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Hybrid pencil beam model (HPBM) based on photon characteristic line algorithm has been presented to get accurate three-dimensional (3D) dose distribution for lung radiotherapy in small fields. In the model, we introduced a scattering factor to accurately describe the transport behavior of scattered photons and secondary electrons, combined with the equivalent depth correction and the weighted density correction. The pencil beam kernels of heterogeneous lung phantoms were redefined by the scattering factor and depth dose for a reference field by photon characteristic line algorithm. Subsequently, the 3D dose distribution in lung phantoms with density of 0.1, 0.26, and 0.4 g/cm3, was calculated by the Finite-size pencil beam algorithm in five regular fields and an irregular field for 6 MV photon beam. The dose distributions obtained by the HPBM are in agreement with those obtained by the MC simulations, with a relative error of less than 3% in most of the cases. However, there are apparent discrepancies at media interfaces and lung anterior portion. Moreover, at media interfaces, relative dose errors of the two methods decrease with the increase in field size and lung density. The depth range in which relative errors is greater than 3% increases with the increase in field size at lung anterior portion. In these examples, maximum relative errors are between 5 and 29%. Nevertheless, it is shown that the HPBM based on photon characteristic line algorithm has potential research values in lung dose calculation under conditions of small fields.

Extreme winds may expose overhead transmission lines to loads that may result in the collapse of transmission towers leading to severe economic losses. This paper develops a modelling framework to assess the fragility of transmission towers under extreme winds such as tropical storms. To this end, the wind loading on a transmission tower is represented by a combination of three wind load components (i.e., the transverse and longitudinal tower loads as well as the wire load) expressed in terms of three key wind load-related input parameters (wind speed, wind angle of attack and horizontal span of the transmission line). The wind load-carrying capacity of towers is accordingly defined by a three-dimensional convex-curve surface with the three wind load components as the principle axes. A kriging surrogate model is established for the tower capacity surface as a function of uncertain structural parameters, based on the results from the nonlinear static analysis of the tower and Latin-hypercube sampling. Accordingly, the limit state function would suggest tower failure if the wind load effect exceeds the tower capacity defined by the surface. In this framework, the tower fragility is established by the Monte Carlo simulation. If the wind intensity, wind direction and line configuration are known, the wind load components can be evaluated. Utilizing the surrogate model, the capacity surfaces of sample towers are also obtained in terms of the simulated uncertain structural parameters simulated. Comparison between the estimated wind load components and the simulated sample surfaces yields the fragility curve. The proposed framework is demonstrated by a numerical example, as well as an application to a typhoon scenario analysis in which the failure probability of a real-world long-distance transmission line is assessed.

Wind loading on a transmission tower structure is jointly influenced by the wind field, structural parameters, and the geo-spatial configuration of the transmission line. Considering the multi-parametric effect, this paper aims at developing a limit capacity model for transmission towers under strong winds. To this end, the limit capacity of the tower is expressed via two equivalent means: one is the limit wind speed as a function of the wind angle of attack and the span of transmission line, the other is a limit capacity surface with three fundamental wind load components as the principal axes. An adaptive kriging surrogate modeling is constructed to approximate the function/surface with structural uncertainties considered. The performance of the surrogate model is improved by adding support points and then evaluated by the overall accuracy validation and local error check. A numerical example demonstrating the feasibility of the surrogate modeling for the limit capacity of the transmission tower under winds is presented. Finally, a fragility assessment concerning a practical transmission line and towers subjected to typhoons is accomplished using the established limit capacity model of the tower.

A wind tunnel test on the aero-elastic model of UHV transmission tower line system was carried out for researching tower line system's dynamic behavior under different wind speeds. The effect of wires' vibration on tower was particularly addressed in the paper. For comparison, the single tower model and tower line system model were involved. Both alongwind and crosswind responses of tower were investigated. The wire's dynamic strain was traced synchronously for exploring the coupling vibration effect of tower line system. Comparing the responses of the single tower model and the tower line model, it is found that 70–90% displacement and strain are induced by wires. This action is more prominent in the alongwind direction. However, the peak response values of the tower line model are smaller than those of the single tower model. Test results in frequency domain indicate that the dynamic behavior of the tower becomes more susceptible to wind speed when it connects with wires. As to the tower line system, the response power spectra of the tower and the conductors show the tendency of moving to lower and higher frequency region respectively with the crests weakened and vibration energy dispersed when wind speed increases.