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Evaluation of the ray-casting analytical algorithm for pencil beam scanning proton therapy

PHYSICS IN MEDICINE AND BIOLOGY 2019年第6期64卷 art. no. 065021-art. no. 065021页

作者： Winterhalter, Carla Zepter, Stefan Shim, Sojin Meier, Gabriel Bolsi, Alessandra Fredh, Anna Hrbacek, Jan Oxley, David Zhang, Ye Weber, Damien C. Lomax, Antony Safai, Sairos Paul Scherrer Inst Ctr Proton Therapy Villigen Switzerland Swiss Fed Inst Technol Dept Phys Zurich Switzerland Swiss Fed Inst Technol Dept Mech & Proc Engn Zurich Switzerland EPF Lausanne Sect Phys Lausanne Switzerland Univ Hosp Bern Radiat Oncol Dept Bern Switzerland Univ Hosp Zurich Radiat Oncol Dept Zurich Switzerland

For pencil beam scanned (PBS) proton therapy, analytical dose calculation engines are still typically used for the optimisation process, and often for the final evaluation of the plan. Recently however, the suitability of analytical calculations for planning PBS treatments has been questioned. Conceptually, the two main approaches for these analytical dose calculations are the ray-casting (RC) and the pencil-beam (PB) method. In this study, we compare dose distributions and dosimetric indices, calculated on both the clinical dose calculation grid and as a function of dose grid resolution, to Monte Carlo (MC) calculations. The analysis is done using a comprehensive set of clinical plans which represent a wide choice of treatment sites. When analysing dose difference histograms for relative treatment plans, pencil beam calculations with double grid resolution perform best, with on average 97.7%/91.9% (RC), 97.9%/92.7% (RC, double grid resolution), 97.6%/91.0% (PB) and 98.6%/94.0% (PB, double grid resolution) of voxels agreeing within +/- 5%/+/- 3% between the analytical and the MC calculations. Even though these point-to-point dose comparison shows differences between analytical and MC calculations, for all algorithms, clinically relevant dosimetric indices agree within +/- 4% for the PTV and within +/- 5% for critical organs. While the clinical agreement depends on the treatment site, there is no substantial difference of indices between the different algorithms. The pencil-beam approach however comes at a higher computational cost than the ray-casting calculation. In conclusion, we would recommend using the ray-casting algorithm for fast dose optimization and subsequently combine it with one MC calculation to scale the absolute dose and assure the quality of the treatment plan.

关键词： proton therapy pencil beam scanning Monte Carlo simulation analytical algorithm ray-casting algorithm pencil-beam algorithm

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An analytical algorithm for assessing dynamic characteristics of a triple-tower double-cable suspension bridge

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STRUCTURAL ENGINEERING AND MECHANICS 2024年第4期90卷 325-343页

作者： Zhang, Wen-ming Chen, Yu-peng Wang, Shi-han Lu, Xiao-fan Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China Southeast Univ State Key Lab Safety Durabil & Hlth Operat Long Sp Nanjing 210096 Peoples R China

Triple -tower double -cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double -cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple -tower double -cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second -order torsion frequencies of double -cable suspension bridges are much higher than those of single -cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

关键词： analytical algorithm double-cable dynamic characteristics free vibration suspension bridge triple-tower

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Comments on "An analytical algorithm for generalized low-rank approximations of matrices"

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PATTERN RECOGNITION 2008年第6期41卷 2133-2135页

作者： Hu, Yafeng Lv, Hairong Zhang, Xianda Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

Low rank approximations of matrices have been widely used in pattern recognition and machine learning. Based on a sequence of matrices, a generalized low rank approximation problem was presented and an iterative scheme was given by Liang and Shi recently proposed an analytical scheme for this approximation problem. In this paper, we identify the weakness in their scheme and prove that their algorithm is incorrect. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： low rank approximation analytical algorithm iterative algorithm

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analytical algorithm for determining anchor span strand tensions in the suspension bridge's free-cable state

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STRUCTURES 2024年 65卷

作者： Zhang, Wen-ming Zhang, Xiao-yi Chen, Yu-peng Shen, Xing-hang Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China

