Ultrawideband radar is commonly used in the frequency range of 50-500 MHz to detect buried pipes at a depth of about 1-2 m depending on the soil characteristics. The typical feature used to locate the pipes is the hyperbolic pattern of the time of flight generated by a linear scan of the antenna above the surface. When the pipes are close together, the hyperbolas overlap, and a straightforward least squares fit is not possible. The Hough transform provides one possible solution. This paper extends the Hough transform by introducing a weighting factor depending on the differentials of the unknown parameters with respect to the experimental errors, namely, the probe position error and the time-of-flight error. This enables optimally placed sets of data pairs to be given greater weight than "ill-conditioned" sets, as for example when all data pairs lie near one end of the arc. The result is a decrease in the background amplitude with respect to the maximum of the peaks in the Hough accumulator space. It is shown that this improvement persists even when many arcs are present. A mathematical analysis with analytical results is given for the case of four unknowns: pipe radius R, pipe center position (Y, Z), and soil propagation velocity V. The results are presented through simulations introducing controlled uncertainties in the probe position, the time of flight, and its bin size. The simulations demonstrate the correlations that occur between the radius, depth, and velocity for given experimental uncertainties.

This paper analyses front propagation of the equation $\upsilon_{\tau}=[D(\upsilon)\upsilon_{x}]_{x}+f(\upsilon) \tau\ge 0, x\in R,$ where $f$ is a monostable (i.e. Fisher-type) nonlinear reaction term and $D(\upsilon)$ changes its sign once, from positive to negative values, in the interval $\upsilon \in [0, 1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $\upsilon$ at time $\tau$ and position $x$. The existence of infinitely many traveling wave solutions is proven. These fronts are parameterized by their wave speed and monotonically connect the stationary states $\upsilon \equiv 0$ and $\upsilon \equiv 1$. In the degenerate case, i.e. when $D(0) = 0$ and/or $D(1) = 0$, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both.

This paper develops a Failure Mode, Effects and Criticality Analysis (FMECA) for a heating, ventilation and air conditioning (HVAC) system in railway. HVAC is a safety critical system which must ensure emergency ventilation in case of fire and in case of loss of primary ventilation functions. A study of the HVAC’s critical areas is mandatory to optimize its reliability and availability and consequently to guarantee a low operation and maintenance cost. The first part of the paper describes the FMECA which is performed and reported to highlight the main criticalities of the HVAC system under analysis. Secondly, the paper deals with the problem of the evaluation of a threshold risk value, which can distinguish negligible and critical failure modes. Literature barely considers the problem of an objective risk threshold estimation. Therefore, a new analytical method based on finite difference is introduced to find a univocal risk threshold value. The method is then tested on two Risk Priority Number datasets related to the same HVAC. The threshold obtained in both cases is a good tradeoff between the risk mitigation and the cost investment for the corrective actions required to mitigate the risk level. Finally, the threshold obtained with the proposed method is compared with the methods available in literature. The comparison shows that the proposed finite difference method is a well-structured technique, with a low computational cost. Furthermore, the proposed approach provides results in line with the literature, but it completely deletes the problem of subjectivity.

Some basic properties of regularly varying sequences are presented here and applied to the study of the asymptotic behavior of decreasing solutions of half-linear difference equations. Relations with the classification of nonoscillatory solutions and with the notion of recessive solutions are also discussed.