A new simple method of implicit time integration for dynamic problems of engineering structures

Zhou, Jun; Zhou, Youhe

doi:10.1007/s10409-006-0050-5

Cited by 9 publications

(8 citation statements)

References 26 publications

(34 reference statements)

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“…In the study of [42], the crown volume of was evaluated by measuring the volume using the sphere equation and had a relative bias of 16.4%. Another study [44] illustrated that crown volume calculated from geometrical formulas was feasible with an average relative RMSE of the flabellate formula of 12.5%. Liang et al [45] compared the crown volume calculated from the ovoid equation and the measured value, which resulted in a relative error of between 7% and 10%.…”

Section: Data Acquisitionmentioning

confidence: 99%

Estimation of the Three-Dimension Green Volume Based on UAV RGB Images: A Case Study in YueYaTan Park in Kunming, China

Hong

Liu

et al. 2023

Forests

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Three-dimension green volume (3DGV) is a quantitative index that measures the crown space occupied by growing plants. It is often used to evaluate the environmental and climatic benefits of urban green space (UGS). We proposed the Mean of neighboring pixels (MNP) algorithm based on unmanned aerial vehicle (UAV) RGB images to estimate the 3DGV in YueYaTan Park in Kunming, China. First, we mapped the vegetated area by the RF algorithm based on visible vegetation indices and texture features, which obtained a producer accuracy (PA) of 98.24% and a user accuracy (UA) of 97.68%. Second, the Canopy Height Mode (CHM) of the vegetated area was built by using the Digital Surface Model (DSM) and Digital Terrain Model (DTM), and the vegetation coverage in specific cells (1.6 m × 1.6 m) was calculated based on the vegetation map. Then, we used the Mean of neighboring pixels (MNP) algorithm to estimate 3DGV based on the cell area, canopy height, and vegetation coverage. Third, the 3DGV based on the MNP algorithm (3DGV_MNP), the Convex hull algorithm (3DGV_Con), and the Voxel algorithm (3DGV_Voxel) were compared with the 3DGV based on the field data (3DGV_FD). Our results indicate that the deviation of 3DGV_MNP for plots (Relative Bias = 15.18%, Relative RMSE = 19.63%) is less than 3DGV_Con (Relative Bias = 24.12%, Relative RMSE = 29.56%) and 3DGV_Voxel (Relative Bias = 30.77%, Relative RMSE = 37.49%). In addition, the deviation of 3DGV_MNP (Relative Bias = 17.31%, Relative RMSE = 19.94%) is also less than 3DGV_Con (Relative Bias = 24.19%, Relative RMSE = 25.77%), and 3DGV_Voxel (Relative Bias = 27.81%, Relative RMSE = 29.57%) for individual trees. Therefore, it is concluded that the 3DGV estimation can be realized by using the Neighboring pixels algorithm. Further, this method performed better than estimation based on tree detection in UGS. There was 377,223.21 m3 of 3DGV in YueYaTan Park. This study provides a rapid and effective method for 3DGV estimation based on UAV RGB images.

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Section: Data Acquisitionmentioning

confidence: 99%

Estimation of the Three-Dimension Green Volume Based on UAV RGB Images: A Case Study in YueYaTan Park in Kunming, China

Hong

Liu

et al. 2023

Forests

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“…Substituting equation ( 12) in equation ( 8), D ζ and E ζ are determined incrementally In numerical integration methods, selecting the control parameters is crucial. Meanwhile, to be unconditionally stable, the stability conditions of the scheme can be reduced to the form (Zhou and Zhou, 2007) 8 > > < > > :…”

Section: Linearizationmentioning

confidence: 99%

“…On the other hand, the order of accuracy in displacement and velocity is O (Δt 4 ). Thus, the order of accuracy is higher than simple methods such as Newmark-β and the Wilson-θ (Zhou and Zhou, 2007). The implicit algorithm of time integration can be expressed aswhere ζ 1 and ζ 2 are the control parameters (Zhou and Zhou, 2007).…”

Section: State Vector and Transfer Matricesmentioning

confidence: 99%

“…Thus, the order of accuracy is higher than simple methods such as Newmark-β and the Wilson-θ (Zhou and Zhou, 2007). The implicit algorithm of time integration can be expressed aswhere ζ 1 and ζ 2 are the control parameters (Zhou and Zhou, 2007). Using the first relation in equation (25), the acceleration in terms of displacement can be written as…”

Section: State Vector and Transfer Matricesmentioning

confidence: 99%

“…Figure 2. The conditional and unconditional stability regions based on ζ 1 and ζ 2(Zhou and Zhou, 2007).…”

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confidence: 99%

See 2 more Smart Citations

Efficient technique in computational dynamic modeling of a flexible manipulator with large deformation

Feyzollahzadeh

Bamdad

2022

Journal of Vibration and Control

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In the flexible manipulators, the links could be modeled using rigid elements and torsional springs, and similarly, the flexibility in actuators could be represented with the equivalent springs. This study applies the discrete time transfer matrix method for the dynamic analysis of flexible manipulators with large deformations. On a first-priority basis, transfer matrices are determined, including all the flexible link/joint mechanism components. A single transfer matrix is established for prismatic and rotational actuators with equivalent springs to build the robotic transfer matrix library. On the second priority, to reduce the computation time, a novel algorithm is developed. In the proposed flexible link discretization, the first element of the flexible link is considered as a function of other elements. It is designed to build a mathematical model as closely as possible to the realistic model with fewer elements. It is presented that this modeling technique can employ discrete data extracted by the sensors. The simulation primarily focuses on developing flexible beam/joint models validated in ADAMS. Besides, the dynamic behavior of a flexible PR robot with external forces acting on the linkage system is analyzed and examined. The result shows that the proposed modeling method affords a low computational time while the manipulator control needs to manage fast responses.

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Numerical Method and Computer Simulation for Analysis of Vehicle–Track Coupled Dynamics

Zhai

2019

Vehicle–Track Coupled Dynamics

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A new simple method of implicit time integration for dynamic problems of engineering structures

Cited by 9 publications

References 26 publications

Estimation of the Three-Dimension Green Volume Based on UAV RGB Images: A Case Study in YueYaTan Park in Kunming, China

Estimation of the Three-Dimension Green Volume Based on UAV RGB Images: A Case Study in YueYaTan Park in Kunming, China

Efficient technique in computational dynamic modeling of a flexible manipulator with large deformation

Numerical Method and Computer Simulation for Analysis of Vehicle–Track Coupled Dynamics

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