Anchor span strand tensions have a large bearing on the overall structural safety of the suspension bridge. Precise estimation of anchor span strand tensions and construction parameters in the free-cable state is critical for geometric form design of main cable and for realizing proper strand tensions in the completed bridge state. Given the complex geometric form of anchor span strands, calculating strand tensions remains highly challenging. To calculate strand tensions in the anchor span in the free-cable state, a system of equations is built based on geometric compatibility conditions and mechanical equilibrium conditions in the anchor span. The calculation of anchor span strand tensions in the free-cable state requires using the unstrained lengths of strands in the completed bridge state, which links the free-cable state with the completed bridge state. This study proposes an analytical algorithm for the unstrained lengths of the anchor span strands. Strand tension is calculated from the three-dimensional steering angle because the anchor span strand has a spatial geometric form. Then, the strand elongation is estimated, and the unstrained length of the strand is obtained accordingly. Based on the conservation of the unstrained lengths of strands, we further estimate the strand tension in the anchor span and the prerotation angle of the splay saddle in the free-cable state. The above calculation of parameters lays a solid foundation for suspension bridge construction. The proposed method is applied to the engineering case of the Jindong Bridge with a main span of 730 m in Kunming, China, to verify the algorithm's feasibility.

关键词： Suspension bridge Anchor span Strand tension Free-cable state analytical algorithm

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RETRIEVAL OF WATER QUALITY PARAMETERS BY NEURAL NETWORK AND analytical algorithm IN GUANTING RESERVOIR IN HEBEI PROVINCE IN CHINA

RETRIEVAL OF WATER QUALITY PARAMETERS BY NEURAL NETWORK AND ...

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IEEE International Geoscience and Remote Sensing Symposium (IGARSS)

作者： Lan, Xinyu Guo, Ziqi Tian, Ye Lei, Xia Wang, Jie Chinese Acad Sci Inst Remote Sensing & Digital Earth State Key Lab Remote Sensing Sci Beijing 100101 Peoples R China

ISBN: (纸本)9781479979295

Based on the measured spectra in the research area of Guangting reservoir, we build the model to retrieve chlorophyll-a, suspended solid and yellow substance. The paper mainly achieved the following results: we adopted matrix inversion method and L-M & NN method to analyse the water quality parameters, the selection schemes of the spectral band include REF, DER, RAN method, and then use the Guanting Reservoir experiment data for inspection and comparative analysis. The results showed that: the retrieval accuracy of L-M & NN method was better than matrix inversion method for three ocean color elements, the RAN weighted method overall had better retrieval accuracy. For C-chla, acdom (440), the best scheme in band selection is RAN, REF showed better retrieval accuracy for Cs.

关键词： Case II water Water Quality Parameters Neural Network analytical algorithm

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A Novel Time Delay Controlling UWB Array Based On analytical algorithm

A Novel Time Delay Controlling UWB Array Based On Analytical...

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IEEE International Symposium on Antennas and Propagation

作者： Li, Pengcheng Pan, Jin Yang, Deqiang Univ Elect Sci & Technol China Chengdu 610054 Peoples R China

ISBN: (纸本)9781467304627

In this paper, a new design of time controlling time domain ultra wide band (UWB) antenna array based on software radio technology (SRT) analytical algorithm is presented. With the novel design array, automatic scan of synthetic pattern is realized. Theoretical analysis and computation is employed to set accurate delay time for each element of the array. Scanning angle can be reached to +/- 30 degrees. It has high precision and speed, and it is a promising choice for ground penetrating radar (GPR), nondestructive testing (NDT).

关键词： Time domain UWB delay time analytical algorithm scanning angle

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A fast analytical algorithm for generating CGH of 3D scene

A fast analytical algorithm for generating CGH of 3D scene

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Conference on Practical Holography XXIV - Materials and Applications

作者： Liu, Yuanzhi Dong, Jianwen Pu, Yiying Chen, Bingchu He, Hexiang Deng, Zilan Wang, Hezhou Sun Yat Sen Zhongshan Univ State Key Lab Optoelect Mat & Technol Guangzhou 510275 Guangdong Peoples R China

ISBN: (纸本)9780819480156

We present a set of analytical formula on describing the diffraction field of the three dimensional (3D) triangular-mesh-based model. The advantage of the proposed method is that it can avoid using the numerical algorithm - Fast Fourier Transform, which leads to a depth-of-field limitation by the Whittaker-Shannon sampling theorem. We employ the proposed method to generate the hologram of 3D texture model derived from the real scene or 3D design software. In order to further increase the computation speed, we have rendered a real scene by employing the GPU platform. Our homemade GPU algorithm performs hundreds of times faster than those of CPU. As we developed a general phase adjustment technique for polygon-based algorithm, the holographic reconstructed scenes possess high performance.

