the Riemann surface of logarithmic function if sigma is an irrational number. It is assumed that w = w ( z ) w=w\left(z) , a is an element of C { 0 } a, and that the function f f is analytic in a neighbourhood of the origin in C x C . Considering sigma to be an integer, a rational, or an irrational number, for each of the above-mentioned cases, the existence is proved of analytic solutions w = w (z ) w=w(z) in a domain that is part of a neighbourhood of the point z = 0 z=0 in C or in the Riemann surface of either a rational or a logarithmic function. Within this domain, the property lim z -> 0 w (z) = 0 is proved and an asymptotic behaviour of w (z) s established. Several examples and figures illustrate the results derived. The blow-up phenomenon is discussed as well.
- ItemDiagnostics of Interturn Short Circuits in PMSMs With Online Fault Indicators Estimation(IEEE, 2024-02-27) Zezula, Lukáš; Kozovský, Matúš; Blaha, PetrThis article presents novel model-based diagnostics of interturn short circuits in permanent magnet synchronous machines that enable estimating fault location and its severity, even during transients. The proposed method utilizes recursive parametric estimation and model comparison approaches cast in a decision-making framework to track motor parameters and fault indicators from a machine's discrete-time model. The discrete-time prototype is derived from an advanced motor model that reflects the stator winding arrangement in a motor's case. The fault detection is then performed by tracking the changes in the estimated probability density function of the electrical parameters, using the Kullback–Leibler divergence. The fault location is subsequently evaluated by performing a recursive comparison of the predefined fault models in the different phases, utilizing a growing-window approach. Ultimately, a parametric estimation algorithm applied to the fault current model allows identifying the fault severity. The diagnostic algorithm has been validated via laboratory experiments, and its capabilities are compared with other approaches enabling severity estimation.
- ItemCapacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)(sigma network, 2024-01-03) Rebenda, Josef; Pátíková, Zuzana; Chvátal, Martin; Rogovchenko, Svitlana; Bakke, Trris Kolen; Croft, TonyThis report describes the final meeting of the project "Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)" held at the Tomas Bata University in Zlín, Czech Republic (June 12-14, 2023). Provision of mathematics and statistics learning support (MSLS) is developing rapidly in many parts of the world and activity in Norway and the Czech Republic has been accelerated significantly through this EEA Grants funded project. Representatives of each of the five partner institutions worked on creating a summary of good practices in tutor training, designing learning resources, and in delivering, monitoring and evaluation of mathematics and statistics support. Provision varied considerably across the institutions and the centres represented demonstrated diverse and innovative ways in which mathematics support is evolving. Outputs from the project include a Handbook on good practice and a booklet concerned with mathematics support centre tutor training, including pedagogic training and learning resources for the development of the tutors as described below. Finally, consideration turned to the value of establishing a professional network to continue this important work. The report will be relevant to other international groups interested in working in university level mathematics and statistics support.
- ItemRobust perception systems for automated, connected, and electrified vehicles: advances from EU project ArchitectECA2030(Elsevier, 2023-12-13) Recekenzaun, Jakob; Solmaz, Selim; Goelles, Thomas; Hilbert, Marc; Weimer, Daniel; Mayer, Peter; Chromý, Adam; Hentschel, Uwe; Modler, Niels; Toth, Mate; Hennecke, MarcusThe perception supply chain (SC1) of the ArchitectECA2030 project investigates failure modes, fault detection, and residual risk in perception systems of electrified, connected, and automated (ECA) vehicles. This accounts for the needs of a reliable understanding of the surrounding environment. The three demonstrators of SC1, described in this paper, address steps of a typical ECA usage cycle: charge - drive - restart charging. The foreign object detection (FOD) demonstrator improves safety within a wireless charging system. The robust physical sensors demonstrator creates a more robust perception by detecting failures within fused and single sensor data. The position enhancement demonstrator improves vehicle localization in areas with reduced GNSS signal coverage. All demonstrators are linked to the challenges that occur during the ECA vehicle usage cycle
- ItemRecursive Variational Inference for Total Least-Squares(IEEE, 2023-06-26) Friml, Dominik; Václavek, PavelThis letter analyzes methods for deriving credible intervals to facilitate errors-in-variables identification by expanding on Bayesian total least squares. The credible intervals are approximated employing Laplace and variational approximations of the intractable posterior density function. Three recursive identification algorithms providing an approximation of the credible intervals for inference with the Bingham and the Gaussian priors are proposed. The introduced algorithms are evaluated on numerical experiments, and a practical example of application on battery cell total capacity estimation compared to the state-of-the-art algorithms is presented.