Errors in Fitting Radial Dose Function of Cobalt Sources for Brachytherapy With 3-5 Degree Polynomials

Belousov, A. V.; Belianov, A. A.; Черняев, А.П.

doi:10.18786/2072-0505-2016-44-2-140-147

Cited by 1 publication

(3 citation statements)

References 7 publications

(11 reference statements)

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“…In constructing the cusp catastrophe model of the horizontal displacement cusp of the foundation pit, the polynomial of the time series of the measured deformation values is established based on the real-time data. Here, we take the quadratic polynomial as an example to illustrate the derivation process of the cusp catastrophe model, and the quadratic polynomial fitting function is as follows where U t is the deformation function, t is the time variable, and a i is the fitting parameter ( i = 0, 1, 2, 3, 4).…”

Section: Resultsmentioning

confidence: 99%

“…Here, we take the quadratic polynomial as an example to illustrate the derivation process of the cusp catastrophe model, and the quadratic polynomial fitting function is as follows. 44 where U t is the deformation function, t is the time variable, and a i is the fitting parameter ( i = 0, 1, 2, 3, 4).…”

Section: Resultsmentioning

confidence: 99%

“…Here, we take the quadratic polynomial as an example to illustrate the derivation process of the cusp catastrophe model, and the quadratic polynomial fitting function is as follows. 44 =…”

Section: Building Of the Horizontal Cusp Catastrophementioning

confidence: 99%

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Monitoring and Prediction of Horizontal Displacement of Underground Enclosure Piles in Subway Foundation Pits

et al. 2023

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Urban rail transportation and underground space development and utilization are initiatives to solve urban traffic congestion. The monitoring and prediction of the stability of underground enclosure piles in foundation pits is a key index for the dynamic evaluation of the stability of underground space engineering. In this paper, we focused on the problem that the dynamic prediction accuracy and stability of foundation pit retaining piles in the Qingdao area are not high. Based on the analysis of various time function curves and the physical meaning of the parameters, we proposed the Adjusted-Logistic time function model, which introduces three physical parameters to adjust the deformation velocity and deformation acceleration in different stages for better accuracy. It could predict the deformation process of underground enclosure piles under different geological engineering conditions. It was verified in the field that the root-mean-square error (RMSE) of the Adjusted-Logistic function was 0.5316, MAE was 0.3752, and R 2 was 0.9937, which were better than those of Gompertz, Weibull, and Knothe time function models. Meanwhile, it showed that with the increase of excavation depth, the maximum horizontal displacement of the underground enclosure piles gradually decreased and finally stabilized at 0.62−0.71 H. We established a catastrophe model of the horizontal displacement cusp at the observation point of the underground enclosure piles by using the time series of the measured data. It could determine the weak location of the underground enclosure pile stability and realize the multipoint warning of the foundation pit stability, which would ensure safe construction.

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Section: Resultsmentioning

confidence: 99%