关键词： Computer generated hologram 3D display analytical algorithm graphic processing units

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An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans

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ENGINEERING STRUCTURES 2019年 199卷 109595-000页

作者： Zhang, Wen-ming Yang, Chao-yu Wang, Zhi-wei Liu, Zhao Southeast Univ Minist Educ Key Lab Concrete & Prestressed Concrete Struct Nanjing Jiangsu Peoples R China

Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique "central tower effect" of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient betw

关键词： Three-tower suspension bridge Unequal-length main spans Central tower effect analytical algorithm Central tower stiffness GRG method

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Comparative Study of Seafloor Topography Prediction from Gravity-Geologic Method and analytical algorithm

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REMOTE SENSING 2024年第17期16卷 3154-3154页

作者： Tian, Yuwei Xu, Huan Yu, Jinhai Wang, Qiuyu Jia, Yongjun Chen, Xin Univ Chinese Acad Sci Coll Earth & Planetary Sci Key Lab Computat Geodynam Beijing 100049 Peoples R China Natl Satellite Ocean Applicat Serv Beijing 100081 Peoples R China Naval Res Inst Tianjin 300061 Peoples R China

Seafloor topography prediction can fill in sea areas without ship sounding data. However, the dependence of various topographic prediction algorithms on ship soundings varies significantly. Hence, this study explores the impact of the number and distributions of ship soundings on topographic prediction using the gravity-geologic method (GGM) and an analytical algorithm. Firstly, this study investigates the influence of ship sounding coverage on the two algorithms. The simulation results demonstrate that increasing coverage from 5.40% to 31.80%, coupled with more uniform distributions across the study area, substantially reduces the RMS error of the GGM. Specifically, the RMS error decreases from 238.68 m to 42.90 m, an improvement of 82.03%. The analytical algorithm maintains a consistent RMS error of 40.39 m because it does not depend on ship soundings. Furthermore, we select a 1 degrees x 1 degrees sea area (134.8 degrees-135.8 degrees E, 30.0 degrees-31.0 degrees N), and the ship soundings are divided into two control groups, Part I and Part II, with coverages of 8.19% and 33.19%, respectively. When Part II is used for calculation, the RMS error of the GGM decreases from 204.17 m to 126.95 m compared to when Part I is used, while the analytical algorithm exhibits an RMS error of 167.94 m. The findings indicate that the prediction accuracy of the GGM is significantly affected by ship soundings, whereas the analytical algorithm is more stable and independent of ship soundings. Based on simulation experiments and realistic examples, when the effective ship soundings coverage exceeds 30%, the GGM may have more advantages. Conversely, the analytical algorithm may be better. This suggests that effectively combining and utilizing different algorithms based on the ship sounding coverage can improve the accuracy of topographic prediction. This will provide a basis for integrating multiple algorithms to construct a global seafloor topography model.

关键词： seafloor topography gravity anomaly analytical algorithm gravity-geologic method numerical simulation

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A Nonlinear analytical algorithm for Predicting the Probabilistic Mass Flow of a Radial District Heating Network

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ENERGIES 2019年第7期12卷 1215页

作者： Sun, Guoqiang Wang, Wenxue Wu, Yi Hu, Wei Yang, Zijun Wei, Zhinong Zang, Haixiang Chen, Sheng Hohai Univ Coll Energy & Elect Engn Nanjing 211100 Jiangsu Peoples R China State Grid Jiangsu Power Co Nanjing 210024 Jiangsu Peoples R China

This paper develops a nonlinear analytical algorithm for predicting the probabilistic mass flow of radial district heating networks based on the principle of heat transfer and basic pipe network theory. The use of a nonlinear mass flow model provides more accurate probabilistic operation information for district heating networks with stochastic heat demands than existing probabilistic power flow analytical algorithms based on a linear mass flow model. Moreover, the computation is efficient because our approach does not require repeated nonlinear mass flow calculations. Test results on a 23-node district heating network case indicate that the proposed approach provides an accurate and efficient estimation of probabilistic operation conditions.

关键词： integrated energy system district heating network probabilistic mass flow analysis nonlinear model analytical algorithm

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